Research ArticleDistributed Link Scheduling Algorithm Based on SuccessiveInterference Cancellation in MIMO Wireless Networks

Junhua Wu Dandan Lin Guangshun Li Yuncui Liu and Yanmin Yin

School of Information Science and Engineering Qufu Normal University Rizhao China

Correspondence should be addressed to Guangshun Li 30752585qqcom

Received 6 March 2019 Accepted 15 May 2019 Published 19 June 2019

Guest Editor Zaobo He

Copyright copy 2019 Junhua Wu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The performance of multiple input multiple output (MIMO) wireless networks is limited mainly by concurrent interference amongsensor nodes Effective link scheduling algorithms with the technology of successive interference cancellation (SIC) can maximizethroughput inMIMOwireless networks Most previous works on link scheduling inMIMOwireless networks did not consider SICIn this paper we propose aMIMO-SIC (MSIC) algorithm under the SINRmodel First amathematical framework is established forthe cross-layer optimization of routing and scheduling with constraints of traffic balance and link capacity Second the interferenceregions are divided to characterize the level of interference between links Finallywe propose a distributed link scheduling algorithmbased on MSIC to eliminate the interference between competing links in the MIMO network Experimental results show thatthe MSIC algorithm can increase the end-to-end throughput per unit by approximately 73 on average compared with non-SICalgorithms

1 Introduction

Due to the explosiveness of big data many new high-performance requirements of network throughput real-timeperformance security privacy and bandwidth have beenput forward [1ndash4] It is consequently challenging to designefficient link scheduling algorithms to improve communi-cation efficiency in wireless communication Wireless net-work multiple input multiple output (MIMO) technologycan transmit multiple data streams simultaneously withoutincreasing bandwidth and enhance data throughput MIMOhas therefore attracted increasing attention[5 6]

MIMO refers to the technology of using multiple trans-mitting antennas and multiple receiving antennas in wire-less transmission which is a major technology of smartantennas in wireless communication networks The mainidea of MIMO is to combine the signals of the receivingand sending antennas to increase transmission reliability anddata throughput [7 8] The architecture of MIMO wirelesscommunication networks is shown in Figure 1

However concurrent links also generate some problemsin communication interference which reduces the success

probability of communication links [9] The reason is thatdue to transmission interference of adjacent channels mixedsuperimposed signals will reach the receiver node [10 11]The cumulative interference effect of the link depends notonly on itself but also on concurrent links When conflictoccurs between concurrent links transmissions fail due tobad interference In wireless networks MIMO gain is closelyrelated to link scheduling

The link scheduling problem focuses on the study ofcapacity optimization and throughput maximization [12] andcan be divided into the following two types of problemsOne is the maximum independent set link (MISL) problem[13] also known as the capacity maximization problem orsingle-slot link scheduling problem In this problem given aset of communication links the largest subset of concurrentlinks that can be transmitted simultaneously in the same timeslot must be identified The other type of problem is theshortest link scheduling (SLS) problem [14 15] also knownas the delay minimization problem This problem refers toscheduling a given set of links with a minimum of time slotsThis paper studies the former problem namely designing a

HindawiWireless Communications and Mobile ComputingVolume 2019 Article ID 9083282 12 pageshttpsdoiorg10115520199083282

2 Wireless Communications and Mobile Computing

Server

BS 1

BS 2

BS 3

IP Gateway

user 1

user 2

user 3

Figure 1 The architecture of a MIMO wireless communication network

link algorithm that schedules as many links as possible in thesame time slot

There are many factors that affect the link schedulingproblem such as different choices of centralized [16] or dis-tributed algorithms [17 18] Before the centralized algorithmis executed various information of the network node isbroadcast to the execution node such as the set of neighborsand the transmit power of the node As the network scaleincreases the time complexity of centralized algorithms willincrease dramatically However the distributed algorithmonly needs to obtain the corresponding information of theneighbors during the execution process Such informationexchange can be achieved only by a broadcast and therunning time of the algorithm is independent of the networkscale

In addition establishing a reasonable interference modelis the key to designing a correct and efficient link schedulingalgorithmThemost commonly used interference models canbe classified into the protocol interference model [19] andSINR (signal-to-interference-plus-noise ratio) interferencemodel [20 21] Under the protocolmodel the transmission ofa link is deemed successful if no other links within a certaintransmission range are active Therefore the coexistencerelationship between two links is mainly determined by thegeometry Due to its simplicity the protocol model has beenwidely used By contrast under the SINR model the coex-istence relationship depends on its own channel conditionand the level of the aggregated interference Specifically atransmission of a link is said to be successful if its SINR valueis greater than a predetermined threshold One challengeunder the SINR model is that multiple links can transmitsuccessfully through a common channel even if they observesome interference signal from each other in marked contrastto the protocol model Furthermore the link relationship isa function of the distance to the neighboring links and theirstatus which may change over timeTherefore the link coex-istence relationship under the SINR model is ldquomultilateralrdquo

and ldquodynamicrdquo As a result link scheduling under the SINRmodel is much more complicated The literature [22] provesthe robustness of SINR models with geometric path loss TheSINR model opens a new avenue for more efficient resourceallocation

SIC is an effective physical layer technology for mul-tipacket reception to combat interference and it allowsother concurrent transmission links to decode correctly[20] According to the descending order of the receiversrsquopower level SIC regards the interference signals as a usefulsignal obeying a specific structure As SIC is able to resolvethe collision more simultaneous transmission and higherperformance could be expected [23 24] We therefore focuson link scheduling in MIMO wireless networks with SICHowever there has been little work on exploring SIC inMIMO networks based on the SINR model

The main contributions of this paper are as follows Wepropose a distributed link scheduling algorithm in MIMOwireless networks with SIC to maximize the link throughputFirst based on the characteristics of MIMO and SIC wepropose a combination of these two technologies to estab-lish the MSIC model and a mathematical framework isestablished for cross-layer optimization of scheduling withconstraints of traffic balance and link capacity Second dueto the global characteristic of the interference localization ofthe interference and division of the interference regions areconsidered Finally a distributed link scheduling algorithmbased on MSIC to generate a feasible scheduling set isproposed

The rest of this article is organized as follows the first andsecond parts describe the background and current situationIn the third part the MSIC network model is constructedbased on SIC technology and the cross-layer optimizationproblem is modeled In the fourth part the interferenceregions are divided and the detailed process of the distributedlink scheduling algorithm based on theMSIC networkmodelis given The fifth part provides experimental results The

Wireless Communications and Mobile Computing 3

last part summarizes the paper and puts forward the futuredevelopment trends

2 Related Work

The link scheduling problemhas been the subject of extensiveresearch Moscibroda et al first defined the link schedulingproblem and introduced the concept of scheduling com-plexity under the SINR model [25] Goussevkaia et alproved that the link scheduling problem is NP-hard [26]Dinitz considered single-slot scheduling and gave the firstdistributed algorithm [27] Although his goal was to designa distributed algorithm the technique relies mainly on themachine learning theory of the algorithm Qian et al [21]first developed a new ldquoMIMO-piperdquo model that captured therate-reliability trade-off in MIMO communications How-ever the ldquoconservative schedulingrdquo achieves a suboptimalperformance Choi et al combined a two-segment queuestructure and carrier sensing technology to design a fullydistributed link scheduling algorithm based on the SINRmodel [17] In [28] Chen et al proposed a low-complexityapproximate optimal scheduling algorithm based on a cross-entropy optimization framework

Most previous work in MIMO wireless networks didnot consider SIC We therefore focus on link scheduling inMIMO wireless networks with SIC The effectiveness of SIChas been verified recently [29] In [30] Lv et al studiedlink scheduling in a network with SIC but ignored theeffects of aggregate interference Then in 2012 they tookthe lead in researching link scheduling under the SINRmodel in wireless networks with SIC [20] The algorithmconsiders the influence of cumulative interference but itis a greedy algorithm based on independent sets that canobtain an approximate optimal schedule In [24] Kontiket al proposed a heuristic algorithm based on the columngeneration method using SIC technology to study the prob-lem of minimized scheduling length in single-hop wirelessnetworks The performance of this algorithm is very closeto the optimal linear programming algorithm and has betterrobustness SIC technology was shown to effectively improvenetwork performance

In addition due to the degree of freedom (DoF) ofMIMO network throughput can be improved by spatialmultiplexing (SM)Therefore the problem of link schedulingbased on DoF has also been extensively studied Based on theDoF concept Sultan et al [31] proposed a handover standardthat maximizes the capacity of the downlink channel whenuplink capacity is maintained at a certain level To furtherimprove the overall performance of the network the datalink layer the network layer and the transmission layerneed to be designed cooperatively for optimization Thelayered protocol architecture with network adaptability hasreceived widespread attention such as the joint routing andscheduling optimization scheme [6] and joint power controland link scheduling optimization scheme [32 33] but thereare still many limitations in the practical applications of theseoptimization schemesTherefore a mathematical frameworkis established in this paper for the cross-layer optimization

of routing and scheduling with constraints of traffic balanceand link capacity

3 The System Model

31 Network Model When the links are transmitted in theSINR model if the signal at the expected receiver is higherthan a given threshold the link is transmitted successfully[17] that is

119878119868119873119877푟푖 =119875푟푖 (119904푖)119868푟푖 + 1198730

ge 120573 (1)

where 119875푟푖 (119904푖) is the received power at receiver 119903푖 from sender119904푖 119868푟푖 is the aggregated interference from the active links in theneighbors of link 119897푖1198730 is the background noise and 120573 is theminimum SINR threshold required for receiver 119903푖 to decodesignals successfully

Consider a set of MIMO networks consisting of 119899 com-munication links 119871 = 1198971 119897푛 where each link 119897푖 includes asender 119904푖 and a receiver 119903푖 The Euclidean distance between 119904푗and 119903푖 is 119889푗푖 = 119889(119904푗 119903푖) Thus the length of link 119897푖 is 119889푖푖 If 119904푖 isthe intended sender (1) can be converted into

119878119868119873119877푟푖 =119875 (119904푖) 119889 (119904푖 119903푖)

훼

1198730 + sum푠푗isin푆푡푠푖119875 (119904푗) 119889 (119904푗 119903푖)

훼

=119875푙푖119889푖푖

훼

1198730 + sum푙푗isin퐿耠푙푖

119875푙푗119889푗푖훼

(2)

where119875(119904푗) is the transmission power from sender 119904푗 120572 is thepath-loss factor 119878푡 is the set of all senders that are transmittedconcurrently in the same time slot 119905 as the expected sender 119871耠is a set of links that are simultaneously scheduled in the sametime slot

Assume that all nodes are static and apply MIMO tech-nology with119872 antennas A node communicates with othersthrough wireless links and each node has an input links set119871푖푛푖 and an output links set 119871표푢푡푖 of node 119894 Suppose a timeframe consists of 119879 slots and the state of a link subset in atime slot 119905 (1 le 119905 le 119879) depends on link scheduling For agiven slot 119905 the data flow from sender 119904푗 to 119903푖 can be expressedas a signal vector x푗 = [1199091푗 119909

2푗 119909

푀푗 ]

푇 and the MIMO signal119910푗푖 received by receiver 119903푖 from sender 119904푗 can be expressed asthe following

119910푗푖 = 120572푗푖Vdagger푗푖H

dagger푗푖U푗A푗x푗 + sum

푘isin퐼푖푘 =푗

120572푘푖Vdagger푗푖H

dagger푘푖U푘A푘x푘

+ Vdagger푗푖n푖

(3)

where H푘푖 isin 119862푀times푀 is the channel matrix between sender119904푘 and receiver 119903푖 and is normalized to mean power 1 ◻dagger isthe Hermitian operations of the corresponding matrix U푘 isin119862푀times푀 is the unitary transmitting precoding matrix at sender119904푘 A푗 isin 119877푀times푀and A푗 = diagradic119901푗 radic119901푗 radic119901푗 is the real-valued diagonal transmit amplitude matrix where 119901푗 is thetransmission power of the corresponding sender 119904푗 V푗푖 isin

4 Wireless Communications and Mobile Computing

yx

Ｏ1

Ｏ2

（1 1

（1 2

（2 1

（2 2

v1

v2

Figure 2 Multi-antennaWireless Channel

119862푀times푀 is the unitary receiving decoding matrix at receiver 119903푖for signals from sender 119904푗ni isin 119862푀times1 is awhiteGaussiannoisevector with variance 1198730 per element 2 is the norm of thevector Figure 2 shows that the sender and receiver 2-antennaarray and MIMO channel are used at both ends To simplifycalculations assuming that data streams are uncorrelated theSINR for the n-th element in 119910푗푖 is given by the following

119878119868119873119877푛푗푖 =119901푗1205722푗푖

100381710038171003817100381710038171003817k푛dagger

푗푖Hdagger푗푖u

푛푗

1003817100381710038171003817100381710038172

1198730 + sum푘isin퐼푖푘 =푗 119901푘1205722푘푖10038171003817100381710038171003817k

푛dagger

푗푖Hdagger푘푖U푘

100381710038171003817100381710038172

(4)

32 MSIC Model The manner in which interference isdealt with effectively affects the performance of the linkscheduling algorithm in MIMO networks The MSIC modelis constructed based on SIC under the SINR model Themain idea of SIC is that the power level of the signals from119870 senders received at 119903푖 are in descending order 119875푟푖 (119904퐾) ge119875푟푖(119904퐾minus1) 119875푟푖 (119904푖) 119875푟푖 (1199042) ge 119875푟푖 (1199041) [20] If the strongestsignal dissatisfies the SINR constraint the process of SICends Otherwise this signal will be decoded while othersignals are considered interference and noise If it is theexpected signal then the transmission is successful if notthis signal is removed and the remaining signals are decodedsequentially until the expected signal is decoded successfully

In detail the SIC model needs to satisfy the followingconstraints Receiver 119903푖 tries to decode signal from sender 119904푛in the order 119896 119896minus1 119899Then the signal with received power119875푟푖(119904푛) can be decoded successfully if and only if

119904119905119890119901 1119875푟푖 (119904푘)

1198730 + sum푘minus1푗isin퐼푖푗=1

119875푟푖 (119904푗)ge 120573푘푖

119904119905119890119901 2119875푟푖 (119904푘minus1)

1198730 + sum푘minus2푗isin퐼푖푗=1

119875푟푖 (119904푗)ge 120573(푘minus1)푖

sdot sdot sdot

119904119905119890119901 (119896 minus 119899 + 1)119875푟푖 (119904푛)

1198730 + sum푛minus1푗isin퐼푖푗=1

119875푟푖 (119904푗)ge 120573푛푖

(5)

If signal 119910푖푖 wants to be decoded correctly it must satisfythe MSIC constraints shown in

119878119868119873119877푛푗푖 =119901푗1205722푗푖

100381710038171003817100381710038171003817k푛dagger

푗푖Hdagger푗푖u

푛푗

1003817100381710038171003817100381710038172

1198730 + sum푘isin퐼푖푘lt푗119901푘1205722푘푖

10038171003817100381710038171003817k푛dagger

푗푖Hdagger푘푖U푘

100381710038171003817100381710038172ge 120573푗푖

forall119895 119904119905 119875푟푖 (119904푖) lt 119875푟푖 (119904푗)

119878119868119873119877푛푖푖 =119901푖1205722푖푖

100381710038171003817100381710038171003817k푛dagger

푖푖 Hdagger푖푖u

푛푖

1003817100381710038171003817100381710038172

1198730 + sum푘isin퐼푖푘lt푖119901푘1205722푘푖

10038171003817100381710038171003817k푛dagger

푖푖 Hdagger푘푖U푘

100381710038171003817100381710038172ge 120573푖푖

(6)

Because SIC is used the receiver can sequentially cancelall interference signals that are stronger than its expectedsignal if those stronger signals satisfy (6)Therefore it is onlynecessary to consider the residual interference at the senderwhich is weaker than the expected signal Specifically theresidual SINR from sender 119904푗 to receiver 119903푖 at time slot 119905 isdefined as follows

119903-119878119868119873119877푗푖 [119905]

=119901푗1205722푗푖

100381710038171003817100381710038171003817k푛dagger

푗푖Hdagger푗푖u

푛푗

1003817100381710038171003817100381710038172

1198730 + sum푝푘훼2푘푖k푛dagger푘푖Hdagger푘푖U푘2le푝푗훼2푗푖k푛

dagger

푗푖 Hdagger푗푖u푛푗 2

푘isin퐼푖푘 =푗119901푘1205722푘푖

10038171003817100381710038171003817k푛dagger

푗푖Hdagger푘푖U푘

100381710038171003817100381710038172

ge 120573푗푖

(7)

where sender 119904푘 in the summation formula includes allsendersrsquo signals with weaker power than node 119904푗

33 Problem Model Consider the problem of throughputmaximization in MIMO wireless networks This paper trans-forms the cross-layer joint scheduling problem into conges-tion control routing and scheduling problems By using localinformation the congestion control problem is solved at thesource node of each flow and the routing and schedulingare transformed into the problem of flow balance and linkcapacity constraint which facilitates distributed deploymentand ensures network throughput

Let 119865 denote a set of active link session flows thatdescribes the flow routing in the network Denote 119904(119891) and119889(119891) as the source and destination nodes of session flow119891 isin 119865 respectively Υ(119891) represents the reachable end-to-end throughput of session flow 119891 isin 119865 and Υmin is theminimum reachable end-to-end throughput in all sessionsthat is Υmin = min푓isin퐹Υ(119891) Υ푙(119891) represents the number ofdata rates caused by session flow 119891 isin 119865 on link 119897 The goal ofthis paper is tomaximize theminimum reachable end-to-endthroughput Υmin to maximize network throughput

Wireless Communications and Mobile Computing 5

We assume a half-duplex node on a MIMO node If node119894 isin 119873 is a sender in time slot 119905 the binary variable 119904푖(119905) is1 otherwise it is 0 Similarly if node 119894 isin 119873 is a receiver intime slot 119905 the binary variable 119903푖(119905) is 1 otherwise it is 0 Forhalf-duplex mode the constraint can be written as follows

119904푖 (119905) + 119903푖 (119905) le 1 (1 le 119894 le 119873 1 le 119905 le 119879) (8)

Denote 119909푙(119905) as the number of data streams over link119897 If node 119894 is not a sender then there is sum푙isin퐿표푢푡푖

119909푙(119905) =0 Otherwise in order to satisfy the DoF constraint at thesending node the total number of outgoing data streamsshould be positive and cannot exceed the number of antennasit owns that is 1 le sum푙isin퐿표푢푡푖

119909푙(119905) le 119872 These two cases can besummarized as follows

119904푖 (119905) le sum푙isin퐿표푢푡푖

119909푙 (119905) le 119872119904푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879) (9)

Similarly according to whether node 119894 is an active receiverwe have the following constraint at the receiving node

119903푖 (119905) le sum푙isin퐿푖푛푖

119909푙 (119905) le 119872119903푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879) (10)

For the congestion control problem of the transport layereach flow 119891 in the network determines the data rate of thenext slot independently according to the local congestionqueue information of the node in the current time slot 119880푓푖 (119905)represents the congestion queue length of flow 119891 at node 119894in time slot 119905 and U(119905) = [119880푓푖 (119905)] (119894 isin 119873 119891 isin 119865) is the setof all congestion queues According to the input and outputmode of each node the local congestion queue informationis updated dynamically as follows 119880푓푖 (119905 + 1) = 119880푓푖 (119905) +sum푙isin퐿푖푛푖

119909푙(119905)minussum푙isin퐿표푢푡푖119909푙(119905)+v푓(119905) and the initialized condition

queue is satisfied with119880푓푖 (0) = 0The source session flow119891 iscompressed into a source rate v푓(119905) before being pushed intothe queue Since the local congestion queue length of eachnode determines the upper limit of the data sum that can betransmitted in the current time slot 119905 there are the followingconstraints

sum푙isin퐿표푢푡푖

119909푙 (119905) le 119880푓푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879 119891 isin 119865) (11)

The session flow 119891 in the network determines the data rateof the next time slot according to the congestion queueconstraint Meanwhile in order to guarantee the strongrobustness of the network the following inequalities must besatisfied

lim푇㨀rarrinfin

1119879

푇minus1

sum푡=0

sum푖isin푁

sum푓isin퐹

119864 119880푓푖 (119905) lt infin (12)

For routing and scheduling problems 119863 =maxsum푙isin퐿 119903푙(119891) lowast max푓isin퐹119906푠푙(119891) minus 119906푑푙(119891) and eachlink 119897 can use local congestion queue information to find aflow 119891lowast that satisfies 119891lowast = argmax푓isin퐹119906s푙(119891) minus 119906푑푙(119891) Let119908푙 = 119906푠푙(119891

lowast) minus 119906푑푙(119891lowast) as the weight of link 119897 (119908푙 can also

be understood as the queue length at link 119897 with flow 119891lowast)To solve routing and scheduling problems we will propose adistributed algorithm in Section 4 to generate an active set119871푆耠 of concurrent links In each time slot the links in set 119871푆耠can send data to the receivers (we assume that in each timeslot each active link transmits a packet) Let 119863 be convertedinto the following form

119863 = maxsum푙isin퐿

Υ푙 (119891lowast) sdot 119908푙 (13)

To achieve the goal of maximizing the minimum end-to-end throughput Υmin a feasible routing scheduling alsoneeds to satisfy the following two constraints flow balanceconstraints and the link capacity constraint We have thefollowing flow balance constraints

(a) at the source node we have

sum푙isin퐿표푢푡푖

Υ푙 (119891) = Υ (119891) (119894 = 119904 (119891) 119891 isin 119865) (14)

(b) at each relay node we have

sum푙isin퐿푖푛푖

Υ푙 (119891) = sum푙isin퐿표푢푡푖

Υ푙 (119891)

(1 le 119894 le 119873 119894 = 119904 (119891) 119894 = 119889 (119891) 119891 isin 119865)(15)

(c) at the destination node we have

sum푙isin퐿푖푛푖

Υ푙 (119891) = Υ (119891) (119894 = d (119891) 119891 isin 119865) (16)

It is easy to verify that as long as any two of these equationsare satisfied the other one will also be satisfied Therefore itis sufficient to satisfy the first two equations

It is assumed that a fixed modulation and encodingscheme is used for each data stream and that each data streamcorresponds to one unit data rate Since the total data rate onlink 119897 cannot exceed the average rate of the link we have thefollowing link capacity constraint

sum푓isin퐹

Υ푙 (119891) le1119879

푇

sum푡=1

119909푙 (119905) (17)

where the right side represents the average throughput on link119897 of a frame (119879 time slots) Putting all the constraints togetherwe have the expression for the throughput maximizationproblem

max Υmin

st Υmin le Υ (119891) (119891 isin 119865)

119903-119878119868119873119877푗푖 [119905]

=119901푗1205722푗푖

100381710038171003817100381710038171003817k푛dagger

푗푖Hdagger푗푖u

푛푗

1003817100381710038171003817100381710038172

1198730 + sum푝푘훼2푘푖k푛dagger푘푖Hdagger푘푖U푘2le푝푗훼2푗푖k푛

dagger

푗푖 Hdagger푗푖u푛푗2

푘isin퐼푖푘 =푗119901푘1205722푘푖

10038171003817100381710038171003817k푛dagger

푗푖Hdagger푘푖U푘

100381710038171003817100381710038172

ge 120573푗푖

119904푖 (119905) + 119903푖 (119905) le 1 (1 le 119894 le 119873 1 le 119905 le 119879)

6 Wireless Communications and Mobile Computing

ＦＣ

ＦＣ

ＦＣ

ＦＣ

ＬＣＭＣ

Figure 3 Division of Interference Regions

119904푖 (119905) le sum푙isin퐿표푢푡푖

119909푙 (119905) le 119872119904푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879)

119903푖 (119905) le sum푙isin퐿푖푛푖

119909푙 (119905) le 119872119903푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879)

sum푙isin퐿표푢푡푖

119909푙 (119905) le 119880푓푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879 119891 isin 119865)

lim푇㨀rarrinfin

1119879

푇minus1

sum푡=0

sum푖isin푁

sum푓isin퐹

119864 119880푓푖 (119905) lt infin

sum푙isin퐿표푢푡푖

Υ푙 (119891) = Υ (119891) (119894 = 119904 (119891) 119891 isin 119865)

sum푙isin퐿푖푛푖

Υ푙 (119891) = sum푙isin퐿표푢푡푖

Υ푙 (119891)

(1 le 119894 le 119873 119894 = 119904 (119891) 119894 = 119889 (119891) 119891 isin 119865)

sum푓isin퐹

Υ푙 (119891) le1119879

푇

sum푡=1

119909푙 (119905)

(18)

4 Distributed Link SchedulingAlgorithm Based on MSIC

41 Division of Interference Regions Due to the character-istics of transmission loss the receiving power 119875푟푖 (119904푗) ofdifferent links is also different [34] The total interference atreceiver 119903푖 is expressed as follows

119868푟푖 = sum푠푗isin푆푡푠푖

119875 (119904푗)

119889 (119904푗 119903푖)훼 = sum

푠푗isin푆푡푠푖

119875푟푖 (119904푗) (19)

The scheduling problem of using SIC under the SINRmodel has been proved to be NP-hard [20] If the strongersignal in the network satisfies (5) it can be decoded andremoved due to the adoption of SIC Therefore the strengthof the receiving power does not completely measure theinterference generated by the link In this paper in orderto describe the interference localization the interferenceregions are defined to measure the level of interference

Different interference regions 119860 푙푖 119861푙푖 and 119862푙푖are divided

according to (19) 119860 푙푖 119861푙푖 and 119862푙푖 are concentric ring (circu-

lar) regions centered on receiver 119903푖 of link 119897푖 respectively asshown in Figure 3 (the red circular region is 119860 푙푖

the bluering region is 119861푙푖 and the black dotted ring region is 119862푙푖)The interference generated by the active link in the 119860 푙푖

and119861푙푖 regions will interrupt the transmission of link 119897푖 and theset of concurrent links in these regions is denoted as 119871푆 Thecumulative interference generated by the active link in the 119862푙푖region has a negligible effect on the receiver of link 119897푖

According to (2) the maximum cumulative interferencevalue that link 119897푖 can tolerate is the following

119868푟푖 le 119868max푙푖

le119875푙푖120573119889푖푖

훼 (20)

Therefore in order to satisfy the MSIC constraints thesum of the cumulative interference values at receiver 119903푖 of link119897푖 cannot exceed 119868max

푙푖 If the total interference in the 119860 푙푖

and119861푙푖 regions is (1 minus 119898)119868

max푙푖

and the total interference in the 119862푙푖region is119898119868max

푙푖 then we have

(1 minus 119898) 119868max푙푖

+ 119898119868max푙푖

le 119868max푙푖

(21)Assuming that the link 119897푗 at receiver 119903푖 from sender 119904푗 isin 119860 푙푖is stronger than link 119897푖 from sender 119904푖 SIC is used That is

Wireless Communications and Mobile Computing 7

Start

End

Initialization

MSIC feasibility judgment

Add link l to acc l

Remove link l from seq l

Update concurrent link set Ls

MSIC feasibility test

Yes

No

No

Yes

Figure 4 Distributed MSIC scheduling algorithm flow chart

receiver 119903푖 uses SIC to decode these strong signals continu-ously before decoding the expected signal from sender 119904푖 Letall links in a feasible set 119871푆 of concurrent links be transmittedsuccessfully When any link 119897푗 is added to the set 119871푆耠 sube 119871푆 thelink transmission will fail Obviously 119871푆耠 is the maximum setof concurrent links and 119871푆耠 must satisfy the constraints in(7)

42 Distributed MSIC Scheduling Algorithm In this sectionbased on the CSMACA mechanism and MSIC constraintswe design the distributed single-slot MSIC algorithm to solvethe scheduling problems If the links 119897 isin 119871耠 in the networkcan be transmitted concurrently then 119871耠 can be defined as ascheduling set In each scheduling time slot each linkwill runscheduling algorithms to generate a new feasible schedulingset 119871푆耠

Next considering the MSIC model and interferenceregions division introduced above a distributed link schedul-ing algorithm is proposed under the MSIC constraints Thealgorithm flow chart is shown in Figure 4 Three states of thelink are defined Active Inactive and Standby The four setscorrespond to different states where 119904119894119888 is the active link setthat satisfies the MSIC constraint and can be scheduled in thecurrent scheduling time slot 119886119888119888 is the standby link set thathas not been judged byMSIC constraints 119897119900119888 is the local cachelink set in the standby state and 119904119890119902 is the candidate link set inthe inactive state Therefore the state of a link in the currentslot can be distinguished by the set of links to which the linkcurrently belongs

(1) Initialization Stage At the beginning of each schedulingcycle each link 119897 maintains two sets of local links set 119886119888119888푙and set 119904119890119902푙 The links contained in the set 119886119888119888푙 are added to

a feasible set 119871푆 of concurrent links in a certain schedulingcycle and the links contained in set 119904119890119902푙 are candidate linksto be added into set 119871푆 At the beginning of each schedulingcycle initializing 119886119888119888푙 = Oslash and 119904119890119902푙 = 119897 119860 푙 cup 119861푙

(2) MSIC Feasibility Judgment Stage Each scheduling cycleconsists of several slots and in each slot each link 119897 makes adecision about whether it should be added to 119886119888119888푙 or removedfrom 119904119890119902푙 At the beginning of each scheduling slot all linksin the set 119904119890119902푙 are weighted for comparisonThe sender of link119897 broadcasts its weight information 119908푙 to all links 119896 whosesender is located in the 119860 푙 region of link 119897 If link 119897 has thelargest weight among all links in 119904119890119902푙 it will run Algorithm 1to try to add itself to 119886119888119888푙

The detailed process is as follows The sender of link 119897broadcasts a Requestmessage to links in 119860 푙cup119861푙 first If thereis a collision all of the links select a random back-off timeand wait for it If there is no collision the sender of all linksin 119860 푙 cup 119861푙 will add link 119897 to set 119897119900119888푙 When link 119897 is added tothe current schedule any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙 will determinewhether it remains feasible under the MSIC constraints Thespecific judgment process is as follows For each link 119897耠 isin119886119888119888푙cup119897119900119888푙 the set of linkswith sender 119904푙耠 isin 119886119888119888푙耠cup119897119900119888푙耠cap119860 푙耠and receiver 119903푙耠 is defined as the MSIC link set 119904119894119888푙耠 TheMSICconstraints will be satisfied when any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙satisfies the following conditions (i) the total interference 119868푙耠coming from set 119861푙耠 does not exceed (1 minus119898)119868max

푙耠 (ii) all links119896 isin 119904119894119888푙耠 are feasible that is the total interference 119868푘 comingfrom set 119861푘 does not exceed (1 minus 119898)119868max

푘 According to the above procedure if any link 119897耠 isin 119886119888119888푙 cup

119897119900119888푙 does not satisfy the MSIC constraints the sender oflink 119897耠 will send an Error message to link 119897 indicating thatlink 119897 cannot be added to set 119871푆 (the current scheduling isnot feasible due to the strong interference caused by link119897) If link 119897 isin 119897119900119888푙 does not receive any Error messagesfrom its neighbors it adds link 119897 to set 119886119888119888푙 and removeslink 119897 from 119904119890119902푙 and 119897119900119888푙 Then the sender broadcasts aSuccess message to all its neighbors to update their link sets119886119888119888 119904119890119902 and 119897119900119888 Otherwise it removes link 119897 from 119904119890119902푙and 119897119900119888푙 and then broadcasts a Remove message to all itsneighbors to update their link sets 119904119890119902 and 119897119900119888 After the aboveprocess is performed until a new link is added to 119871푆 thecurrent scheduling process is still feasible under the MSICconstraints

(3) MSIC Feasibility Test Stage After a new 119871푆耠 is generatedin each slot all links 119897 isin 119904119890119902푙 need to make the followingdecision about whether the MSIC constraints are satisfiedFor each link 119897 isin 119904119890119902푙 the set of links with sender 119904푙 isin119886119888119888푙 cap 119860 푙 and receiver 119903푙 is defined as another MSIC linkset 119904119894119888푙耠 Similar to the first procedure any link 119897 isin 119904119890119902푙 thatsatisfies any of the following conditions will dissatisfy theMSIC constraints (i) the total interference 119868푙耠 coming fromset 119861푙 exceeds (1 minus 119898)119868max

푙 or (ii) for any link 119896耠 isin 119904119894119888푙耠 is notfeasible that is the total interference 119868푘耠 coming from set 119861푘耠exceeds (1 minus119898)119868max

푘耠 After the above process if there is a link119897 in 119904119890119902푙 that does not satisfy the MSIC constraints the senderwill remove link 119897 from 119904119890119902푙 and broadcast a Remove messageto all its neighbors to update their link sets 119904119890119902 and 119886119888119888 The

8 Wireless Communications and Mobile Computing

1 sets of int 119886119888119888푙 119904119890119902푙 119897119900119888푙 119904119894119888푙耠 119904119894119888푙耠 initialize2 119886119888119888푙 larr997888 Oslash and 119904119890119902푙 larr997888 119897 119860 푙 cup 119861푙3 Sender of link 119897 broadcasts Requestmessage to links in 119860 푙 cup 119861푙4 for link 119897耠 isin 119860 푙 cup 119861푙 cap 119886119888119888푙 cup 119897119900119888푙 do MSIC feasibility judgment5 if sender of link 119897耠 receives Requestmessage from sender of link 119897 then6 sender of link 119897耠 adds link 119897 into 119897119900119888푘7 sender of link 119897耠 calculates cumulative interference 119868푙耠 8 if 119868푙耠 gt (1 minus 119898)119868max

푙耠then

9 Sender of link 119897耠 broadcasts Error message to sender of link 11989710 else11 Generate 119904119894119888푙耠 12 for 119896 isin 119904119894119888푙耠 do13 Link 119896 calculates cumulative interference 119868푘14 if 119868푘 gt (1 minus 119898)119868max

푘 then15 Sender of link 119897耠 broadcasts Error message to sender of link 11989716 end if17 end for18 end if19 end if20end for21 if sender of link 119897 does not receive Error messages then Generate concurrent links set22 119886119888119888푙 larr997888 119886119888119888푙 cup 11989723 119904119890119902푙 larr997888 119904119890119902푙11989724 119897119900119888푙 larr997888 119897119900119888푙11989725 Sender of link 119897 broadcasts Successmessage to all its neighbors to update their link sets 119886119888119888 119904119890119902 and 11989711990011988826 Goto Algorithm 227 else28 119904119890119902푙 larr997888 119904119890119902푙119897 Does not satisfy MSIC feasibility conditions29 Sender of link 119897 broadcasts Removemessage to all its neighbors to update their local link sets 119904119890119902 and 11989711990011988830 end if

Algorithm 1 Distributed MSIC Scheduling Algorithm (MSIC feasibility judgment)

above process ensures that each link in 119904119890119902푙 satisfies theMSICconstraints under the current scheduling

In the distributed algorithm the number of time slots ineach scheduling cycle is a fixed value In each scheduling sloteach link will run the distributed scheduling algorithm togenerate a new feasible scheduling set 119871푆耠 during schedulingOnce the scheduling is completed the selected link willtransmit a packet during the transmission cycle

43 Theoretical Proof of Algorithm

Theorem 1 The set 119871푆 of scheduling generated by the MSICalgorithm is feasible

Proof Based on the MSIC algorithm under interferenceregions division each link will run the algorithm indepen-dently in each scheduling slot to generate a new feasiblescheduling set 119871푆耠 From Algorithm 2 it is known that aftera new set 119871푆耠 is generated in each time slot all links 119897 isin 119904119890119902푙need to be tested to determine if theMSIC constraints are stillsatisfied To ensure that each link in 119904119890119902푙 satisfies the MSICconstraints under the current scheduling any link 119897 that doesnot satisfy the MSIC constraints will be removed from 119904119890119902푙Therefore the interference links cannot be scheduled at thesame time that is the links in the current set 119871푆耠 are feasiblewhich ensures the feasibility of the algorithm

Theorem 2 The time complexity of the MSIC algorithm is119874(1198962)

Proof In the process of MSIC feasibility judgment of Algo-rithm 1 it is necessary to judge the MSIC constraints formula(4) of any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙 and decide whether to add thelink to the current scheduling set This process requires twoloop statements to be executed with the algorithm executioncomplexity of 119874(1198962) where 119896 represents the number ofconcurrently transmitted signals After Algorithm 1 generatesa new set 119871푆耠 the MSIC feasibility test is performed inAlgorithm 2 The MSIC constraints condition needs to betested again for all links 119897 isin 119904119890119902푙 to ensure that any link in119904119890119902푙 satisfies the MSIC constraints This process also needsto execute two loop statements with the algorithm executioncomplexity of119874(1198962) Therefore the total algorithm executioncomplexity is 119874(1198962)

Theorem 3 The messages complexity of the MSIC algorithmis 119874(119899)

Proof The message complexity of sending a Request broad-cast message is 119874(1) To find a set of links that can be con-currently given by a network of 119899 links an MSIC constraintjudgment is performed for each link of 119897耠 isin 119860 푙 cup 119861푙 cap119886119888119888푙 cup 119897119900119888푙 and the number of Error or Success messages

Wireless Communications and Mobile Computing 9

1 sets of int 119868푘耠 119868푗耠 119904119894119888푘耠2 for link 119896 isin 119860 푙 cup 119861푙 cap 119904119890119902푙 do MSIC feasibility test3 if the sender of link 119896 receives a Successmessage from the sender of link 119897 then4 Link 119896 calculates the cumulative interference 119868푘耠5 if 119868푘耠 gt (1 minus 119898)119868max

푘 then6 The sender of link 119896 broadcasts a Removemessage to its neighbors to update their link sets 1199041198901199027 else8 Generate 119904119894119888푘耠9 for 119895 isin 119904119894119888푘耠 do10 Link 119895 calculates the cumulative interference 119868푗耠11 if 119868푗耠 gt (1 minus 119898)119868max

푗 then12 The sender of link 119896 broadcasts a Removemessage to its neighbors to update their link sets 11990411989011990213 end if14 end for15 end if16 end if17 end for

Algorithm 2 Distributed MSIC Scheduling Algorithm (MSIC feasibility test)

sent is at most 119899 minus 1 For each link of 119896 isin 119860 푙 cup 119861푙 cap 119904119890119902푙a feasibility test is performed and the number of Remove orSuccess messages is up to 119899 minus 1 When the execution of thealgorithm ends the total number of messages used is up to119874(119899)

5 Experimental Results

In this section the distributed single-slot scheduling probleminMIMOwireless networks is studied under the SINRmodelThe simulation is the average of 50 trials obtained on anetwork with 100 links The network size is 600 lowast 600 andthe distance between the sender and the receiver is selectedwithin the range of [20 40] The SINR parameters are set asfollows the threshold value is 120573 = 3 the path loss index is120572 = 22 the background noise power is119873 = 4times10minus7 and theuniform power is 119875 = 2 and 119875 = 10

First the relationship between the size of different net-works and the number of successful transmissions of linksis studied The simulation results are shown in Figure 5Under different power allocations the number of successfultransmissions of the link increases as the network sizeincreases and a larger transmission power can generate alarger neighbor size which is benefited by the gain of thetransmission power However when the network size is largethe neighbor size reaches the upper bound and the gain fromincreasing the power becomes very small At the same timelarger power will also cause more interference to other linksAt this time the impact of the interference on transmission isgreater than the benefit of the network scale increase whichmakes it impossible to satisfy the SINR constraint conditionalthough it improves its own successful transmission proba-bility and reduces the total size of the successful transmissionof the linkTherefore the transmission scale cannot be soughtblindly by increasing the power and a larger-scale schedulingset can be realized by controlling the network scale

20 50 100 150 200 250 300 350 400 450 500 550 6000

10

20

30

40

50

60

70

80

90

Network sizeP=10P=2

Num

ber o

f suc

cess

ful t

rans

miss

ions

Figure 5 The relationship between network size and number ofsuccessful transmissions

Next we compare the number of concurrent link trans-missions of different algorithms At the network layer therouting algorithm based on the least hops is adopted Forconvenience the distance data rate bandwidth and trans-mission power of the data stream are all normalized to 1

First the MSIC algorithm is compared with the recursivelargest first (RLF) algorithm and the smallest degree first(SDF) algorithm in [20] The results in Figure 6 show thatthe MSIC algorithm can obtain a larger link schedulingscale compared with the other two algorithms After theSIC is used all signals with high power in the interferenceregions can be decoded and removed firstly and thus theinterference reached at the receiver is smaller and a larger setof concurrent links can be obtained

10 Wireless Communications and Mobile Computing

0 10 20 30 40 50 60 70 800

5

10

15

20

25

30

Scheduling slot

MIMORLF

SDFMSIC

Num

ber o

f con

curr

ent l

ink

tran

smiss

ions

Figure 6 Comparison of the number of concurrent link transmis-sions of different algorithms

Then we study the effect of the parameter 119898 on thenumber of concurrent link transmissions Figure 7 shows thatthe number of concurrent links decreases as the parameter119898 increases When 119898 is smaller the interference radius ofeach link in the network is larger and there are more linksthat can participate in scheduling The number of concurrentlinks in each selected scheduling configuration is larger andthe data flow rate is higher At this time the network hasstronger interference management ability As the parametersbecome larger the interference in the network is largerthereby allowing fewer links to be transmitted concurrentlyThe MSIC algorithm can reduce partial interference andincrease the number of concurrent transmission links When119898 = 04 there is a close interference region radius betweenMSIC and MIMO so119898 = 04 is set here

Next we study the influence of the number of antennason network performanceThenumber of antennas is changedfrom 2 to 6 and the test is repeated 100 times We then takethe average value of each flow of 100 tests Ideally we assumethat the transmission rate of one link is equal to the capacityof the point-to-point MIMO link without other transmissioninterference As shown inFigure 8 throughput is nearly linearwith the number of antennas and the MSIC algorithm canachieve a higherminimumflow throughput and a higher totalthroughput in the network

To show more detail the flow rate gains for the four flowsessions are given in Figure 9 The simulation results showthat MSIC brings significant throughput gain toMIMOwire-less networks The network flow rate with SIC functionalityis more than half of the network rate without interferencecancellation whichmeans that the reachable unit end-to-endthroughput is increased by approximately 73on average dueto the application of SIC Therefore the MSIC algorithm hasobvious advantages in improving network throughput

01 02 03 04 05 06 07 08 0940

45

50

55

60

65

70

Parameter mMIMOMSIC

The n

umbe

r of c

oncu

rren

t tra

nsm

issio

ns

Figure 7The relationship between parameterm and the number ofconcurrent transmissions

6 Conclusions and Future Work

In this paper the MSIC scheduling algorithm based on SICin MIMO wireless networks is proposed First the MSICconstraints model is constructed under the SINR interfer-ence model Then interference region division is carriedout to describe the level of interference between links Afeasible scheduling set is generated by the distributed linkscheduling algorithm to coordinate the link transmissionand the interference between competing links in the MIMOnetwork is cancelled Experimental results show that thedistributed MSIC scheduling algorithm can bring significantperformance gain to wireless networks

Since the algorithm is premised on satisfying the thresh-old constraint of SINR the algorithm ends when the SINRvalue is less than the current threshold Therefore the nextresearch goal is how to solve the link scheduling problemwhen the SINR value is less than threshold

With the rapid development of the social economy theapplication of modern communication technology has beencontinuously promoted in various fields and the capacityrequirement for networks is increasing In addition dueto the complexity of the network environment a singletechnology will not have a sufficient effect on interferencecancellation Therefore in future wireless communicationnetworks a variety of joint applications of multiple interfer-ence cancellation technologies will be needed How to com-bine these technologies efficiently and achieve a reasonableoptimization combination is an important research direction

Data Availability

The simulation data used to support the findings of this studyare included within the article

Wireless Communications and Mobile Computing 11

2 25 3 35 4 45 5 55 61

2

3

4

5

6

7

8

9 x 105

Number of antennas

MIMOSDF

RLFMSIC

Min

imum

flow

thro

ughp

ut (b

ps)

(a) Minimum flow throughput

2 25 3 35 4 45 5 55 62

3

4

5

6

7

8

9

10

11 x 106

Number of antennas

MIMOSDF

RLFMSIC

Tota

l thr

ough

put (

bps)

(b) Total throughput

Figure 8 The relationship between antenna number and throughput

1 2 3 40

01

02

03

04

05

06

07

08

FlowMSICRLFMIMO

048046

056

033

054057

035

057061

028 032

043

The a

chie

vabl

e flow

rate

s

Figure 9 The gains of data flow rate for the four flow sessions

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (61672321 61771289 and 61832012)

Shandong provincial Graduate Education Innovation Pro-gram (SDYY14052 and SDYY15049) Qufu Normal Uni-versity Science and Technology Project (xkj201525) Shan-dong province agricultural machinery equipment researchand development innovation project (2018YZ002) ShandongProvincial Specialized Degree Postgraduate Teaching CaseLibrary Construction Program and Shandong ProvincialPostgraduate Education Quality Curriculum ConstructionProgram The authors thank the School of InformationScience and Engineering Qufu Normal University

References

[1] S Cheng Z Cai J Li and H Gao ldquoExtracting kernel datasetfrom big sensory data in wireless sensor networksrdquo IEEETransactions on Knowledge and Data Engineering vol 29 no4 pp 813ndash827 2017

[2] S Cheng Z Cai J Li and X Fang ldquoDrawing dominant datasetfrom big sensory data in wireless sensor networksrdquo in Pro-ceedings of the IEEE Conference on Computer Communications(INFOCOM rsquo15) pp 531ndash539 Hong Kong April 2015

[3] X Zheng and Z Cai ldquoReal-time big data delivery in wirelessnetworks a case study on video deliveryrdquo IEEE Transactions onIndustrial Informatics vol 13 no 4 pp 2048ndash2057 2017

[4] Z Cai andX Zheng ldquoA private and efficientmechanism for datauploading in smart cyber-physical systemsrdquo IEEE Transactionson Network Science and Engineering 2018

[5] L Lu G Y Li A L Swindlehurst A Ashikhmin and R ZhangldquoAn overview of massive MIMO benefits and challengesrdquo IEEEJournal of Selected Topics in Signal Processing vol 8 no 5 pp742ndash758 2014

[6] H Liu L Luo D Wu J Yu and D Chen ldquoRouting spectrumaccess and scheduling in multi-hop multi-channel wirelessnetworks with MIMO linksrdquo EURASIP Journal on Wireless

12 Wireless Communications and Mobile Computing

Communications and Networking vol 15 no 1 article no 652015

[7] B Hamdaoui and K G Shin ldquoCharacterization and analysis ofmulti-hop wireless mimo network throughputrdquo in Proceedingsof the Eighth ACM International Symposium on Mobile Ad HocNetworking and Computing pp 120ndash129 Montreal QuebecCanada September 2007

[8] L Jiang and J Walrand ldquoA distributed CSMA algorithm forthroughput and utility maximization in wireless networksrdquoIEEEACM Transactions on Networking vol 18 no 3 pp 960ndash972 2010

[9] H Yu O Bejarano and L Zhong ldquoCombating Inter-cellInterference in 80211ac-based multi-user MIMO networksrdquo inProceedings of the 20th ACM Annual International Conferenceon Mobile Computing and Networking (MobiCom rsquo14) pp 141ndash152 Maui Hawaii USA September 2014

[10] L B Le E Modiano C Joo and N B Shroff ldquoLongest-queue-first scheduling under SINR interferencemodelrdquo in Proceedingsof the 11th ACM International Symposium on Mobile Ad HocNetworking and Computing MobiHoc 2010 pp 41ndash50 USASeptember 2010

[11] J Li S Cheng Z Cai J Yu C Wang and Y Li ldquoApproximateholistic aggregation in wireless sensor networksrdquo ACM Trans-actions on Sensor Networks vol 13 no 2 article no 11 2017

[12] Y Zhou X Li M Liu X Mao S Tang and Z Li ldquoThroughputoptimizing localized link scheduling for multihop wireless net-works under physical interferencemodelrdquo IEEETransactions onParallel and Distributed Systems vol 25 no 10 pp 2708ndash27202014

[13] G Pei and A K S Vullikanti ldquoDistributed approximation algo-rithms for maximum link scheduling and local broadcasting inthe physical interferencemodelrdquo inProceedings of the 32nd IEEEConference on Computer Communications (IEEE INFOCOMrsquo13) pp 1339ndash1347 Turin Italy April 2013

[14] J Yu B Huang X Cheng and M Atiquzzaman ldquoShortest linkscheduling algorithms in wireless networks under the SINRmodelrdquo IEEE Transactions on Vehicular Technology vol 66 no3 pp 2643ndash2657 2017

[15] P J Wan X Xu and O Frieder ldquoShortest link scheduling withpower control under physical interferencemodelrdquo inProceedingof the Sixth International Conference on Mobile Ad-Hoc andSensor Networks pp 74ndash78 2010

[16] M Nabli F Abdelkefi W Ajib and M Siala ldquoEfficient central-ized link scheduling algorithms in wireless mesh networksrdquo inProceedings of the 10th International Wireless Communicationsand Mobile Computing Conference IWCMC 2014 pp 660ndash665Cyprus August 2014

[17] J-G Choi C Joo J Zhang and N B Shroff ldquoDistributed linkscheduling under SINR model in multihop wireless networksrdquoIEEEACM Transactions on Networking vol 22 no 4 pp 1204ndash1217 2014

[18] J Park and S Lee ldquoDistributed MIMO Ad-hoc networks Linkscheduling power allocation and cooperative beamformingrdquoIEEE Transactions on Vehicular Technology vol 61 no 6 pp2586ndash2598 2012

[19] Y Shi Y Thomas H J Liu and S Kompella ldquoHow tocorrectly use the protocol interference model for multi-hopwireless networksrdquo in Proceedings of the 10th ACM InternationalSymposium on Mobile Ad Hoc Networking and ComputingMobiHocrsquo09 pp 239ndash248 USA May 2009

[20] S Lv XWang andX Zhou ldquoScheduling under the SINRmodelin ad hoc networks with successive interference cancellationrdquoComputer Engineering and Science vol 34 no 2 pp 1ndash5 2012

[21] D Qian D Zheng J Zhang and N Shroff ldquoCSMA-baseddistributed scheduling in multi-hop MIMO networks underSINR modelrdquo in Proceedings of the IEEE INFOCOM 2010 pp1ndash9 USA March 2010

[22] O Goussevskaia M M Halldorsson and R WattenhoferldquoAlgorithms for wireless capacityrdquo IEEEACM Transactions onNetworking vol 22 no 3 pp 745ndash755 2014

[23] O Goussevskaia and RWattenhofer ldquoScheduling wireless linkswith successive interference cancellationrdquo in Proceedings of the21st International Conference onComputer Communications andNetworks ICCCN 2012 pp 1ndash7 Germany August 2012

[24] M Kontik and S C Ergen ldquoScheduling in single-hop multipleaccess wireless networks with successive interference cancella-tionrdquo IEEE Wireless Communications Letters vol 3 no 2 pp197ndash200 2014

[25] T Moscibroda R Wattenhofer and A Zollinger ldquoTopologycontrol meets SINR the scheduling complexity of arbitrarytopologiesrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 310ndash321 Florence Italy May 2006

[26] O Goussevskaia R Wattenhofer M M Halldorsson and EWelzl ldquoCapacity of arbitrary wireless networksrdquo in Proceedingsof the 28th Conference on Computer Communications (IEEEINFOCOM rsquo09) pp 1872ndash1880 Rio de Janeiro Brazil April2009

[27] M Dinitz ldquoDistributed algorithms for approximating wirelessnetwork capacityrdquo in Proceedings of the IEEE INFOCOM pp 1ndash9 IEEE San Diego Calif USA March 2010

[28] J Chen C Wen S Jin and K Wong ldquoA low complexitypilot scheduling algorithm for massive MIMOrdquo IEEE WirelessCommunications Letters vol 6 no 1 pp 18ndash21 2017

[29] D Halperin T Anderson and D Wetherall ldquoTaking thesting out of carrier sense interference cancellation for wirelessLANsrdquo in Proceedings of the 14th ACM Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo08) pp 339ndash350 September 2008

[30] S LvW Zhuang XWang andX Zhou ldquoScheduling inwirelessad hoc networks with successive interference cancellationrdquo inProceedings of the IEEE INFOCOM 2011 - IEEE Conference onComputer Communications pp 1287ndash1295 Shanghai ChinaApril 2011

[31] R Sultan L Song K G Seddik and Z Han ldquoFull-duplexmeetsmultiuser MIMO comparisons and analysisrdquo IEEE Transac-tions on Vehicular Technology vol 66 no 1 pp 455ndash467 2017

[32] X Zheng Z Cai J Li and H Gao ldquoA study on application-aware scheduling in wireless networksrdquo IEEE Transactions onMobile Computing vol 16 no 7 pp 1787ndash1801 2017

[33] X Li Y Shi X Wang C Xu and M Sheng ldquoEfficient linkscheduling with joint power control and successive interferencecancellation in wireless networksrdquo Science China InformationSciences vol 59 no 12 pp 1ndash15 2016

[34] L Qu J He and C Assi ldquoDistributed link scheduling inwireless networks with interference cancellation capabilitiesrdquoin Proceedings of the 15th IEEE International Symposium on aWorld ofWireless Mobile andMultimedia Networks WoWMoM2014 pp 1ndash7 Australia 2014

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Wireless Communications and Mobile Computing 3

last part summarizes the paper and puts forward the futuredevelopment trends

2 Related Work

The link scheduling problemhas been the subject of extensiveresearch Moscibroda et al first defined the link schedulingproblem and introduced the concept of scheduling com-plexity under the SINR model [25] Goussevkaia et alproved that the link scheduling problem is NP-hard [26]Dinitz considered single-slot scheduling and gave the firstdistributed algorithm [27] Although his goal was to designa distributed algorithm the technique relies mainly on themachine learning theory of the algorithm Qian et al [21]first developed a new ldquoMIMO-piperdquo model that captured therate-reliability trade-off in MIMO communications How-ever the ldquoconservative schedulingrdquo achieves a suboptimalperformance Choi et al combined a two-segment queuestructure and carrier sensing technology to design a fullydistributed link scheduling algorithm based on the SINRmodel [17] In [28] Chen et al proposed a low-complexityapproximate optimal scheduling algorithm based on a cross-entropy optimization framework

Most previous work in MIMO wireless networks didnot consider SIC We therefore focus on link scheduling inMIMO wireless networks with SIC The effectiveness of SIChas been verified recently [29] In [30] Lv et al studiedlink scheduling in a network with SIC but ignored theeffects of aggregate interference Then in 2012 they tookthe lead in researching link scheduling under the SINRmodel in wireless networks with SIC [20] The algorithmconsiders the influence of cumulative interference but itis a greedy algorithm based on independent sets that canobtain an approximate optimal schedule In [24] Kontiket al proposed a heuristic algorithm based on the columngeneration method using SIC technology to study the prob-lem of minimized scheduling length in single-hop wirelessnetworks The performance of this algorithm is very closeto the optimal linear programming algorithm and has betterrobustness SIC technology was shown to effectively improvenetwork performance

In addition due to the degree of freedom (DoF) ofMIMO network throughput can be improved by spatialmultiplexing (SM)Therefore the problem of link schedulingbased on DoF has also been extensively studied Based on theDoF concept Sultan et al [31] proposed a handover standardthat maximizes the capacity of the downlink channel whenuplink capacity is maintained at a certain level To furtherimprove the overall performance of the network the datalink layer the network layer and the transmission layerneed to be designed cooperatively for optimization Thelayered protocol architecture with network adaptability hasreceived widespread attention such as the joint routing andscheduling optimization scheme [6] and joint power controland link scheduling optimization scheme [32 33] but thereare still many limitations in the practical applications of theseoptimization schemesTherefore a mathematical frameworkis established in this paper for the cross-layer optimization

of routing and scheduling with constraints of traffic balanceand link capacity

3 The System Model

31 Network Model When the links are transmitted in theSINR model if the signal at the expected receiver is higherthan a given threshold the link is transmitted successfully[17] that is

119878119868119873119877푟푖 =119875푟푖 (119904푖)119868푟푖 + 1198730

ge 120573 (1)

where 119875푟푖 (119904푖) is the received power at receiver 119903푖 from sender119904푖 119868푟푖 is the aggregated interference from the active links in theneighbors of link 119897푖1198730 is the background noise and 120573 is theminimum SINR threshold required for receiver 119903푖 to decodesignals successfully

Consider a set of MIMO networks consisting of 119899 com-munication links 119871 = 1198971 119897푛 where each link 119897푖 includes asender 119904푖 and a receiver 119903푖 The Euclidean distance between 119904푗and 119903푖 is 119889푗푖 = 119889(119904푗 119903푖) Thus the length of link 119897푖 is 119889푖푖 If 119904푖 isthe intended sender (1) can be converted into

119878119868119873119877푟푖 =119875 (119904푖) 119889 (119904푖 119903푖)

훼

1198730 + sum푠푗isin푆푡푠푖119875 (119904푗) 119889 (119904푗 119903푖)

훼

=119875푙푖119889푖푖

훼

1198730 + sum푙푗isin퐿耠푙푖

119875푙푗119889푗푖훼

(2)

where119875(119904푗) is the transmission power from sender 119904푗 120572 is thepath-loss factor 119878푡 is the set of all senders that are transmittedconcurrently in the same time slot 119905 as the expected sender 119871耠is a set of links that are simultaneously scheduled in the sametime slot

Assume that all nodes are static and apply MIMO tech-nology with119872 antennas A node communicates with othersthrough wireless links and each node has an input links set119871푖푛푖 and an output links set 119871표푢푡푖 of node 119894 Suppose a timeframe consists of 119879 slots and the state of a link subset in atime slot 119905 (1 le 119905 le 119879) depends on link scheduling For agiven slot 119905 the data flow from sender 119904푗 to 119903푖 can be expressedas a signal vector x푗 = [1199091푗 119909

2푗 119909

푀푗 ]

푇 and the MIMO signal119910푗푖 received by receiver 119903푖 from sender 119904푗 can be expressed asthe following

119910푗푖 = 120572푗푖Vdagger푗푖H

dagger푗푖U푗A푗x푗 + sum

푘isin퐼푖푘 =푗

120572푘푖Vdagger푗푖H

dagger푘푖U푘A푘x푘

+ Vdagger푗푖n푖

(3)

where H푘푖 isin 119862푀times푀 is the channel matrix between sender119904푘 and receiver 119903푖 and is normalized to mean power 1 ◻dagger isthe Hermitian operations of the corresponding matrix U푘 isin119862푀times푀 is the unitary transmitting precoding matrix at sender119904푘 A푗 isin 119877푀times푀and A푗 = diagradic119901푗 radic119901푗 radic119901푗 is the real-valued diagonal transmit amplitude matrix where 119901푗 is thetransmission power of the corresponding sender 119904푗 V푗푖 isin

4 Wireless Communications and Mobile Computing

yx

Ｏ1

Ｏ2

（1 1

（1 2

（2 1

（2 2

v1

v2

Figure 2 Multi-antennaWireless Channel

119862푀times푀 is the unitary receiving decoding matrix at receiver 119903푖for signals from sender 119904푗ni isin 119862푀times1 is awhiteGaussiannoisevector with variance 1198730 per element 2 is the norm of thevector Figure 2 shows that the sender and receiver 2-antennaarray and MIMO channel are used at both ends To simplifycalculations assuming that data streams are uncorrelated theSINR for the n-th element in 119910푗푖 is given by the following

119878119868119873119877푛푗푖 =119901푗1205722푗푖

100381710038171003817100381710038171003817k푛dagger

푗푖Hdagger푗푖u

푛푗

1003817100381710038171003817100381710038172

1198730 + sum푘isin퐼푖푘 =푗 119901푘1205722푘푖10038171003817100381710038171003817k

푛dagger

푗푖Hdagger푘푖U푘

100381710038171003817100381710038172

(4)

32 MSIC Model The manner in which interference isdealt with effectively affects the performance of the linkscheduling algorithm in MIMO networks The MSIC modelis constructed based on SIC under the SINR model Themain idea of SIC is that the power level of the signals from119870 senders received at 119903푖 are in descending order 119875푟푖 (119904퐾) ge119875푟푖(119904퐾minus1) 119875푟푖 (119904푖) 119875푟푖 (1199042) ge 119875푟푖 (1199041) [20] If the strongestsignal dissatisfies the SINR constraint the process of SICends Otherwise this signal will be decoded while othersignals are considered interference and noise If it is theexpected signal then the transmission is successful if notthis signal is removed and the remaining signals are decodedsequentially until the expected signal is decoded successfully

In detail the SIC model needs to satisfy the followingconstraints Receiver 119903푖 tries to decode signal from sender 119904푛in the order 119896 119896minus1 119899Then the signal with received power119875푟푖(119904푛) can be decoded successfully if and only if

119904119905119890119901 1119875푟푖 (119904푘)

1198730 + sum푘minus1푗isin퐼푖푗=1

119875푟푖 (119904푗)ge 120573푘푖

119904119905119890119901 2119875푟푖 (119904푘minus1)

1198730 + sum푘minus2푗isin퐼푖푗=1

119875푟푖 (119904푗)ge 120573(푘minus1)푖

sdot sdot sdot

119904119905119890119901 (119896 minus 119899 + 1)119875푟푖 (119904푛)

1198730 + sum푛minus1푗isin퐼푖푗=1

119875푟푖 (119904푗)ge 120573푛푖

(5)

If signal 119910푖푖 wants to be decoded correctly it must satisfythe MSIC constraints shown in

119878119868119873119877푛푗푖 =119901푗1205722푗푖

100381710038171003817100381710038171003817k푛dagger

푗푖Hdagger푗푖u

푛푗

1003817100381710038171003817100381710038172

1198730 + sum푘isin퐼푖푘lt푗119901푘1205722푘푖

10038171003817100381710038171003817k푛dagger

푗푖Hdagger푘푖U푘

100381710038171003817100381710038172ge 120573푗푖

forall119895 119904119905 119875푟푖 (119904푖) lt 119875푟푖 (119904푗)

119878119868119873119877푛푖푖 =119901푖1205722푖푖

100381710038171003817100381710038171003817k푛dagger

푖푖 Hdagger푖푖u

푛푖

1003817100381710038171003817100381710038172

1198730 + sum푘isin퐼푖푘lt푖119901푘1205722푘푖

10038171003817100381710038171003817k푛dagger

푖푖 Hdagger푘푖U푘

100381710038171003817100381710038172ge 120573푖푖

(6)

Because SIC is used the receiver can sequentially cancelall interference signals that are stronger than its expectedsignal if those stronger signals satisfy (6)Therefore it is onlynecessary to consider the residual interference at the senderwhich is weaker than the expected signal Specifically theresidual SINR from sender 119904푗 to receiver 119903푖 at time slot 119905 isdefined as follows

119903-119878119868119873119877푗푖 [119905]

=119901푗1205722푗푖

100381710038171003817100381710038171003817k푛dagger

푗푖Hdagger푗푖u

푛푗

1003817100381710038171003817100381710038172

1198730 + sum푝푘훼2푘푖k푛dagger푘푖Hdagger푘푖U푘2le푝푗훼2푗푖k푛

dagger

푗푖 Hdagger푗푖u푛푗 2

푘isin퐼푖푘 =푗119901푘1205722푘푖

10038171003817100381710038171003817k푛dagger

푗푖Hdagger푘푖U푘

100381710038171003817100381710038172

ge 120573푗푖

(7)

where sender 119904푘 in the summation formula includes allsendersrsquo signals with weaker power than node 119904푗

33 Problem Model Consider the problem of throughputmaximization in MIMO wireless networks This paper trans-forms the cross-layer joint scheduling problem into conges-tion control routing and scheduling problems By using localinformation the congestion control problem is solved at thesource node of each flow and the routing and schedulingare transformed into the problem of flow balance and linkcapacity constraint which facilitates distributed deploymentand ensures network throughput

Let 119865 denote a set of active link session flows thatdescribes the flow routing in the network Denote 119904(119891) and119889(119891) as the source and destination nodes of session flow119891 isin 119865 respectively Υ(119891) represents the reachable end-to-end throughput of session flow 119891 isin 119865 and Υmin is theminimum reachable end-to-end throughput in all sessionsthat is Υmin = min푓isin퐹Υ(119891) Υ푙(119891) represents the number ofdata rates caused by session flow 119891 isin 119865 on link 119897 The goal ofthis paper is tomaximize theminimum reachable end-to-endthroughput Υmin to maximize network throughput

Wireless Communications and Mobile Computing 5

We assume a half-duplex node on a MIMO node If node119894 isin 119873 is a sender in time slot 119905 the binary variable 119904푖(119905) is1 otherwise it is 0 Similarly if node 119894 isin 119873 is a receiver intime slot 119905 the binary variable 119903푖(119905) is 1 otherwise it is 0 Forhalf-duplex mode the constraint can be written as follows

119904푖 (119905) + 119903푖 (119905) le 1 (1 le 119894 le 119873 1 le 119905 le 119879) (8)

Denote 119909푙(119905) as the number of data streams over link119897 If node 119894 is not a sender then there is sum푙isin퐿표푢푡푖

119909푙(119905) =0 Otherwise in order to satisfy the DoF constraint at thesending node the total number of outgoing data streamsshould be positive and cannot exceed the number of antennasit owns that is 1 le sum푙isin퐿표푢푡푖

119909푙(119905) le 119872 These two cases can besummarized as follows

119904푖 (119905) le sum푙isin퐿표푢푡푖

119909푙 (119905) le 119872119904푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879) (9)

Similarly according to whether node 119894 is an active receiverwe have the following constraint at the receiving node

119903푖 (119905) le sum푙isin퐿푖푛푖

119909푙 (119905) le 119872119903푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879) (10)

For the congestion control problem of the transport layereach flow 119891 in the network determines the data rate of thenext slot independently according to the local congestionqueue information of the node in the current time slot 119880푓푖 (119905)represents the congestion queue length of flow 119891 at node 119894in time slot 119905 and U(119905) = [119880푓푖 (119905)] (119894 isin 119873 119891 isin 119865) is the setof all congestion queues According to the input and outputmode of each node the local congestion queue informationis updated dynamically as follows 119880푓푖 (119905 + 1) = 119880푓푖 (119905) +sum푙isin퐿푖푛푖

119909푙(119905)minussum푙isin퐿표푢푡푖119909푙(119905)+v푓(119905) and the initialized condition

queue is satisfied with119880푓푖 (0) = 0The source session flow119891 iscompressed into a source rate v푓(119905) before being pushed intothe queue Since the local congestion queue length of eachnode determines the upper limit of the data sum that can betransmitted in the current time slot 119905 there are the followingconstraints

sum푙isin퐿표푢푡푖

119909푙 (119905) le 119880푓푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879 119891 isin 119865) (11)

The session flow 119891 in the network determines the data rateof the next time slot according to the congestion queueconstraint Meanwhile in order to guarantee the strongrobustness of the network the following inequalities must besatisfied

lim푇㨀rarrinfin

1119879

푇minus1

sum푡=0

sum푖isin푁

sum푓isin퐹

119864 119880푓푖 (119905) lt infin (12)

For routing and scheduling problems 119863 =maxsum푙isin퐿 119903푙(119891) lowast max푓isin퐹119906푠푙(119891) minus 119906푑푙(119891) and eachlink 119897 can use local congestion queue information to find aflow 119891lowast that satisfies 119891lowast = argmax푓isin퐹119906s푙(119891) minus 119906푑푙(119891) Let119908푙 = 119906푠푙(119891

lowast) minus 119906푑푙(119891lowast) as the weight of link 119897 (119908푙 can also

be understood as the queue length at link 119897 with flow 119891lowast)To solve routing and scheduling problems we will propose adistributed algorithm in Section 4 to generate an active set119871푆耠 of concurrent links In each time slot the links in set 119871푆耠can send data to the receivers (we assume that in each timeslot each active link transmits a packet) Let 119863 be convertedinto the following form

119863 = maxsum푙isin퐿

Υ푙 (119891lowast) sdot 119908푙 (13)

To achieve the goal of maximizing the minimum end-to-end throughput Υmin a feasible routing scheduling alsoneeds to satisfy the following two constraints flow balanceconstraints and the link capacity constraint We have thefollowing flow balance constraints

(a) at the source node we have

sum푙isin퐿표푢푡푖

Υ푙 (119891) = Υ (119891) (119894 = 119904 (119891) 119891 isin 119865) (14)

(b) at each relay node we have

sum푙isin퐿푖푛푖

Υ푙 (119891) = sum푙isin퐿표푢푡푖

Υ푙 (119891)

(1 le 119894 le 119873 119894 = 119904 (119891) 119894 = 119889 (119891) 119891 isin 119865)(15)

(c) at the destination node we have

sum푙isin퐿푖푛푖

Υ푙 (119891) = Υ (119891) (119894 = d (119891) 119891 isin 119865) (16)

It is easy to verify that as long as any two of these equationsare satisfied the other one will also be satisfied Therefore itis sufficient to satisfy the first two equations

It is assumed that a fixed modulation and encodingscheme is used for each data stream and that each data streamcorresponds to one unit data rate Since the total data rate onlink 119897 cannot exceed the average rate of the link we have thefollowing link capacity constraint

sum푓isin퐹

Υ푙 (119891) le1119879

푇

sum푡=1

119909푙 (119905) (17)

where the right side represents the average throughput on link119897 of a frame (119879 time slots) Putting all the constraints togetherwe have the expression for the throughput maximizationproblem

max Υmin

st Υmin le Υ (119891) (119891 isin 119865)

119903-119878119868119873119877푗푖 [119905]

=119901푗1205722푗푖

100381710038171003817100381710038171003817k푛dagger

푗푖Hdagger푗푖u

푛푗

1003817100381710038171003817100381710038172

1198730 + sum푝푘훼2푘푖k푛dagger푘푖Hdagger푘푖U푘2le푝푗훼2푗푖k푛

dagger

푗푖 Hdagger푗푖u푛푗2

푘isin퐼푖푘 =푗119901푘1205722푘푖

10038171003817100381710038171003817k푛dagger

푗푖Hdagger푘푖U푘

100381710038171003817100381710038172

ge 120573푗푖

119904푖 (119905) + 119903푖 (119905) le 1 (1 le 119894 le 119873 1 le 119905 le 119879)

6 Wireless Communications and Mobile Computing

ＦＣ

ＦＣ

ＦＣ

ＦＣ

ＬＣＭＣ

Figure 3 Division of Interference Regions

119904푖 (119905) le sum푙isin퐿표푢푡푖

119909푙 (119905) le 119872119904푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879)

119903푖 (119905) le sum푙isin퐿푖푛푖

119909푙 (119905) le 119872119903푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879)

sum푙isin퐿표푢푡푖

119909푙 (119905) le 119880푓푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879 119891 isin 119865)

lim푇㨀rarrinfin

1119879

푇minus1

sum푡=0

sum푖isin푁

sum푓isin퐹

119864 119880푓푖 (119905) lt infin

sum푙isin퐿표푢푡푖

Υ푙 (119891) = Υ (119891) (119894 = 119904 (119891) 119891 isin 119865)

sum푙isin퐿푖푛푖

Υ푙 (119891) = sum푙isin퐿표푢푡푖

Υ푙 (119891)

(1 le 119894 le 119873 119894 = 119904 (119891) 119894 = 119889 (119891) 119891 isin 119865)

sum푓isin퐹

Υ푙 (119891) le1119879

푇

sum푡=1

119909푙 (119905)

(18)

4 Distributed Link SchedulingAlgorithm Based on MSIC

41 Division of Interference Regions Due to the character-istics of transmission loss the receiving power 119875푟푖 (119904푗) ofdifferent links is also different [34] The total interference atreceiver 119903푖 is expressed as follows

119868푟푖 = sum푠푗isin푆푡푠푖

119875 (119904푗)

119889 (119904푗 119903푖)훼 = sum

푠푗isin푆푡푠푖

119875푟푖 (119904푗) (19)

The scheduling problem of using SIC under the SINRmodel has been proved to be NP-hard [20] If the strongersignal in the network satisfies (5) it can be decoded andremoved due to the adoption of SIC Therefore the strengthof the receiving power does not completely measure theinterference generated by the link In this paper in orderto describe the interference localization the interferenceregions are defined to measure the level of interference

Different interference regions 119860 푙푖 119861푙푖 and 119862푙푖are divided

according to (19) 119860 푙푖 119861푙푖 and 119862푙푖 are concentric ring (circu-

lar) regions centered on receiver 119903푖 of link 119897푖 respectively asshown in Figure 3 (the red circular region is 119860 푙푖

the bluering region is 119861푙푖 and the black dotted ring region is 119862푙푖)The interference generated by the active link in the 119860 푙푖

and119861푙푖 regions will interrupt the transmission of link 119897푖 and theset of concurrent links in these regions is denoted as 119871푆 Thecumulative interference generated by the active link in the 119862푙푖region has a negligible effect on the receiver of link 119897푖

According to (2) the maximum cumulative interferencevalue that link 119897푖 can tolerate is the following

119868푟푖 le 119868max푙푖

le119875푙푖120573119889푖푖

훼 (20)

Therefore in order to satisfy the MSIC constraints thesum of the cumulative interference values at receiver 119903푖 of link119897푖 cannot exceed 119868max

푙푖 If the total interference in the 119860 푙푖

and119861푙푖 regions is (1 minus 119898)119868

max푙푖

and the total interference in the 119862푙푖region is119898119868max

푙푖 then we have

(1 minus 119898) 119868max푙푖

+ 119898119868max푙푖

le 119868max푙푖

(21)Assuming that the link 119897푗 at receiver 119903푖 from sender 119904푗 isin 119860 푙푖is stronger than link 119897푖 from sender 119904푖 SIC is used That is

Wireless Communications and Mobile Computing 7

Start

End

Initialization

MSIC feasibility judgment

Add link l to acc l

Remove link l from seq l

Update concurrent link set Ls

MSIC feasibility test

Yes

No

No

Yes

Figure 4 Distributed MSIC scheduling algorithm flow chart

receiver 119903푖 uses SIC to decode these strong signals continu-ously before decoding the expected signal from sender 119904푖 Letall links in a feasible set 119871푆 of concurrent links be transmittedsuccessfully When any link 119897푗 is added to the set 119871푆耠 sube 119871푆 thelink transmission will fail Obviously 119871푆耠 is the maximum setof concurrent links and 119871푆耠 must satisfy the constraints in(7)

42 Distributed MSIC Scheduling Algorithm In this sectionbased on the CSMACA mechanism and MSIC constraintswe design the distributed single-slot MSIC algorithm to solvethe scheduling problems If the links 119897 isin 119871耠 in the networkcan be transmitted concurrently then 119871耠 can be defined as ascheduling set In each scheduling time slot each linkwill runscheduling algorithms to generate a new feasible schedulingset 119871푆耠

Next considering the MSIC model and interferenceregions division introduced above a distributed link schedul-ing algorithm is proposed under the MSIC constraints Thealgorithm flow chart is shown in Figure 4 Three states of thelink are defined Active Inactive and Standby The four setscorrespond to different states where 119904119894119888 is the active link setthat satisfies the MSIC constraint and can be scheduled in thecurrent scheduling time slot 119886119888119888 is the standby link set thathas not been judged byMSIC constraints 119897119900119888 is the local cachelink set in the standby state and 119904119890119902 is the candidate link set inthe inactive state Therefore the state of a link in the currentslot can be distinguished by the set of links to which the linkcurrently belongs

(1) Initialization Stage At the beginning of each schedulingcycle each link 119897 maintains two sets of local links set 119886119888119888푙and set 119904119890119902푙 The links contained in the set 119886119888119888푙 are added to

a feasible set 119871푆 of concurrent links in a certain schedulingcycle and the links contained in set 119904119890119902푙 are candidate linksto be added into set 119871푆 At the beginning of each schedulingcycle initializing 119886119888119888푙 = Oslash and 119904119890119902푙 = 119897 119860 푙 cup 119861푙

(2) MSIC Feasibility Judgment Stage Each scheduling cycleconsists of several slots and in each slot each link 119897 makes adecision about whether it should be added to 119886119888119888푙 or removedfrom 119904119890119902푙 At the beginning of each scheduling slot all linksin the set 119904119890119902푙 are weighted for comparisonThe sender of link119897 broadcasts its weight information 119908푙 to all links 119896 whosesender is located in the 119860 푙 region of link 119897 If link 119897 has thelargest weight among all links in 119904119890119902푙 it will run Algorithm 1to try to add itself to 119886119888119888푙

The detailed process is as follows The sender of link 119897broadcasts a Requestmessage to links in 119860 푙cup119861푙 first If thereis a collision all of the links select a random back-off timeand wait for it If there is no collision the sender of all linksin 119860 푙 cup 119861푙 will add link 119897 to set 119897119900119888푙 When link 119897 is added tothe current schedule any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙 will determinewhether it remains feasible under the MSIC constraints Thespecific judgment process is as follows For each link 119897耠 isin119886119888119888푙cup119897119900119888푙 the set of linkswith sender 119904푙耠 isin 119886119888119888푙耠cup119897119900119888푙耠cap119860 푙耠and receiver 119903푙耠 is defined as the MSIC link set 119904119894119888푙耠 TheMSICconstraints will be satisfied when any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙satisfies the following conditions (i) the total interference 119868푙耠coming from set 119861푙耠 does not exceed (1 minus119898)119868max

푙耠 (ii) all links119896 isin 119904119894119888푙耠 are feasible that is the total interference 119868푘 comingfrom set 119861푘 does not exceed (1 minus 119898)119868max

푘 According to the above procedure if any link 119897耠 isin 119886119888119888푙 cup

119897119900119888푙 does not satisfy the MSIC constraints the sender oflink 119897耠 will send an Error message to link 119897 indicating thatlink 119897 cannot be added to set 119871푆 (the current scheduling isnot feasible due to the strong interference caused by link119897) If link 119897 isin 119897119900119888푙 does not receive any Error messagesfrom its neighbors it adds link 119897 to set 119886119888119888푙 and removeslink 119897 from 119904119890119902푙 and 119897119900119888푙 Then the sender broadcasts aSuccess message to all its neighbors to update their link sets119886119888119888 119904119890119902 and 119897119900119888 Otherwise it removes link 119897 from 119904119890119902푙and 119897119900119888푙 and then broadcasts a Remove message to all itsneighbors to update their link sets 119904119890119902 and 119897119900119888 After the aboveprocess is performed until a new link is added to 119871푆 thecurrent scheduling process is still feasible under the MSICconstraints

(3) MSIC Feasibility Test Stage After a new 119871푆耠 is generatedin each slot all links 119897 isin 119904119890119902푙 need to make the followingdecision about whether the MSIC constraints are satisfiedFor each link 119897 isin 119904119890119902푙 the set of links with sender 119904푙 isin119886119888119888푙 cap 119860 푙 and receiver 119903푙 is defined as another MSIC linkset 119904119894119888푙耠 Similar to the first procedure any link 119897 isin 119904119890119902푙 thatsatisfies any of the following conditions will dissatisfy theMSIC constraints (i) the total interference 119868푙耠 coming fromset 119861푙 exceeds (1 minus 119898)119868max

푙 or (ii) for any link 119896耠 isin 119904119894119888푙耠 is notfeasible that is the total interference 119868푘耠 coming from set 119861푘耠exceeds (1 minus119898)119868max

푘耠 After the above process if there is a link119897 in 119904119890119902푙 that does not satisfy the MSIC constraints the senderwill remove link 119897 from 119904119890119902푙 and broadcast a Remove messageto all its neighbors to update their link sets 119904119890119902 and 119886119888119888 The

8 Wireless Communications and Mobile Computing

1 sets of int 119886119888119888푙 119904119890119902푙 119897119900119888푙 119904119894119888푙耠 119904119894119888푙耠 initialize2 119886119888119888푙 larr997888 Oslash and 119904119890119902푙 larr997888 119897 119860 푙 cup 119861푙3 Sender of link 119897 broadcasts Requestmessage to links in 119860 푙 cup 119861푙4 for link 119897耠 isin 119860 푙 cup 119861푙 cap 119886119888119888푙 cup 119897119900119888푙 do MSIC feasibility judgment5 if sender of link 119897耠 receives Requestmessage from sender of link 119897 then6 sender of link 119897耠 adds link 119897 into 119897119900119888푘7 sender of link 119897耠 calculates cumulative interference 119868푙耠 8 if 119868푙耠 gt (1 minus 119898)119868max

푙耠then

9 Sender of link 119897耠 broadcasts Error message to sender of link 11989710 else11 Generate 119904119894119888푙耠 12 for 119896 isin 119904119894119888푙耠 do13 Link 119896 calculates cumulative interference 119868푘14 if 119868푘 gt (1 minus 119898)119868max

푘 then15 Sender of link 119897耠 broadcasts Error message to sender of link 11989716 end if17 end for18 end if19 end if20end for21 if sender of link 119897 does not receive Error messages then Generate concurrent links set22 119886119888119888푙 larr997888 119886119888119888푙 cup 11989723 119904119890119902푙 larr997888 119904119890119902푙11989724 119897119900119888푙 larr997888 119897119900119888푙11989725 Sender of link 119897 broadcasts Successmessage to all its neighbors to update their link sets 119886119888119888 119904119890119902 and 11989711990011988826 Goto Algorithm 227 else28 119904119890119902푙 larr997888 119904119890119902푙119897 Does not satisfy MSIC feasibility conditions29 Sender of link 119897 broadcasts Removemessage to all its neighbors to update their local link sets 119904119890119902 and 11989711990011988830 end if

Algorithm 1 Distributed MSIC Scheduling Algorithm (MSIC feasibility judgment)

above process ensures that each link in 119904119890119902푙 satisfies theMSICconstraints under the current scheduling

In the distributed algorithm the number of time slots ineach scheduling cycle is a fixed value In each scheduling sloteach link will run the distributed scheduling algorithm togenerate a new feasible scheduling set 119871푆耠 during schedulingOnce the scheduling is completed the selected link willtransmit a packet during the transmission cycle

43 Theoretical Proof of Algorithm

Theorem 1 The set 119871푆 of scheduling generated by the MSICalgorithm is feasible

Proof Based on the MSIC algorithm under interferenceregions division each link will run the algorithm indepen-dently in each scheduling slot to generate a new feasiblescheduling set 119871푆耠 From Algorithm 2 it is known that aftera new set 119871푆耠 is generated in each time slot all links 119897 isin 119904119890119902푙need to be tested to determine if theMSIC constraints are stillsatisfied To ensure that each link in 119904119890119902푙 satisfies the MSICconstraints under the current scheduling any link 119897 that doesnot satisfy the MSIC constraints will be removed from 119904119890119902푙Therefore the interference links cannot be scheduled at thesame time that is the links in the current set 119871푆耠 are feasiblewhich ensures the feasibility of the algorithm

Theorem 2 The time complexity of the MSIC algorithm is119874(1198962)

Proof In the process of MSIC feasibility judgment of Algo-rithm 1 it is necessary to judge the MSIC constraints formula(4) of any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙 and decide whether to add thelink to the current scheduling set This process requires twoloop statements to be executed with the algorithm executioncomplexity of 119874(1198962) where 119896 represents the number ofconcurrently transmitted signals After Algorithm 1 generatesa new set 119871푆耠 the MSIC feasibility test is performed inAlgorithm 2 The MSIC constraints condition needs to betested again for all links 119897 isin 119904119890119902푙 to ensure that any link in119904119890119902푙 satisfies the MSIC constraints This process also needsto execute two loop statements with the algorithm executioncomplexity of119874(1198962) Therefore the total algorithm executioncomplexity is 119874(1198962)

Theorem 3 The messages complexity of the MSIC algorithmis 119874(119899)

Proof The message complexity of sending a Request broad-cast message is 119874(1) To find a set of links that can be con-currently given by a network of 119899 links an MSIC constraintjudgment is performed for each link of 119897耠 isin 119860 푙 cup 119861푙 cap119886119888119888푙 cup 119897119900119888푙 and the number of Error or Success messages

Wireless Communications and Mobile Computing 9

1 sets of int 119868푘耠 119868푗耠 119904119894119888푘耠2 for link 119896 isin 119860 푙 cup 119861푙 cap 119904119890119902푙 do MSIC feasibility test3 if the sender of link 119896 receives a Successmessage from the sender of link 119897 then4 Link 119896 calculates the cumulative interference 119868푘耠5 if 119868푘耠 gt (1 minus 119898)119868max

푘 then6 The sender of link 119896 broadcasts a Removemessage to its neighbors to update their link sets 1199041198901199027 else8 Generate 119904119894119888푘耠9 for 119895 isin 119904119894119888푘耠 do10 Link 119895 calculates the cumulative interference 119868푗耠11 if 119868푗耠 gt (1 minus 119898)119868max

푗 then12 The sender of link 119896 broadcasts a Removemessage to its neighbors to update their link sets 11990411989011990213 end if14 end for15 end if16 end if17 end for

Algorithm 2 Distributed MSIC Scheduling Algorithm (MSIC feasibility test)

sent is at most 119899 minus 1 For each link of 119896 isin 119860 푙 cup 119861푙 cap 119904119890119902푙a feasibility test is performed and the number of Remove orSuccess messages is up to 119899 minus 1 When the execution of thealgorithm ends the total number of messages used is up to119874(119899)

5 Experimental Results

In this section the distributed single-slot scheduling probleminMIMOwireless networks is studied under the SINRmodelThe simulation is the average of 50 trials obtained on anetwork with 100 links The network size is 600 lowast 600 andthe distance between the sender and the receiver is selectedwithin the range of [20 40] The SINR parameters are set asfollows the threshold value is 120573 = 3 the path loss index is120572 = 22 the background noise power is119873 = 4times10minus7 and theuniform power is 119875 = 2 and 119875 = 10

First the relationship between the size of different net-works and the number of successful transmissions of linksis studied The simulation results are shown in Figure 5Under different power allocations the number of successfultransmissions of the link increases as the network sizeincreases and a larger transmission power can generate alarger neighbor size which is benefited by the gain of thetransmission power However when the network size is largethe neighbor size reaches the upper bound and the gain fromincreasing the power becomes very small At the same timelarger power will also cause more interference to other linksAt this time the impact of the interference on transmission isgreater than the benefit of the network scale increase whichmakes it impossible to satisfy the SINR constraint conditionalthough it improves its own successful transmission proba-bility and reduces the total size of the successful transmissionof the linkTherefore the transmission scale cannot be soughtblindly by increasing the power and a larger-scale schedulingset can be realized by controlling the network scale

20 50 100 150 200 250 300 350 400 450 500 550 6000

10

20

30

40

50

60

70

80

90

Network sizeP=10P=2

Num

ber o

f suc

cess

ful t

rans

miss

ions

Figure 5 The relationship between network size and number ofsuccessful transmissions

Next we compare the number of concurrent link trans-missions of different algorithms At the network layer therouting algorithm based on the least hops is adopted Forconvenience the distance data rate bandwidth and trans-mission power of the data stream are all normalized to 1

First the MSIC algorithm is compared with the recursivelargest first (RLF) algorithm and the smallest degree first(SDF) algorithm in [20] The results in Figure 6 show thatthe MSIC algorithm can obtain a larger link schedulingscale compared with the other two algorithms After theSIC is used all signals with high power in the interferenceregions can be decoded and removed firstly and thus theinterference reached at the receiver is smaller and a larger setof concurrent links can be obtained

10 Wireless Communications and Mobile Computing

0 10 20 30 40 50 60 70 800

5

10

15

20

25

30

Scheduling slot

MIMORLF

SDFMSIC

Num

ber o

f con

curr

ent l

ink

tran

smiss

ions

Figure 6 Comparison of the number of concurrent link transmis-sions of different algorithms

Then we study the effect of the parameter 119898 on thenumber of concurrent link transmissions Figure 7 shows thatthe number of concurrent links decreases as the parameter119898 increases When 119898 is smaller the interference radius ofeach link in the network is larger and there are more linksthat can participate in scheduling The number of concurrentlinks in each selected scheduling configuration is larger andthe data flow rate is higher At this time the network hasstronger interference management ability As the parametersbecome larger the interference in the network is largerthereby allowing fewer links to be transmitted concurrentlyThe MSIC algorithm can reduce partial interference andincrease the number of concurrent transmission links When119898 = 04 there is a close interference region radius betweenMSIC and MIMO so119898 = 04 is set here

Next we study the influence of the number of antennason network performanceThenumber of antennas is changedfrom 2 to 6 and the test is repeated 100 times We then takethe average value of each flow of 100 tests Ideally we assumethat the transmission rate of one link is equal to the capacityof the point-to-point MIMO link without other transmissioninterference As shown inFigure 8 throughput is nearly linearwith the number of antennas and the MSIC algorithm canachieve a higherminimumflow throughput and a higher totalthroughput in the network

To show more detail the flow rate gains for the four flowsessions are given in Figure 9 The simulation results showthat MSIC brings significant throughput gain toMIMOwire-less networks The network flow rate with SIC functionalityis more than half of the network rate without interferencecancellation whichmeans that the reachable unit end-to-endthroughput is increased by approximately 73on average dueto the application of SIC Therefore the MSIC algorithm hasobvious advantages in improving network throughput

01 02 03 04 05 06 07 08 0940

45

50

55

60

65

70

Parameter mMIMOMSIC

The n

umbe

r of c

oncu

rren

t tra

nsm

issio

ns

Figure 7The relationship between parameterm and the number ofconcurrent transmissions

6 Conclusions and Future Work

In this paper the MSIC scheduling algorithm based on SICin MIMO wireless networks is proposed First the MSICconstraints model is constructed under the SINR interfer-ence model Then interference region division is carriedout to describe the level of interference between links Afeasible scheduling set is generated by the distributed linkscheduling algorithm to coordinate the link transmissionand the interference between competing links in the MIMOnetwork is cancelled Experimental results show that thedistributed MSIC scheduling algorithm can bring significantperformance gain to wireless networks

Since the algorithm is premised on satisfying the thresh-old constraint of SINR the algorithm ends when the SINRvalue is less than the current threshold Therefore the nextresearch goal is how to solve the link scheduling problemwhen the SINR value is less than threshold

With the rapid development of the social economy theapplication of modern communication technology has beencontinuously promoted in various fields and the capacityrequirement for networks is increasing In addition dueto the complexity of the network environment a singletechnology will not have a sufficient effect on interferencecancellation Therefore in future wireless communicationnetworks a variety of joint applications of multiple interfer-ence cancellation technologies will be needed How to com-bine these technologies efficiently and achieve a reasonableoptimization combination is an important research direction

Data Availability

The simulation data used to support the findings of this studyare included within the article

Wireless Communications and Mobile Computing 11

2 25 3 35 4 45 5 55 61

2

3

4

5

6

7

8

9 x 105

Number of antennas

MIMOSDF

RLFMSIC

Min

imum

flow

thro

ughp

ut (b

ps)

(a) Minimum flow throughput

2 25 3 35 4 45 5 55 62

3

4

5

6

7

8

9

10

11 x 106

Number of antennas

MIMOSDF

RLFMSIC

Tota

l thr

ough

put (

bps)

(b) Total throughput

Figure 8 The relationship between antenna number and throughput

1 2 3 40

01

02

03

04

05

06

07

08

FlowMSICRLFMIMO

048046

056

033

054057

035

057061

028 032

043

The a

chie

vabl

e flow

rate

s

Figure 9 The gains of data flow rate for the four flow sessions

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (61672321 61771289 and 61832012)

Shandong provincial Graduate Education Innovation Pro-gram (SDYY14052 and SDYY15049) Qufu Normal Uni-versity Science and Technology Project (xkj201525) Shan-dong province agricultural machinery equipment researchand development innovation project (2018YZ002) ShandongProvincial Specialized Degree Postgraduate Teaching CaseLibrary Construction Program and Shandong ProvincialPostgraduate Education Quality Curriculum ConstructionProgram The authors thank the School of InformationScience and Engineering Qufu Normal University

References

[1] S Cheng Z Cai J Li and H Gao ldquoExtracting kernel datasetfrom big sensory data in wireless sensor networksrdquo IEEETransactions on Knowledge and Data Engineering vol 29 no4 pp 813ndash827 2017

[2] S Cheng Z Cai J Li and X Fang ldquoDrawing dominant datasetfrom big sensory data in wireless sensor networksrdquo in Pro-ceedings of the IEEE Conference on Computer Communications(INFOCOM rsquo15) pp 531ndash539 Hong Kong April 2015

[3] X Zheng and Z Cai ldquoReal-time big data delivery in wirelessnetworks a case study on video deliveryrdquo IEEE Transactions onIndustrial Informatics vol 13 no 4 pp 2048ndash2057 2017

[4] Z Cai andX Zheng ldquoA private and efficientmechanism for datauploading in smart cyber-physical systemsrdquo IEEE Transactionson Network Science and Engineering 2018

[5] L Lu G Y Li A L Swindlehurst A Ashikhmin and R ZhangldquoAn overview of massive MIMO benefits and challengesrdquo IEEEJournal of Selected Topics in Signal Processing vol 8 no 5 pp742ndash758 2014

[6] H Liu L Luo D Wu J Yu and D Chen ldquoRouting spectrumaccess and scheduling in multi-hop multi-channel wirelessnetworks with MIMO linksrdquo EURASIP Journal on Wireless

12 Wireless Communications and Mobile Computing

Communications and Networking vol 15 no 1 article no 652015

[7] B Hamdaoui and K G Shin ldquoCharacterization and analysis ofmulti-hop wireless mimo network throughputrdquo in Proceedingsof the Eighth ACM International Symposium on Mobile Ad HocNetworking and Computing pp 120ndash129 Montreal QuebecCanada September 2007

[8] L Jiang and J Walrand ldquoA distributed CSMA algorithm forthroughput and utility maximization in wireless networksrdquoIEEEACM Transactions on Networking vol 18 no 3 pp 960ndash972 2010

[9] H Yu O Bejarano and L Zhong ldquoCombating Inter-cellInterference in 80211ac-based multi-user MIMO networksrdquo inProceedings of the 20th ACM Annual International Conferenceon Mobile Computing and Networking (MobiCom rsquo14) pp 141ndash152 Maui Hawaii USA September 2014

[10] L B Le E Modiano C Joo and N B Shroff ldquoLongest-queue-first scheduling under SINR interferencemodelrdquo in Proceedingsof the 11th ACM International Symposium on Mobile Ad HocNetworking and Computing MobiHoc 2010 pp 41ndash50 USASeptember 2010

[11] J Li S Cheng Z Cai J Yu C Wang and Y Li ldquoApproximateholistic aggregation in wireless sensor networksrdquo ACM Trans-actions on Sensor Networks vol 13 no 2 article no 11 2017

[12] Y Zhou X Li M Liu X Mao S Tang and Z Li ldquoThroughputoptimizing localized link scheduling for multihop wireless net-works under physical interferencemodelrdquo IEEETransactions onParallel and Distributed Systems vol 25 no 10 pp 2708ndash27202014

[13] G Pei and A K S Vullikanti ldquoDistributed approximation algo-rithms for maximum link scheduling and local broadcasting inthe physical interferencemodelrdquo inProceedings of the 32nd IEEEConference on Computer Communications (IEEE INFOCOMrsquo13) pp 1339ndash1347 Turin Italy April 2013

[14] J Yu B Huang X Cheng and M Atiquzzaman ldquoShortest linkscheduling algorithms in wireless networks under the SINRmodelrdquo IEEE Transactions on Vehicular Technology vol 66 no3 pp 2643ndash2657 2017

[15] P J Wan X Xu and O Frieder ldquoShortest link scheduling withpower control under physical interferencemodelrdquo inProceedingof the Sixth International Conference on Mobile Ad-Hoc andSensor Networks pp 74ndash78 2010

[16] M Nabli F Abdelkefi W Ajib and M Siala ldquoEfficient central-ized link scheduling algorithms in wireless mesh networksrdquo inProceedings of the 10th International Wireless Communicationsand Mobile Computing Conference IWCMC 2014 pp 660ndash665Cyprus August 2014

[17] J-G Choi C Joo J Zhang and N B Shroff ldquoDistributed linkscheduling under SINR model in multihop wireless networksrdquoIEEEACM Transactions on Networking vol 22 no 4 pp 1204ndash1217 2014

[18] J Park and S Lee ldquoDistributed MIMO Ad-hoc networks Linkscheduling power allocation and cooperative beamformingrdquoIEEE Transactions on Vehicular Technology vol 61 no 6 pp2586ndash2598 2012

[19] Y Shi Y Thomas H J Liu and S Kompella ldquoHow tocorrectly use the protocol interference model for multi-hopwireless networksrdquo in Proceedings of the 10th ACM InternationalSymposium on Mobile Ad Hoc Networking and ComputingMobiHocrsquo09 pp 239ndash248 USA May 2009

[20] S Lv XWang andX Zhou ldquoScheduling under the SINRmodelin ad hoc networks with successive interference cancellationrdquoComputer Engineering and Science vol 34 no 2 pp 1ndash5 2012

[21] D Qian D Zheng J Zhang and N Shroff ldquoCSMA-baseddistributed scheduling in multi-hop MIMO networks underSINR modelrdquo in Proceedings of the IEEE INFOCOM 2010 pp1ndash9 USA March 2010

[22] O Goussevskaia M M Halldorsson and R WattenhoferldquoAlgorithms for wireless capacityrdquo IEEEACM Transactions onNetworking vol 22 no 3 pp 745ndash755 2014

[23] O Goussevskaia and RWattenhofer ldquoScheduling wireless linkswith successive interference cancellationrdquo in Proceedings of the21st International Conference onComputer Communications andNetworks ICCCN 2012 pp 1ndash7 Germany August 2012

[24] M Kontik and S C Ergen ldquoScheduling in single-hop multipleaccess wireless networks with successive interference cancella-tionrdquo IEEE Wireless Communications Letters vol 3 no 2 pp197ndash200 2014

[25] T Moscibroda R Wattenhofer and A Zollinger ldquoTopologycontrol meets SINR the scheduling complexity of arbitrarytopologiesrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 310ndash321 Florence Italy May 2006

[26] O Goussevskaia R Wattenhofer M M Halldorsson and EWelzl ldquoCapacity of arbitrary wireless networksrdquo in Proceedingsof the 28th Conference on Computer Communications (IEEEINFOCOM rsquo09) pp 1872ndash1880 Rio de Janeiro Brazil April2009

[27] M Dinitz ldquoDistributed algorithms for approximating wirelessnetwork capacityrdquo in Proceedings of the IEEE INFOCOM pp 1ndash9 IEEE San Diego Calif USA March 2010

[28] J Chen C Wen S Jin and K Wong ldquoA low complexitypilot scheduling algorithm for massive MIMOrdquo IEEE WirelessCommunications Letters vol 6 no 1 pp 18ndash21 2017

[29] D Halperin T Anderson and D Wetherall ldquoTaking thesting out of carrier sense interference cancellation for wirelessLANsrdquo in Proceedings of the 14th ACM Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo08) pp 339ndash350 September 2008

[30] S LvW Zhuang XWang andX Zhou ldquoScheduling inwirelessad hoc networks with successive interference cancellationrdquo inProceedings of the IEEE INFOCOM 2011 - IEEE Conference onComputer Communications pp 1287ndash1295 Shanghai ChinaApril 2011

[31] R Sultan L Song K G Seddik and Z Han ldquoFull-duplexmeetsmultiuser MIMO comparisons and analysisrdquo IEEE Transac-tions on Vehicular Technology vol 66 no 1 pp 455ndash467 2017

[32] X Zheng Z Cai J Li and H Gao ldquoA study on application-aware scheduling in wireless networksrdquo IEEE Transactions onMobile Computing vol 16 no 7 pp 1787ndash1801 2017

[33] X Li Y Shi X Wang C Xu and M Sheng ldquoEfficient linkscheduling with joint power control and successive interferencecancellation in wireless networksrdquo Science China InformationSciences vol 59 no 12 pp 1ndash15 2016

[34] L Qu J He and C Assi ldquoDistributed link scheduling inwireless networks with interference cancellation capabilitiesrdquoin Proceedings of the 15th IEEE International Symposium on aWorld ofWireless Mobile andMultimedia Networks WoWMoM2014 pp 1ndash7 Australia 2014

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4 Wireless Communications and Mobile Computing

yx

Ｏ1

Ｏ2

（1 1

（1 2

（2 1

（2 2

v1

v2

Figure 2 Multi-antennaWireless Channel

119862푀times푀 is the unitary receiving decoding matrix at receiver 119903푖for signals from sender 119904푗ni isin 119862푀times1 is awhiteGaussiannoisevector with variance 1198730 per element 2 is the norm of thevector Figure 2 shows that the sender and receiver 2-antennaarray and MIMO channel are used at both ends To simplifycalculations assuming that data streams are uncorrelated theSINR for the n-th element in 119910푗푖 is given by the following

119878119868119873119877푛푗푖 =119901푗1205722푗푖

100381710038171003817100381710038171003817k푛dagger

푗푖Hdagger푗푖u

푛푗

1003817100381710038171003817100381710038172

1198730 + sum푘isin퐼푖푘 =푗 119901푘1205722푘푖10038171003817100381710038171003817k

푛dagger

푗푖Hdagger푘푖U푘

100381710038171003817100381710038172

(4)

32 MSIC Model The manner in which interference isdealt with effectively affects the performance of the linkscheduling algorithm in MIMO networks The MSIC modelis constructed based on SIC under the SINR model Themain idea of SIC is that the power level of the signals from119870 senders received at 119903푖 are in descending order 119875푟푖 (119904퐾) ge119875푟푖(119904퐾minus1) 119875푟푖 (119904푖) 119875푟푖 (1199042) ge 119875푟푖 (1199041) [20] If the strongestsignal dissatisfies the SINR constraint the process of SICends Otherwise this signal will be decoded while othersignals are considered interference and noise If it is theexpected signal then the transmission is successful if notthis signal is removed and the remaining signals are decodedsequentially until the expected signal is decoded successfully

In detail the SIC model needs to satisfy the followingconstraints Receiver 119903푖 tries to decode signal from sender 119904푛in the order 119896 119896minus1 119899Then the signal with received power119875푟푖(119904푛) can be decoded successfully if and only if

119904119905119890119901 1119875푟푖 (119904푘)

1198730 + sum푘minus1푗isin퐼푖푗=1

119875푟푖 (119904푗)ge 120573푘푖

119904119905119890119901 2119875푟푖 (119904푘minus1)

1198730 + sum푘minus2푗isin퐼푖푗=1

119875푟푖 (119904푗)ge 120573(푘minus1)푖

sdot sdot sdot

119904119905119890119901 (119896 minus 119899 + 1)119875푟푖 (119904푛)

1198730 + sum푛minus1푗isin퐼푖푗=1

119875푟푖 (119904푗)ge 120573푛푖

(5)

If signal 119910푖푖 wants to be decoded correctly it must satisfythe MSIC constraints shown in

119878119868119873119877푛푗푖 =119901푗1205722푗푖

100381710038171003817100381710038171003817k푛dagger

푗푖Hdagger푗푖u

푛푗

1003817100381710038171003817100381710038172

1198730 + sum푘isin퐼푖푘lt푗119901푘1205722푘푖

10038171003817100381710038171003817k푛dagger

푗푖Hdagger푘푖U푘

100381710038171003817100381710038172ge 120573푗푖

forall119895 119904119905 119875푟푖 (119904푖) lt 119875푟푖 (119904푗)

119878119868119873119877푛푖푖 =119901푖1205722푖푖

100381710038171003817100381710038171003817k푛dagger

푖푖 Hdagger푖푖u

푛푖

1003817100381710038171003817100381710038172

1198730 + sum푘isin퐼푖푘lt푖119901푘1205722푘푖

10038171003817100381710038171003817k푛dagger

푖푖 Hdagger푘푖U푘

100381710038171003817100381710038172ge 120573푖푖

(6)

Because SIC is used the receiver can sequentially cancelall interference signals that are stronger than its expectedsignal if those stronger signals satisfy (6)Therefore it is onlynecessary to consider the residual interference at the senderwhich is weaker than the expected signal Specifically theresidual SINR from sender 119904푗 to receiver 119903푖 at time slot 119905 isdefined as follows

119903-119878119868119873119877푗푖 [119905]

=119901푗1205722푗푖

100381710038171003817100381710038171003817k푛dagger

푗푖Hdagger푗푖u

푛푗

1003817100381710038171003817100381710038172

1198730 + sum푝푘훼2푘푖k푛dagger푘푖Hdagger푘푖U푘2le푝푗훼2푗푖k푛

dagger

푗푖 Hdagger푗푖u푛푗 2

푘isin퐼푖푘 =푗119901푘1205722푘푖

10038171003817100381710038171003817k푛dagger

푗푖Hdagger푘푖U푘

100381710038171003817100381710038172

ge 120573푗푖

(7)

where sender 119904푘 in the summation formula includes allsendersrsquo signals with weaker power than node 119904푗

33 Problem Model Consider the problem of throughputmaximization in MIMO wireless networks This paper trans-forms the cross-layer joint scheduling problem into conges-tion control routing and scheduling problems By using localinformation the congestion control problem is solved at thesource node of each flow and the routing and schedulingare transformed into the problem of flow balance and linkcapacity constraint which facilitates distributed deploymentand ensures network throughput

Let 119865 denote a set of active link session flows thatdescribes the flow routing in the network Denote 119904(119891) and119889(119891) as the source and destination nodes of session flow119891 isin 119865 respectively Υ(119891) represents the reachable end-to-end throughput of session flow 119891 isin 119865 and Υmin is theminimum reachable end-to-end throughput in all sessionsthat is Υmin = min푓isin퐹Υ(119891) Υ푙(119891) represents the number ofdata rates caused by session flow 119891 isin 119865 on link 119897 The goal ofthis paper is tomaximize theminimum reachable end-to-endthroughput Υmin to maximize network throughput

Wireless Communications and Mobile Computing 5

We assume a half-duplex node on a MIMO node If node119894 isin 119873 is a sender in time slot 119905 the binary variable 119904푖(119905) is1 otherwise it is 0 Similarly if node 119894 isin 119873 is a receiver intime slot 119905 the binary variable 119903푖(119905) is 1 otherwise it is 0 Forhalf-duplex mode the constraint can be written as follows

119904푖 (119905) + 119903푖 (119905) le 1 (1 le 119894 le 119873 1 le 119905 le 119879) (8)

Denote 119909푙(119905) as the number of data streams over link119897 If node 119894 is not a sender then there is sum푙isin퐿표푢푡푖

119909푙(119905) =0 Otherwise in order to satisfy the DoF constraint at thesending node the total number of outgoing data streamsshould be positive and cannot exceed the number of antennasit owns that is 1 le sum푙isin퐿표푢푡푖

119909푙(119905) le 119872 These two cases can besummarized as follows

119904푖 (119905) le sum푙isin퐿표푢푡푖

119909푙 (119905) le 119872119904푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879) (9)

Similarly according to whether node 119894 is an active receiverwe have the following constraint at the receiving node

119903푖 (119905) le sum푙isin퐿푖푛푖

119909푙 (119905) le 119872119903푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879) (10)

For the congestion control problem of the transport layereach flow 119891 in the network determines the data rate of thenext slot independently according to the local congestionqueue information of the node in the current time slot 119880푓푖 (119905)represents the congestion queue length of flow 119891 at node 119894in time slot 119905 and U(119905) = [119880푓푖 (119905)] (119894 isin 119873 119891 isin 119865) is the setof all congestion queues According to the input and outputmode of each node the local congestion queue informationis updated dynamically as follows 119880푓푖 (119905 + 1) = 119880푓푖 (119905) +sum푙isin퐿푖푛푖

119909푙(119905)minussum푙isin퐿표푢푡푖119909푙(119905)+v푓(119905) and the initialized condition

queue is satisfied with119880푓푖 (0) = 0The source session flow119891 iscompressed into a source rate v푓(119905) before being pushed intothe queue Since the local congestion queue length of eachnode determines the upper limit of the data sum that can betransmitted in the current time slot 119905 there are the followingconstraints

sum푙isin퐿표푢푡푖

119909푙 (119905) le 119880푓푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879 119891 isin 119865) (11)

The session flow 119891 in the network determines the data rateof the next time slot according to the congestion queueconstraint Meanwhile in order to guarantee the strongrobustness of the network the following inequalities must besatisfied

lim푇㨀rarrinfin

1119879

푇minus1

sum푡=0

sum푖isin푁

sum푓isin퐹

119864 119880푓푖 (119905) lt infin (12)

For routing and scheduling problems 119863 =maxsum푙isin퐿 119903푙(119891) lowast max푓isin퐹119906푠푙(119891) minus 119906푑푙(119891) and eachlink 119897 can use local congestion queue information to find aflow 119891lowast that satisfies 119891lowast = argmax푓isin퐹119906s푙(119891) minus 119906푑푙(119891) Let119908푙 = 119906푠푙(119891

lowast) minus 119906푑푙(119891lowast) as the weight of link 119897 (119908푙 can also

be understood as the queue length at link 119897 with flow 119891lowast)To solve routing and scheduling problems we will propose adistributed algorithm in Section 4 to generate an active set119871푆耠 of concurrent links In each time slot the links in set 119871푆耠can send data to the receivers (we assume that in each timeslot each active link transmits a packet) Let 119863 be convertedinto the following form

119863 = maxsum푙isin퐿

Υ푙 (119891lowast) sdot 119908푙 (13)

To achieve the goal of maximizing the minimum end-to-end throughput Υmin a feasible routing scheduling alsoneeds to satisfy the following two constraints flow balanceconstraints and the link capacity constraint We have thefollowing flow balance constraints

(a) at the source node we have

sum푙isin퐿표푢푡푖

Υ푙 (119891) = Υ (119891) (119894 = 119904 (119891) 119891 isin 119865) (14)

(b) at each relay node we have

sum푙isin퐿푖푛푖

Υ푙 (119891) = sum푙isin퐿표푢푡푖

Υ푙 (119891)

(1 le 119894 le 119873 119894 = 119904 (119891) 119894 = 119889 (119891) 119891 isin 119865)(15)

(c) at the destination node we have

sum푙isin퐿푖푛푖

Υ푙 (119891) = Υ (119891) (119894 = d (119891) 119891 isin 119865) (16)

It is easy to verify that as long as any two of these equationsare satisfied the other one will also be satisfied Therefore itis sufficient to satisfy the first two equations

It is assumed that a fixed modulation and encodingscheme is used for each data stream and that each data streamcorresponds to one unit data rate Since the total data rate onlink 119897 cannot exceed the average rate of the link we have thefollowing link capacity constraint

sum푓isin퐹

Υ푙 (119891) le1119879

푇

sum푡=1

119909푙 (119905) (17)

where the right side represents the average throughput on link119897 of a frame (119879 time slots) Putting all the constraints togetherwe have the expression for the throughput maximizationproblem

max Υmin

st Υmin le Υ (119891) (119891 isin 119865)

119903-119878119868119873119877푗푖 [119905]

=119901푗1205722푗푖

100381710038171003817100381710038171003817k푛dagger

푗푖Hdagger푗푖u

푛푗

1003817100381710038171003817100381710038172

1198730 + sum푝푘훼2푘푖k푛dagger푘푖Hdagger푘푖U푘2le푝푗훼2푗푖k푛

dagger

푗푖 Hdagger푗푖u푛푗2

푘isin퐼푖푘 =푗119901푘1205722푘푖

10038171003817100381710038171003817k푛dagger

푗푖Hdagger푘푖U푘

100381710038171003817100381710038172

ge 120573푗푖

119904푖 (119905) + 119903푖 (119905) le 1 (1 le 119894 le 119873 1 le 119905 le 119879)

6 Wireless Communications and Mobile Computing

ＦＣ

ＦＣ

ＦＣ

ＦＣ

ＬＣＭＣ

Figure 3 Division of Interference Regions

119904푖 (119905) le sum푙isin퐿표푢푡푖

119909푙 (119905) le 119872119904푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879)

119903푖 (119905) le sum푙isin퐿푖푛푖

119909푙 (119905) le 119872119903푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879)

sum푙isin퐿표푢푡푖

119909푙 (119905) le 119880푓푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879 119891 isin 119865)

lim푇㨀rarrinfin

1119879

푇minus1

sum푡=0

sum푖isin푁

sum푓isin퐹

119864 119880푓푖 (119905) lt infin

sum푙isin퐿표푢푡푖

Υ푙 (119891) = Υ (119891) (119894 = 119904 (119891) 119891 isin 119865)

sum푙isin퐿푖푛푖

Υ푙 (119891) = sum푙isin퐿표푢푡푖

Υ푙 (119891)

(1 le 119894 le 119873 119894 = 119904 (119891) 119894 = 119889 (119891) 119891 isin 119865)

sum푓isin퐹

Υ푙 (119891) le1119879

푇

sum푡=1

119909푙 (119905)

(18)

4 Distributed Link SchedulingAlgorithm Based on MSIC

41 Division of Interference Regions Due to the character-istics of transmission loss the receiving power 119875푟푖 (119904푗) ofdifferent links is also different [34] The total interference atreceiver 119903푖 is expressed as follows

119868푟푖 = sum푠푗isin푆푡푠푖

119875 (119904푗)

119889 (119904푗 119903푖)훼 = sum

푠푗isin푆푡푠푖

119875푟푖 (119904푗) (19)

The scheduling problem of using SIC under the SINRmodel has been proved to be NP-hard [20] If the strongersignal in the network satisfies (5) it can be decoded andremoved due to the adoption of SIC Therefore the strengthof the receiving power does not completely measure theinterference generated by the link In this paper in orderto describe the interference localization the interferenceregions are defined to measure the level of interference

Different interference regions 119860 푙푖 119861푙푖 and 119862푙푖are divided

according to (19) 119860 푙푖 119861푙푖 and 119862푙푖 are concentric ring (circu-

lar) regions centered on receiver 119903푖 of link 119897푖 respectively asshown in Figure 3 (the red circular region is 119860 푙푖

the bluering region is 119861푙푖 and the black dotted ring region is 119862푙푖)The interference generated by the active link in the 119860 푙푖

and119861푙푖 regions will interrupt the transmission of link 119897푖 and theset of concurrent links in these regions is denoted as 119871푆 Thecumulative interference generated by the active link in the 119862푙푖region has a negligible effect on the receiver of link 119897푖

According to (2) the maximum cumulative interferencevalue that link 119897푖 can tolerate is the following

119868푟푖 le 119868max푙푖

le119875푙푖120573119889푖푖

훼 (20)

Therefore in order to satisfy the MSIC constraints thesum of the cumulative interference values at receiver 119903푖 of link119897푖 cannot exceed 119868max

푙푖 If the total interference in the 119860 푙푖

and119861푙푖 regions is (1 minus 119898)119868

max푙푖

and the total interference in the 119862푙푖region is119898119868max

푙푖 then we have

(1 minus 119898) 119868max푙푖

+ 119898119868max푙푖

le 119868max푙푖

(21)Assuming that the link 119897푗 at receiver 119903푖 from sender 119904푗 isin 119860 푙푖is stronger than link 119897푖 from sender 119904푖 SIC is used That is

Wireless Communications and Mobile Computing 7

Start

End

Initialization

MSIC feasibility judgment

Add link l to acc l

Remove link l from seq l

Update concurrent link set Ls

MSIC feasibility test

Yes

No

No

Yes

Figure 4 Distributed MSIC scheduling algorithm flow chart

receiver 119903푖 uses SIC to decode these strong signals continu-ously before decoding the expected signal from sender 119904푖 Letall links in a feasible set 119871푆 of concurrent links be transmittedsuccessfully When any link 119897푗 is added to the set 119871푆耠 sube 119871푆 thelink transmission will fail Obviously 119871푆耠 is the maximum setof concurrent links and 119871푆耠 must satisfy the constraints in(7)

42 Distributed MSIC Scheduling Algorithm In this sectionbased on the CSMACA mechanism and MSIC constraintswe design the distributed single-slot MSIC algorithm to solvethe scheduling problems If the links 119897 isin 119871耠 in the networkcan be transmitted concurrently then 119871耠 can be defined as ascheduling set In each scheduling time slot each linkwill runscheduling algorithms to generate a new feasible schedulingset 119871푆耠

Next considering the MSIC model and interferenceregions division introduced above a distributed link schedul-ing algorithm is proposed under the MSIC constraints Thealgorithm flow chart is shown in Figure 4 Three states of thelink are defined Active Inactive and Standby The four setscorrespond to different states where 119904119894119888 is the active link setthat satisfies the MSIC constraint and can be scheduled in thecurrent scheduling time slot 119886119888119888 is the standby link set thathas not been judged byMSIC constraints 119897119900119888 is the local cachelink set in the standby state and 119904119890119902 is the candidate link set inthe inactive state Therefore the state of a link in the currentslot can be distinguished by the set of links to which the linkcurrently belongs

(1) Initialization Stage At the beginning of each schedulingcycle each link 119897 maintains two sets of local links set 119886119888119888푙and set 119904119890119902푙 The links contained in the set 119886119888119888푙 are added to

a feasible set 119871푆 of concurrent links in a certain schedulingcycle and the links contained in set 119904119890119902푙 are candidate linksto be added into set 119871푆 At the beginning of each schedulingcycle initializing 119886119888119888푙 = Oslash and 119904119890119902푙 = 119897 119860 푙 cup 119861푙

(2) MSIC Feasibility Judgment Stage Each scheduling cycleconsists of several slots and in each slot each link 119897 makes adecision about whether it should be added to 119886119888119888푙 or removedfrom 119904119890119902푙 At the beginning of each scheduling slot all linksin the set 119904119890119902푙 are weighted for comparisonThe sender of link119897 broadcasts its weight information 119908푙 to all links 119896 whosesender is located in the 119860 푙 region of link 119897 If link 119897 has thelargest weight among all links in 119904119890119902푙 it will run Algorithm 1to try to add itself to 119886119888119888푙

The detailed process is as follows The sender of link 119897broadcasts a Requestmessage to links in 119860 푙cup119861푙 first If thereis a collision all of the links select a random back-off timeand wait for it If there is no collision the sender of all linksin 119860 푙 cup 119861푙 will add link 119897 to set 119897119900119888푙 When link 119897 is added tothe current schedule any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙 will determinewhether it remains feasible under the MSIC constraints Thespecific judgment process is as follows For each link 119897耠 isin119886119888119888푙cup119897119900119888푙 the set of linkswith sender 119904푙耠 isin 119886119888119888푙耠cup119897119900119888푙耠cap119860 푙耠and receiver 119903푙耠 is defined as the MSIC link set 119904119894119888푙耠 TheMSICconstraints will be satisfied when any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙satisfies the following conditions (i) the total interference 119868푙耠coming from set 119861푙耠 does not exceed (1 minus119898)119868max

푙耠 (ii) all links119896 isin 119904119894119888푙耠 are feasible that is the total interference 119868푘 comingfrom set 119861푘 does not exceed (1 minus 119898)119868max

푘 According to the above procedure if any link 119897耠 isin 119886119888119888푙 cup

119897119900119888푙 does not satisfy the MSIC constraints the sender oflink 119897耠 will send an Error message to link 119897 indicating thatlink 119897 cannot be added to set 119871푆 (the current scheduling isnot feasible due to the strong interference caused by link119897) If link 119897 isin 119897119900119888푙 does not receive any Error messagesfrom its neighbors it adds link 119897 to set 119886119888119888푙 and removeslink 119897 from 119904119890119902푙 and 119897119900119888푙 Then the sender broadcasts aSuccess message to all its neighbors to update their link sets119886119888119888 119904119890119902 and 119897119900119888 Otherwise it removes link 119897 from 119904119890119902푙and 119897119900119888푙 and then broadcasts a Remove message to all itsneighbors to update their link sets 119904119890119902 and 119897119900119888 After the aboveprocess is performed until a new link is added to 119871푆 thecurrent scheduling process is still feasible under the MSICconstraints

(3) MSIC Feasibility Test Stage After a new 119871푆耠 is generatedin each slot all links 119897 isin 119904119890119902푙 need to make the followingdecision about whether the MSIC constraints are satisfiedFor each link 119897 isin 119904119890119902푙 the set of links with sender 119904푙 isin119886119888119888푙 cap 119860 푙 and receiver 119903푙 is defined as another MSIC linkset 119904119894119888푙耠 Similar to the first procedure any link 119897 isin 119904119890119902푙 thatsatisfies any of the following conditions will dissatisfy theMSIC constraints (i) the total interference 119868푙耠 coming fromset 119861푙 exceeds (1 minus 119898)119868max

푙 or (ii) for any link 119896耠 isin 119904119894119888푙耠 is notfeasible that is the total interference 119868푘耠 coming from set 119861푘耠exceeds (1 minus119898)119868max

푘耠 After the above process if there is a link119897 in 119904119890119902푙 that does not satisfy the MSIC constraints the senderwill remove link 119897 from 119904119890119902푙 and broadcast a Remove messageto all its neighbors to update their link sets 119904119890119902 and 119886119888119888 The

8 Wireless Communications and Mobile Computing

1 sets of int 119886119888119888푙 119904119890119902푙 119897119900119888푙 119904119894119888푙耠 119904119894119888푙耠 initialize2 119886119888119888푙 larr997888 Oslash and 119904119890119902푙 larr997888 119897 119860 푙 cup 119861푙3 Sender of link 119897 broadcasts Requestmessage to links in 119860 푙 cup 119861푙4 for link 119897耠 isin 119860 푙 cup 119861푙 cap 119886119888119888푙 cup 119897119900119888푙 do MSIC feasibility judgment5 if sender of link 119897耠 receives Requestmessage from sender of link 119897 then6 sender of link 119897耠 adds link 119897 into 119897119900119888푘7 sender of link 119897耠 calculates cumulative interference 119868푙耠 8 if 119868푙耠 gt (1 minus 119898)119868max

푙耠then

9 Sender of link 119897耠 broadcasts Error message to sender of link 11989710 else11 Generate 119904119894119888푙耠 12 for 119896 isin 119904119894119888푙耠 do13 Link 119896 calculates cumulative interference 119868푘14 if 119868푘 gt (1 minus 119898)119868max

푘 then15 Sender of link 119897耠 broadcasts Error message to sender of link 11989716 end if17 end for18 end if19 end if20end for21 if sender of link 119897 does not receive Error messages then Generate concurrent links set22 119886119888119888푙 larr997888 119886119888119888푙 cup 11989723 119904119890119902푙 larr997888 119904119890119902푙11989724 119897119900119888푙 larr997888 119897119900119888푙11989725 Sender of link 119897 broadcasts Successmessage to all its neighbors to update their link sets 119886119888119888 119904119890119902 and 11989711990011988826 Goto Algorithm 227 else28 119904119890119902푙 larr997888 119904119890119902푙119897 Does not satisfy MSIC feasibility conditions29 Sender of link 119897 broadcasts Removemessage to all its neighbors to update their local link sets 119904119890119902 and 11989711990011988830 end if

Algorithm 1 Distributed MSIC Scheduling Algorithm (MSIC feasibility judgment)

above process ensures that each link in 119904119890119902푙 satisfies theMSICconstraints under the current scheduling

In the distributed algorithm the number of time slots ineach scheduling cycle is a fixed value In each scheduling sloteach link will run the distributed scheduling algorithm togenerate a new feasible scheduling set 119871푆耠 during schedulingOnce the scheduling is completed the selected link willtransmit a packet during the transmission cycle

43 Theoretical Proof of Algorithm

Theorem 1 The set 119871푆 of scheduling generated by the MSICalgorithm is feasible

Proof Based on the MSIC algorithm under interferenceregions division each link will run the algorithm indepen-dently in each scheduling slot to generate a new feasiblescheduling set 119871푆耠 From Algorithm 2 it is known that aftera new set 119871푆耠 is generated in each time slot all links 119897 isin 119904119890119902푙need to be tested to determine if theMSIC constraints are stillsatisfied To ensure that each link in 119904119890119902푙 satisfies the MSICconstraints under the current scheduling any link 119897 that doesnot satisfy the MSIC constraints will be removed from 119904119890119902푙Therefore the interference links cannot be scheduled at thesame time that is the links in the current set 119871푆耠 are feasiblewhich ensures the feasibility of the algorithm

Theorem 2 The time complexity of the MSIC algorithm is119874(1198962)

Proof In the process of MSIC feasibility judgment of Algo-rithm 1 it is necessary to judge the MSIC constraints formula(4) of any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙 and decide whether to add thelink to the current scheduling set This process requires twoloop statements to be executed with the algorithm executioncomplexity of 119874(1198962) where 119896 represents the number ofconcurrently transmitted signals After Algorithm 1 generatesa new set 119871푆耠 the MSIC feasibility test is performed inAlgorithm 2 The MSIC constraints condition needs to betested again for all links 119897 isin 119904119890119902푙 to ensure that any link in119904119890119902푙 satisfies the MSIC constraints This process also needsto execute two loop statements with the algorithm executioncomplexity of119874(1198962) Therefore the total algorithm executioncomplexity is 119874(1198962)

Theorem 3 The messages complexity of the MSIC algorithmis 119874(119899)

Proof The message complexity of sending a Request broad-cast message is 119874(1) To find a set of links that can be con-currently given by a network of 119899 links an MSIC constraintjudgment is performed for each link of 119897耠 isin 119860 푙 cup 119861푙 cap119886119888119888푙 cup 119897119900119888푙 and the number of Error or Success messages

Wireless Communications and Mobile Computing 9

1 sets of int 119868푘耠 119868푗耠 119904119894119888푘耠2 for link 119896 isin 119860 푙 cup 119861푙 cap 119904119890119902푙 do MSIC feasibility test3 if the sender of link 119896 receives a Successmessage from the sender of link 119897 then4 Link 119896 calculates the cumulative interference 119868푘耠5 if 119868푘耠 gt (1 minus 119898)119868max

푘 then6 The sender of link 119896 broadcasts a Removemessage to its neighbors to update their link sets 1199041198901199027 else8 Generate 119904119894119888푘耠9 for 119895 isin 119904119894119888푘耠 do10 Link 119895 calculates the cumulative interference 119868푗耠11 if 119868푗耠 gt (1 minus 119898)119868max

푗 then12 The sender of link 119896 broadcasts a Removemessage to its neighbors to update their link sets 11990411989011990213 end if14 end for15 end if16 end if17 end for

Algorithm 2 Distributed MSIC Scheduling Algorithm (MSIC feasibility test)

sent is at most 119899 minus 1 For each link of 119896 isin 119860 푙 cup 119861푙 cap 119904119890119902푙a feasibility test is performed and the number of Remove orSuccess messages is up to 119899 minus 1 When the execution of thealgorithm ends the total number of messages used is up to119874(119899)

5 Experimental Results

In this section the distributed single-slot scheduling probleminMIMOwireless networks is studied under the SINRmodelThe simulation is the average of 50 trials obtained on anetwork with 100 links The network size is 600 lowast 600 andthe distance between the sender and the receiver is selectedwithin the range of [20 40] The SINR parameters are set asfollows the threshold value is 120573 = 3 the path loss index is120572 = 22 the background noise power is119873 = 4times10minus7 and theuniform power is 119875 = 2 and 119875 = 10

First the relationship between the size of different net-works and the number of successful transmissions of linksis studied The simulation results are shown in Figure 5Under different power allocations the number of successfultransmissions of the link increases as the network sizeincreases and a larger transmission power can generate alarger neighbor size which is benefited by the gain of thetransmission power However when the network size is largethe neighbor size reaches the upper bound and the gain fromincreasing the power becomes very small At the same timelarger power will also cause more interference to other linksAt this time the impact of the interference on transmission isgreater than the benefit of the network scale increase whichmakes it impossible to satisfy the SINR constraint conditionalthough it improves its own successful transmission proba-bility and reduces the total size of the successful transmissionof the linkTherefore the transmission scale cannot be soughtblindly by increasing the power and a larger-scale schedulingset can be realized by controlling the network scale

20 50 100 150 200 250 300 350 400 450 500 550 6000

10

20

30

40

50

60

70

80

90

Network sizeP=10P=2

Num

ber o

f suc

cess

ful t

rans

miss

ions

Figure 5 The relationship between network size and number ofsuccessful transmissions

Next we compare the number of concurrent link trans-missions of different algorithms At the network layer therouting algorithm based on the least hops is adopted Forconvenience the distance data rate bandwidth and trans-mission power of the data stream are all normalized to 1

First the MSIC algorithm is compared with the recursivelargest first (RLF) algorithm and the smallest degree first(SDF) algorithm in [20] The results in Figure 6 show thatthe MSIC algorithm can obtain a larger link schedulingscale compared with the other two algorithms After theSIC is used all signals with high power in the interferenceregions can be decoded and removed firstly and thus theinterference reached at the receiver is smaller and a larger setof concurrent links can be obtained

10 Wireless Communications and Mobile Computing

0 10 20 30 40 50 60 70 800

5

10

15

20

25

30

Scheduling slot

MIMORLF

SDFMSIC

Num

ber o

f con

curr

ent l

ink

tran

smiss

ions

Figure 6 Comparison of the number of concurrent link transmis-sions of different algorithms

Then we study the effect of the parameter 119898 on thenumber of concurrent link transmissions Figure 7 shows thatthe number of concurrent links decreases as the parameter119898 increases When 119898 is smaller the interference radius ofeach link in the network is larger and there are more linksthat can participate in scheduling The number of concurrentlinks in each selected scheduling configuration is larger andthe data flow rate is higher At this time the network hasstronger interference management ability As the parametersbecome larger the interference in the network is largerthereby allowing fewer links to be transmitted concurrentlyThe MSIC algorithm can reduce partial interference andincrease the number of concurrent transmission links When119898 = 04 there is a close interference region radius betweenMSIC and MIMO so119898 = 04 is set here

Next we study the influence of the number of antennason network performanceThenumber of antennas is changedfrom 2 to 6 and the test is repeated 100 times We then takethe average value of each flow of 100 tests Ideally we assumethat the transmission rate of one link is equal to the capacityof the point-to-point MIMO link without other transmissioninterference As shown inFigure 8 throughput is nearly linearwith the number of antennas and the MSIC algorithm canachieve a higherminimumflow throughput and a higher totalthroughput in the network

To show more detail the flow rate gains for the four flowsessions are given in Figure 9 The simulation results showthat MSIC brings significant throughput gain toMIMOwire-less networks The network flow rate with SIC functionalityis more than half of the network rate without interferencecancellation whichmeans that the reachable unit end-to-endthroughput is increased by approximately 73on average dueto the application of SIC Therefore the MSIC algorithm hasobvious advantages in improving network throughput

01 02 03 04 05 06 07 08 0940

45

50

55

60

65

70

Parameter mMIMOMSIC

The n

umbe

r of c

oncu

rren

t tra

nsm

issio

ns

Figure 7The relationship between parameterm and the number ofconcurrent transmissions

6 Conclusions and Future Work

In this paper the MSIC scheduling algorithm based on SICin MIMO wireless networks is proposed First the MSICconstraints model is constructed under the SINR interfer-ence model Then interference region division is carriedout to describe the level of interference between links Afeasible scheduling set is generated by the distributed linkscheduling algorithm to coordinate the link transmissionand the interference between competing links in the MIMOnetwork is cancelled Experimental results show that thedistributed MSIC scheduling algorithm can bring significantperformance gain to wireless networks

Since the algorithm is premised on satisfying the thresh-old constraint of SINR the algorithm ends when the SINRvalue is less than the current threshold Therefore the nextresearch goal is how to solve the link scheduling problemwhen the SINR value is less than threshold

With the rapid development of the social economy theapplication of modern communication technology has beencontinuously promoted in various fields and the capacityrequirement for networks is increasing In addition dueto the complexity of the network environment a singletechnology will not have a sufficient effect on interferencecancellation Therefore in future wireless communicationnetworks a variety of joint applications of multiple interfer-ence cancellation technologies will be needed How to com-bine these technologies efficiently and achieve a reasonableoptimization combination is an important research direction

Data Availability

The simulation data used to support the findings of this studyare included within the article

Wireless Communications and Mobile Computing 11

2 25 3 35 4 45 5 55 61

2

3

4

5

6

7

8

9 x 105

Number of antennas

MIMOSDF

RLFMSIC

Min

imum

flow

thro

ughp

ut (b

ps)

(a) Minimum flow throughput

2 25 3 35 4 45 5 55 62

3

4

5

6

7

8

9

10

11 x 106

Number of antennas

MIMOSDF

RLFMSIC

Tota

l thr

ough

put (

bps)

(b) Total throughput

Figure 8 The relationship between antenna number and throughput

1 2 3 40

01

02

03

04

05

06

07

08

FlowMSICRLFMIMO

048046

056

033

054057

035

057061

028 032

043

The a

chie

vabl

e flow

rate

s

Figure 9 The gains of data flow rate for the four flow sessions

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (61672321 61771289 and 61832012)

Shandong provincial Graduate Education Innovation Pro-gram (SDYY14052 and SDYY15049) Qufu Normal Uni-versity Science and Technology Project (xkj201525) Shan-dong province agricultural machinery equipment researchand development innovation project (2018YZ002) ShandongProvincial Specialized Degree Postgraduate Teaching CaseLibrary Construction Program and Shandong ProvincialPostgraduate Education Quality Curriculum ConstructionProgram The authors thank the School of InformationScience and Engineering Qufu Normal University

References

[1] S Cheng Z Cai J Li and H Gao ldquoExtracting kernel datasetfrom big sensory data in wireless sensor networksrdquo IEEETransactions on Knowledge and Data Engineering vol 29 no4 pp 813ndash827 2017

[2] S Cheng Z Cai J Li and X Fang ldquoDrawing dominant datasetfrom big sensory data in wireless sensor networksrdquo in Pro-ceedings of the IEEE Conference on Computer Communications(INFOCOM rsquo15) pp 531ndash539 Hong Kong April 2015

[3] X Zheng and Z Cai ldquoReal-time big data delivery in wirelessnetworks a case study on video deliveryrdquo IEEE Transactions onIndustrial Informatics vol 13 no 4 pp 2048ndash2057 2017

[4] Z Cai andX Zheng ldquoA private and efficientmechanism for datauploading in smart cyber-physical systemsrdquo IEEE Transactionson Network Science and Engineering 2018

[5] L Lu G Y Li A L Swindlehurst A Ashikhmin and R ZhangldquoAn overview of massive MIMO benefits and challengesrdquo IEEEJournal of Selected Topics in Signal Processing vol 8 no 5 pp742ndash758 2014

[6] H Liu L Luo D Wu J Yu and D Chen ldquoRouting spectrumaccess and scheduling in multi-hop multi-channel wirelessnetworks with MIMO linksrdquo EURASIP Journal on Wireless

12 Wireless Communications and Mobile Computing

Communications and Networking vol 15 no 1 article no 652015

[7] B Hamdaoui and K G Shin ldquoCharacterization and analysis ofmulti-hop wireless mimo network throughputrdquo in Proceedingsof the Eighth ACM International Symposium on Mobile Ad HocNetworking and Computing pp 120ndash129 Montreal QuebecCanada September 2007

[8] L Jiang and J Walrand ldquoA distributed CSMA algorithm forthroughput and utility maximization in wireless networksrdquoIEEEACM Transactions on Networking vol 18 no 3 pp 960ndash972 2010

[9] H Yu O Bejarano and L Zhong ldquoCombating Inter-cellInterference in 80211ac-based multi-user MIMO networksrdquo inProceedings of the 20th ACM Annual International Conferenceon Mobile Computing and Networking (MobiCom rsquo14) pp 141ndash152 Maui Hawaii USA September 2014

[10] L B Le E Modiano C Joo and N B Shroff ldquoLongest-queue-first scheduling under SINR interferencemodelrdquo in Proceedingsof the 11th ACM International Symposium on Mobile Ad HocNetworking and Computing MobiHoc 2010 pp 41ndash50 USASeptember 2010

[11] J Li S Cheng Z Cai J Yu C Wang and Y Li ldquoApproximateholistic aggregation in wireless sensor networksrdquo ACM Trans-actions on Sensor Networks vol 13 no 2 article no 11 2017

[12] Y Zhou X Li M Liu X Mao S Tang and Z Li ldquoThroughputoptimizing localized link scheduling for multihop wireless net-works under physical interferencemodelrdquo IEEETransactions onParallel and Distributed Systems vol 25 no 10 pp 2708ndash27202014

[13] G Pei and A K S Vullikanti ldquoDistributed approximation algo-rithms for maximum link scheduling and local broadcasting inthe physical interferencemodelrdquo inProceedings of the 32nd IEEEConference on Computer Communications (IEEE INFOCOMrsquo13) pp 1339ndash1347 Turin Italy April 2013

[14] J Yu B Huang X Cheng and M Atiquzzaman ldquoShortest linkscheduling algorithms in wireless networks under the SINRmodelrdquo IEEE Transactions on Vehicular Technology vol 66 no3 pp 2643ndash2657 2017

[15] P J Wan X Xu and O Frieder ldquoShortest link scheduling withpower control under physical interferencemodelrdquo inProceedingof the Sixth International Conference on Mobile Ad-Hoc andSensor Networks pp 74ndash78 2010

[16] M Nabli F Abdelkefi W Ajib and M Siala ldquoEfficient central-ized link scheduling algorithms in wireless mesh networksrdquo inProceedings of the 10th International Wireless Communicationsand Mobile Computing Conference IWCMC 2014 pp 660ndash665Cyprus August 2014

[17] J-G Choi C Joo J Zhang and N B Shroff ldquoDistributed linkscheduling under SINR model in multihop wireless networksrdquoIEEEACM Transactions on Networking vol 22 no 4 pp 1204ndash1217 2014

[18] J Park and S Lee ldquoDistributed MIMO Ad-hoc networks Linkscheduling power allocation and cooperative beamformingrdquoIEEE Transactions on Vehicular Technology vol 61 no 6 pp2586ndash2598 2012

[19] Y Shi Y Thomas H J Liu and S Kompella ldquoHow tocorrectly use the protocol interference model for multi-hopwireless networksrdquo in Proceedings of the 10th ACM InternationalSymposium on Mobile Ad Hoc Networking and ComputingMobiHocrsquo09 pp 239ndash248 USA May 2009

[20] S Lv XWang andX Zhou ldquoScheduling under the SINRmodelin ad hoc networks with successive interference cancellationrdquoComputer Engineering and Science vol 34 no 2 pp 1ndash5 2012

[21] D Qian D Zheng J Zhang and N Shroff ldquoCSMA-baseddistributed scheduling in multi-hop MIMO networks underSINR modelrdquo in Proceedings of the IEEE INFOCOM 2010 pp1ndash9 USA March 2010

[22] O Goussevskaia M M Halldorsson and R WattenhoferldquoAlgorithms for wireless capacityrdquo IEEEACM Transactions onNetworking vol 22 no 3 pp 745ndash755 2014

[23] O Goussevskaia and RWattenhofer ldquoScheduling wireless linkswith successive interference cancellationrdquo in Proceedings of the21st International Conference onComputer Communications andNetworks ICCCN 2012 pp 1ndash7 Germany August 2012

[24] M Kontik and S C Ergen ldquoScheduling in single-hop multipleaccess wireless networks with successive interference cancella-tionrdquo IEEE Wireless Communications Letters vol 3 no 2 pp197ndash200 2014

[25] T Moscibroda R Wattenhofer and A Zollinger ldquoTopologycontrol meets SINR the scheduling complexity of arbitrarytopologiesrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 310ndash321 Florence Italy May 2006

[26] O Goussevskaia R Wattenhofer M M Halldorsson and EWelzl ldquoCapacity of arbitrary wireless networksrdquo in Proceedingsof the 28th Conference on Computer Communications (IEEEINFOCOM rsquo09) pp 1872ndash1880 Rio de Janeiro Brazil April2009

[27] M Dinitz ldquoDistributed algorithms for approximating wirelessnetwork capacityrdquo in Proceedings of the IEEE INFOCOM pp 1ndash9 IEEE San Diego Calif USA March 2010

[28] J Chen C Wen S Jin and K Wong ldquoA low complexitypilot scheduling algorithm for massive MIMOrdquo IEEE WirelessCommunications Letters vol 6 no 1 pp 18ndash21 2017

[29] D Halperin T Anderson and D Wetherall ldquoTaking thesting out of carrier sense interference cancellation for wirelessLANsrdquo in Proceedings of the 14th ACM Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo08) pp 339ndash350 September 2008

[30] S LvW Zhuang XWang andX Zhou ldquoScheduling inwirelessad hoc networks with successive interference cancellationrdquo inProceedings of the IEEE INFOCOM 2011 - IEEE Conference onComputer Communications pp 1287ndash1295 Shanghai ChinaApril 2011

[31] R Sultan L Song K G Seddik and Z Han ldquoFull-duplexmeetsmultiuser MIMO comparisons and analysisrdquo IEEE Transac-tions on Vehicular Technology vol 66 no 1 pp 455ndash467 2017

[32] X Zheng Z Cai J Li and H Gao ldquoA study on application-aware scheduling in wireless networksrdquo IEEE Transactions onMobile Computing vol 16 no 7 pp 1787ndash1801 2017

[33] X Li Y Shi X Wang C Xu and M Sheng ldquoEfficient linkscheduling with joint power control and successive interferencecancellation in wireless networksrdquo Science China InformationSciences vol 59 no 12 pp 1ndash15 2016

[34] L Qu J He and C Assi ldquoDistributed link scheduling inwireless networks with interference cancellation capabilitiesrdquoin Proceedings of the 15th IEEE International Symposium on aWorld ofWireless Mobile andMultimedia Networks WoWMoM2014 pp 1ndash7 Australia 2014

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Wireless Communications and Mobile Computing 5

We assume a half-duplex node on a MIMO node If node119894 isin 119873 is a sender in time slot 119905 the binary variable 119904푖(119905) is1 otherwise it is 0 Similarly if node 119894 isin 119873 is a receiver intime slot 119905 the binary variable 119903푖(119905) is 1 otherwise it is 0 Forhalf-duplex mode the constraint can be written as follows

119904푖 (119905) + 119903푖 (119905) le 1 (1 le 119894 le 119873 1 le 119905 le 119879) (8)

Denote 119909푙(119905) as the number of data streams over link119897 If node 119894 is not a sender then there is sum푙isin퐿표푢푡푖

119909푙(119905) =0 Otherwise in order to satisfy the DoF constraint at thesending node the total number of outgoing data streamsshould be positive and cannot exceed the number of antennasit owns that is 1 le sum푙isin퐿표푢푡푖

119909푙(119905) le 119872 These two cases can besummarized as follows

119904푖 (119905) le sum푙isin퐿표푢푡푖

119909푙 (119905) le 119872119904푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879) (9)

Similarly according to whether node 119894 is an active receiverwe have the following constraint at the receiving node

119903푖 (119905) le sum푙isin퐿푖푛푖

119909푙 (119905) le 119872119903푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879) (10)

For the congestion control problem of the transport layereach flow 119891 in the network determines the data rate of thenext slot independently according to the local congestionqueue information of the node in the current time slot 119880푓푖 (119905)represents the congestion queue length of flow 119891 at node 119894in time slot 119905 and U(119905) = [119880푓푖 (119905)] (119894 isin 119873 119891 isin 119865) is the setof all congestion queues According to the input and outputmode of each node the local congestion queue informationis updated dynamically as follows 119880푓푖 (119905 + 1) = 119880푓푖 (119905) +sum푙isin퐿푖푛푖

119909푙(119905)minussum푙isin퐿표푢푡푖119909푙(119905)+v푓(119905) and the initialized condition

queue is satisfied with119880푓푖 (0) = 0The source session flow119891 iscompressed into a source rate v푓(119905) before being pushed intothe queue Since the local congestion queue length of eachnode determines the upper limit of the data sum that can betransmitted in the current time slot 119905 there are the followingconstraints

sum푙isin퐿표푢푡푖

119909푙 (119905) le 119880푓푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879 119891 isin 119865) (11)

The session flow 119891 in the network determines the data rateof the next time slot according to the congestion queueconstraint Meanwhile in order to guarantee the strongrobustness of the network the following inequalities must besatisfied

lim푇㨀rarrinfin

1119879

푇minus1

sum푡=0

sum푖isin푁

sum푓isin퐹

119864 119880푓푖 (119905) lt infin (12)

For routing and scheduling problems 119863 =maxsum푙isin퐿 119903푙(119891) lowast max푓isin퐹119906푠푙(119891) minus 119906푑푙(119891) and eachlink 119897 can use local congestion queue information to find aflow 119891lowast that satisfies 119891lowast = argmax푓isin퐹119906s푙(119891) minus 119906푑푙(119891) Let119908푙 = 119906푠푙(119891

lowast) minus 119906푑푙(119891lowast) as the weight of link 119897 (119908푙 can also

be understood as the queue length at link 119897 with flow 119891lowast)To solve routing and scheduling problems we will propose adistributed algorithm in Section 4 to generate an active set119871푆耠 of concurrent links In each time slot the links in set 119871푆耠can send data to the receivers (we assume that in each timeslot each active link transmits a packet) Let 119863 be convertedinto the following form

119863 = maxsum푙isin퐿

Υ푙 (119891lowast) sdot 119908푙 (13)

To achieve the goal of maximizing the minimum end-to-end throughput Υmin a feasible routing scheduling alsoneeds to satisfy the following two constraints flow balanceconstraints and the link capacity constraint We have thefollowing flow balance constraints

(a) at the source node we have

sum푙isin퐿표푢푡푖

Υ푙 (119891) = Υ (119891) (119894 = 119904 (119891) 119891 isin 119865) (14)

(b) at each relay node we have

sum푙isin퐿푖푛푖

Υ푙 (119891) = sum푙isin퐿표푢푡푖

Υ푙 (119891)

(1 le 119894 le 119873 119894 = 119904 (119891) 119894 = 119889 (119891) 119891 isin 119865)(15)

(c) at the destination node we have

sum푙isin퐿푖푛푖

Υ푙 (119891) = Υ (119891) (119894 = d (119891) 119891 isin 119865) (16)

It is easy to verify that as long as any two of these equationsare satisfied the other one will also be satisfied Therefore itis sufficient to satisfy the first two equations

It is assumed that a fixed modulation and encodingscheme is used for each data stream and that each data streamcorresponds to one unit data rate Since the total data rate onlink 119897 cannot exceed the average rate of the link we have thefollowing link capacity constraint

sum푓isin퐹

Υ푙 (119891) le1119879

푇

sum푡=1

119909푙 (119905) (17)

where the right side represents the average throughput on link119897 of a frame (119879 time slots) Putting all the constraints togetherwe have the expression for the throughput maximizationproblem

max Υmin

st Υmin le Υ (119891) (119891 isin 119865)

119903-119878119868119873119877푗푖 [119905]

=119901푗1205722푗푖

100381710038171003817100381710038171003817k푛dagger

푗푖Hdagger푗푖u

푛푗

1003817100381710038171003817100381710038172

1198730 + sum푝푘훼2푘푖k푛dagger푘푖Hdagger푘푖U푘2le푝푗훼2푗푖k푛

dagger

푗푖 Hdagger푗푖u푛푗2

푘isin퐼푖푘 =푗119901푘1205722푘푖

10038171003817100381710038171003817k푛dagger

푗푖Hdagger푘푖U푘

100381710038171003817100381710038172

ge 120573푗푖

119904푖 (119905) + 119903푖 (119905) le 1 (1 le 119894 le 119873 1 le 119905 le 119879)

6 Wireless Communications and Mobile Computing

ＦＣ

ＦＣ

ＦＣ

ＦＣ

ＬＣＭＣ

Figure 3 Division of Interference Regions

119904푖 (119905) le sum푙isin퐿표푢푡푖

119909푙 (119905) le 119872119904푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879)

119903푖 (119905) le sum푙isin퐿푖푛푖

119909푙 (119905) le 119872119903푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879)

sum푙isin퐿표푢푡푖

119909푙 (119905) le 119880푓푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879 119891 isin 119865)

lim푇㨀rarrinfin

1119879

푇minus1

sum푡=0

sum푖isin푁

sum푓isin퐹

119864 119880푓푖 (119905) lt infin

sum푙isin퐿표푢푡푖

Υ푙 (119891) = Υ (119891) (119894 = 119904 (119891) 119891 isin 119865)

sum푙isin퐿푖푛푖

Υ푙 (119891) = sum푙isin퐿표푢푡푖

Υ푙 (119891)

(1 le 119894 le 119873 119894 = 119904 (119891) 119894 = 119889 (119891) 119891 isin 119865)

sum푓isin퐹

Υ푙 (119891) le1119879

푇

sum푡=1

119909푙 (119905)

(18)

4 Distributed Link SchedulingAlgorithm Based on MSIC

41 Division of Interference Regions Due to the character-istics of transmission loss the receiving power 119875푟푖 (119904푗) ofdifferent links is also different [34] The total interference atreceiver 119903푖 is expressed as follows

119868푟푖 = sum푠푗isin푆푡푠푖

119875 (119904푗)

119889 (119904푗 119903푖)훼 = sum

푠푗isin푆푡푠푖

119875푟푖 (119904푗) (19)

The scheduling problem of using SIC under the SINRmodel has been proved to be NP-hard [20] If the strongersignal in the network satisfies (5) it can be decoded andremoved due to the adoption of SIC Therefore the strengthof the receiving power does not completely measure theinterference generated by the link In this paper in orderto describe the interference localization the interferenceregions are defined to measure the level of interference

Different interference regions 119860 푙푖 119861푙푖 and 119862푙푖are divided

according to (19) 119860 푙푖 119861푙푖 and 119862푙푖 are concentric ring (circu-

lar) regions centered on receiver 119903푖 of link 119897푖 respectively asshown in Figure 3 (the red circular region is 119860 푙푖

the bluering region is 119861푙푖 and the black dotted ring region is 119862푙푖)The interference generated by the active link in the 119860 푙푖

and119861푙푖 regions will interrupt the transmission of link 119897푖 and theset of concurrent links in these regions is denoted as 119871푆 Thecumulative interference generated by the active link in the 119862푙푖region has a negligible effect on the receiver of link 119897푖

According to (2) the maximum cumulative interferencevalue that link 119897푖 can tolerate is the following

119868푟푖 le 119868max푙푖

le119875푙푖120573119889푖푖

훼 (20)

Therefore in order to satisfy the MSIC constraints thesum of the cumulative interference values at receiver 119903푖 of link119897푖 cannot exceed 119868max

푙푖 If the total interference in the 119860 푙푖

and119861푙푖 regions is (1 minus 119898)119868

max푙푖

and the total interference in the 119862푙푖region is119898119868max

푙푖 then we have

(1 minus 119898) 119868max푙푖

+ 119898119868max푙푖

le 119868max푙푖

(21)Assuming that the link 119897푗 at receiver 119903푖 from sender 119904푗 isin 119860 푙푖is stronger than link 119897푖 from sender 119904푖 SIC is used That is

Wireless Communications and Mobile Computing 7

Start

End

Initialization

MSIC feasibility judgment

Add link l to acc l

Remove link l from seq l

Update concurrent link set Ls

MSIC feasibility test

Yes

No

No

Yes

Figure 4 Distributed MSIC scheduling algorithm flow chart

receiver 119903푖 uses SIC to decode these strong signals continu-ously before decoding the expected signal from sender 119904푖 Letall links in a feasible set 119871푆 of concurrent links be transmittedsuccessfully When any link 119897푗 is added to the set 119871푆耠 sube 119871푆 thelink transmission will fail Obviously 119871푆耠 is the maximum setof concurrent links and 119871푆耠 must satisfy the constraints in(7)

42 Distributed MSIC Scheduling Algorithm In this sectionbased on the CSMACA mechanism and MSIC constraintswe design the distributed single-slot MSIC algorithm to solvethe scheduling problems If the links 119897 isin 119871耠 in the networkcan be transmitted concurrently then 119871耠 can be defined as ascheduling set In each scheduling time slot each linkwill runscheduling algorithms to generate a new feasible schedulingset 119871푆耠

Next considering the MSIC model and interferenceregions division introduced above a distributed link schedul-ing algorithm is proposed under the MSIC constraints Thealgorithm flow chart is shown in Figure 4 Three states of thelink are defined Active Inactive and Standby The four setscorrespond to different states where 119904119894119888 is the active link setthat satisfies the MSIC constraint and can be scheduled in thecurrent scheduling time slot 119886119888119888 is the standby link set thathas not been judged byMSIC constraints 119897119900119888 is the local cachelink set in the standby state and 119904119890119902 is the candidate link set inthe inactive state Therefore the state of a link in the currentslot can be distinguished by the set of links to which the linkcurrently belongs

(1) Initialization Stage At the beginning of each schedulingcycle each link 119897 maintains two sets of local links set 119886119888119888푙and set 119904119890119902푙 The links contained in the set 119886119888119888푙 are added to

a feasible set 119871푆 of concurrent links in a certain schedulingcycle and the links contained in set 119904119890119902푙 are candidate linksto be added into set 119871푆 At the beginning of each schedulingcycle initializing 119886119888119888푙 = Oslash and 119904119890119902푙 = 119897 119860 푙 cup 119861푙

(2) MSIC Feasibility Judgment Stage Each scheduling cycleconsists of several slots and in each slot each link 119897 makes adecision about whether it should be added to 119886119888119888푙 or removedfrom 119904119890119902푙 At the beginning of each scheduling slot all linksin the set 119904119890119902푙 are weighted for comparisonThe sender of link119897 broadcasts its weight information 119908푙 to all links 119896 whosesender is located in the 119860 푙 region of link 119897 If link 119897 has thelargest weight among all links in 119904119890119902푙 it will run Algorithm 1to try to add itself to 119886119888119888푙

The detailed process is as follows The sender of link 119897broadcasts a Requestmessage to links in 119860 푙cup119861푙 first If thereis a collision all of the links select a random back-off timeand wait for it If there is no collision the sender of all linksin 119860 푙 cup 119861푙 will add link 119897 to set 119897119900119888푙 When link 119897 is added tothe current schedule any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙 will determinewhether it remains feasible under the MSIC constraints Thespecific judgment process is as follows For each link 119897耠 isin119886119888119888푙cup119897119900119888푙 the set of linkswith sender 119904푙耠 isin 119886119888119888푙耠cup119897119900119888푙耠cap119860 푙耠and receiver 119903푙耠 is defined as the MSIC link set 119904119894119888푙耠 TheMSICconstraints will be satisfied when any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙satisfies the following conditions (i) the total interference 119868푙耠coming from set 119861푙耠 does not exceed (1 minus119898)119868max

푙耠 (ii) all links119896 isin 119904119894119888푙耠 are feasible that is the total interference 119868푘 comingfrom set 119861푘 does not exceed (1 minus 119898)119868max

푘 According to the above procedure if any link 119897耠 isin 119886119888119888푙 cup

119897119900119888푙 does not satisfy the MSIC constraints the sender oflink 119897耠 will send an Error message to link 119897 indicating thatlink 119897 cannot be added to set 119871푆 (the current scheduling isnot feasible due to the strong interference caused by link119897) If link 119897 isin 119897119900119888푙 does not receive any Error messagesfrom its neighbors it adds link 119897 to set 119886119888119888푙 and removeslink 119897 from 119904119890119902푙 and 119897119900119888푙 Then the sender broadcasts aSuccess message to all its neighbors to update their link sets119886119888119888 119904119890119902 and 119897119900119888 Otherwise it removes link 119897 from 119904119890119902푙and 119897119900119888푙 and then broadcasts a Remove message to all itsneighbors to update their link sets 119904119890119902 and 119897119900119888 After the aboveprocess is performed until a new link is added to 119871푆 thecurrent scheduling process is still feasible under the MSICconstraints

(3) MSIC Feasibility Test Stage After a new 119871푆耠 is generatedin each slot all links 119897 isin 119904119890119902푙 need to make the followingdecision about whether the MSIC constraints are satisfiedFor each link 119897 isin 119904119890119902푙 the set of links with sender 119904푙 isin119886119888119888푙 cap 119860 푙 and receiver 119903푙 is defined as another MSIC linkset 119904119894119888푙耠 Similar to the first procedure any link 119897 isin 119904119890119902푙 thatsatisfies any of the following conditions will dissatisfy theMSIC constraints (i) the total interference 119868푙耠 coming fromset 119861푙 exceeds (1 minus 119898)119868max

푙 or (ii) for any link 119896耠 isin 119904119894119888푙耠 is notfeasible that is the total interference 119868푘耠 coming from set 119861푘耠exceeds (1 minus119898)119868max

푘耠 After the above process if there is a link119897 in 119904119890119902푙 that does not satisfy the MSIC constraints the senderwill remove link 119897 from 119904119890119902푙 and broadcast a Remove messageto all its neighbors to update their link sets 119904119890119902 and 119886119888119888 The

8 Wireless Communications and Mobile Computing

1 sets of int 119886119888119888푙 119904119890119902푙 119897119900119888푙 119904119894119888푙耠 119904119894119888푙耠 initialize2 119886119888119888푙 larr997888 Oslash and 119904119890119902푙 larr997888 119897 119860 푙 cup 119861푙3 Sender of link 119897 broadcasts Requestmessage to links in 119860 푙 cup 119861푙4 for link 119897耠 isin 119860 푙 cup 119861푙 cap 119886119888119888푙 cup 119897119900119888푙 do MSIC feasibility judgment5 if sender of link 119897耠 receives Requestmessage from sender of link 119897 then6 sender of link 119897耠 adds link 119897 into 119897119900119888푘7 sender of link 119897耠 calculates cumulative interference 119868푙耠 8 if 119868푙耠 gt (1 minus 119898)119868max

푙耠then

9 Sender of link 119897耠 broadcasts Error message to sender of link 11989710 else11 Generate 119904119894119888푙耠 12 for 119896 isin 119904119894119888푙耠 do13 Link 119896 calculates cumulative interference 119868푘14 if 119868푘 gt (1 minus 119898)119868max

푘 then15 Sender of link 119897耠 broadcasts Error message to sender of link 11989716 end if17 end for18 end if19 end if20end for21 if sender of link 119897 does not receive Error messages then Generate concurrent links set22 119886119888119888푙 larr997888 119886119888119888푙 cup 11989723 119904119890119902푙 larr997888 119904119890119902푙11989724 119897119900119888푙 larr997888 119897119900119888푙11989725 Sender of link 119897 broadcasts Successmessage to all its neighbors to update their link sets 119886119888119888 119904119890119902 and 11989711990011988826 Goto Algorithm 227 else28 119904119890119902푙 larr997888 119904119890119902푙119897 Does not satisfy MSIC feasibility conditions29 Sender of link 119897 broadcasts Removemessage to all its neighbors to update their local link sets 119904119890119902 and 11989711990011988830 end if

Algorithm 1 Distributed MSIC Scheduling Algorithm (MSIC feasibility judgment)

above process ensures that each link in 119904119890119902푙 satisfies theMSICconstraints under the current scheduling

In the distributed algorithm the number of time slots ineach scheduling cycle is a fixed value In each scheduling sloteach link will run the distributed scheduling algorithm togenerate a new feasible scheduling set 119871푆耠 during schedulingOnce the scheduling is completed the selected link willtransmit a packet during the transmission cycle

43 Theoretical Proof of Algorithm

Theorem 1 The set 119871푆 of scheduling generated by the MSICalgorithm is feasible

Proof Based on the MSIC algorithm under interferenceregions division each link will run the algorithm indepen-dently in each scheduling slot to generate a new feasiblescheduling set 119871푆耠 From Algorithm 2 it is known that aftera new set 119871푆耠 is generated in each time slot all links 119897 isin 119904119890119902푙need to be tested to determine if theMSIC constraints are stillsatisfied To ensure that each link in 119904119890119902푙 satisfies the MSICconstraints under the current scheduling any link 119897 that doesnot satisfy the MSIC constraints will be removed from 119904119890119902푙Therefore the interference links cannot be scheduled at thesame time that is the links in the current set 119871푆耠 are feasiblewhich ensures the feasibility of the algorithm

Theorem 2 The time complexity of the MSIC algorithm is119874(1198962)

Proof In the process of MSIC feasibility judgment of Algo-rithm 1 it is necessary to judge the MSIC constraints formula(4) of any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙 and decide whether to add thelink to the current scheduling set This process requires twoloop statements to be executed with the algorithm executioncomplexity of 119874(1198962) where 119896 represents the number ofconcurrently transmitted signals After Algorithm 1 generatesa new set 119871푆耠 the MSIC feasibility test is performed inAlgorithm 2 The MSIC constraints condition needs to betested again for all links 119897 isin 119904119890119902푙 to ensure that any link in119904119890119902푙 satisfies the MSIC constraints This process also needsto execute two loop statements with the algorithm executioncomplexity of119874(1198962) Therefore the total algorithm executioncomplexity is 119874(1198962)

Theorem 3 The messages complexity of the MSIC algorithmis 119874(119899)

Proof The message complexity of sending a Request broad-cast message is 119874(1) To find a set of links that can be con-currently given by a network of 119899 links an MSIC constraintjudgment is performed for each link of 119897耠 isin 119860 푙 cup 119861푙 cap119886119888119888푙 cup 119897119900119888푙 and the number of Error or Success messages

Wireless Communications and Mobile Computing 9

1 sets of int 119868푘耠 119868푗耠 119904119894119888푘耠2 for link 119896 isin 119860 푙 cup 119861푙 cap 119904119890119902푙 do MSIC feasibility test3 if the sender of link 119896 receives a Successmessage from the sender of link 119897 then4 Link 119896 calculates the cumulative interference 119868푘耠5 if 119868푘耠 gt (1 minus 119898)119868max

푘 then6 The sender of link 119896 broadcasts a Removemessage to its neighbors to update their link sets 1199041198901199027 else8 Generate 119904119894119888푘耠9 for 119895 isin 119904119894119888푘耠 do10 Link 119895 calculates the cumulative interference 119868푗耠11 if 119868푗耠 gt (1 minus 119898)119868max

푗 then12 The sender of link 119896 broadcasts a Removemessage to its neighbors to update their link sets 11990411989011990213 end if14 end for15 end if16 end if17 end for

Algorithm 2 Distributed MSIC Scheduling Algorithm (MSIC feasibility test)

sent is at most 119899 minus 1 For each link of 119896 isin 119860 푙 cup 119861푙 cap 119904119890119902푙a feasibility test is performed and the number of Remove orSuccess messages is up to 119899 minus 1 When the execution of thealgorithm ends the total number of messages used is up to119874(119899)

5 Experimental Results

In this section the distributed single-slot scheduling probleminMIMOwireless networks is studied under the SINRmodelThe simulation is the average of 50 trials obtained on anetwork with 100 links The network size is 600 lowast 600 andthe distance between the sender and the receiver is selectedwithin the range of [20 40] The SINR parameters are set asfollows the threshold value is 120573 = 3 the path loss index is120572 = 22 the background noise power is119873 = 4times10minus7 and theuniform power is 119875 = 2 and 119875 = 10

First the relationship between the size of different net-works and the number of successful transmissions of linksis studied The simulation results are shown in Figure 5Under different power allocations the number of successfultransmissions of the link increases as the network sizeincreases and a larger transmission power can generate alarger neighbor size which is benefited by the gain of thetransmission power However when the network size is largethe neighbor size reaches the upper bound and the gain fromincreasing the power becomes very small At the same timelarger power will also cause more interference to other linksAt this time the impact of the interference on transmission isgreater than the benefit of the network scale increase whichmakes it impossible to satisfy the SINR constraint conditionalthough it improves its own successful transmission proba-bility and reduces the total size of the successful transmissionof the linkTherefore the transmission scale cannot be soughtblindly by increasing the power and a larger-scale schedulingset can be realized by controlling the network scale

20 50 100 150 200 250 300 350 400 450 500 550 6000

10

20

30

40

50

60

70

80

90

Network sizeP=10P=2

Num

ber o

f suc

cess

ful t

rans

miss

ions

Figure 5 The relationship between network size and number ofsuccessful transmissions

Next we compare the number of concurrent link trans-missions of different algorithms At the network layer therouting algorithm based on the least hops is adopted Forconvenience the distance data rate bandwidth and trans-mission power of the data stream are all normalized to 1

First the MSIC algorithm is compared with the recursivelargest first (RLF) algorithm and the smallest degree first(SDF) algorithm in [20] The results in Figure 6 show thatthe MSIC algorithm can obtain a larger link schedulingscale compared with the other two algorithms After theSIC is used all signals with high power in the interferenceregions can be decoded and removed firstly and thus theinterference reached at the receiver is smaller and a larger setof concurrent links can be obtained

10 Wireless Communications and Mobile Computing

0 10 20 30 40 50 60 70 800

5

10

15

20

25

30

Scheduling slot

MIMORLF

SDFMSIC

Num

ber o

f con

curr

ent l

ink

tran

smiss

ions

Figure 6 Comparison of the number of concurrent link transmis-sions of different algorithms

Then we study the effect of the parameter 119898 on thenumber of concurrent link transmissions Figure 7 shows thatthe number of concurrent links decreases as the parameter119898 increases When 119898 is smaller the interference radius ofeach link in the network is larger and there are more linksthat can participate in scheduling The number of concurrentlinks in each selected scheduling configuration is larger andthe data flow rate is higher At this time the network hasstronger interference management ability As the parametersbecome larger the interference in the network is largerthereby allowing fewer links to be transmitted concurrentlyThe MSIC algorithm can reduce partial interference andincrease the number of concurrent transmission links When119898 = 04 there is a close interference region radius betweenMSIC and MIMO so119898 = 04 is set here

Next we study the influence of the number of antennason network performanceThenumber of antennas is changedfrom 2 to 6 and the test is repeated 100 times We then takethe average value of each flow of 100 tests Ideally we assumethat the transmission rate of one link is equal to the capacityof the point-to-point MIMO link without other transmissioninterference As shown inFigure 8 throughput is nearly linearwith the number of antennas and the MSIC algorithm canachieve a higherminimumflow throughput and a higher totalthroughput in the network

To show more detail the flow rate gains for the four flowsessions are given in Figure 9 The simulation results showthat MSIC brings significant throughput gain toMIMOwire-less networks The network flow rate with SIC functionalityis more than half of the network rate without interferencecancellation whichmeans that the reachable unit end-to-endthroughput is increased by approximately 73on average dueto the application of SIC Therefore the MSIC algorithm hasobvious advantages in improving network throughput

01 02 03 04 05 06 07 08 0940

45

50

55

60

65

70

Parameter mMIMOMSIC

The n

umbe

r of c

oncu

rren

t tra

nsm

issio

ns

Figure 7The relationship between parameterm and the number ofconcurrent transmissions

6 Conclusions and Future Work

In this paper the MSIC scheduling algorithm based on SICin MIMO wireless networks is proposed First the MSICconstraints model is constructed under the SINR interfer-ence model Then interference region division is carriedout to describe the level of interference between links Afeasible scheduling set is generated by the distributed linkscheduling algorithm to coordinate the link transmissionand the interference between competing links in the MIMOnetwork is cancelled Experimental results show that thedistributed MSIC scheduling algorithm can bring significantperformance gain to wireless networks

Since the algorithm is premised on satisfying the thresh-old constraint of SINR the algorithm ends when the SINRvalue is less than the current threshold Therefore the nextresearch goal is how to solve the link scheduling problemwhen the SINR value is less than threshold

With the rapid development of the social economy theapplication of modern communication technology has beencontinuously promoted in various fields and the capacityrequirement for networks is increasing In addition dueto the complexity of the network environment a singletechnology will not have a sufficient effect on interferencecancellation Therefore in future wireless communicationnetworks a variety of joint applications of multiple interfer-ence cancellation technologies will be needed How to com-bine these technologies efficiently and achieve a reasonableoptimization combination is an important research direction

Data Availability

The simulation data used to support the findings of this studyare included within the article

Wireless Communications and Mobile Computing 11

2 25 3 35 4 45 5 55 61

2

3

4

5

6

7

8

9 x 105

Number of antennas

MIMOSDF

RLFMSIC

Min

imum

flow

thro

ughp

ut (b

ps)

(a) Minimum flow throughput

2 25 3 35 4 45 5 55 62

3

4

5

6

7

8

9

10

11 x 106

Number of antennas

MIMOSDF

RLFMSIC

Tota

l thr

ough

put (

bps)

(b) Total throughput

Figure 8 The relationship between antenna number and throughput

1 2 3 40

01

02

03

04

05

06

07

08

FlowMSICRLFMIMO

048046

056

033

054057

035

057061

028 032

043

The a

chie

vabl

e flow

rate

s

Figure 9 The gains of data flow rate for the four flow sessions

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (61672321 61771289 and 61832012)

Shandong provincial Graduate Education Innovation Pro-gram (SDYY14052 and SDYY15049) Qufu Normal Uni-versity Science and Technology Project (xkj201525) Shan-dong province agricultural machinery equipment researchand development innovation project (2018YZ002) ShandongProvincial Specialized Degree Postgraduate Teaching CaseLibrary Construction Program and Shandong ProvincialPostgraduate Education Quality Curriculum ConstructionProgram The authors thank the School of InformationScience and Engineering Qufu Normal University

References

[1] S Cheng Z Cai J Li and H Gao ldquoExtracting kernel datasetfrom big sensory data in wireless sensor networksrdquo IEEETransactions on Knowledge and Data Engineering vol 29 no4 pp 813ndash827 2017

[2] S Cheng Z Cai J Li and X Fang ldquoDrawing dominant datasetfrom big sensory data in wireless sensor networksrdquo in Pro-ceedings of the IEEE Conference on Computer Communications(INFOCOM rsquo15) pp 531ndash539 Hong Kong April 2015

[3] X Zheng and Z Cai ldquoReal-time big data delivery in wirelessnetworks a case study on video deliveryrdquo IEEE Transactions onIndustrial Informatics vol 13 no 4 pp 2048ndash2057 2017

[4] Z Cai andX Zheng ldquoA private and efficientmechanism for datauploading in smart cyber-physical systemsrdquo IEEE Transactionson Network Science and Engineering 2018

[5] L Lu G Y Li A L Swindlehurst A Ashikhmin and R ZhangldquoAn overview of massive MIMO benefits and challengesrdquo IEEEJournal of Selected Topics in Signal Processing vol 8 no 5 pp742ndash758 2014

[6] H Liu L Luo D Wu J Yu and D Chen ldquoRouting spectrumaccess and scheduling in multi-hop multi-channel wirelessnetworks with MIMO linksrdquo EURASIP Journal on Wireless

12 Wireless Communications and Mobile Computing

Communications and Networking vol 15 no 1 article no 652015

[7] B Hamdaoui and K G Shin ldquoCharacterization and analysis ofmulti-hop wireless mimo network throughputrdquo in Proceedingsof the Eighth ACM International Symposium on Mobile Ad HocNetworking and Computing pp 120ndash129 Montreal QuebecCanada September 2007

[8] L Jiang and J Walrand ldquoA distributed CSMA algorithm forthroughput and utility maximization in wireless networksrdquoIEEEACM Transactions on Networking vol 18 no 3 pp 960ndash972 2010

[9] H Yu O Bejarano and L Zhong ldquoCombating Inter-cellInterference in 80211ac-based multi-user MIMO networksrdquo inProceedings of the 20th ACM Annual International Conferenceon Mobile Computing and Networking (MobiCom rsquo14) pp 141ndash152 Maui Hawaii USA September 2014

[10] L B Le E Modiano C Joo and N B Shroff ldquoLongest-queue-first scheduling under SINR interferencemodelrdquo in Proceedingsof the 11th ACM International Symposium on Mobile Ad HocNetworking and Computing MobiHoc 2010 pp 41ndash50 USASeptember 2010

[11] J Li S Cheng Z Cai J Yu C Wang and Y Li ldquoApproximateholistic aggregation in wireless sensor networksrdquo ACM Trans-actions on Sensor Networks vol 13 no 2 article no 11 2017

[12] Y Zhou X Li M Liu X Mao S Tang and Z Li ldquoThroughputoptimizing localized link scheduling for multihop wireless net-works under physical interferencemodelrdquo IEEETransactions onParallel and Distributed Systems vol 25 no 10 pp 2708ndash27202014

[13] G Pei and A K S Vullikanti ldquoDistributed approximation algo-rithms for maximum link scheduling and local broadcasting inthe physical interferencemodelrdquo inProceedings of the 32nd IEEEConference on Computer Communications (IEEE INFOCOMrsquo13) pp 1339ndash1347 Turin Italy April 2013

[14] J Yu B Huang X Cheng and M Atiquzzaman ldquoShortest linkscheduling algorithms in wireless networks under the SINRmodelrdquo IEEE Transactions on Vehicular Technology vol 66 no3 pp 2643ndash2657 2017

[15] P J Wan X Xu and O Frieder ldquoShortest link scheduling withpower control under physical interferencemodelrdquo inProceedingof the Sixth International Conference on Mobile Ad-Hoc andSensor Networks pp 74ndash78 2010

[16] M Nabli F Abdelkefi W Ajib and M Siala ldquoEfficient central-ized link scheduling algorithms in wireless mesh networksrdquo inProceedings of the 10th International Wireless Communicationsand Mobile Computing Conference IWCMC 2014 pp 660ndash665Cyprus August 2014

[17] J-G Choi C Joo J Zhang and N B Shroff ldquoDistributed linkscheduling under SINR model in multihop wireless networksrdquoIEEEACM Transactions on Networking vol 22 no 4 pp 1204ndash1217 2014

[18] J Park and S Lee ldquoDistributed MIMO Ad-hoc networks Linkscheduling power allocation and cooperative beamformingrdquoIEEE Transactions on Vehicular Technology vol 61 no 6 pp2586ndash2598 2012

[19] Y Shi Y Thomas H J Liu and S Kompella ldquoHow tocorrectly use the protocol interference model for multi-hopwireless networksrdquo in Proceedings of the 10th ACM InternationalSymposium on Mobile Ad Hoc Networking and ComputingMobiHocrsquo09 pp 239ndash248 USA May 2009

[20] S Lv XWang andX Zhou ldquoScheduling under the SINRmodelin ad hoc networks with successive interference cancellationrdquoComputer Engineering and Science vol 34 no 2 pp 1ndash5 2012

[21] D Qian D Zheng J Zhang and N Shroff ldquoCSMA-baseddistributed scheduling in multi-hop MIMO networks underSINR modelrdquo in Proceedings of the IEEE INFOCOM 2010 pp1ndash9 USA March 2010

[22] O Goussevskaia M M Halldorsson and R WattenhoferldquoAlgorithms for wireless capacityrdquo IEEEACM Transactions onNetworking vol 22 no 3 pp 745ndash755 2014

[23] O Goussevskaia and RWattenhofer ldquoScheduling wireless linkswith successive interference cancellationrdquo in Proceedings of the21st International Conference onComputer Communications andNetworks ICCCN 2012 pp 1ndash7 Germany August 2012

[24] M Kontik and S C Ergen ldquoScheduling in single-hop multipleaccess wireless networks with successive interference cancella-tionrdquo IEEE Wireless Communications Letters vol 3 no 2 pp197ndash200 2014

[25] T Moscibroda R Wattenhofer and A Zollinger ldquoTopologycontrol meets SINR the scheduling complexity of arbitrarytopologiesrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 310ndash321 Florence Italy May 2006

[26] O Goussevskaia R Wattenhofer M M Halldorsson and EWelzl ldquoCapacity of arbitrary wireless networksrdquo in Proceedingsof the 28th Conference on Computer Communications (IEEEINFOCOM rsquo09) pp 1872ndash1880 Rio de Janeiro Brazil April2009

[27] M Dinitz ldquoDistributed algorithms for approximating wirelessnetwork capacityrdquo in Proceedings of the IEEE INFOCOM pp 1ndash9 IEEE San Diego Calif USA March 2010

[28] J Chen C Wen S Jin and K Wong ldquoA low complexitypilot scheduling algorithm for massive MIMOrdquo IEEE WirelessCommunications Letters vol 6 no 1 pp 18ndash21 2017

[29] D Halperin T Anderson and D Wetherall ldquoTaking thesting out of carrier sense interference cancellation for wirelessLANsrdquo in Proceedings of the 14th ACM Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo08) pp 339ndash350 September 2008

[30] S LvW Zhuang XWang andX Zhou ldquoScheduling inwirelessad hoc networks with successive interference cancellationrdquo inProceedings of the IEEE INFOCOM 2011 - IEEE Conference onComputer Communications pp 1287ndash1295 Shanghai ChinaApril 2011

[31] R Sultan L Song K G Seddik and Z Han ldquoFull-duplexmeetsmultiuser MIMO comparisons and analysisrdquo IEEE Transac-tions on Vehicular Technology vol 66 no 1 pp 455ndash467 2017

[32] X Zheng Z Cai J Li and H Gao ldquoA study on application-aware scheduling in wireless networksrdquo IEEE Transactions onMobile Computing vol 16 no 7 pp 1787ndash1801 2017

[33] X Li Y Shi X Wang C Xu and M Sheng ldquoEfficient linkscheduling with joint power control and successive interferencecancellation in wireless networksrdquo Science China InformationSciences vol 59 no 12 pp 1ndash15 2016

[34] L Qu J He and C Assi ldquoDistributed link scheduling inwireless networks with interference cancellation capabilitiesrdquoin Proceedings of the 15th IEEE International Symposium on aWorld ofWireless Mobile andMultimedia Networks WoWMoM2014 pp 1ndash7 Australia 2014

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6 Wireless Communications and Mobile Computing

ＦＣ

ＦＣ

ＦＣ

ＦＣ

ＬＣＭＣ

Figure 3 Division of Interference Regions

119904푖 (119905) le sum푙isin퐿표푢푡푖

119909푙 (119905) le 119872119904푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879)

119903푖 (119905) le sum푙isin퐿푖푛푖

119909푙 (119905) le 119872119903푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879)

sum푙isin퐿표푢푡푖

119909푙 (119905) le 119880푓푖 (119905) (1 le 119894 le 119873 1 le 119905 le 119879 119891 isin 119865)

lim푇㨀rarrinfin

1119879

푇minus1

sum푡=0

sum푖isin푁

sum푓isin퐹

119864 119880푓푖 (119905) lt infin

sum푙isin퐿표푢푡푖

Υ푙 (119891) = Υ (119891) (119894 = 119904 (119891) 119891 isin 119865)

sum푙isin퐿푖푛푖

Υ푙 (119891) = sum푙isin퐿표푢푡푖

Υ푙 (119891)

(1 le 119894 le 119873 119894 = 119904 (119891) 119894 = 119889 (119891) 119891 isin 119865)

sum푓isin퐹

Υ푙 (119891) le1119879

푇

sum푡=1

119909푙 (119905)

(18)

4 Distributed Link SchedulingAlgorithm Based on MSIC

41 Division of Interference Regions Due to the character-istics of transmission loss the receiving power 119875푟푖 (119904푗) ofdifferent links is also different [34] The total interference atreceiver 119903푖 is expressed as follows

119868푟푖 = sum푠푗isin푆푡푠푖

119875 (119904푗)

119889 (119904푗 119903푖)훼 = sum

푠푗isin푆푡푠푖

119875푟푖 (119904푗) (19)

The scheduling problem of using SIC under the SINRmodel has been proved to be NP-hard [20] If the strongersignal in the network satisfies (5) it can be decoded andremoved due to the adoption of SIC Therefore the strengthof the receiving power does not completely measure theinterference generated by the link In this paper in orderto describe the interference localization the interferenceregions are defined to measure the level of interference

Different interference regions 119860 푙푖 119861푙푖 and 119862푙푖are divided

according to (19) 119860 푙푖 119861푙푖 and 119862푙푖 are concentric ring (circu-

lar) regions centered on receiver 119903푖 of link 119897푖 respectively asshown in Figure 3 (the red circular region is 119860 푙푖

the bluering region is 119861푙푖 and the black dotted ring region is 119862푙푖)The interference generated by the active link in the 119860 푙푖

and119861푙푖 regions will interrupt the transmission of link 119897푖 and theset of concurrent links in these regions is denoted as 119871푆 Thecumulative interference generated by the active link in the 119862푙푖region has a negligible effect on the receiver of link 119897푖

According to (2) the maximum cumulative interferencevalue that link 119897푖 can tolerate is the following

119868푟푖 le 119868max푙푖

le119875푙푖120573119889푖푖

훼 (20)

Therefore in order to satisfy the MSIC constraints thesum of the cumulative interference values at receiver 119903푖 of link119897푖 cannot exceed 119868max

푙푖 If the total interference in the 119860 푙푖

and119861푙푖 regions is (1 minus 119898)119868

max푙푖

and the total interference in the 119862푙푖region is119898119868max

푙푖 then we have

(1 minus 119898) 119868max푙푖

+ 119898119868max푙푖

le 119868max푙푖

(21)Assuming that the link 119897푗 at receiver 119903푖 from sender 119904푗 isin 119860 푙푖is stronger than link 119897푖 from sender 119904푖 SIC is used That is

Wireless Communications and Mobile Computing 7

Start

End

Initialization

MSIC feasibility judgment

Add link l to acc l

Remove link l from seq l

Update concurrent link set Ls

MSIC feasibility test

Yes

No

No

Yes

Figure 4 Distributed MSIC scheduling algorithm flow chart

receiver 119903푖 uses SIC to decode these strong signals continu-ously before decoding the expected signal from sender 119904푖 Letall links in a feasible set 119871푆 of concurrent links be transmittedsuccessfully When any link 119897푗 is added to the set 119871푆耠 sube 119871푆 thelink transmission will fail Obviously 119871푆耠 is the maximum setof concurrent links and 119871푆耠 must satisfy the constraints in(7)

42 Distributed MSIC Scheduling Algorithm In this sectionbased on the CSMACA mechanism and MSIC constraintswe design the distributed single-slot MSIC algorithm to solvethe scheduling problems If the links 119897 isin 119871耠 in the networkcan be transmitted concurrently then 119871耠 can be defined as ascheduling set In each scheduling time slot each linkwill runscheduling algorithms to generate a new feasible schedulingset 119871푆耠

Next considering the MSIC model and interferenceregions division introduced above a distributed link schedul-ing algorithm is proposed under the MSIC constraints Thealgorithm flow chart is shown in Figure 4 Three states of thelink are defined Active Inactive and Standby The four setscorrespond to different states where 119904119894119888 is the active link setthat satisfies the MSIC constraint and can be scheduled in thecurrent scheduling time slot 119886119888119888 is the standby link set thathas not been judged byMSIC constraints 119897119900119888 is the local cachelink set in the standby state and 119904119890119902 is the candidate link set inthe inactive state Therefore the state of a link in the currentslot can be distinguished by the set of links to which the linkcurrently belongs

(1) Initialization Stage At the beginning of each schedulingcycle each link 119897 maintains two sets of local links set 119886119888119888푙and set 119904119890119902푙 The links contained in the set 119886119888119888푙 are added to

a feasible set 119871푆 of concurrent links in a certain schedulingcycle and the links contained in set 119904119890119902푙 are candidate linksto be added into set 119871푆 At the beginning of each schedulingcycle initializing 119886119888119888푙 = Oslash and 119904119890119902푙 = 119897 119860 푙 cup 119861푙

(2) MSIC Feasibility Judgment Stage Each scheduling cycleconsists of several slots and in each slot each link 119897 makes adecision about whether it should be added to 119886119888119888푙 or removedfrom 119904119890119902푙 At the beginning of each scheduling slot all linksin the set 119904119890119902푙 are weighted for comparisonThe sender of link119897 broadcasts its weight information 119908푙 to all links 119896 whosesender is located in the 119860 푙 region of link 119897 If link 119897 has thelargest weight among all links in 119904119890119902푙 it will run Algorithm 1to try to add itself to 119886119888119888푙

The detailed process is as follows The sender of link 119897broadcasts a Requestmessage to links in 119860 푙cup119861푙 first If thereis a collision all of the links select a random back-off timeand wait for it If there is no collision the sender of all linksin 119860 푙 cup 119861푙 will add link 119897 to set 119897119900119888푙 When link 119897 is added tothe current schedule any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙 will determinewhether it remains feasible under the MSIC constraints Thespecific judgment process is as follows For each link 119897耠 isin119886119888119888푙cup119897119900119888푙 the set of linkswith sender 119904푙耠 isin 119886119888119888푙耠cup119897119900119888푙耠cap119860 푙耠and receiver 119903푙耠 is defined as the MSIC link set 119904119894119888푙耠 TheMSICconstraints will be satisfied when any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙satisfies the following conditions (i) the total interference 119868푙耠coming from set 119861푙耠 does not exceed (1 minus119898)119868max

푙耠 (ii) all links119896 isin 119904119894119888푙耠 are feasible that is the total interference 119868푘 comingfrom set 119861푘 does not exceed (1 minus 119898)119868max

푘 According to the above procedure if any link 119897耠 isin 119886119888119888푙 cup

119897119900119888푙 does not satisfy the MSIC constraints the sender oflink 119897耠 will send an Error message to link 119897 indicating thatlink 119897 cannot be added to set 119871푆 (the current scheduling isnot feasible due to the strong interference caused by link119897) If link 119897 isin 119897119900119888푙 does not receive any Error messagesfrom its neighbors it adds link 119897 to set 119886119888119888푙 and removeslink 119897 from 119904119890119902푙 and 119897119900119888푙 Then the sender broadcasts aSuccess message to all its neighbors to update their link sets119886119888119888 119904119890119902 and 119897119900119888 Otherwise it removes link 119897 from 119904119890119902푙and 119897119900119888푙 and then broadcasts a Remove message to all itsneighbors to update their link sets 119904119890119902 and 119897119900119888 After the aboveprocess is performed until a new link is added to 119871푆 thecurrent scheduling process is still feasible under the MSICconstraints

(3) MSIC Feasibility Test Stage After a new 119871푆耠 is generatedin each slot all links 119897 isin 119904119890119902푙 need to make the followingdecision about whether the MSIC constraints are satisfiedFor each link 119897 isin 119904119890119902푙 the set of links with sender 119904푙 isin119886119888119888푙 cap 119860 푙 and receiver 119903푙 is defined as another MSIC linkset 119904119894119888푙耠 Similar to the first procedure any link 119897 isin 119904119890119902푙 thatsatisfies any of the following conditions will dissatisfy theMSIC constraints (i) the total interference 119868푙耠 coming fromset 119861푙 exceeds (1 minus 119898)119868max

푙 or (ii) for any link 119896耠 isin 119904119894119888푙耠 is notfeasible that is the total interference 119868푘耠 coming from set 119861푘耠exceeds (1 minus119898)119868max

푘耠 After the above process if there is a link119897 in 119904119890119902푙 that does not satisfy the MSIC constraints the senderwill remove link 119897 from 119904119890119902푙 and broadcast a Remove messageto all its neighbors to update their link sets 119904119890119902 and 119886119888119888 The

8 Wireless Communications and Mobile Computing

1 sets of int 119886119888119888푙 119904119890119902푙 119897119900119888푙 119904119894119888푙耠 119904119894119888푙耠 initialize2 119886119888119888푙 larr997888 Oslash and 119904119890119902푙 larr997888 119897 119860 푙 cup 119861푙3 Sender of link 119897 broadcasts Requestmessage to links in 119860 푙 cup 119861푙4 for link 119897耠 isin 119860 푙 cup 119861푙 cap 119886119888119888푙 cup 119897119900119888푙 do MSIC feasibility judgment5 if sender of link 119897耠 receives Requestmessage from sender of link 119897 then6 sender of link 119897耠 adds link 119897 into 119897119900119888푘7 sender of link 119897耠 calculates cumulative interference 119868푙耠 8 if 119868푙耠 gt (1 minus 119898)119868max

푙耠then

9 Sender of link 119897耠 broadcasts Error message to sender of link 11989710 else11 Generate 119904119894119888푙耠 12 for 119896 isin 119904119894119888푙耠 do13 Link 119896 calculates cumulative interference 119868푘14 if 119868푘 gt (1 minus 119898)119868max

푘 then15 Sender of link 119897耠 broadcasts Error message to sender of link 11989716 end if17 end for18 end if19 end if20end for21 if sender of link 119897 does not receive Error messages then Generate concurrent links set22 119886119888119888푙 larr997888 119886119888119888푙 cup 11989723 119904119890119902푙 larr997888 119904119890119902푙11989724 119897119900119888푙 larr997888 119897119900119888푙11989725 Sender of link 119897 broadcasts Successmessage to all its neighbors to update their link sets 119886119888119888 119904119890119902 and 11989711990011988826 Goto Algorithm 227 else28 119904119890119902푙 larr997888 119904119890119902푙119897 Does not satisfy MSIC feasibility conditions29 Sender of link 119897 broadcasts Removemessage to all its neighbors to update their local link sets 119904119890119902 and 11989711990011988830 end if

Algorithm 1 Distributed MSIC Scheduling Algorithm (MSIC feasibility judgment)

above process ensures that each link in 119904119890119902푙 satisfies theMSICconstraints under the current scheduling

In the distributed algorithm the number of time slots ineach scheduling cycle is a fixed value In each scheduling sloteach link will run the distributed scheduling algorithm togenerate a new feasible scheduling set 119871푆耠 during schedulingOnce the scheduling is completed the selected link willtransmit a packet during the transmission cycle

43 Theoretical Proof of Algorithm

Theorem 1 The set 119871푆 of scheduling generated by the MSICalgorithm is feasible

Proof Based on the MSIC algorithm under interferenceregions division each link will run the algorithm indepen-dently in each scheduling slot to generate a new feasiblescheduling set 119871푆耠 From Algorithm 2 it is known that aftera new set 119871푆耠 is generated in each time slot all links 119897 isin 119904119890119902푙need to be tested to determine if theMSIC constraints are stillsatisfied To ensure that each link in 119904119890119902푙 satisfies the MSICconstraints under the current scheduling any link 119897 that doesnot satisfy the MSIC constraints will be removed from 119904119890119902푙Therefore the interference links cannot be scheduled at thesame time that is the links in the current set 119871푆耠 are feasiblewhich ensures the feasibility of the algorithm

Theorem 2 The time complexity of the MSIC algorithm is119874(1198962)

Proof In the process of MSIC feasibility judgment of Algo-rithm 1 it is necessary to judge the MSIC constraints formula(4) of any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙 and decide whether to add thelink to the current scheduling set This process requires twoloop statements to be executed with the algorithm executioncomplexity of 119874(1198962) where 119896 represents the number ofconcurrently transmitted signals After Algorithm 1 generatesa new set 119871푆耠 the MSIC feasibility test is performed inAlgorithm 2 The MSIC constraints condition needs to betested again for all links 119897 isin 119904119890119902푙 to ensure that any link in119904119890119902푙 satisfies the MSIC constraints This process also needsto execute two loop statements with the algorithm executioncomplexity of119874(1198962) Therefore the total algorithm executioncomplexity is 119874(1198962)

Theorem 3 The messages complexity of the MSIC algorithmis 119874(119899)

Proof The message complexity of sending a Request broad-cast message is 119874(1) To find a set of links that can be con-currently given by a network of 119899 links an MSIC constraintjudgment is performed for each link of 119897耠 isin 119860 푙 cup 119861푙 cap119886119888119888푙 cup 119897119900119888푙 and the number of Error or Success messages

Wireless Communications and Mobile Computing 9

1 sets of int 119868푘耠 119868푗耠 119904119894119888푘耠2 for link 119896 isin 119860 푙 cup 119861푙 cap 119904119890119902푙 do MSIC feasibility test3 if the sender of link 119896 receives a Successmessage from the sender of link 119897 then4 Link 119896 calculates the cumulative interference 119868푘耠5 if 119868푘耠 gt (1 minus 119898)119868max

푘 then6 The sender of link 119896 broadcasts a Removemessage to its neighbors to update their link sets 1199041198901199027 else8 Generate 119904119894119888푘耠9 for 119895 isin 119904119894119888푘耠 do10 Link 119895 calculates the cumulative interference 119868푗耠11 if 119868푗耠 gt (1 minus 119898)119868max

푗 then12 The sender of link 119896 broadcasts a Removemessage to its neighbors to update their link sets 11990411989011990213 end if14 end for15 end if16 end if17 end for

Algorithm 2 Distributed MSIC Scheduling Algorithm (MSIC feasibility test)

sent is at most 119899 minus 1 For each link of 119896 isin 119860 푙 cup 119861푙 cap 119904119890119902푙a feasibility test is performed and the number of Remove orSuccess messages is up to 119899 minus 1 When the execution of thealgorithm ends the total number of messages used is up to119874(119899)

5 Experimental Results

In this section the distributed single-slot scheduling probleminMIMOwireless networks is studied under the SINRmodelThe simulation is the average of 50 trials obtained on anetwork with 100 links The network size is 600 lowast 600 andthe distance between the sender and the receiver is selectedwithin the range of [20 40] The SINR parameters are set asfollows the threshold value is 120573 = 3 the path loss index is120572 = 22 the background noise power is119873 = 4times10minus7 and theuniform power is 119875 = 2 and 119875 = 10

First the relationship between the size of different net-works and the number of successful transmissions of linksis studied The simulation results are shown in Figure 5Under different power allocations the number of successfultransmissions of the link increases as the network sizeincreases and a larger transmission power can generate alarger neighbor size which is benefited by the gain of thetransmission power However when the network size is largethe neighbor size reaches the upper bound and the gain fromincreasing the power becomes very small At the same timelarger power will also cause more interference to other linksAt this time the impact of the interference on transmission isgreater than the benefit of the network scale increase whichmakes it impossible to satisfy the SINR constraint conditionalthough it improves its own successful transmission proba-bility and reduces the total size of the successful transmissionof the linkTherefore the transmission scale cannot be soughtblindly by increasing the power and a larger-scale schedulingset can be realized by controlling the network scale

20 50 100 150 200 250 300 350 400 450 500 550 6000

10

20

30

40

50

60

70

80

90

Network sizeP=10P=2

Num

ber o

f suc

cess

ful t

rans

miss

ions

Figure 5 The relationship between network size and number ofsuccessful transmissions

Next we compare the number of concurrent link trans-missions of different algorithms At the network layer therouting algorithm based on the least hops is adopted Forconvenience the distance data rate bandwidth and trans-mission power of the data stream are all normalized to 1

First the MSIC algorithm is compared with the recursivelargest first (RLF) algorithm and the smallest degree first(SDF) algorithm in [20] The results in Figure 6 show thatthe MSIC algorithm can obtain a larger link schedulingscale compared with the other two algorithms After theSIC is used all signals with high power in the interferenceregions can be decoded and removed firstly and thus theinterference reached at the receiver is smaller and a larger setof concurrent links can be obtained

10 Wireless Communications and Mobile Computing

0 10 20 30 40 50 60 70 800

5

10

15

20

25

30

Scheduling slot

MIMORLF

SDFMSIC

Num

ber o

f con

curr

ent l

ink

tran

smiss

ions

Figure 6 Comparison of the number of concurrent link transmis-sions of different algorithms

Then we study the effect of the parameter 119898 on thenumber of concurrent link transmissions Figure 7 shows thatthe number of concurrent links decreases as the parameter119898 increases When 119898 is smaller the interference radius ofeach link in the network is larger and there are more linksthat can participate in scheduling The number of concurrentlinks in each selected scheduling configuration is larger andthe data flow rate is higher At this time the network hasstronger interference management ability As the parametersbecome larger the interference in the network is largerthereby allowing fewer links to be transmitted concurrentlyThe MSIC algorithm can reduce partial interference andincrease the number of concurrent transmission links When119898 = 04 there is a close interference region radius betweenMSIC and MIMO so119898 = 04 is set here

Next we study the influence of the number of antennason network performanceThenumber of antennas is changedfrom 2 to 6 and the test is repeated 100 times We then takethe average value of each flow of 100 tests Ideally we assumethat the transmission rate of one link is equal to the capacityof the point-to-point MIMO link without other transmissioninterference As shown inFigure 8 throughput is nearly linearwith the number of antennas and the MSIC algorithm canachieve a higherminimumflow throughput and a higher totalthroughput in the network

To show more detail the flow rate gains for the four flowsessions are given in Figure 9 The simulation results showthat MSIC brings significant throughput gain toMIMOwire-less networks The network flow rate with SIC functionalityis more than half of the network rate without interferencecancellation whichmeans that the reachable unit end-to-endthroughput is increased by approximately 73on average dueto the application of SIC Therefore the MSIC algorithm hasobvious advantages in improving network throughput

01 02 03 04 05 06 07 08 0940

45

50

55

60

65

70

Parameter mMIMOMSIC

The n

umbe

r of c

oncu

rren

t tra

nsm

issio

ns

Figure 7The relationship between parameterm and the number ofconcurrent transmissions

6 Conclusions and Future Work

In this paper the MSIC scheduling algorithm based on SICin MIMO wireless networks is proposed First the MSICconstraints model is constructed under the SINR interfer-ence model Then interference region division is carriedout to describe the level of interference between links Afeasible scheduling set is generated by the distributed linkscheduling algorithm to coordinate the link transmissionand the interference between competing links in the MIMOnetwork is cancelled Experimental results show that thedistributed MSIC scheduling algorithm can bring significantperformance gain to wireless networks

Since the algorithm is premised on satisfying the thresh-old constraint of SINR the algorithm ends when the SINRvalue is less than the current threshold Therefore the nextresearch goal is how to solve the link scheduling problemwhen the SINR value is less than threshold

With the rapid development of the social economy theapplication of modern communication technology has beencontinuously promoted in various fields and the capacityrequirement for networks is increasing In addition dueto the complexity of the network environment a singletechnology will not have a sufficient effect on interferencecancellation Therefore in future wireless communicationnetworks a variety of joint applications of multiple interfer-ence cancellation technologies will be needed How to com-bine these technologies efficiently and achieve a reasonableoptimization combination is an important research direction

Data Availability

The simulation data used to support the findings of this studyare included within the article

Wireless Communications and Mobile Computing 11

2 25 3 35 4 45 5 55 61

2

3

4

5

6

7

8

9 x 105

Number of antennas

MIMOSDF

RLFMSIC

Min

imum

flow

thro

ughp

ut (b

ps)

(a) Minimum flow throughput

2 25 3 35 4 45 5 55 62

3

4

5

6

7

8

9

10

11 x 106

Number of antennas

MIMOSDF

RLFMSIC

Tota

l thr

ough

put (

bps)

(b) Total throughput

Figure 8 The relationship between antenna number and throughput

1 2 3 40

01

02

03

04

05

06

07

08

FlowMSICRLFMIMO

048046

056

033

054057

035

057061

028 032

043

The a

chie

vabl

e flow

rate

s

Figure 9 The gains of data flow rate for the four flow sessions

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (61672321 61771289 and 61832012)

Shandong provincial Graduate Education Innovation Pro-gram (SDYY14052 and SDYY15049) Qufu Normal Uni-versity Science and Technology Project (xkj201525) Shan-dong province agricultural machinery equipment researchand development innovation project (2018YZ002) ShandongProvincial Specialized Degree Postgraduate Teaching CaseLibrary Construction Program and Shandong ProvincialPostgraduate Education Quality Curriculum ConstructionProgram The authors thank the School of InformationScience and Engineering Qufu Normal University

References

[1] S Cheng Z Cai J Li and H Gao ldquoExtracting kernel datasetfrom big sensory data in wireless sensor networksrdquo IEEETransactions on Knowledge and Data Engineering vol 29 no4 pp 813ndash827 2017

[2] S Cheng Z Cai J Li and X Fang ldquoDrawing dominant datasetfrom big sensory data in wireless sensor networksrdquo in Pro-ceedings of the IEEE Conference on Computer Communications(INFOCOM rsquo15) pp 531ndash539 Hong Kong April 2015

[3] X Zheng and Z Cai ldquoReal-time big data delivery in wirelessnetworks a case study on video deliveryrdquo IEEE Transactions onIndustrial Informatics vol 13 no 4 pp 2048ndash2057 2017

[4] Z Cai andX Zheng ldquoA private and efficientmechanism for datauploading in smart cyber-physical systemsrdquo IEEE Transactionson Network Science and Engineering 2018

[5] L Lu G Y Li A L Swindlehurst A Ashikhmin and R ZhangldquoAn overview of massive MIMO benefits and challengesrdquo IEEEJournal of Selected Topics in Signal Processing vol 8 no 5 pp742ndash758 2014

[6] H Liu L Luo D Wu J Yu and D Chen ldquoRouting spectrumaccess and scheduling in multi-hop multi-channel wirelessnetworks with MIMO linksrdquo EURASIP Journal on Wireless

12 Wireless Communications and Mobile Computing

Communications and Networking vol 15 no 1 article no 652015

[7] B Hamdaoui and K G Shin ldquoCharacterization and analysis ofmulti-hop wireless mimo network throughputrdquo in Proceedingsof the Eighth ACM International Symposium on Mobile Ad HocNetworking and Computing pp 120ndash129 Montreal QuebecCanada September 2007

[8] L Jiang and J Walrand ldquoA distributed CSMA algorithm forthroughput and utility maximization in wireless networksrdquoIEEEACM Transactions on Networking vol 18 no 3 pp 960ndash972 2010

[9] H Yu O Bejarano and L Zhong ldquoCombating Inter-cellInterference in 80211ac-based multi-user MIMO networksrdquo inProceedings of the 20th ACM Annual International Conferenceon Mobile Computing and Networking (MobiCom rsquo14) pp 141ndash152 Maui Hawaii USA September 2014

[10] L B Le E Modiano C Joo and N B Shroff ldquoLongest-queue-first scheduling under SINR interferencemodelrdquo in Proceedingsof the 11th ACM International Symposium on Mobile Ad HocNetworking and Computing MobiHoc 2010 pp 41ndash50 USASeptember 2010

[11] J Li S Cheng Z Cai J Yu C Wang and Y Li ldquoApproximateholistic aggregation in wireless sensor networksrdquo ACM Trans-actions on Sensor Networks vol 13 no 2 article no 11 2017

[12] Y Zhou X Li M Liu X Mao S Tang and Z Li ldquoThroughputoptimizing localized link scheduling for multihop wireless net-works under physical interferencemodelrdquo IEEETransactions onParallel and Distributed Systems vol 25 no 10 pp 2708ndash27202014

[13] G Pei and A K S Vullikanti ldquoDistributed approximation algo-rithms for maximum link scheduling and local broadcasting inthe physical interferencemodelrdquo inProceedings of the 32nd IEEEConference on Computer Communications (IEEE INFOCOMrsquo13) pp 1339ndash1347 Turin Italy April 2013

[14] J Yu B Huang X Cheng and M Atiquzzaman ldquoShortest linkscheduling algorithms in wireless networks under the SINRmodelrdquo IEEE Transactions on Vehicular Technology vol 66 no3 pp 2643ndash2657 2017

[15] P J Wan X Xu and O Frieder ldquoShortest link scheduling withpower control under physical interferencemodelrdquo inProceedingof the Sixth International Conference on Mobile Ad-Hoc andSensor Networks pp 74ndash78 2010

[16] M Nabli F Abdelkefi W Ajib and M Siala ldquoEfficient central-ized link scheduling algorithms in wireless mesh networksrdquo inProceedings of the 10th International Wireless Communicationsand Mobile Computing Conference IWCMC 2014 pp 660ndash665Cyprus August 2014

[17] J-G Choi C Joo J Zhang and N B Shroff ldquoDistributed linkscheduling under SINR model in multihop wireless networksrdquoIEEEACM Transactions on Networking vol 22 no 4 pp 1204ndash1217 2014

[18] J Park and S Lee ldquoDistributed MIMO Ad-hoc networks Linkscheduling power allocation and cooperative beamformingrdquoIEEE Transactions on Vehicular Technology vol 61 no 6 pp2586ndash2598 2012

[19] Y Shi Y Thomas H J Liu and S Kompella ldquoHow tocorrectly use the protocol interference model for multi-hopwireless networksrdquo in Proceedings of the 10th ACM InternationalSymposium on Mobile Ad Hoc Networking and ComputingMobiHocrsquo09 pp 239ndash248 USA May 2009

[20] S Lv XWang andX Zhou ldquoScheduling under the SINRmodelin ad hoc networks with successive interference cancellationrdquoComputer Engineering and Science vol 34 no 2 pp 1ndash5 2012

[21] D Qian D Zheng J Zhang and N Shroff ldquoCSMA-baseddistributed scheduling in multi-hop MIMO networks underSINR modelrdquo in Proceedings of the IEEE INFOCOM 2010 pp1ndash9 USA March 2010

[22] O Goussevskaia M M Halldorsson and R WattenhoferldquoAlgorithms for wireless capacityrdquo IEEEACM Transactions onNetworking vol 22 no 3 pp 745ndash755 2014

[23] O Goussevskaia and RWattenhofer ldquoScheduling wireless linkswith successive interference cancellationrdquo in Proceedings of the21st International Conference onComputer Communications andNetworks ICCCN 2012 pp 1ndash7 Germany August 2012

[24] M Kontik and S C Ergen ldquoScheduling in single-hop multipleaccess wireless networks with successive interference cancella-tionrdquo IEEE Wireless Communications Letters vol 3 no 2 pp197ndash200 2014

[25] T Moscibroda R Wattenhofer and A Zollinger ldquoTopologycontrol meets SINR the scheduling complexity of arbitrarytopologiesrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 310ndash321 Florence Italy May 2006

[26] O Goussevskaia R Wattenhofer M M Halldorsson and EWelzl ldquoCapacity of arbitrary wireless networksrdquo in Proceedingsof the 28th Conference on Computer Communications (IEEEINFOCOM rsquo09) pp 1872ndash1880 Rio de Janeiro Brazil April2009

[27] M Dinitz ldquoDistributed algorithms for approximating wirelessnetwork capacityrdquo in Proceedings of the IEEE INFOCOM pp 1ndash9 IEEE San Diego Calif USA March 2010

[28] J Chen C Wen S Jin and K Wong ldquoA low complexitypilot scheduling algorithm for massive MIMOrdquo IEEE WirelessCommunications Letters vol 6 no 1 pp 18ndash21 2017

[29] D Halperin T Anderson and D Wetherall ldquoTaking thesting out of carrier sense interference cancellation for wirelessLANsrdquo in Proceedings of the 14th ACM Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo08) pp 339ndash350 September 2008

[30] S LvW Zhuang XWang andX Zhou ldquoScheduling inwirelessad hoc networks with successive interference cancellationrdquo inProceedings of the IEEE INFOCOM 2011 - IEEE Conference onComputer Communications pp 1287ndash1295 Shanghai ChinaApril 2011

[31] R Sultan L Song K G Seddik and Z Han ldquoFull-duplexmeetsmultiuser MIMO comparisons and analysisrdquo IEEE Transac-tions on Vehicular Technology vol 66 no 1 pp 455ndash467 2017

[32] X Zheng Z Cai J Li and H Gao ldquoA study on application-aware scheduling in wireless networksrdquo IEEE Transactions onMobile Computing vol 16 no 7 pp 1787ndash1801 2017

[33] X Li Y Shi X Wang C Xu and M Sheng ldquoEfficient linkscheduling with joint power control and successive interferencecancellation in wireless networksrdquo Science China InformationSciences vol 59 no 12 pp 1ndash15 2016

[34] L Qu J He and C Assi ldquoDistributed link scheduling inwireless networks with interference cancellation capabilitiesrdquoin Proceedings of the 15th IEEE International Symposium on aWorld ofWireless Mobile andMultimedia Networks WoWMoM2014 pp 1ndash7 Australia 2014

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Wireless Communications and Mobile Computing 7

Start

End

Initialization

MSIC feasibility judgment

Add link l to acc l

Remove link l from seq l

Update concurrent link set Ls

MSIC feasibility test

Yes

No

No

Yes

Figure 4 Distributed MSIC scheduling algorithm flow chart

receiver 119903푖 uses SIC to decode these strong signals continu-ously before decoding the expected signal from sender 119904푖 Letall links in a feasible set 119871푆 of concurrent links be transmittedsuccessfully When any link 119897푗 is added to the set 119871푆耠 sube 119871푆 thelink transmission will fail Obviously 119871푆耠 is the maximum setof concurrent links and 119871푆耠 must satisfy the constraints in(7)

42 Distributed MSIC Scheduling Algorithm In this sectionbased on the CSMACA mechanism and MSIC constraintswe design the distributed single-slot MSIC algorithm to solvethe scheduling problems If the links 119897 isin 119871耠 in the networkcan be transmitted concurrently then 119871耠 can be defined as ascheduling set In each scheduling time slot each linkwill runscheduling algorithms to generate a new feasible schedulingset 119871푆耠

Next considering the MSIC model and interferenceregions division introduced above a distributed link schedul-ing algorithm is proposed under the MSIC constraints Thealgorithm flow chart is shown in Figure 4 Three states of thelink are defined Active Inactive and Standby The four setscorrespond to different states where 119904119894119888 is the active link setthat satisfies the MSIC constraint and can be scheduled in thecurrent scheduling time slot 119886119888119888 is the standby link set thathas not been judged byMSIC constraints 119897119900119888 is the local cachelink set in the standby state and 119904119890119902 is the candidate link set inthe inactive state Therefore the state of a link in the currentslot can be distinguished by the set of links to which the linkcurrently belongs

(1) Initialization Stage At the beginning of each schedulingcycle each link 119897 maintains two sets of local links set 119886119888119888푙and set 119904119890119902푙 The links contained in the set 119886119888119888푙 are added to

a feasible set 119871푆 of concurrent links in a certain schedulingcycle and the links contained in set 119904119890119902푙 are candidate linksto be added into set 119871푆 At the beginning of each schedulingcycle initializing 119886119888119888푙 = Oslash and 119904119890119902푙 = 119897 119860 푙 cup 119861푙

(2) MSIC Feasibility Judgment Stage Each scheduling cycleconsists of several slots and in each slot each link 119897 makes adecision about whether it should be added to 119886119888119888푙 or removedfrom 119904119890119902푙 At the beginning of each scheduling slot all linksin the set 119904119890119902푙 are weighted for comparisonThe sender of link119897 broadcasts its weight information 119908푙 to all links 119896 whosesender is located in the 119860 푙 region of link 119897 If link 119897 has thelargest weight among all links in 119904119890119902푙 it will run Algorithm 1to try to add itself to 119886119888119888푙

The detailed process is as follows The sender of link 119897broadcasts a Requestmessage to links in 119860 푙cup119861푙 first If thereis a collision all of the links select a random back-off timeand wait for it If there is no collision the sender of all linksin 119860 푙 cup 119861푙 will add link 119897 to set 119897119900119888푙 When link 119897 is added tothe current schedule any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙 will determinewhether it remains feasible under the MSIC constraints Thespecific judgment process is as follows For each link 119897耠 isin119886119888119888푙cup119897119900119888푙 the set of linkswith sender 119904푙耠 isin 119886119888119888푙耠cup119897119900119888푙耠cap119860 푙耠and receiver 119903푙耠 is defined as the MSIC link set 119904119894119888푙耠 TheMSICconstraints will be satisfied when any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙satisfies the following conditions (i) the total interference 119868푙耠coming from set 119861푙耠 does not exceed (1 minus119898)119868max

푙耠 (ii) all links119896 isin 119904119894119888푙耠 are feasible that is the total interference 119868푘 comingfrom set 119861푘 does not exceed (1 minus 119898)119868max

푘 According to the above procedure if any link 119897耠 isin 119886119888119888푙 cup

119897119900119888푙 does not satisfy the MSIC constraints the sender oflink 119897耠 will send an Error message to link 119897 indicating thatlink 119897 cannot be added to set 119871푆 (the current scheduling isnot feasible due to the strong interference caused by link119897) If link 119897 isin 119897119900119888푙 does not receive any Error messagesfrom its neighbors it adds link 119897 to set 119886119888119888푙 and removeslink 119897 from 119904119890119902푙 and 119897119900119888푙 Then the sender broadcasts aSuccess message to all its neighbors to update their link sets119886119888119888 119904119890119902 and 119897119900119888 Otherwise it removes link 119897 from 119904119890119902푙and 119897119900119888푙 and then broadcasts a Remove message to all itsneighbors to update their link sets 119904119890119902 and 119897119900119888 After the aboveprocess is performed until a new link is added to 119871푆 thecurrent scheduling process is still feasible under the MSICconstraints

(3) MSIC Feasibility Test Stage After a new 119871푆耠 is generatedin each slot all links 119897 isin 119904119890119902푙 need to make the followingdecision about whether the MSIC constraints are satisfiedFor each link 119897 isin 119904119890119902푙 the set of links with sender 119904푙 isin119886119888119888푙 cap 119860 푙 and receiver 119903푙 is defined as another MSIC linkset 119904119894119888푙耠 Similar to the first procedure any link 119897 isin 119904119890119902푙 thatsatisfies any of the following conditions will dissatisfy theMSIC constraints (i) the total interference 119868푙耠 coming fromset 119861푙 exceeds (1 minus 119898)119868max

푙 or (ii) for any link 119896耠 isin 119904119894119888푙耠 is notfeasible that is the total interference 119868푘耠 coming from set 119861푘耠exceeds (1 minus119898)119868max

푘耠 After the above process if there is a link119897 in 119904119890119902푙 that does not satisfy the MSIC constraints the senderwill remove link 119897 from 119904119890119902푙 and broadcast a Remove messageto all its neighbors to update their link sets 119904119890119902 and 119886119888119888 The

8 Wireless Communications and Mobile Computing

1 sets of int 119886119888119888푙 119904119890119902푙 119897119900119888푙 119904119894119888푙耠 119904119894119888푙耠 initialize2 119886119888119888푙 larr997888 Oslash and 119904119890119902푙 larr997888 119897 119860 푙 cup 119861푙3 Sender of link 119897 broadcasts Requestmessage to links in 119860 푙 cup 119861푙4 for link 119897耠 isin 119860 푙 cup 119861푙 cap 119886119888119888푙 cup 119897119900119888푙 do MSIC feasibility judgment5 if sender of link 119897耠 receives Requestmessage from sender of link 119897 then6 sender of link 119897耠 adds link 119897 into 119897119900119888푘7 sender of link 119897耠 calculates cumulative interference 119868푙耠 8 if 119868푙耠 gt (1 minus 119898)119868max

푙耠then

9 Sender of link 119897耠 broadcasts Error message to sender of link 11989710 else11 Generate 119904119894119888푙耠 12 for 119896 isin 119904119894119888푙耠 do13 Link 119896 calculates cumulative interference 119868푘14 if 119868푘 gt (1 minus 119898)119868max

푘 then15 Sender of link 119897耠 broadcasts Error message to sender of link 11989716 end if17 end for18 end if19 end if20end for21 if sender of link 119897 does not receive Error messages then Generate concurrent links set22 119886119888119888푙 larr997888 119886119888119888푙 cup 11989723 119904119890119902푙 larr997888 119904119890119902푙11989724 119897119900119888푙 larr997888 119897119900119888푙11989725 Sender of link 119897 broadcasts Successmessage to all its neighbors to update their link sets 119886119888119888 119904119890119902 and 11989711990011988826 Goto Algorithm 227 else28 119904119890119902푙 larr997888 119904119890119902푙119897 Does not satisfy MSIC feasibility conditions29 Sender of link 119897 broadcasts Removemessage to all its neighbors to update their local link sets 119904119890119902 and 11989711990011988830 end if

Algorithm 1 Distributed MSIC Scheduling Algorithm (MSIC feasibility judgment)

above process ensures that each link in 119904119890119902푙 satisfies theMSICconstraints under the current scheduling

In the distributed algorithm the number of time slots ineach scheduling cycle is a fixed value In each scheduling sloteach link will run the distributed scheduling algorithm togenerate a new feasible scheduling set 119871푆耠 during schedulingOnce the scheduling is completed the selected link willtransmit a packet during the transmission cycle

43 Theoretical Proof of Algorithm

Theorem 1 The set 119871푆 of scheduling generated by the MSICalgorithm is feasible

Proof Based on the MSIC algorithm under interferenceregions division each link will run the algorithm indepen-dently in each scheduling slot to generate a new feasiblescheduling set 119871푆耠 From Algorithm 2 it is known that aftera new set 119871푆耠 is generated in each time slot all links 119897 isin 119904119890119902푙need to be tested to determine if theMSIC constraints are stillsatisfied To ensure that each link in 119904119890119902푙 satisfies the MSICconstraints under the current scheduling any link 119897 that doesnot satisfy the MSIC constraints will be removed from 119904119890119902푙Therefore the interference links cannot be scheduled at thesame time that is the links in the current set 119871푆耠 are feasiblewhich ensures the feasibility of the algorithm

Theorem 2 The time complexity of the MSIC algorithm is119874(1198962)

Proof In the process of MSIC feasibility judgment of Algo-rithm 1 it is necessary to judge the MSIC constraints formula(4) of any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙 and decide whether to add thelink to the current scheduling set This process requires twoloop statements to be executed with the algorithm executioncomplexity of 119874(1198962) where 119896 represents the number ofconcurrently transmitted signals After Algorithm 1 generatesa new set 119871푆耠 the MSIC feasibility test is performed inAlgorithm 2 The MSIC constraints condition needs to betested again for all links 119897 isin 119904119890119902푙 to ensure that any link in119904119890119902푙 satisfies the MSIC constraints This process also needsto execute two loop statements with the algorithm executioncomplexity of119874(1198962) Therefore the total algorithm executioncomplexity is 119874(1198962)

Theorem 3 The messages complexity of the MSIC algorithmis 119874(119899)

Proof The message complexity of sending a Request broad-cast message is 119874(1) To find a set of links that can be con-currently given by a network of 119899 links an MSIC constraintjudgment is performed for each link of 119897耠 isin 119860 푙 cup 119861푙 cap119886119888119888푙 cup 119897119900119888푙 and the number of Error or Success messages

Wireless Communications and Mobile Computing 9

1 sets of int 119868푘耠 119868푗耠 119904119894119888푘耠2 for link 119896 isin 119860 푙 cup 119861푙 cap 119904119890119902푙 do MSIC feasibility test3 if the sender of link 119896 receives a Successmessage from the sender of link 119897 then4 Link 119896 calculates the cumulative interference 119868푘耠5 if 119868푘耠 gt (1 minus 119898)119868max

푘 then6 The sender of link 119896 broadcasts a Removemessage to its neighbors to update their link sets 1199041198901199027 else8 Generate 119904119894119888푘耠9 for 119895 isin 119904119894119888푘耠 do10 Link 119895 calculates the cumulative interference 119868푗耠11 if 119868푗耠 gt (1 minus 119898)119868max

푗 then12 The sender of link 119896 broadcasts a Removemessage to its neighbors to update their link sets 11990411989011990213 end if14 end for15 end if16 end if17 end for

Algorithm 2 Distributed MSIC Scheduling Algorithm (MSIC feasibility test)

sent is at most 119899 minus 1 For each link of 119896 isin 119860 푙 cup 119861푙 cap 119904119890119902푙a feasibility test is performed and the number of Remove orSuccess messages is up to 119899 minus 1 When the execution of thealgorithm ends the total number of messages used is up to119874(119899)

5 Experimental Results

In this section the distributed single-slot scheduling probleminMIMOwireless networks is studied under the SINRmodelThe simulation is the average of 50 trials obtained on anetwork with 100 links The network size is 600 lowast 600 andthe distance between the sender and the receiver is selectedwithin the range of [20 40] The SINR parameters are set asfollows the threshold value is 120573 = 3 the path loss index is120572 = 22 the background noise power is119873 = 4times10minus7 and theuniform power is 119875 = 2 and 119875 = 10

First the relationship between the size of different net-works and the number of successful transmissions of linksis studied The simulation results are shown in Figure 5Under different power allocations the number of successfultransmissions of the link increases as the network sizeincreases and a larger transmission power can generate alarger neighbor size which is benefited by the gain of thetransmission power However when the network size is largethe neighbor size reaches the upper bound and the gain fromincreasing the power becomes very small At the same timelarger power will also cause more interference to other linksAt this time the impact of the interference on transmission isgreater than the benefit of the network scale increase whichmakes it impossible to satisfy the SINR constraint conditionalthough it improves its own successful transmission proba-bility and reduces the total size of the successful transmissionof the linkTherefore the transmission scale cannot be soughtblindly by increasing the power and a larger-scale schedulingset can be realized by controlling the network scale

20 50 100 150 200 250 300 350 400 450 500 550 6000

10

20

30

40

50

60

70

80

90

Network sizeP=10P=2

Num

ber o

f suc

cess

ful t

rans

miss

ions

Figure 5 The relationship between network size and number ofsuccessful transmissions

Next we compare the number of concurrent link trans-missions of different algorithms At the network layer therouting algorithm based on the least hops is adopted Forconvenience the distance data rate bandwidth and trans-mission power of the data stream are all normalized to 1

First the MSIC algorithm is compared with the recursivelargest first (RLF) algorithm and the smallest degree first(SDF) algorithm in [20] The results in Figure 6 show thatthe MSIC algorithm can obtain a larger link schedulingscale compared with the other two algorithms After theSIC is used all signals with high power in the interferenceregions can be decoded and removed firstly and thus theinterference reached at the receiver is smaller and a larger setof concurrent links can be obtained

10 Wireless Communications and Mobile Computing

0 10 20 30 40 50 60 70 800

5

10

15

20

25

30

Scheduling slot

MIMORLF

SDFMSIC

Num

ber o

f con

curr

ent l

ink

tran

smiss

ions

Figure 6 Comparison of the number of concurrent link transmis-sions of different algorithms

Then we study the effect of the parameter 119898 on thenumber of concurrent link transmissions Figure 7 shows thatthe number of concurrent links decreases as the parameter119898 increases When 119898 is smaller the interference radius ofeach link in the network is larger and there are more linksthat can participate in scheduling The number of concurrentlinks in each selected scheduling configuration is larger andthe data flow rate is higher At this time the network hasstronger interference management ability As the parametersbecome larger the interference in the network is largerthereby allowing fewer links to be transmitted concurrentlyThe MSIC algorithm can reduce partial interference andincrease the number of concurrent transmission links When119898 = 04 there is a close interference region radius betweenMSIC and MIMO so119898 = 04 is set here

Next we study the influence of the number of antennason network performanceThenumber of antennas is changedfrom 2 to 6 and the test is repeated 100 times We then takethe average value of each flow of 100 tests Ideally we assumethat the transmission rate of one link is equal to the capacityof the point-to-point MIMO link without other transmissioninterference As shown inFigure 8 throughput is nearly linearwith the number of antennas and the MSIC algorithm canachieve a higherminimumflow throughput and a higher totalthroughput in the network

To show more detail the flow rate gains for the four flowsessions are given in Figure 9 The simulation results showthat MSIC brings significant throughput gain toMIMOwire-less networks The network flow rate with SIC functionalityis more than half of the network rate without interferencecancellation whichmeans that the reachable unit end-to-endthroughput is increased by approximately 73on average dueto the application of SIC Therefore the MSIC algorithm hasobvious advantages in improving network throughput

01 02 03 04 05 06 07 08 0940

45

50

55

60

65

70

Parameter mMIMOMSIC

The n

umbe

r of c

oncu

rren

t tra

nsm

issio

ns

Figure 7The relationship between parameterm and the number ofconcurrent transmissions

6 Conclusions and Future Work

In this paper the MSIC scheduling algorithm based on SICin MIMO wireless networks is proposed First the MSICconstraints model is constructed under the SINR interfer-ence model Then interference region division is carriedout to describe the level of interference between links Afeasible scheduling set is generated by the distributed linkscheduling algorithm to coordinate the link transmissionand the interference between competing links in the MIMOnetwork is cancelled Experimental results show that thedistributed MSIC scheduling algorithm can bring significantperformance gain to wireless networks

Since the algorithm is premised on satisfying the thresh-old constraint of SINR the algorithm ends when the SINRvalue is less than the current threshold Therefore the nextresearch goal is how to solve the link scheduling problemwhen the SINR value is less than threshold

With the rapid development of the social economy theapplication of modern communication technology has beencontinuously promoted in various fields and the capacityrequirement for networks is increasing In addition dueto the complexity of the network environment a singletechnology will not have a sufficient effect on interferencecancellation Therefore in future wireless communicationnetworks a variety of joint applications of multiple interfer-ence cancellation technologies will be needed How to com-bine these technologies efficiently and achieve a reasonableoptimization combination is an important research direction

Data Availability

The simulation data used to support the findings of this studyare included within the article

Wireless Communications and Mobile Computing 11

2 25 3 35 4 45 5 55 61

2

3

4

5

6

7

8

9 x 105

Number of antennas

MIMOSDF

RLFMSIC

Min

imum

flow

thro

ughp

ut (b

ps)

(a) Minimum flow throughput

2 25 3 35 4 45 5 55 62

3

4

5

6

7

8

9

10

11 x 106

Number of antennas

MIMOSDF

RLFMSIC

Tota

l thr

ough

put (

bps)

(b) Total throughput

Figure 8 The relationship between antenna number and throughput

1 2 3 40

01

02

03

04

05

06

07

08

FlowMSICRLFMIMO

048046

056

033

054057

035

057061

028 032

043

The a

chie

vabl

e flow

rate

s

Figure 9 The gains of data flow rate for the four flow sessions

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (61672321 61771289 and 61832012)

Shandong provincial Graduate Education Innovation Pro-gram (SDYY14052 and SDYY15049) Qufu Normal Uni-versity Science and Technology Project (xkj201525) Shan-dong province agricultural machinery equipment researchand development innovation project (2018YZ002) ShandongProvincial Specialized Degree Postgraduate Teaching CaseLibrary Construction Program and Shandong ProvincialPostgraduate Education Quality Curriculum ConstructionProgram The authors thank the School of InformationScience and Engineering Qufu Normal University

References

[1] S Cheng Z Cai J Li and H Gao ldquoExtracting kernel datasetfrom big sensory data in wireless sensor networksrdquo IEEETransactions on Knowledge and Data Engineering vol 29 no4 pp 813ndash827 2017

[2] S Cheng Z Cai J Li and X Fang ldquoDrawing dominant datasetfrom big sensory data in wireless sensor networksrdquo in Pro-ceedings of the IEEE Conference on Computer Communications(INFOCOM rsquo15) pp 531ndash539 Hong Kong April 2015

[3] X Zheng and Z Cai ldquoReal-time big data delivery in wirelessnetworks a case study on video deliveryrdquo IEEE Transactions onIndustrial Informatics vol 13 no 4 pp 2048ndash2057 2017

[4] Z Cai andX Zheng ldquoA private and efficientmechanism for datauploading in smart cyber-physical systemsrdquo IEEE Transactionson Network Science and Engineering 2018

[5] L Lu G Y Li A L Swindlehurst A Ashikhmin and R ZhangldquoAn overview of massive MIMO benefits and challengesrdquo IEEEJournal of Selected Topics in Signal Processing vol 8 no 5 pp742ndash758 2014

[6] H Liu L Luo D Wu J Yu and D Chen ldquoRouting spectrumaccess and scheduling in multi-hop multi-channel wirelessnetworks with MIMO linksrdquo EURASIP Journal on Wireless

12 Wireless Communications and Mobile Computing

Communications and Networking vol 15 no 1 article no 652015

[7] B Hamdaoui and K G Shin ldquoCharacterization and analysis ofmulti-hop wireless mimo network throughputrdquo in Proceedingsof the Eighth ACM International Symposium on Mobile Ad HocNetworking and Computing pp 120ndash129 Montreal QuebecCanada September 2007

[8] L Jiang and J Walrand ldquoA distributed CSMA algorithm forthroughput and utility maximization in wireless networksrdquoIEEEACM Transactions on Networking vol 18 no 3 pp 960ndash972 2010

[9] H Yu O Bejarano and L Zhong ldquoCombating Inter-cellInterference in 80211ac-based multi-user MIMO networksrdquo inProceedings of the 20th ACM Annual International Conferenceon Mobile Computing and Networking (MobiCom rsquo14) pp 141ndash152 Maui Hawaii USA September 2014

[10] L B Le E Modiano C Joo and N B Shroff ldquoLongest-queue-first scheduling under SINR interferencemodelrdquo in Proceedingsof the 11th ACM International Symposium on Mobile Ad HocNetworking and Computing MobiHoc 2010 pp 41ndash50 USASeptember 2010

[11] J Li S Cheng Z Cai J Yu C Wang and Y Li ldquoApproximateholistic aggregation in wireless sensor networksrdquo ACM Trans-actions on Sensor Networks vol 13 no 2 article no 11 2017

[12] Y Zhou X Li M Liu X Mao S Tang and Z Li ldquoThroughputoptimizing localized link scheduling for multihop wireless net-works under physical interferencemodelrdquo IEEETransactions onParallel and Distributed Systems vol 25 no 10 pp 2708ndash27202014

[13] G Pei and A K S Vullikanti ldquoDistributed approximation algo-rithms for maximum link scheduling and local broadcasting inthe physical interferencemodelrdquo inProceedings of the 32nd IEEEConference on Computer Communications (IEEE INFOCOMrsquo13) pp 1339ndash1347 Turin Italy April 2013

[14] J Yu B Huang X Cheng and M Atiquzzaman ldquoShortest linkscheduling algorithms in wireless networks under the SINRmodelrdquo IEEE Transactions on Vehicular Technology vol 66 no3 pp 2643ndash2657 2017

[15] P J Wan X Xu and O Frieder ldquoShortest link scheduling withpower control under physical interferencemodelrdquo inProceedingof the Sixth International Conference on Mobile Ad-Hoc andSensor Networks pp 74ndash78 2010

[16] M Nabli F Abdelkefi W Ajib and M Siala ldquoEfficient central-ized link scheduling algorithms in wireless mesh networksrdquo inProceedings of the 10th International Wireless Communicationsand Mobile Computing Conference IWCMC 2014 pp 660ndash665Cyprus August 2014

[17] J-G Choi C Joo J Zhang and N B Shroff ldquoDistributed linkscheduling under SINR model in multihop wireless networksrdquoIEEEACM Transactions on Networking vol 22 no 4 pp 1204ndash1217 2014

[18] J Park and S Lee ldquoDistributed MIMO Ad-hoc networks Linkscheduling power allocation and cooperative beamformingrdquoIEEE Transactions on Vehicular Technology vol 61 no 6 pp2586ndash2598 2012

[19] Y Shi Y Thomas H J Liu and S Kompella ldquoHow tocorrectly use the protocol interference model for multi-hopwireless networksrdquo in Proceedings of the 10th ACM InternationalSymposium on Mobile Ad Hoc Networking and ComputingMobiHocrsquo09 pp 239ndash248 USA May 2009

[20] S Lv XWang andX Zhou ldquoScheduling under the SINRmodelin ad hoc networks with successive interference cancellationrdquoComputer Engineering and Science vol 34 no 2 pp 1ndash5 2012

[21] D Qian D Zheng J Zhang and N Shroff ldquoCSMA-baseddistributed scheduling in multi-hop MIMO networks underSINR modelrdquo in Proceedings of the IEEE INFOCOM 2010 pp1ndash9 USA March 2010

[22] O Goussevskaia M M Halldorsson and R WattenhoferldquoAlgorithms for wireless capacityrdquo IEEEACM Transactions onNetworking vol 22 no 3 pp 745ndash755 2014

[23] O Goussevskaia and RWattenhofer ldquoScheduling wireless linkswith successive interference cancellationrdquo in Proceedings of the21st International Conference onComputer Communications andNetworks ICCCN 2012 pp 1ndash7 Germany August 2012

[24] M Kontik and S C Ergen ldquoScheduling in single-hop multipleaccess wireless networks with successive interference cancella-tionrdquo IEEE Wireless Communications Letters vol 3 no 2 pp197ndash200 2014

[25] T Moscibroda R Wattenhofer and A Zollinger ldquoTopologycontrol meets SINR the scheduling complexity of arbitrarytopologiesrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 310ndash321 Florence Italy May 2006

[26] O Goussevskaia R Wattenhofer M M Halldorsson and EWelzl ldquoCapacity of arbitrary wireless networksrdquo in Proceedingsof the 28th Conference on Computer Communications (IEEEINFOCOM rsquo09) pp 1872ndash1880 Rio de Janeiro Brazil April2009

[27] M Dinitz ldquoDistributed algorithms for approximating wirelessnetwork capacityrdquo in Proceedings of the IEEE INFOCOM pp 1ndash9 IEEE San Diego Calif USA March 2010

[28] J Chen C Wen S Jin and K Wong ldquoA low complexitypilot scheduling algorithm for massive MIMOrdquo IEEE WirelessCommunications Letters vol 6 no 1 pp 18ndash21 2017

[29] D Halperin T Anderson and D Wetherall ldquoTaking thesting out of carrier sense interference cancellation for wirelessLANsrdquo in Proceedings of the 14th ACM Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo08) pp 339ndash350 September 2008

[30] S LvW Zhuang XWang andX Zhou ldquoScheduling inwirelessad hoc networks with successive interference cancellationrdquo inProceedings of the IEEE INFOCOM 2011 - IEEE Conference onComputer Communications pp 1287ndash1295 Shanghai ChinaApril 2011

[31] R Sultan L Song K G Seddik and Z Han ldquoFull-duplexmeetsmultiuser MIMO comparisons and analysisrdquo IEEE Transac-tions on Vehicular Technology vol 66 no 1 pp 455ndash467 2017

[32] X Zheng Z Cai J Li and H Gao ldquoA study on application-aware scheduling in wireless networksrdquo IEEE Transactions onMobile Computing vol 16 no 7 pp 1787ndash1801 2017

[33] X Li Y Shi X Wang C Xu and M Sheng ldquoEfficient linkscheduling with joint power control and successive interferencecancellation in wireless networksrdquo Science China InformationSciences vol 59 no 12 pp 1ndash15 2016

[34] L Qu J He and C Assi ldquoDistributed link scheduling inwireless networks with interference cancellation capabilitiesrdquoin Proceedings of the 15th IEEE International Symposium on aWorld ofWireless Mobile andMultimedia Networks WoWMoM2014 pp 1ndash7 Australia 2014

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

8 Wireless Communications and Mobile Computing

1 sets of int 119886119888119888푙 119904119890119902푙 119897119900119888푙 119904119894119888푙耠 119904119894119888푙耠 initialize2 119886119888119888푙 larr997888 Oslash and 119904119890119902푙 larr997888 119897 119860 푙 cup 119861푙3 Sender of link 119897 broadcasts Requestmessage to links in 119860 푙 cup 119861푙4 for link 119897耠 isin 119860 푙 cup 119861푙 cap 119886119888119888푙 cup 119897119900119888푙 do MSIC feasibility judgment5 if sender of link 119897耠 receives Requestmessage from sender of link 119897 then6 sender of link 119897耠 adds link 119897 into 119897119900119888푘7 sender of link 119897耠 calculates cumulative interference 119868푙耠 8 if 119868푙耠 gt (1 minus 119898)119868max

푙耠then

9 Sender of link 119897耠 broadcasts Error message to sender of link 11989710 else11 Generate 119904119894119888푙耠 12 for 119896 isin 119904119894119888푙耠 do13 Link 119896 calculates cumulative interference 119868푘14 if 119868푘 gt (1 minus 119898)119868max

푘 then15 Sender of link 119897耠 broadcasts Error message to sender of link 11989716 end if17 end for18 end if19 end if20end for21 if sender of link 119897 does not receive Error messages then Generate concurrent links set22 119886119888119888푙 larr997888 119886119888119888푙 cup 11989723 119904119890119902푙 larr997888 119904119890119902푙11989724 119897119900119888푙 larr997888 119897119900119888푙11989725 Sender of link 119897 broadcasts Successmessage to all its neighbors to update their link sets 119886119888119888 119904119890119902 and 11989711990011988826 Goto Algorithm 227 else28 119904119890119902푙 larr997888 119904119890119902푙119897 Does not satisfy MSIC feasibility conditions29 Sender of link 119897 broadcasts Removemessage to all its neighbors to update their local link sets 119904119890119902 and 11989711990011988830 end if

Algorithm 1 Distributed MSIC Scheduling Algorithm (MSIC feasibility judgment)

above process ensures that each link in 119904119890119902푙 satisfies theMSICconstraints under the current scheduling

In the distributed algorithm the number of time slots ineach scheduling cycle is a fixed value In each scheduling sloteach link will run the distributed scheduling algorithm togenerate a new feasible scheduling set 119871푆耠 during schedulingOnce the scheduling is completed the selected link willtransmit a packet during the transmission cycle

43 Theoretical Proof of Algorithm

Theorem 1 The set 119871푆 of scheduling generated by the MSICalgorithm is feasible

Proof Based on the MSIC algorithm under interferenceregions division each link will run the algorithm indepen-dently in each scheduling slot to generate a new feasiblescheduling set 119871푆耠 From Algorithm 2 it is known that aftera new set 119871푆耠 is generated in each time slot all links 119897 isin 119904119890119902푙need to be tested to determine if theMSIC constraints are stillsatisfied To ensure that each link in 119904119890119902푙 satisfies the MSICconstraints under the current scheduling any link 119897 that doesnot satisfy the MSIC constraints will be removed from 119904119890119902푙Therefore the interference links cannot be scheduled at thesame time that is the links in the current set 119871푆耠 are feasiblewhich ensures the feasibility of the algorithm

Theorem 2 The time complexity of the MSIC algorithm is119874(1198962)

Proof In the process of MSIC feasibility judgment of Algo-rithm 1 it is necessary to judge the MSIC constraints formula(4) of any link 119897耠 isin 119886119888119888푙 cup 119897119900119888푙 and decide whether to add thelink to the current scheduling set This process requires twoloop statements to be executed with the algorithm executioncomplexity of 119874(1198962) where 119896 represents the number ofconcurrently transmitted signals After Algorithm 1 generatesa new set 119871푆耠 the MSIC feasibility test is performed inAlgorithm 2 The MSIC constraints condition needs to betested again for all links 119897 isin 119904119890119902푙 to ensure that any link in119904119890119902푙 satisfies the MSIC constraints This process also needsto execute two loop statements with the algorithm executioncomplexity of119874(1198962) Therefore the total algorithm executioncomplexity is 119874(1198962)

Theorem 3 The messages complexity of the MSIC algorithmis 119874(119899)

Proof The message complexity of sending a Request broad-cast message is 119874(1) To find a set of links that can be con-currently given by a network of 119899 links an MSIC constraintjudgment is performed for each link of 119897耠 isin 119860 푙 cup 119861푙 cap119886119888119888푙 cup 119897119900119888푙 and the number of Error or Success messages

Wireless Communications and Mobile Computing 9

1 sets of int 119868푘耠 119868푗耠 119904119894119888푘耠2 for link 119896 isin 119860 푙 cup 119861푙 cap 119904119890119902푙 do MSIC feasibility test3 if the sender of link 119896 receives a Successmessage from the sender of link 119897 then4 Link 119896 calculates the cumulative interference 119868푘耠5 if 119868푘耠 gt (1 minus 119898)119868max

푘 then6 The sender of link 119896 broadcasts a Removemessage to its neighbors to update their link sets 1199041198901199027 else8 Generate 119904119894119888푘耠9 for 119895 isin 119904119894119888푘耠 do10 Link 119895 calculates the cumulative interference 119868푗耠11 if 119868푗耠 gt (1 minus 119898)119868max

푗 then12 The sender of link 119896 broadcasts a Removemessage to its neighbors to update their link sets 11990411989011990213 end if14 end for15 end if16 end if17 end for

Algorithm 2 Distributed MSIC Scheduling Algorithm (MSIC feasibility test)

sent is at most 119899 minus 1 For each link of 119896 isin 119860 푙 cup 119861푙 cap 119904119890119902푙a feasibility test is performed and the number of Remove orSuccess messages is up to 119899 minus 1 When the execution of thealgorithm ends the total number of messages used is up to119874(119899)

5 Experimental Results

In this section the distributed single-slot scheduling probleminMIMOwireless networks is studied under the SINRmodelThe simulation is the average of 50 trials obtained on anetwork with 100 links The network size is 600 lowast 600 andthe distance between the sender and the receiver is selectedwithin the range of [20 40] The SINR parameters are set asfollows the threshold value is 120573 = 3 the path loss index is120572 = 22 the background noise power is119873 = 4times10minus7 and theuniform power is 119875 = 2 and 119875 = 10

First the relationship between the size of different net-works and the number of successful transmissions of linksis studied The simulation results are shown in Figure 5Under different power allocations the number of successfultransmissions of the link increases as the network sizeincreases and a larger transmission power can generate alarger neighbor size which is benefited by the gain of thetransmission power However when the network size is largethe neighbor size reaches the upper bound and the gain fromincreasing the power becomes very small At the same timelarger power will also cause more interference to other linksAt this time the impact of the interference on transmission isgreater than the benefit of the network scale increase whichmakes it impossible to satisfy the SINR constraint conditionalthough it improves its own successful transmission proba-bility and reduces the total size of the successful transmissionof the linkTherefore the transmission scale cannot be soughtblindly by increasing the power and a larger-scale schedulingset can be realized by controlling the network scale

20 50 100 150 200 250 300 350 400 450 500 550 6000

10

20

30

40

50

60

70

80

90

Network sizeP=10P=2

Num

ber o

f suc

cess

ful t

rans

miss

ions

Figure 5 The relationship between network size and number ofsuccessful transmissions

Next we compare the number of concurrent link trans-missions of different algorithms At the network layer therouting algorithm based on the least hops is adopted Forconvenience the distance data rate bandwidth and trans-mission power of the data stream are all normalized to 1

First the MSIC algorithm is compared with the recursivelargest first (RLF) algorithm and the smallest degree first(SDF) algorithm in [20] The results in Figure 6 show thatthe MSIC algorithm can obtain a larger link schedulingscale compared with the other two algorithms After theSIC is used all signals with high power in the interferenceregions can be decoded and removed firstly and thus theinterference reached at the receiver is smaller and a larger setof concurrent links can be obtained

10 Wireless Communications and Mobile Computing

0 10 20 30 40 50 60 70 800

5

10

15

20

25

30

Scheduling slot

MIMORLF

SDFMSIC

Num

ber o

f con

curr

ent l

ink

tran

smiss

ions

Figure 6 Comparison of the number of concurrent link transmis-sions of different algorithms

Then we study the effect of the parameter 119898 on thenumber of concurrent link transmissions Figure 7 shows thatthe number of concurrent links decreases as the parameter119898 increases When 119898 is smaller the interference radius ofeach link in the network is larger and there are more linksthat can participate in scheduling The number of concurrentlinks in each selected scheduling configuration is larger andthe data flow rate is higher At this time the network hasstronger interference management ability As the parametersbecome larger the interference in the network is largerthereby allowing fewer links to be transmitted concurrentlyThe MSIC algorithm can reduce partial interference andincrease the number of concurrent transmission links When119898 = 04 there is a close interference region radius betweenMSIC and MIMO so119898 = 04 is set here

Next we study the influence of the number of antennason network performanceThenumber of antennas is changedfrom 2 to 6 and the test is repeated 100 times We then takethe average value of each flow of 100 tests Ideally we assumethat the transmission rate of one link is equal to the capacityof the point-to-point MIMO link without other transmissioninterference As shown inFigure 8 throughput is nearly linearwith the number of antennas and the MSIC algorithm canachieve a higherminimumflow throughput and a higher totalthroughput in the network

To show more detail the flow rate gains for the four flowsessions are given in Figure 9 The simulation results showthat MSIC brings significant throughput gain toMIMOwire-less networks The network flow rate with SIC functionalityis more than half of the network rate without interferencecancellation whichmeans that the reachable unit end-to-endthroughput is increased by approximately 73on average dueto the application of SIC Therefore the MSIC algorithm hasobvious advantages in improving network throughput

01 02 03 04 05 06 07 08 0940

45

50

55

60

65

70

Parameter mMIMOMSIC

The n

umbe

r of c

oncu

rren

t tra

nsm

issio

ns

Figure 7The relationship between parameterm and the number ofconcurrent transmissions

6 Conclusions and Future Work

In this paper the MSIC scheduling algorithm based on SICin MIMO wireless networks is proposed First the MSICconstraints model is constructed under the SINR interfer-ence model Then interference region division is carriedout to describe the level of interference between links Afeasible scheduling set is generated by the distributed linkscheduling algorithm to coordinate the link transmissionand the interference between competing links in the MIMOnetwork is cancelled Experimental results show that thedistributed MSIC scheduling algorithm can bring significantperformance gain to wireless networks

Since the algorithm is premised on satisfying the thresh-old constraint of SINR the algorithm ends when the SINRvalue is less than the current threshold Therefore the nextresearch goal is how to solve the link scheduling problemwhen the SINR value is less than threshold

With the rapid development of the social economy theapplication of modern communication technology has beencontinuously promoted in various fields and the capacityrequirement for networks is increasing In addition dueto the complexity of the network environment a singletechnology will not have a sufficient effect on interferencecancellation Therefore in future wireless communicationnetworks a variety of joint applications of multiple interfer-ence cancellation technologies will be needed How to com-bine these technologies efficiently and achieve a reasonableoptimization combination is an important research direction

Data Availability

The simulation data used to support the findings of this studyare included within the article

Wireless Communications and Mobile Computing 11

2 25 3 35 4 45 5 55 61

2

3

4

5

6

7

8

9 x 105

Number of antennas

MIMOSDF

RLFMSIC

Min

imum

flow

thro

ughp

ut (b

ps)

(a) Minimum flow throughput

2 25 3 35 4 45 5 55 62

3

4

5

6

7

8

9

10

11 x 106

Number of antennas

MIMOSDF

RLFMSIC

Tota

l thr

ough

put (

bps)

(b) Total throughput

Figure 8 The relationship between antenna number and throughput

1 2 3 40

01

02

03

04

05

06

07

08

FlowMSICRLFMIMO

048046

056

033

054057

035

057061

028 032

043

The a

chie

vabl

e flow

rate

s

Figure 9 The gains of data flow rate for the four flow sessions

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (61672321 61771289 and 61832012)

Shandong provincial Graduate Education Innovation Pro-gram (SDYY14052 and SDYY15049) Qufu Normal Uni-versity Science and Technology Project (xkj201525) Shan-dong province agricultural machinery equipment researchand development innovation project (2018YZ002) ShandongProvincial Specialized Degree Postgraduate Teaching CaseLibrary Construction Program and Shandong ProvincialPostgraduate Education Quality Curriculum ConstructionProgram The authors thank the School of InformationScience and Engineering Qufu Normal University

References

[1] S Cheng Z Cai J Li and H Gao ldquoExtracting kernel datasetfrom big sensory data in wireless sensor networksrdquo IEEETransactions on Knowledge and Data Engineering vol 29 no4 pp 813ndash827 2017

[2] S Cheng Z Cai J Li and X Fang ldquoDrawing dominant datasetfrom big sensory data in wireless sensor networksrdquo in Pro-ceedings of the IEEE Conference on Computer Communications(INFOCOM rsquo15) pp 531ndash539 Hong Kong April 2015

[3] X Zheng and Z Cai ldquoReal-time big data delivery in wirelessnetworks a case study on video deliveryrdquo IEEE Transactions onIndustrial Informatics vol 13 no 4 pp 2048ndash2057 2017

[4] Z Cai andX Zheng ldquoA private and efficientmechanism for datauploading in smart cyber-physical systemsrdquo IEEE Transactionson Network Science and Engineering 2018

[5] L Lu G Y Li A L Swindlehurst A Ashikhmin and R ZhangldquoAn overview of massive MIMO benefits and challengesrdquo IEEEJournal of Selected Topics in Signal Processing vol 8 no 5 pp742ndash758 2014

[6] H Liu L Luo D Wu J Yu and D Chen ldquoRouting spectrumaccess and scheduling in multi-hop multi-channel wirelessnetworks with MIMO linksrdquo EURASIP Journal on Wireless

12 Wireless Communications and Mobile Computing

Communications and Networking vol 15 no 1 article no 652015

[7] B Hamdaoui and K G Shin ldquoCharacterization and analysis ofmulti-hop wireless mimo network throughputrdquo in Proceedingsof the Eighth ACM International Symposium on Mobile Ad HocNetworking and Computing pp 120ndash129 Montreal QuebecCanada September 2007

[8] L Jiang and J Walrand ldquoA distributed CSMA algorithm forthroughput and utility maximization in wireless networksrdquoIEEEACM Transactions on Networking vol 18 no 3 pp 960ndash972 2010

[9] H Yu O Bejarano and L Zhong ldquoCombating Inter-cellInterference in 80211ac-based multi-user MIMO networksrdquo inProceedings of the 20th ACM Annual International Conferenceon Mobile Computing and Networking (MobiCom rsquo14) pp 141ndash152 Maui Hawaii USA September 2014

[10] L B Le E Modiano C Joo and N B Shroff ldquoLongest-queue-first scheduling under SINR interferencemodelrdquo in Proceedingsof the 11th ACM International Symposium on Mobile Ad HocNetworking and Computing MobiHoc 2010 pp 41ndash50 USASeptember 2010

[11] J Li S Cheng Z Cai J Yu C Wang and Y Li ldquoApproximateholistic aggregation in wireless sensor networksrdquo ACM Trans-actions on Sensor Networks vol 13 no 2 article no 11 2017

[12] Y Zhou X Li M Liu X Mao S Tang and Z Li ldquoThroughputoptimizing localized link scheduling for multihop wireless net-works under physical interferencemodelrdquo IEEETransactions onParallel and Distributed Systems vol 25 no 10 pp 2708ndash27202014

[13] G Pei and A K S Vullikanti ldquoDistributed approximation algo-rithms for maximum link scheduling and local broadcasting inthe physical interferencemodelrdquo inProceedings of the 32nd IEEEConference on Computer Communications (IEEE INFOCOMrsquo13) pp 1339ndash1347 Turin Italy April 2013

[14] J Yu B Huang X Cheng and M Atiquzzaman ldquoShortest linkscheduling algorithms in wireless networks under the SINRmodelrdquo IEEE Transactions on Vehicular Technology vol 66 no3 pp 2643ndash2657 2017

[15] P J Wan X Xu and O Frieder ldquoShortest link scheduling withpower control under physical interferencemodelrdquo inProceedingof the Sixth International Conference on Mobile Ad-Hoc andSensor Networks pp 74ndash78 2010

[16] M Nabli F Abdelkefi W Ajib and M Siala ldquoEfficient central-ized link scheduling algorithms in wireless mesh networksrdquo inProceedings of the 10th International Wireless Communicationsand Mobile Computing Conference IWCMC 2014 pp 660ndash665Cyprus August 2014

[17] J-G Choi C Joo J Zhang and N B Shroff ldquoDistributed linkscheduling under SINR model in multihop wireless networksrdquoIEEEACM Transactions on Networking vol 22 no 4 pp 1204ndash1217 2014

[18] J Park and S Lee ldquoDistributed MIMO Ad-hoc networks Linkscheduling power allocation and cooperative beamformingrdquoIEEE Transactions on Vehicular Technology vol 61 no 6 pp2586ndash2598 2012

[19] Y Shi Y Thomas H J Liu and S Kompella ldquoHow tocorrectly use the protocol interference model for multi-hopwireless networksrdquo in Proceedings of the 10th ACM InternationalSymposium on Mobile Ad Hoc Networking and ComputingMobiHocrsquo09 pp 239ndash248 USA May 2009

[20] S Lv XWang andX Zhou ldquoScheduling under the SINRmodelin ad hoc networks with successive interference cancellationrdquoComputer Engineering and Science vol 34 no 2 pp 1ndash5 2012

[21] D Qian D Zheng J Zhang and N Shroff ldquoCSMA-baseddistributed scheduling in multi-hop MIMO networks underSINR modelrdquo in Proceedings of the IEEE INFOCOM 2010 pp1ndash9 USA March 2010

[22] O Goussevskaia M M Halldorsson and R WattenhoferldquoAlgorithms for wireless capacityrdquo IEEEACM Transactions onNetworking vol 22 no 3 pp 745ndash755 2014

[23] O Goussevskaia and RWattenhofer ldquoScheduling wireless linkswith successive interference cancellationrdquo in Proceedings of the21st International Conference onComputer Communications andNetworks ICCCN 2012 pp 1ndash7 Germany August 2012

[24] M Kontik and S C Ergen ldquoScheduling in single-hop multipleaccess wireless networks with successive interference cancella-tionrdquo IEEE Wireless Communications Letters vol 3 no 2 pp197ndash200 2014

[25] T Moscibroda R Wattenhofer and A Zollinger ldquoTopologycontrol meets SINR the scheduling complexity of arbitrarytopologiesrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 310ndash321 Florence Italy May 2006

[26] O Goussevskaia R Wattenhofer M M Halldorsson and EWelzl ldquoCapacity of arbitrary wireless networksrdquo in Proceedingsof the 28th Conference on Computer Communications (IEEEINFOCOM rsquo09) pp 1872ndash1880 Rio de Janeiro Brazil April2009

[27] M Dinitz ldquoDistributed algorithms for approximating wirelessnetwork capacityrdquo in Proceedings of the IEEE INFOCOM pp 1ndash9 IEEE San Diego Calif USA March 2010

[28] J Chen C Wen S Jin and K Wong ldquoA low complexitypilot scheduling algorithm for massive MIMOrdquo IEEE WirelessCommunications Letters vol 6 no 1 pp 18ndash21 2017

[29] D Halperin T Anderson and D Wetherall ldquoTaking thesting out of carrier sense interference cancellation for wirelessLANsrdquo in Proceedings of the 14th ACM Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo08) pp 339ndash350 September 2008

[30] S LvW Zhuang XWang andX Zhou ldquoScheduling inwirelessad hoc networks with successive interference cancellationrdquo inProceedings of the IEEE INFOCOM 2011 - IEEE Conference onComputer Communications pp 1287ndash1295 Shanghai ChinaApril 2011

[31] R Sultan L Song K G Seddik and Z Han ldquoFull-duplexmeetsmultiuser MIMO comparisons and analysisrdquo IEEE Transac-tions on Vehicular Technology vol 66 no 1 pp 455ndash467 2017

[32] X Zheng Z Cai J Li and H Gao ldquoA study on application-aware scheduling in wireless networksrdquo IEEE Transactions onMobile Computing vol 16 no 7 pp 1787ndash1801 2017

[33] X Li Y Shi X Wang C Xu and M Sheng ldquoEfficient linkscheduling with joint power control and successive interferencecancellation in wireless networksrdquo Science China InformationSciences vol 59 no 12 pp 1ndash15 2016

[34] L Qu J He and C Assi ldquoDistributed link scheduling inwireless networks with interference cancellation capabilitiesrdquoin Proceedings of the 15th IEEE International Symposium on aWorld ofWireless Mobile andMultimedia Networks WoWMoM2014 pp 1ndash7 Australia 2014

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Wireless Communications and Mobile Computing 9

1 sets of int 119868푘耠 119868푗耠 119904119894119888푘耠2 for link 119896 isin 119860 푙 cup 119861푙 cap 119904119890119902푙 do MSIC feasibility test3 if the sender of link 119896 receives a Successmessage from the sender of link 119897 then4 Link 119896 calculates the cumulative interference 119868푘耠5 if 119868푘耠 gt (1 minus 119898)119868max

푘 then6 The sender of link 119896 broadcasts a Removemessage to its neighbors to update their link sets 1199041198901199027 else8 Generate 119904119894119888푘耠9 for 119895 isin 119904119894119888푘耠 do10 Link 119895 calculates the cumulative interference 119868푗耠11 if 119868푗耠 gt (1 minus 119898)119868max

푗 then12 The sender of link 119896 broadcasts a Removemessage to its neighbors to update their link sets 11990411989011990213 end if14 end for15 end if16 end if17 end for

Algorithm 2 Distributed MSIC Scheduling Algorithm (MSIC feasibility test)

sent is at most 119899 minus 1 For each link of 119896 isin 119860 푙 cup 119861푙 cap 119904119890119902푙a feasibility test is performed and the number of Remove orSuccess messages is up to 119899 minus 1 When the execution of thealgorithm ends the total number of messages used is up to119874(119899)

5 Experimental Results

In this section the distributed single-slot scheduling probleminMIMOwireless networks is studied under the SINRmodelThe simulation is the average of 50 trials obtained on anetwork with 100 links The network size is 600 lowast 600 andthe distance between the sender and the receiver is selectedwithin the range of [20 40] The SINR parameters are set asfollows the threshold value is 120573 = 3 the path loss index is120572 = 22 the background noise power is119873 = 4times10minus7 and theuniform power is 119875 = 2 and 119875 = 10

First the relationship between the size of different net-works and the number of successful transmissions of linksis studied The simulation results are shown in Figure 5Under different power allocations the number of successfultransmissions of the link increases as the network sizeincreases and a larger transmission power can generate alarger neighbor size which is benefited by the gain of thetransmission power However when the network size is largethe neighbor size reaches the upper bound and the gain fromincreasing the power becomes very small At the same timelarger power will also cause more interference to other linksAt this time the impact of the interference on transmission isgreater than the benefit of the network scale increase whichmakes it impossible to satisfy the SINR constraint conditionalthough it improves its own successful transmission proba-bility and reduces the total size of the successful transmissionof the linkTherefore the transmission scale cannot be soughtblindly by increasing the power and a larger-scale schedulingset can be realized by controlling the network scale

20 50 100 150 200 250 300 350 400 450 500 550 6000

10

20

30

40

50

60

70

80

90

Network sizeP=10P=2

Num

ber o

f suc

cess

ful t

rans

miss

ions

Figure 5 The relationship between network size and number ofsuccessful transmissions

Next we compare the number of concurrent link trans-missions of different algorithms At the network layer therouting algorithm based on the least hops is adopted Forconvenience the distance data rate bandwidth and trans-mission power of the data stream are all normalized to 1

First the MSIC algorithm is compared with the recursivelargest first (RLF) algorithm and the smallest degree first(SDF) algorithm in [20] The results in Figure 6 show thatthe MSIC algorithm can obtain a larger link schedulingscale compared with the other two algorithms After theSIC is used all signals with high power in the interferenceregions can be decoded and removed firstly and thus theinterference reached at the receiver is smaller and a larger setof concurrent links can be obtained

10 Wireless Communications and Mobile Computing

0 10 20 30 40 50 60 70 800

5

10

15

20

25

30

Scheduling slot

MIMORLF

SDFMSIC

Num

ber o

f con

curr

ent l

ink

tran

smiss

ions

Figure 6 Comparison of the number of concurrent link transmis-sions of different algorithms

Then we study the effect of the parameter 119898 on thenumber of concurrent link transmissions Figure 7 shows thatthe number of concurrent links decreases as the parameter119898 increases When 119898 is smaller the interference radius ofeach link in the network is larger and there are more linksthat can participate in scheduling The number of concurrentlinks in each selected scheduling configuration is larger andthe data flow rate is higher At this time the network hasstronger interference management ability As the parametersbecome larger the interference in the network is largerthereby allowing fewer links to be transmitted concurrentlyThe MSIC algorithm can reduce partial interference andincrease the number of concurrent transmission links When119898 = 04 there is a close interference region radius betweenMSIC and MIMO so119898 = 04 is set here

Next we study the influence of the number of antennason network performanceThenumber of antennas is changedfrom 2 to 6 and the test is repeated 100 times We then takethe average value of each flow of 100 tests Ideally we assumethat the transmission rate of one link is equal to the capacityof the point-to-point MIMO link without other transmissioninterference As shown inFigure 8 throughput is nearly linearwith the number of antennas and the MSIC algorithm canachieve a higherminimumflow throughput and a higher totalthroughput in the network

To show more detail the flow rate gains for the four flowsessions are given in Figure 9 The simulation results showthat MSIC brings significant throughput gain toMIMOwire-less networks The network flow rate with SIC functionalityis more than half of the network rate without interferencecancellation whichmeans that the reachable unit end-to-endthroughput is increased by approximately 73on average dueto the application of SIC Therefore the MSIC algorithm hasobvious advantages in improving network throughput

01 02 03 04 05 06 07 08 0940

45

50

55

60

65

70

Parameter mMIMOMSIC

The n

umbe

r of c

oncu

rren

t tra

nsm

issio

ns

Figure 7The relationship between parameterm and the number ofconcurrent transmissions

6 Conclusions and Future Work

In this paper the MSIC scheduling algorithm based on SICin MIMO wireless networks is proposed First the MSICconstraints model is constructed under the SINR interfer-ence model Then interference region division is carriedout to describe the level of interference between links Afeasible scheduling set is generated by the distributed linkscheduling algorithm to coordinate the link transmissionand the interference between competing links in the MIMOnetwork is cancelled Experimental results show that thedistributed MSIC scheduling algorithm can bring significantperformance gain to wireless networks

Since the algorithm is premised on satisfying the thresh-old constraint of SINR the algorithm ends when the SINRvalue is less than the current threshold Therefore the nextresearch goal is how to solve the link scheduling problemwhen the SINR value is less than threshold

With the rapid development of the social economy theapplication of modern communication technology has beencontinuously promoted in various fields and the capacityrequirement for networks is increasing In addition dueto the complexity of the network environment a singletechnology will not have a sufficient effect on interferencecancellation Therefore in future wireless communicationnetworks a variety of joint applications of multiple interfer-ence cancellation technologies will be needed How to com-bine these technologies efficiently and achieve a reasonableoptimization combination is an important research direction

Data Availability

The simulation data used to support the findings of this studyare included within the article

Wireless Communications and Mobile Computing 11

2 25 3 35 4 45 5 55 61

2

3

4

5

6

7

8

9 x 105

Number of antennas

MIMOSDF

RLFMSIC

Min

imum

flow

thro

ughp

ut (b

ps)

(a) Minimum flow throughput

2 25 3 35 4 45 5 55 62

3

4

5

6

7

8

9

10

11 x 106

Number of antennas

MIMOSDF

RLFMSIC

Tota

l thr

ough

put (

bps)

(b) Total throughput

Figure 8 The relationship between antenna number and throughput

1 2 3 40

01

02

03

04

05

06

07

08

FlowMSICRLFMIMO

048046

056

033

054057

035

057061

028 032

043

The a

chie

vabl

e flow

rate

s

Figure 9 The gains of data flow rate for the four flow sessions

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (61672321 61771289 and 61832012)

Shandong provincial Graduate Education Innovation Pro-gram (SDYY14052 and SDYY15049) Qufu Normal Uni-versity Science and Technology Project (xkj201525) Shan-dong province agricultural machinery equipment researchand development innovation project (2018YZ002) ShandongProvincial Specialized Degree Postgraduate Teaching CaseLibrary Construction Program and Shandong ProvincialPostgraduate Education Quality Curriculum ConstructionProgram The authors thank the School of InformationScience and Engineering Qufu Normal University

References

[1] S Cheng Z Cai J Li and H Gao ldquoExtracting kernel datasetfrom big sensory data in wireless sensor networksrdquo IEEETransactions on Knowledge and Data Engineering vol 29 no4 pp 813ndash827 2017

[2] S Cheng Z Cai J Li and X Fang ldquoDrawing dominant datasetfrom big sensory data in wireless sensor networksrdquo in Pro-ceedings of the IEEE Conference on Computer Communications(INFOCOM rsquo15) pp 531ndash539 Hong Kong April 2015

[3] X Zheng and Z Cai ldquoReal-time big data delivery in wirelessnetworks a case study on video deliveryrdquo IEEE Transactions onIndustrial Informatics vol 13 no 4 pp 2048ndash2057 2017

[4] Z Cai andX Zheng ldquoA private and efficientmechanism for datauploading in smart cyber-physical systemsrdquo IEEE Transactionson Network Science and Engineering 2018

[5] L Lu G Y Li A L Swindlehurst A Ashikhmin and R ZhangldquoAn overview of massive MIMO benefits and challengesrdquo IEEEJournal of Selected Topics in Signal Processing vol 8 no 5 pp742ndash758 2014

[6] H Liu L Luo D Wu J Yu and D Chen ldquoRouting spectrumaccess and scheduling in multi-hop multi-channel wirelessnetworks with MIMO linksrdquo EURASIP Journal on Wireless

12 Wireless Communications and Mobile Computing

Communications and Networking vol 15 no 1 article no 652015

[7] B Hamdaoui and K G Shin ldquoCharacterization and analysis ofmulti-hop wireless mimo network throughputrdquo in Proceedingsof the Eighth ACM International Symposium on Mobile Ad HocNetworking and Computing pp 120ndash129 Montreal QuebecCanada September 2007

[8] L Jiang and J Walrand ldquoA distributed CSMA algorithm forthroughput and utility maximization in wireless networksrdquoIEEEACM Transactions on Networking vol 18 no 3 pp 960ndash972 2010

[9] H Yu O Bejarano and L Zhong ldquoCombating Inter-cellInterference in 80211ac-based multi-user MIMO networksrdquo inProceedings of the 20th ACM Annual International Conferenceon Mobile Computing and Networking (MobiCom rsquo14) pp 141ndash152 Maui Hawaii USA September 2014

[10] L B Le E Modiano C Joo and N B Shroff ldquoLongest-queue-first scheduling under SINR interferencemodelrdquo in Proceedingsof the 11th ACM International Symposium on Mobile Ad HocNetworking and Computing MobiHoc 2010 pp 41ndash50 USASeptember 2010

[11] J Li S Cheng Z Cai J Yu C Wang and Y Li ldquoApproximateholistic aggregation in wireless sensor networksrdquo ACM Trans-actions on Sensor Networks vol 13 no 2 article no 11 2017

[12] Y Zhou X Li M Liu X Mao S Tang and Z Li ldquoThroughputoptimizing localized link scheduling for multihop wireless net-works under physical interferencemodelrdquo IEEETransactions onParallel and Distributed Systems vol 25 no 10 pp 2708ndash27202014

[13] G Pei and A K S Vullikanti ldquoDistributed approximation algo-rithms for maximum link scheduling and local broadcasting inthe physical interferencemodelrdquo inProceedings of the 32nd IEEEConference on Computer Communications (IEEE INFOCOMrsquo13) pp 1339ndash1347 Turin Italy April 2013

[14] J Yu B Huang X Cheng and M Atiquzzaman ldquoShortest linkscheduling algorithms in wireless networks under the SINRmodelrdquo IEEE Transactions on Vehicular Technology vol 66 no3 pp 2643ndash2657 2017

[15] P J Wan X Xu and O Frieder ldquoShortest link scheduling withpower control under physical interferencemodelrdquo inProceedingof the Sixth International Conference on Mobile Ad-Hoc andSensor Networks pp 74ndash78 2010

[16] M Nabli F Abdelkefi W Ajib and M Siala ldquoEfficient central-ized link scheduling algorithms in wireless mesh networksrdquo inProceedings of the 10th International Wireless Communicationsand Mobile Computing Conference IWCMC 2014 pp 660ndash665Cyprus August 2014

[17] J-G Choi C Joo J Zhang and N B Shroff ldquoDistributed linkscheduling under SINR model in multihop wireless networksrdquoIEEEACM Transactions on Networking vol 22 no 4 pp 1204ndash1217 2014

[18] J Park and S Lee ldquoDistributed MIMO Ad-hoc networks Linkscheduling power allocation and cooperative beamformingrdquoIEEE Transactions on Vehicular Technology vol 61 no 6 pp2586ndash2598 2012

[19] Y Shi Y Thomas H J Liu and S Kompella ldquoHow tocorrectly use the protocol interference model for multi-hopwireless networksrdquo in Proceedings of the 10th ACM InternationalSymposium on Mobile Ad Hoc Networking and ComputingMobiHocrsquo09 pp 239ndash248 USA May 2009

[20] S Lv XWang andX Zhou ldquoScheduling under the SINRmodelin ad hoc networks with successive interference cancellationrdquoComputer Engineering and Science vol 34 no 2 pp 1ndash5 2012

[21] D Qian D Zheng J Zhang and N Shroff ldquoCSMA-baseddistributed scheduling in multi-hop MIMO networks underSINR modelrdquo in Proceedings of the IEEE INFOCOM 2010 pp1ndash9 USA March 2010

[22] O Goussevskaia M M Halldorsson and R WattenhoferldquoAlgorithms for wireless capacityrdquo IEEEACM Transactions onNetworking vol 22 no 3 pp 745ndash755 2014

[23] O Goussevskaia and RWattenhofer ldquoScheduling wireless linkswith successive interference cancellationrdquo in Proceedings of the21st International Conference onComputer Communications andNetworks ICCCN 2012 pp 1ndash7 Germany August 2012

[24] M Kontik and S C Ergen ldquoScheduling in single-hop multipleaccess wireless networks with successive interference cancella-tionrdquo IEEE Wireless Communications Letters vol 3 no 2 pp197ndash200 2014

[25] T Moscibroda R Wattenhofer and A Zollinger ldquoTopologycontrol meets SINR the scheduling complexity of arbitrarytopologiesrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 310ndash321 Florence Italy May 2006

[26] O Goussevskaia R Wattenhofer M M Halldorsson and EWelzl ldquoCapacity of arbitrary wireless networksrdquo in Proceedingsof the 28th Conference on Computer Communications (IEEEINFOCOM rsquo09) pp 1872ndash1880 Rio de Janeiro Brazil April2009

[27] M Dinitz ldquoDistributed algorithms for approximating wirelessnetwork capacityrdquo in Proceedings of the IEEE INFOCOM pp 1ndash9 IEEE San Diego Calif USA March 2010

[28] J Chen C Wen S Jin and K Wong ldquoA low complexitypilot scheduling algorithm for massive MIMOrdquo IEEE WirelessCommunications Letters vol 6 no 1 pp 18ndash21 2017

[29] D Halperin T Anderson and D Wetherall ldquoTaking thesting out of carrier sense interference cancellation for wirelessLANsrdquo in Proceedings of the 14th ACM Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo08) pp 339ndash350 September 2008

[30] S LvW Zhuang XWang andX Zhou ldquoScheduling inwirelessad hoc networks with successive interference cancellationrdquo inProceedings of the IEEE INFOCOM 2011 - IEEE Conference onComputer Communications pp 1287ndash1295 Shanghai ChinaApril 2011

[31] R Sultan L Song K G Seddik and Z Han ldquoFull-duplexmeetsmultiuser MIMO comparisons and analysisrdquo IEEE Transac-tions on Vehicular Technology vol 66 no 1 pp 455ndash467 2017

[32] X Zheng Z Cai J Li and H Gao ldquoA study on application-aware scheduling in wireless networksrdquo IEEE Transactions onMobile Computing vol 16 no 7 pp 1787ndash1801 2017

[33] X Li Y Shi X Wang C Xu and M Sheng ldquoEfficient linkscheduling with joint power control and successive interferencecancellation in wireless networksrdquo Science China InformationSciences vol 59 no 12 pp 1ndash15 2016

[34] L Qu J He and C Assi ldquoDistributed link scheduling inwireless networks with interference cancellation capabilitiesrdquoin Proceedings of the 15th IEEE International Symposium on aWorld ofWireless Mobile andMultimedia Networks WoWMoM2014 pp 1ndash7 Australia 2014

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

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Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

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RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

10 Wireless Communications and Mobile Computing

0 10 20 30 40 50 60 70 800

5

10

15

20

25

30

Scheduling slot

MIMORLF

SDFMSIC

Num

ber o

f con

curr

ent l

ink

tran

smiss

ions

Figure 6 Comparison of the number of concurrent link transmis-sions of different algorithms

Then we study the effect of the parameter 119898 on thenumber of concurrent link transmissions Figure 7 shows thatthe number of concurrent links decreases as the parameter119898 increases When 119898 is smaller the interference radius ofeach link in the network is larger and there are more linksthat can participate in scheduling The number of concurrentlinks in each selected scheduling configuration is larger andthe data flow rate is higher At this time the network hasstronger interference management ability As the parametersbecome larger the interference in the network is largerthereby allowing fewer links to be transmitted concurrentlyThe MSIC algorithm can reduce partial interference andincrease the number of concurrent transmission links When119898 = 04 there is a close interference region radius betweenMSIC and MIMO so119898 = 04 is set here

Next we study the influence of the number of antennason network performanceThenumber of antennas is changedfrom 2 to 6 and the test is repeated 100 times We then takethe average value of each flow of 100 tests Ideally we assumethat the transmission rate of one link is equal to the capacityof the point-to-point MIMO link without other transmissioninterference As shown inFigure 8 throughput is nearly linearwith the number of antennas and the MSIC algorithm canachieve a higherminimumflow throughput and a higher totalthroughput in the network

To show more detail the flow rate gains for the four flowsessions are given in Figure 9 The simulation results showthat MSIC brings significant throughput gain toMIMOwire-less networks The network flow rate with SIC functionalityis more than half of the network rate without interferencecancellation whichmeans that the reachable unit end-to-endthroughput is increased by approximately 73on average dueto the application of SIC Therefore the MSIC algorithm hasobvious advantages in improving network throughput

01 02 03 04 05 06 07 08 0940

45

50

55

60

65

70

Parameter mMIMOMSIC

The n

umbe

r of c

oncu

rren

t tra

nsm

issio

ns

Figure 7The relationship between parameterm and the number ofconcurrent transmissions

6 Conclusions and Future Work

In this paper the MSIC scheduling algorithm based on SICin MIMO wireless networks is proposed First the MSICconstraints model is constructed under the SINR interfer-ence model Then interference region division is carriedout to describe the level of interference between links Afeasible scheduling set is generated by the distributed linkscheduling algorithm to coordinate the link transmissionand the interference between competing links in the MIMOnetwork is cancelled Experimental results show that thedistributed MSIC scheduling algorithm can bring significantperformance gain to wireless networks

Since the algorithm is premised on satisfying the thresh-old constraint of SINR the algorithm ends when the SINRvalue is less than the current threshold Therefore the nextresearch goal is how to solve the link scheduling problemwhen the SINR value is less than threshold

With the rapid development of the social economy theapplication of modern communication technology has beencontinuously promoted in various fields and the capacityrequirement for networks is increasing In addition dueto the complexity of the network environment a singletechnology will not have a sufficient effect on interferencecancellation Therefore in future wireless communicationnetworks a variety of joint applications of multiple interfer-ence cancellation technologies will be needed How to com-bine these technologies efficiently and achieve a reasonableoptimization combination is an important research direction

Data Availability

The simulation data used to support the findings of this studyare included within the article

Wireless Communications and Mobile Computing 11

2 25 3 35 4 45 5 55 61

2

3

4

5

6

7

8

9 x 105

Number of antennas

MIMOSDF

RLFMSIC

Min

imum

flow

thro

ughp

ut (b

ps)

(a) Minimum flow throughput

2 25 3 35 4 45 5 55 62

3

4

5

6

7

8

9

10

11 x 106

Number of antennas

MIMOSDF

RLFMSIC

Tota

l thr

ough

put (

bps)

(b) Total throughput

Figure 8 The relationship between antenna number and throughput

1 2 3 40

01

02

03

04

05

06

07

08

FlowMSICRLFMIMO

048046

056

033

054057

035

057061

028 032

043

The a

chie

vabl

e flow

rate

s

Figure 9 The gains of data flow rate for the four flow sessions

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (61672321 61771289 and 61832012)

Shandong provincial Graduate Education Innovation Pro-gram (SDYY14052 and SDYY15049) Qufu Normal Uni-versity Science and Technology Project (xkj201525) Shan-dong province agricultural machinery equipment researchand development innovation project (2018YZ002) ShandongProvincial Specialized Degree Postgraduate Teaching CaseLibrary Construction Program and Shandong ProvincialPostgraduate Education Quality Curriculum ConstructionProgram The authors thank the School of InformationScience and Engineering Qufu Normal University

References

[1] S Cheng Z Cai J Li and H Gao ldquoExtracting kernel datasetfrom big sensory data in wireless sensor networksrdquo IEEETransactions on Knowledge and Data Engineering vol 29 no4 pp 813ndash827 2017

[2] S Cheng Z Cai J Li and X Fang ldquoDrawing dominant datasetfrom big sensory data in wireless sensor networksrdquo in Pro-ceedings of the IEEE Conference on Computer Communications(INFOCOM rsquo15) pp 531ndash539 Hong Kong April 2015

[3] X Zheng and Z Cai ldquoReal-time big data delivery in wirelessnetworks a case study on video deliveryrdquo IEEE Transactions onIndustrial Informatics vol 13 no 4 pp 2048ndash2057 2017

[4] Z Cai andX Zheng ldquoA private and efficientmechanism for datauploading in smart cyber-physical systemsrdquo IEEE Transactionson Network Science and Engineering 2018

[5] L Lu G Y Li A L Swindlehurst A Ashikhmin and R ZhangldquoAn overview of massive MIMO benefits and challengesrdquo IEEEJournal of Selected Topics in Signal Processing vol 8 no 5 pp742ndash758 2014

[6] H Liu L Luo D Wu J Yu and D Chen ldquoRouting spectrumaccess and scheduling in multi-hop multi-channel wirelessnetworks with MIMO linksrdquo EURASIP Journal on Wireless

12 Wireless Communications and Mobile Computing

Communications and Networking vol 15 no 1 article no 652015

[7] B Hamdaoui and K G Shin ldquoCharacterization and analysis ofmulti-hop wireless mimo network throughputrdquo in Proceedingsof the Eighth ACM International Symposium on Mobile Ad HocNetworking and Computing pp 120ndash129 Montreal QuebecCanada September 2007

[8] L Jiang and J Walrand ldquoA distributed CSMA algorithm forthroughput and utility maximization in wireless networksrdquoIEEEACM Transactions on Networking vol 18 no 3 pp 960ndash972 2010

[9] H Yu O Bejarano and L Zhong ldquoCombating Inter-cellInterference in 80211ac-based multi-user MIMO networksrdquo inProceedings of the 20th ACM Annual International Conferenceon Mobile Computing and Networking (MobiCom rsquo14) pp 141ndash152 Maui Hawaii USA September 2014

[10] L B Le E Modiano C Joo and N B Shroff ldquoLongest-queue-first scheduling under SINR interferencemodelrdquo in Proceedingsof the 11th ACM International Symposium on Mobile Ad HocNetworking and Computing MobiHoc 2010 pp 41ndash50 USASeptember 2010

[11] J Li S Cheng Z Cai J Yu C Wang and Y Li ldquoApproximateholistic aggregation in wireless sensor networksrdquo ACM Trans-actions on Sensor Networks vol 13 no 2 article no 11 2017

[12] Y Zhou X Li M Liu X Mao S Tang and Z Li ldquoThroughputoptimizing localized link scheduling for multihop wireless net-works under physical interferencemodelrdquo IEEETransactions onParallel and Distributed Systems vol 25 no 10 pp 2708ndash27202014

[13] G Pei and A K S Vullikanti ldquoDistributed approximation algo-rithms for maximum link scheduling and local broadcasting inthe physical interferencemodelrdquo inProceedings of the 32nd IEEEConference on Computer Communications (IEEE INFOCOMrsquo13) pp 1339ndash1347 Turin Italy April 2013

[14] J Yu B Huang X Cheng and M Atiquzzaman ldquoShortest linkscheduling algorithms in wireless networks under the SINRmodelrdquo IEEE Transactions on Vehicular Technology vol 66 no3 pp 2643ndash2657 2017

[15] P J Wan X Xu and O Frieder ldquoShortest link scheduling withpower control under physical interferencemodelrdquo inProceedingof the Sixth International Conference on Mobile Ad-Hoc andSensor Networks pp 74ndash78 2010

[16] M Nabli F Abdelkefi W Ajib and M Siala ldquoEfficient central-ized link scheduling algorithms in wireless mesh networksrdquo inProceedings of the 10th International Wireless Communicationsand Mobile Computing Conference IWCMC 2014 pp 660ndash665Cyprus August 2014

[17] J-G Choi C Joo J Zhang and N B Shroff ldquoDistributed linkscheduling under SINR model in multihop wireless networksrdquoIEEEACM Transactions on Networking vol 22 no 4 pp 1204ndash1217 2014

[18] J Park and S Lee ldquoDistributed MIMO Ad-hoc networks Linkscheduling power allocation and cooperative beamformingrdquoIEEE Transactions on Vehicular Technology vol 61 no 6 pp2586ndash2598 2012

[19] Y Shi Y Thomas H J Liu and S Kompella ldquoHow tocorrectly use the protocol interference model for multi-hopwireless networksrdquo in Proceedings of the 10th ACM InternationalSymposium on Mobile Ad Hoc Networking and ComputingMobiHocrsquo09 pp 239ndash248 USA May 2009

[20] S Lv XWang andX Zhou ldquoScheduling under the SINRmodelin ad hoc networks with successive interference cancellationrdquoComputer Engineering and Science vol 34 no 2 pp 1ndash5 2012

[21] D Qian D Zheng J Zhang and N Shroff ldquoCSMA-baseddistributed scheduling in multi-hop MIMO networks underSINR modelrdquo in Proceedings of the IEEE INFOCOM 2010 pp1ndash9 USA March 2010

[22] O Goussevskaia M M Halldorsson and R WattenhoferldquoAlgorithms for wireless capacityrdquo IEEEACM Transactions onNetworking vol 22 no 3 pp 745ndash755 2014

[23] O Goussevskaia and RWattenhofer ldquoScheduling wireless linkswith successive interference cancellationrdquo in Proceedings of the21st International Conference onComputer Communications andNetworks ICCCN 2012 pp 1ndash7 Germany August 2012

[24] M Kontik and S C Ergen ldquoScheduling in single-hop multipleaccess wireless networks with successive interference cancella-tionrdquo IEEE Wireless Communications Letters vol 3 no 2 pp197ndash200 2014

[25] T Moscibroda R Wattenhofer and A Zollinger ldquoTopologycontrol meets SINR the scheduling complexity of arbitrarytopologiesrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 310ndash321 Florence Italy May 2006

[26] O Goussevskaia R Wattenhofer M M Halldorsson and EWelzl ldquoCapacity of arbitrary wireless networksrdquo in Proceedingsof the 28th Conference on Computer Communications (IEEEINFOCOM rsquo09) pp 1872ndash1880 Rio de Janeiro Brazil April2009

[27] M Dinitz ldquoDistributed algorithms for approximating wirelessnetwork capacityrdquo in Proceedings of the IEEE INFOCOM pp 1ndash9 IEEE San Diego Calif USA March 2010

[28] J Chen C Wen S Jin and K Wong ldquoA low complexitypilot scheduling algorithm for massive MIMOrdquo IEEE WirelessCommunications Letters vol 6 no 1 pp 18ndash21 2017

[29] D Halperin T Anderson and D Wetherall ldquoTaking thesting out of carrier sense interference cancellation for wirelessLANsrdquo in Proceedings of the 14th ACM Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo08) pp 339ndash350 September 2008

[30] S LvW Zhuang XWang andX Zhou ldquoScheduling inwirelessad hoc networks with successive interference cancellationrdquo inProceedings of the IEEE INFOCOM 2011 - IEEE Conference onComputer Communications pp 1287ndash1295 Shanghai ChinaApril 2011

[31] R Sultan L Song K G Seddik and Z Han ldquoFull-duplexmeetsmultiuser MIMO comparisons and analysisrdquo IEEE Transac-tions on Vehicular Technology vol 66 no 1 pp 455ndash467 2017

[32] X Zheng Z Cai J Li and H Gao ldquoA study on application-aware scheduling in wireless networksrdquo IEEE Transactions onMobile Computing vol 16 no 7 pp 1787ndash1801 2017

[33] X Li Y Shi X Wang C Xu and M Sheng ldquoEfficient linkscheduling with joint power control and successive interferencecancellation in wireless networksrdquo Science China InformationSciences vol 59 no 12 pp 1ndash15 2016

[34] L Qu J He and C Assi ldquoDistributed link scheduling inwireless networks with interference cancellation capabilitiesrdquoin Proceedings of the 15th IEEE International Symposium on aWorld ofWireless Mobile andMultimedia Networks WoWMoM2014 pp 1ndash7 Australia 2014

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Wireless Communications and Mobile Computing 11

2 25 3 35 4 45 5 55 61

2

3

4

5

6

7

8

9 x 105

Number of antennas

MIMOSDF

RLFMSIC

Min

imum

flow

thro

ughp

ut (b

ps)

(a) Minimum flow throughput

2 25 3 35 4 45 5 55 62

3

4

5

6

7

8

9

10

11 x 106

Number of antennas

MIMOSDF

RLFMSIC

Tota

l thr

ough

put (

bps)

(b) Total throughput

Figure 8 The relationship between antenna number and throughput

1 2 3 40

01

02

03

04

05

06

07

08

FlowMSICRLFMIMO

048046

056

033

054057

035

057061

028 032

043

The a

chie

vabl

e flow

rate

s

Figure 9 The gains of data flow rate for the four flow sessions

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (61672321 61771289 and 61832012)

Shandong provincial Graduate Education Innovation Pro-gram (SDYY14052 and SDYY15049) Qufu Normal Uni-versity Science and Technology Project (xkj201525) Shan-dong province agricultural machinery equipment researchand development innovation project (2018YZ002) ShandongProvincial Specialized Degree Postgraduate Teaching CaseLibrary Construction Program and Shandong ProvincialPostgraduate Education Quality Curriculum ConstructionProgram The authors thank the School of InformationScience and Engineering Qufu Normal University

References

[1] S Cheng Z Cai J Li and H Gao ldquoExtracting kernel datasetfrom big sensory data in wireless sensor networksrdquo IEEETransactions on Knowledge and Data Engineering vol 29 no4 pp 813ndash827 2017

[2] S Cheng Z Cai J Li and X Fang ldquoDrawing dominant datasetfrom big sensory data in wireless sensor networksrdquo in Pro-ceedings of the IEEE Conference on Computer Communications(INFOCOM rsquo15) pp 531ndash539 Hong Kong April 2015

[3] X Zheng and Z Cai ldquoReal-time big data delivery in wirelessnetworks a case study on video deliveryrdquo IEEE Transactions onIndustrial Informatics vol 13 no 4 pp 2048ndash2057 2017

[4] Z Cai andX Zheng ldquoA private and efficientmechanism for datauploading in smart cyber-physical systemsrdquo IEEE Transactionson Network Science and Engineering 2018

[5] L Lu G Y Li A L Swindlehurst A Ashikhmin and R ZhangldquoAn overview of massive MIMO benefits and challengesrdquo IEEEJournal of Selected Topics in Signal Processing vol 8 no 5 pp742ndash758 2014

[6] H Liu L Luo D Wu J Yu and D Chen ldquoRouting spectrumaccess and scheduling in multi-hop multi-channel wirelessnetworks with MIMO linksrdquo EURASIP Journal on Wireless

12 Wireless Communications and Mobile Computing

Communications and Networking vol 15 no 1 article no 652015

[7] B Hamdaoui and K G Shin ldquoCharacterization and analysis ofmulti-hop wireless mimo network throughputrdquo in Proceedingsof the Eighth ACM International Symposium on Mobile Ad HocNetworking and Computing pp 120ndash129 Montreal QuebecCanada September 2007

[8] L Jiang and J Walrand ldquoA distributed CSMA algorithm forthroughput and utility maximization in wireless networksrdquoIEEEACM Transactions on Networking vol 18 no 3 pp 960ndash972 2010

[9] H Yu O Bejarano and L Zhong ldquoCombating Inter-cellInterference in 80211ac-based multi-user MIMO networksrdquo inProceedings of the 20th ACM Annual International Conferenceon Mobile Computing and Networking (MobiCom rsquo14) pp 141ndash152 Maui Hawaii USA September 2014

[10] L B Le E Modiano C Joo and N B Shroff ldquoLongest-queue-first scheduling under SINR interferencemodelrdquo in Proceedingsof the 11th ACM International Symposium on Mobile Ad HocNetworking and Computing MobiHoc 2010 pp 41ndash50 USASeptember 2010

[11] J Li S Cheng Z Cai J Yu C Wang and Y Li ldquoApproximateholistic aggregation in wireless sensor networksrdquo ACM Trans-actions on Sensor Networks vol 13 no 2 article no 11 2017

[12] Y Zhou X Li M Liu X Mao S Tang and Z Li ldquoThroughputoptimizing localized link scheduling for multihop wireless net-works under physical interferencemodelrdquo IEEETransactions onParallel and Distributed Systems vol 25 no 10 pp 2708ndash27202014

[13] G Pei and A K S Vullikanti ldquoDistributed approximation algo-rithms for maximum link scheduling and local broadcasting inthe physical interferencemodelrdquo inProceedings of the 32nd IEEEConference on Computer Communications (IEEE INFOCOMrsquo13) pp 1339ndash1347 Turin Italy April 2013

[14] J Yu B Huang X Cheng and M Atiquzzaman ldquoShortest linkscheduling algorithms in wireless networks under the SINRmodelrdquo IEEE Transactions on Vehicular Technology vol 66 no3 pp 2643ndash2657 2017

[15] P J Wan X Xu and O Frieder ldquoShortest link scheduling withpower control under physical interferencemodelrdquo inProceedingof the Sixth International Conference on Mobile Ad-Hoc andSensor Networks pp 74ndash78 2010

[16] M Nabli F Abdelkefi W Ajib and M Siala ldquoEfficient central-ized link scheduling algorithms in wireless mesh networksrdquo inProceedings of the 10th International Wireless Communicationsand Mobile Computing Conference IWCMC 2014 pp 660ndash665Cyprus August 2014

[17] J-G Choi C Joo J Zhang and N B Shroff ldquoDistributed linkscheduling under SINR model in multihop wireless networksrdquoIEEEACM Transactions on Networking vol 22 no 4 pp 1204ndash1217 2014

[18] J Park and S Lee ldquoDistributed MIMO Ad-hoc networks Linkscheduling power allocation and cooperative beamformingrdquoIEEE Transactions on Vehicular Technology vol 61 no 6 pp2586ndash2598 2012

[19] Y Shi Y Thomas H J Liu and S Kompella ldquoHow tocorrectly use the protocol interference model for multi-hopwireless networksrdquo in Proceedings of the 10th ACM InternationalSymposium on Mobile Ad Hoc Networking and ComputingMobiHocrsquo09 pp 239ndash248 USA May 2009

[20] S Lv XWang andX Zhou ldquoScheduling under the SINRmodelin ad hoc networks with successive interference cancellationrdquoComputer Engineering and Science vol 34 no 2 pp 1ndash5 2012

[21] D Qian D Zheng J Zhang and N Shroff ldquoCSMA-baseddistributed scheduling in multi-hop MIMO networks underSINR modelrdquo in Proceedings of the IEEE INFOCOM 2010 pp1ndash9 USA March 2010

[22] O Goussevskaia M M Halldorsson and R WattenhoferldquoAlgorithms for wireless capacityrdquo IEEEACM Transactions onNetworking vol 22 no 3 pp 745ndash755 2014

[23] O Goussevskaia and RWattenhofer ldquoScheduling wireless linkswith successive interference cancellationrdquo in Proceedings of the21st International Conference onComputer Communications andNetworks ICCCN 2012 pp 1ndash7 Germany August 2012

[24] M Kontik and S C Ergen ldquoScheduling in single-hop multipleaccess wireless networks with successive interference cancella-tionrdquo IEEE Wireless Communications Letters vol 3 no 2 pp197ndash200 2014

[25] T Moscibroda R Wattenhofer and A Zollinger ldquoTopologycontrol meets SINR the scheduling complexity of arbitrarytopologiesrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 310ndash321 Florence Italy May 2006

[26] O Goussevskaia R Wattenhofer M M Halldorsson and EWelzl ldquoCapacity of arbitrary wireless networksrdquo in Proceedingsof the 28th Conference on Computer Communications (IEEEINFOCOM rsquo09) pp 1872ndash1880 Rio de Janeiro Brazil April2009

[27] M Dinitz ldquoDistributed algorithms for approximating wirelessnetwork capacityrdquo in Proceedings of the IEEE INFOCOM pp 1ndash9 IEEE San Diego Calif USA March 2010

[28] J Chen C Wen S Jin and K Wong ldquoA low complexitypilot scheduling algorithm for massive MIMOrdquo IEEE WirelessCommunications Letters vol 6 no 1 pp 18ndash21 2017

[29] D Halperin T Anderson and D Wetherall ldquoTaking thesting out of carrier sense interference cancellation for wirelessLANsrdquo in Proceedings of the 14th ACM Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo08) pp 339ndash350 September 2008

[30] S LvW Zhuang XWang andX Zhou ldquoScheduling inwirelessad hoc networks with successive interference cancellationrdquo inProceedings of the IEEE INFOCOM 2011 - IEEE Conference onComputer Communications pp 1287ndash1295 Shanghai ChinaApril 2011

[31] R Sultan L Song K G Seddik and Z Han ldquoFull-duplexmeetsmultiuser MIMO comparisons and analysisrdquo IEEE Transac-tions on Vehicular Technology vol 66 no 1 pp 455ndash467 2017

[32] X Zheng Z Cai J Li and H Gao ldquoA study on application-aware scheduling in wireless networksrdquo IEEE Transactions onMobile Computing vol 16 no 7 pp 1787ndash1801 2017

[33] X Li Y Shi X Wang C Xu and M Sheng ldquoEfficient linkscheduling with joint power control and successive interferencecancellation in wireless networksrdquo Science China InformationSciences vol 59 no 12 pp 1ndash15 2016

[34] L Qu J He and C Assi ldquoDistributed link scheduling inwireless networks with interference cancellation capabilitiesrdquoin Proceedings of the 15th IEEE International Symposium on aWorld ofWireless Mobile andMultimedia Networks WoWMoM2014 pp 1ndash7 Australia 2014

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

12 Wireless Communications and Mobile Computing

Communications and Networking vol 15 no 1 article no 652015

[7] B Hamdaoui and K G Shin ldquoCharacterization and analysis ofmulti-hop wireless mimo network throughputrdquo in Proceedingsof the Eighth ACM International Symposium on Mobile Ad HocNetworking and Computing pp 120ndash129 Montreal QuebecCanada September 2007

[8] L Jiang and J Walrand ldquoA distributed CSMA algorithm forthroughput and utility maximization in wireless networksrdquoIEEEACM Transactions on Networking vol 18 no 3 pp 960ndash972 2010

[9] H Yu O Bejarano and L Zhong ldquoCombating Inter-cellInterference in 80211ac-based multi-user MIMO networksrdquo inProceedings of the 20th ACM Annual International Conferenceon Mobile Computing and Networking (MobiCom rsquo14) pp 141ndash152 Maui Hawaii USA September 2014

[10] L B Le E Modiano C Joo and N B Shroff ldquoLongest-queue-first scheduling under SINR interferencemodelrdquo in Proceedingsof the 11th ACM International Symposium on Mobile Ad HocNetworking and Computing MobiHoc 2010 pp 41ndash50 USASeptember 2010

[11] J Li S Cheng Z Cai J Yu C Wang and Y Li ldquoApproximateholistic aggregation in wireless sensor networksrdquo ACM Trans-actions on Sensor Networks vol 13 no 2 article no 11 2017

[12] Y Zhou X Li M Liu X Mao S Tang and Z Li ldquoThroughputoptimizing localized link scheduling for multihop wireless net-works under physical interferencemodelrdquo IEEETransactions onParallel and Distributed Systems vol 25 no 10 pp 2708ndash27202014

[13] G Pei and A K S Vullikanti ldquoDistributed approximation algo-rithms for maximum link scheduling and local broadcasting inthe physical interferencemodelrdquo inProceedings of the 32nd IEEEConference on Computer Communications (IEEE INFOCOMrsquo13) pp 1339ndash1347 Turin Italy April 2013

[14] J Yu B Huang X Cheng and M Atiquzzaman ldquoShortest linkscheduling algorithms in wireless networks under the SINRmodelrdquo IEEE Transactions on Vehicular Technology vol 66 no3 pp 2643ndash2657 2017

[15] P J Wan X Xu and O Frieder ldquoShortest link scheduling withpower control under physical interferencemodelrdquo inProceedingof the Sixth International Conference on Mobile Ad-Hoc andSensor Networks pp 74ndash78 2010

[16] M Nabli F Abdelkefi W Ajib and M Siala ldquoEfficient central-ized link scheduling algorithms in wireless mesh networksrdquo inProceedings of the 10th International Wireless Communicationsand Mobile Computing Conference IWCMC 2014 pp 660ndash665Cyprus August 2014

[17] J-G Choi C Joo J Zhang and N B Shroff ldquoDistributed linkscheduling under SINR model in multihop wireless networksrdquoIEEEACM Transactions on Networking vol 22 no 4 pp 1204ndash1217 2014

[18] J Park and S Lee ldquoDistributed MIMO Ad-hoc networks Linkscheduling power allocation and cooperative beamformingrdquoIEEE Transactions on Vehicular Technology vol 61 no 6 pp2586ndash2598 2012

[19] Y Shi Y Thomas H J Liu and S Kompella ldquoHow tocorrectly use the protocol interference model for multi-hopwireless networksrdquo in Proceedings of the 10th ACM InternationalSymposium on Mobile Ad Hoc Networking and ComputingMobiHocrsquo09 pp 239ndash248 USA May 2009

[20] S Lv XWang andX Zhou ldquoScheduling under the SINRmodelin ad hoc networks with successive interference cancellationrdquoComputer Engineering and Science vol 34 no 2 pp 1ndash5 2012

[21] D Qian D Zheng J Zhang and N Shroff ldquoCSMA-baseddistributed scheduling in multi-hop MIMO networks underSINR modelrdquo in Proceedings of the IEEE INFOCOM 2010 pp1ndash9 USA March 2010

[22] O Goussevskaia M M Halldorsson and R WattenhoferldquoAlgorithms for wireless capacityrdquo IEEEACM Transactions onNetworking vol 22 no 3 pp 745ndash755 2014

[23] O Goussevskaia and RWattenhofer ldquoScheduling wireless linkswith successive interference cancellationrdquo in Proceedings of the21st International Conference onComputer Communications andNetworks ICCCN 2012 pp 1ndash7 Germany August 2012

[24] M Kontik and S C Ergen ldquoScheduling in single-hop multipleaccess wireless networks with successive interference cancella-tionrdquo IEEE Wireless Communications Letters vol 3 no 2 pp197ndash200 2014

[25] T Moscibroda R Wattenhofer and A Zollinger ldquoTopologycontrol meets SINR the scheduling complexity of arbitrarytopologiesrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 310ndash321 Florence Italy May 2006

[26] O Goussevskaia R Wattenhofer M M Halldorsson and EWelzl ldquoCapacity of arbitrary wireless networksrdquo in Proceedingsof the 28th Conference on Computer Communications (IEEEINFOCOM rsquo09) pp 1872ndash1880 Rio de Janeiro Brazil April2009

[27] M Dinitz ldquoDistributed algorithms for approximating wirelessnetwork capacityrdquo in Proceedings of the IEEE INFOCOM pp 1ndash9 IEEE San Diego Calif USA March 2010

[28] J Chen C Wen S Jin and K Wong ldquoA low complexitypilot scheduling algorithm for massive MIMOrdquo IEEE WirelessCommunications Letters vol 6 no 1 pp 18ndash21 2017

[29] D Halperin T Anderson and D Wetherall ldquoTaking thesting out of carrier sense interference cancellation for wirelessLANsrdquo in Proceedings of the 14th ACM Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo08) pp 339ndash350 September 2008

[30] S LvW Zhuang XWang andX Zhou ldquoScheduling inwirelessad hoc networks with successive interference cancellationrdquo inProceedings of the IEEE INFOCOM 2011 - IEEE Conference onComputer Communications pp 1287ndash1295 Shanghai ChinaApril 2011

[31] R Sultan L Song K G Seddik and Z Han ldquoFull-duplexmeetsmultiuser MIMO comparisons and analysisrdquo IEEE Transac-tions on Vehicular Technology vol 66 no 1 pp 455ndash467 2017

[32] X Zheng Z Cai J Li and H Gao ldquoA study on application-aware scheduling in wireless networksrdquo IEEE Transactions onMobile Computing vol 16 no 7 pp 1787ndash1801 2017

[33] X Li Y Shi X Wang C Xu and M Sheng ldquoEfficient linkscheduling with joint power control and successive interferencecancellation in wireless networksrdquo Science China InformationSciences vol 59 no 12 pp 1ndash15 2016

[34] L Qu J He and C Assi ldquoDistributed link scheduling inwireless networks with interference cancellation capabilitiesrdquoin Proceedings of the 15th IEEE International Symposium on aWorld ofWireless Mobile andMultimedia Networks WoWMoM2014 pp 1ndash7 Australia 2014

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom