Research Article Incorporating D2D to Current Cellular Communication Systemdownloads.hindawi.com/journals/misy/2016/2732917.pdf · 2019-07-30 · Research Article Incorporating D2D

Research ArticleIncorporating D2D to Current Cellular Communication System

Mingjun Dai12 Bailu Mao12 Dan Shen12 Xiaohui Lin12 Hui Wang12 and Bin Chen12

1Shenzhen Key Lab of Advanced Communication and Information Process and Shenzhen Key Laboratory of Media SecurityCollege of Information Engineering Shenzhen University 518060 China2State Key Laboratory of Integrated Services Networks Xidian University China

Correspondence should be addressed to Bailu Mao 115624532qqcom

Received 3 November 2015 Accepted 20 January 2016

Academic Editor Qilian Liang

Copyright copy 2016 Mingjun Dai 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

A device-to-device (D2D) group works as relay nodes to aid the information delivery from a source to a destination in cellularcommunication network Within this system we propose a communication mechanism to aid traditional cellular communicationand correspondingly borrow some channel resource from traditional cellular communication system for D2D communication Onone side to aid cellular communication we propose a modified Alamouti scheme which does not modify the operation at the basestation This makes our proposed scheme consistent with previous cellular communication system On the other side there aremany competitive D2D groups that want to potentially utilize the borrowed channel resource from traditional cellular system fordelivering their own informationWemodel this competition as a game and utilize game theory technique to solve this competitionproblem

1 Introduction

In traditional cellular systems data is transmitted from thesource terminal to the destination terminal via a base station(BS) All traffic is forwarded or relayed by the BS even ifthe source and the destination are close to each otherThis relaying-structure has two drawbacks First it incurslong communication latency and high energy consumptionSecond traditional BS can only support limited numberof mobiles communicating simultaneously which does notsuit the exponential growth of mobile terminals especiallymachine-to-machine (M2M) communications which aremainly adopted to collect signals from sensors and then deliv-ered to the Internet [1ndash3]

To tackle these two problems device-to-device (D2D)communication instead of communication via a relay wasproposed as a short-distance communication option [4ndash7] Firstly it reduces communication latency and energyconsumption due to shorter communication range and fewertransmitters Secondly it enlarges system capacity sinceshorter communication range of D2D communication (canbe viewed as a smaller cell) utilizes the spectrum with ahigher utilization rate per area and hence has higher system

capacity There are a lot of application scenarios for D2Dcommunication (1) A group of people climb a mountain orvisit a place (2) A group of friends want to find each otherin a prescheduled place (3) A group of closed-to-each-othercars run in a highway

Due to D2Drsquos advantages as listed above how to embed itinto current cellular system needs to be carefully designedIn particular radio resource (eg the frequency channel)allocation among these two systems is needed There aretwo allocation modes In the first these two systems sharethe radio resource simultaneously which introduces theinterference between the D2D link and cellular link In thesecond these two systems use orthogonal channels

Most of previous works for D2D communicationassumed that D2D users worked in the underlay modenamely Mode One [8ndash11] A radio resource allocation policyforD2D link is proposed in [12]Thework in [13] limits D2Drsquostransmission power to ensure the quality of cellular links Itis also shown in [14] that power control in relay assisted D2Dcommunication may be a better choice which benefits fromhigh transmission capacity and power efficiency

To summarize all those D2D works do not considerthe cooperation between D2D groups with cellular system

Hindawi Publishing CorporationMobile Information SystemsVolume 2016 Article ID 2732917 7 pageshttpdxdoiorg10115520162732917

2 Mobile Information Systems

In this work we let the transmitter of the D2D group helpthe cellular communication namely help the source to relayhis signal to the destination which provides another linkThetwo signals from these two links (one from BS and the otherfrom the D2D group) can be combined in a certain mannerfor example maximum ratio combining (MRC) to enhancethe received signal-to-noise ratio (SNR) which reduces theoutage probability and increases the achieved diversity [15]To implement the above conventional diversity techniqueAlamouti scheme is not compatible since BS needs toperform conjugation on one of the transmission signalsduring the collaboration process We propose a modifiedAlamouti scheme which does not modify the operation atBS namely the operation at the BS is identical to that intraditional cellular system This kind of cooperation canreduce the delivery time required for cellular communicationsystem and hence the saved time can be rewarded to D2Dcommunication

During the communication process free riding howeverexists in the D2D terminal In this paper the game theoreticalframework [16 17] can solve this problem and multi-D2Dgroups power can be controlled by Nash Equilibria [18] Thisscheme can be utilized into high communication efficiencydata collection in 5Gmobile communication system [19ndash22]for example

The organization of this paper is as follows In Section 2we first provide preliminaries and then describe the systemmodel In Section 3 we elaborate the proposed cooperationscheme that incorporates traditional cellular communicationandD2Dcommunication In Section 4we use game theoreti-cal framework to design the competition amongD2D groupsFinally in Section 5 we draw the conclusions

2 Preliminaries and System Model

21 Preliminaries We first describe the decode-and-forward(DF) relaying protocol and then illustrate the Alamoutischeme

211 Decode-and-Forward (DF) Refer to Figure 1 Transmit-ter119860 sends signal toward receiver 119861 via relay 119877 The link gainbetween 119860 and 119877 is 119906 and the link gain between 119877 and 119861 isV The channelrsquos input-output relationship of the two hops ischaracterized by

119910119877= 119906119909119860+ 119908119877

119910119861= V119909119877+ 119908119861

(1)

where 119909119877and 119910

119877denote the output signal and input signal

of relay 119877 respectively In the DF protocol the relay nodefirst tries to decode the message from the received signal Ifthe decoding is successful the relay reencodes the messageusing the same codebook as in source119860 Otherwise the relaysimply keeps silent

212 Alamouti Scheme Refer to Figure 2 Transmitters 1 and2 send signals simultaneously toward destination119863 The link

A B120583 v

R

Figure 1 Illustration of DF

h1D

h2D

D

1

2

Figure 2 Alamouti scheme

gain between transmitter 119894 isin 1 2 and destination 119863 is ℎ119894119863

The channelrsquos input-output relationship is characterized as

119910 [119898] = ℎ1119863 [119898] 1199091 [119898] + ℎ

2119863 [119898] 1199092 [119898] + 119908 [119898] (2)

where 119909119894[119898] denotes the transmitted signal by transmitter 119894

119910[119898] denotes the received signal at destination 119863 and 119908[119898]

denotes the thermal noise at destination119863 all at time slot119898In the Alamouti scheme [23] the two transmitters intend

to send two complex symbols1199061and1199062 respectively over two

consecutive symbol slots During slot 1 transmitter 1 sends 1199061

and transmitter 2 sends 1199062 namely 119909

1[1] = 119906

1 1199092[1] = 119906

2

During slot 2 transmitter 1 sendsminus119906lowast2and transmitter 2 sends

119906lowast

1 namely 119909

1[2] = minus119906

lowast

2 1199092[2] = 119906

lowast

1 If we assume that

the channel gain remains constant over these two consecutivesymbol times namely ℎ

1119863[1] = ℎ

1119863[2] ≜ ℎ

1 ℎ2119863

[1] =

ℎ2119863

[2] ≜ ℎ2 then we have two consecutive received signals

as

119910 [1] = ℎ11199061+ ℎ21199062+ 119908 [1]

119910 [2] = minusℎ1119906lowast

2+ ℎ2119906lowast

1+ 119908 [2]

(3)

Rewriting it into matrix form and performing the conju-gation operation on the lower half matrix we obtain

(

119910 [1]

119910 [2]lowast) = (

ℎ1

ℎ2

ℎlowast

2minusℎlowast

1

)(

1199061

1199062

) + (

119908 [1]

119908 [2]lowast) (4)

We observe that the two columns of the square matrix in(4) are orthogonal Hence the detection problem for 119906

1 1199062

decomposes into two separate orthogonal scalar problems

Remark Throughout this paper we use 119909lowast to denote the

conjugate of the complex number 119909 and 119867dagger to denote the

conjugate transpose of the complex matrix119867

22 System Model Refer to Figure 3 There are two subsys-tems One is the traditional cellular system and the otheris the D2D system Node 119878 communicates with node 119863

via 119861119878 as a relay which composes the traditional cellularsystem The users that are in a small circle form the D2Dcommunication group due to their closeness to each othernamely the communication within this group is one hop

The D2D group may help the source relay its transmittedsignal to the destination which provides another branch of

Mobile Information Systems 3

S

D2D group

D2D group

D2Dgroup

Communication line

Base stationBS

D

Figure 3 Illustration of relay D2D communications

h1DhS1

hS2h2D

S D

1

2

Figure 4 The relay network model

link The two signals arriving at the destination from thesetwo links can be combined in a certain manner for examplemaximum ratio combining (MRC) to enhance the receivedSNR According to Shannonrsquos capacity formula the achievedrate is correspondingly increased which brings the followingbenefitsThe completion time of the 119878-119863 communication linkcan be reduced and the reduced time (reduction of time)maybe rewarded to the D2D users for communication

The cellular communication in the above model can besimplified to the model in Figure 4 where node 1 represents119861119878 and node 2 represents a relay node which is acted bya member of the D2D group We assume node 119894 is subjectto power constraint 119901

119894 119894 isin 119878 1 2 The two relays are

assumed to be operated in full-duplex mode (the half-duplexmode can be easily obtained by halving the transmission timebetween the first and the second hop) We consider the slowfading scenario and the link gains are randomThe link gainsbetween node 119878 and node 119894 and between node 119894 and node 119863

are represented by ℎ119878119894and ℎ119894119863 respectively 119894 isin 1 2

Let 119909119894(119898) be the transmitted symbol from node 119878 to node

119894 at time 119898 119894 isin 119878 1 2 We also let 119910119894(119898) and 119908

119894(119898) be

respectively the received symbol and the thermal noise at

Table 1 Standard Alamouti

BS D2DSlot 1 119906

11199062

Slot 2 minus119906lowast

2119906lowast

1

node 119894 at time 119898 119894 isin 1 2 119863 Each channelrsquos input-outputrelationship is represented by the following formulas

119910119894 (119898) = ℎ

119878119894radic119875119878119909119878 (119898) + 119908

119894 (119898)

119910119863 (119898) =

2

sum

119894=1

ℎ119894119863radic119875119894119909119894 (119898) + 119908

119863 (119898)

(5)

subject to Var119909119878(119898) le 119875

119878and Var119909

119894(119898) le 119875

119894for 119894 = 1 2

and 119908119894(119898) 119908

119863(119898) sim CN(0 119899)

If the decoding in each relay node is successful the outputof the relay node can be represented by

119909119894 (119898) = 119909

119878 (119898) (6)

We assume that 1198751

= 1198752

= 120581119875119878 Define signal-to-

noise ratio (SNR) Γ ≜ 119875119878119899 The received SNR at relay 119894

is denoted by Γ119894(ℎ119878119894) and is equal to |ℎ

119860119894|2Γ The received

SNR at destination 119863 is denoted by Γ119863(ℎ) whose expression

depends on the transmission scheme Correspondingly wedefine 119877

119878(ℎ) as the end-to-end information rate from source

119878 to destination119863 According to Shannonrsquos capacity formulathe end-to-end information rate is equal to

119877119878 (ℎ) = log

2(1 + Γ

119863 (ℎ)) (7)

An outage event occurs if the instantaneous end-to-end rate 119877

119878(ℎ) falls below a certain threshold 119877thd Outage

probability is the probability of occurrence of an outageevent that is 119901out ≜ Pr119877

119878(ℎ) lt 119877thd According to

(7) there is a one-to-one correspondence between 119877119878(ℎ)

and Γ119863(ℎ) Therefore the outage probability can be obtained

by comparing Γ119863(ℎ) with a certain threshold Γthd More

specifically we have 119901out ≜ PrΓ119863(ℎ) lt Γthd

3 Proposed Cooperation Scheme

The key idea is that the D2D group serves as another branchof link for aiding the 119878-119863 communication In this case thereceived signal at 119863 may be enhanced by appropriate signalprocessing method and hence the completion time may beshortened The reward is that the saved time can be grantedto the D2D group for short-distance D2D communication

31 Protocol Description After receiving the signal fromthe source the BS and the D2D group combine Alamoutiprotocol with DF Note that simply using the standard Alam-outi scheme as shown in Section 212 will have drawbackDetailed explanation is as follows

The standard Alamouti schedule is shown in Table 1 Ina transmission block the BS (relay 1) transmits 119906

1and minus119906

lowast

2

in two consecutive time slots respectively We observe that


Table 2 Modified Alamouti

BS D2DSlot 1 119906

1minus119906lowast

2

Slot 2 1199062

119906lowast

1

the BS in the second slots performs a conjugation operationfollowed by a negative operation which is not consistent withtraditional cellular system (for traditional cellular systemthe BS should perform uniform operation on the signalsfor all users namely transmits 119906

1and 119906

2in the block) For

this reason we propose a modified Alamouti scheme whichdoes not need to alter the operation at the BS The modifiedAlamouti schedule is shown in Table 2 We observe that theoperation in the BS (relay 1) is exactly what the BS does intraditional cellular systemTherefore the modified Alamoutischeme can be easily incorporated into traditional cellularsystem in a consistentmannerWe call themodifiedAlamouticombined with DF MADF for short

32 Performance Analysis To analyze the performance ofMADF we rephrase its protocol description Each relay firstdecodes themessage from the received signal If the decodingis successful the relay reencodes the message using the samecodebook adopted in source 119878 Otherwise if the decodingfails the relay will not forward the signal to the destinationThe transmissions of the relays follow the modified Alamoutischeme

After receiving the signal from the source the transmitsymbols of relays are constructed in the following way

119906119894119898

≜ 119909119894 (119898) = 119909

119878 (119898) (8)

where 119894 = 1 2 and 119909119878(119898) is the symbol from the previous

blockAs the modified Alamouti scheme shows in the first time

slot relay 1 transmits 11990611

and relay 2 transmits minus119906lowast22 in the

second time slot relay 1 transmits 11990612

and relay 2 transmits119906lowast

21 Note that the BS transmits the original signal in this block

which is consistent with the operation in traditional cellularsystem The output symbols at destination node119863 are

119910119863 (1) = radic120581119875

119878(ℎ1119863

11990611

+ ℎ2119863

(minus119906lowast

22)) + 119908

119863 (1)

119910119863 (2) = radic120581119875

119878(ℎ1119863

11990612

+ ℎ2119863

(119906lowast

21)) + 119908

119863 (2)

(9)

which is equivalent to

(

119910119863 (1)

119910lowast

119863(2)

) = 119867radic120581119875119878(

119909119878 (1)

119909lowast

119878(2)

) + 119908119863 (10)

where

119867 ≜ (

ℎ1119863

minusℎ2119863

ℎlowast

2119863ℎlowast

1119863

)

119908119863≜ (

119908119863 (1)

119908lowast

2(2)

)

(11)

Multiplying (10) by119867dagger we obtain

119867+(

119910119863 (1)

119910lowast

119863(2)

) = 119867+119867radic120581119875

119878(

119909119878 (1)

119909lowast

119878(2)

) + 119867dagger119908119863 (12)

where119867dagger119867 = diag(120582 120582) and 120582 ≜ |ℎ1119863

|2+ |ℎ2119863

|2

The received SNR at destination119863 is then given by

ΓMADF119863

(ℎ) = Γ119863(Φ1 Φ2)

= (Φ1

1003816100381610038161003816ℎ11198631003816100381610038161003816

2+ Φ2

1003816100381610038161003816ℎ21198631003816100381610038161003816

2) 120581Γ

(13)

where for 119894 = 1 2

Φ119894≜

1 if Γ119894ge Γthd

0 otherwise(14)

We claim the following

Theorem 1 MADF yields a lower outage probability thantraditional cellular network

Proof If BS fails in the decoding then traditional methodfails in the decoding at final destination 119863 since BS willkeep silent In MADF final destination 119863 may or may notbe able to recover the message depending on whether relaytwo succeeds in the decoding and final destination succeedsin the decoding If it is positive then MADF outperformstraditional method Otherwise they have the same outageperformance

If BS succeeds in decoding then traditional cellularmethod achieves received SNR at 119863 as Γ

119863(1 0) = 120581|ℎ

1119863|2Γ

while MADF achieves Γ119863(1 1) = (|ℎ

1119863|2+ |ℎ2119863

|2)120581Γ which

is greater than the traditional cellular system This can betransformed to the fact that MADF outperforms traditionalcellular system in terms of outage performance

Summarizing the above two cases we claim that MADFoutperforms traditional cellular system in terms of outageprobability

Note that the inverse of outage probability represents thetime duration required to finish the information deliveryWe hence conclude that MADF saves delivery time Thesaved time can be rewarded to the D2D group for D2Dcommunication How to utilize this borrowed channel isillustrated in the next section

4 D2D Competition within GameTheoretical Framework

In view of the above description traditional communi-cation framework cannot meet increasingly huge demandof communication Our proposed scheme alleviates suchheavy burden by attracting D2D communication into usingtraditional cellular communication channel Besides suchscheme does not alter the operation at BS and hence can beapplied into current cellular system seamlessly

However in practice there are many D2D groups thatpotentially want to communicate If they want to borrow


the communication channel of the cellular system a fairchannel allocation scheme should be designed for manycompetitors Game theory is a good option for providinga fair resource allocation among many competitors in adistributed fashion Under noncooperative game theoreticalframework where each user is selfish the notion of NashEquilibrium (NE) is normally considered as a good steadystate that evaluates the systems steadiness In an NE stateno user will benefit by unilaterally deviating from the currentstrategy selection [24]

In this section we formulate the competition amongD2Dgroups within noncooperative game theoretical frameworkDetailed mechanism is as follows

Each D2D group wants to communicate within a groupMany D2D groups compete for the channel resource oftraditional cellular system Channel allocation rule is thechannel which will be awarded to the D2D group that acts asrelay for cellular communication On one hand one memberin a D2D group may serve as the relay and hence thisgroup grabs the channel for communication This memberhas power consumption for serving as relay but he enjoysthe D2D communication the other members within thisgroup will benefit without payment for example powerconsumption for relaying On the other hand other D2Dgroups do not have power consumption for relaying but theydo not get the channel resource for D2D communication

We propose a back-off timer based [25] mechanism forthese users to compete for this channel Each user randomlysets a back-off timer The user that times out first will serveas relay and he notifies the other users to stop timingAfterwards the group that contains this user as memberstarts D2D communication

Game Setting Totally there are 119866 D2D groups with all themembers in the 119892th group denoted by setU119892 In D2D group119892 isin 1 2 119866 ≜ G its 119894th member 119898119892

119894randomly picks a

back-off timer 120591119892119894 which is a random variable and follows the

exponential distribution 120591119892119894

sim exp(120582119892119894) Each user chooses

the value separately

Utility Formulation If user119898119892119894lowast serves as relay then his utility

is

U119892

119894lowast = 120572119892

119894lowast119901119892

119894lowast + 120573119892

119894lowast min (120591

1

1 120591

1

1198991

1205912

1 120591

2

1198992

) (15)

where 119901119892

119894lowast is the transmission power of 119898119892

119894lowast when he serves

as relay and 120572119892

119894lowast and 120573

119892

119894lowast are the weighting coefficients for

transmission power 119901119892

119894lowast and weighting time For users with

different power savings 120572119892119894lowast will be different Define 120591

119892

119894lowast ≜

min(12059111 120591

1

1198991

1205912

1 120591

2

1198992

) Actually the above utility iscost and hence the smaller the better The other users withingroup 119892 have utility

U119892

119894= 120573119892

119894min (120591

1

1 120591

1

1198991

1205912

1 120591

2

1198992

) 119894 = 119894lowast (16)

For members in other groups the utility is

Uℎ

119895= 120573ℎ

119895min (120591

1

1 120591

1

1198991

1205912

1 120591

2

1198992

) ℎ = 119892 (17)

Instead of considering each userrsquos utility we consider eachgrouprsquos utility The utility of group 119892 is

U119892=

119899119892

sum

119894=1

U119892

119894=

119899119892

sum

119894=1

120573119892

119894120591119892

119894lowast + 120572119892

119894lowast119901119892

119894lowast (18)

The utility of group ℎ = 119892 is

Uℎ=

119899ℎ

sum

119894=1

Uℎ

119894=

119899ℎ

sum

119894=1

120573ℎ

119894120591119892

119894lowast (19)

We formulate a noncooperative gameThe game involves119866 players with each player being a D2D group Each grouptries to minimize the value of its utility For simplicitywe assume that the duration of each timer follows theexponential distribution exp(120582) with value of parameter 120582

yet to be determined We in the following will derive howeach user determines such a value so that an NE can beobtained We apply the following theorem to obtain NE andthe corresponding values

Theorem 2 The strategies of players in a game form an NE iffor each player given the strategies of other players the expectedcost of player 119894 is the same regardless of its chosen values of back-off times [26]

We apply Theorem 2 to determine the values of 120582rsquosSuppose that user 119898

119892

119894lowast in group 119892 chooses 120591

119892

119894lowast = 120591 On one

hand if 120591 is smaller than all 120591ℎ119894

isin U1 cup U2 sdot sdot sdot cup U119866

119898119892

119894lowast user119898119892

119894lowast serves as relay node to aid traditional cellular

communication after waiting for 120591 units of time and thusthe utility obtained by group 119892 is sum

119899119892

119894=1120573119892

119894120591 + 120572

119892

119894lowast119901119892

119894lowast where

120572119892

119894lowast119901119892

119894lowast denotes relaying power consumption cost andsum

119899119892

119894=1120573119892

119894120591

denotes waiting costOn the other hand if existℎ isin G 119892 such that one member

in group ℎ sets a timer smaller than 120591 and it is the smallestamong all timers of all groups in this case all users in group119892 do not need to aid traditional cellular communication andhence the utility of group 119892 is sum

119899119892

119894=1120573119892

119894120591 Note that we have

min1205911 1205912 120591

119897 sim exp(Σ

119897120582119894) where 120591

119894sim exp(120582

119894) Therefore

120591 is theminimumwithin all groups except group119892Therefore120591 sim exp(120582

minusU119892) where 120582minusU119892 ≜ sum

119866

119892=1sum119899119892

119894=1120582119892

119894minus sum119899119892

119894=1120582119892

119894with

minusU119892 ≜ (cup119866

119896=1U119896) U119892

The expected utility of group 119892 can be written as

int

120591

119904=0

119899119892

sum

119894=1

120573119892

119894119904120582minusU119892119890minus120582minusU119892 119904119889119904

+ int

infin

119904=120591

(

119899119892

sum

119894=1

120573119892

119894120591 + 120572119892

119894lowast119901119892

119894lowast)120582minusU119892119890minus120582minusU119892 119904119889119904

=sum119899119892

119894=1120573119892

119894

120582minusU119892

+ (120572119892

119894lowast119901119892

119894lowast minus

sum119899119892

119894=1120573119892

119894

120582minusU119892

)119890minus120582minusU119892120591

(20)


Thus if 120572119892119894119901119892

119894= sum119899119892

119894=1120573119892

119894120582minusU119892 the strategies form a Nash

EquilibriumThis can be done by choosing

120582U =1

119866 minus 1

119866

sum

119892=1

119899119892

sum

119896=1

sum119899119892

119894=1120573119892

119894

120572119892

119896119901119892

119896

minussum119899119892

119894=1120573119892

119894

120572119892

119894119901119892

119894

(21)

for all U isin U1U2 U

119866 where 120582U denotes the

parameter of exponential distribution that the duration of theminimum timer of this group which is a random variablefollows

Theorem 3 If each group say group 119892 chooses 120591U119892 sim

exp(120582U119892) as set by (21) then these strategies form a NashEquilibrium

The 120582rsquos in a group need to satisfy

119899119892

sum

119894=1

120582119892

119894= 120582U119892 (22)

subject to constraint 120582119892119894gt 0 Detailed values chosen for 120582119892

119894rsquos

may be implemented by voting for a group leader and let himallocate the values that satisfy (22) In practice for simplicitywe can choose 120582119892

119894= 120582U119892119899119892 for all 119894 isin U119892

5 Conclusion

In this work a device-to-device (D2D) group aids the trans-mission of traditional cellular communication We presenta modified Alamouti scheme which does not modify theoperation at BS and hence make the scheme consistent withtraditional cellular communication system The saved timein traditional communication is rewarded to D2D usersfor communication Game theory technique is designedto tackle the competition among many D2D groups thatpotentially want to utilize the rewarded channel for D2Dcommunication

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported by research grant fromNatural Science Foundation of China (6130118261171071 and 61575126) Natural Science Foundation ofGuangdong Province (S2013040016857 2015A030313552)Specialized Research Fund for the Doctoral Programof Higher Education from The Ministry of Education(20134408120004) Distinguished Young Talents inHigher Education of Guangdong (2013LYM 0077)Foundation of Shenzhen City (KQCX20140509172609163GJHS20120621143440025 JCYJ20140418095735590JCYJ20150324140036847 and ZDSY20120612094614154)Xiniuniao from Tencent Research Foundation of the HigherEducation Institute of Guangdong Province (GDJ2014083)

Teaching Reform and Research Project of ShenzhenUniversity (JG2015038) and Natural Science Foundation ofShenzhen University (00002501 00036107)

References

[1] J Kim J Lee J Kim and J Yun ldquoM2M service platforms sur-vey issues and enabling technologiesrdquo IEEE CommunicationsSurveys and Tutorials vol 16 no 1 pp 61ndash76 2014

[2] G Wu S Talwar K Johnsson N Himayat and K D JohnsonldquoM2M from mobile to embedded internetrdquo IEEE Communica-tions Magazine vol 49 no 4 pp 36ndash43 2011

[3] J Du and SW Chao ldquoA study of information security forM2Mof IOTrdquo in Proceedings of the 3rd IEEE International Conferenceon Advanced Computer Theory and Engineering (ICACTE rsquo10)vol 3 pp V3-576ndashV3-579 IEEE Chengdu China August 2010

[4] J C F Li M Lei and F Gao ldquoDevice-to-device (D2D) commu-nication in MU-MIMO cellular networksrdquo in Proceedings of theIEEEGlobal Communications Conference (GLOBECOM rsquo12) pp3583ndash3587 Anaheim Calif USA December 2012

[5] A Altieri P Piantanida L R Vega and C G Galarza ldquoOnfundamental trade-offs of device-to-device communicationsin large wireless networksrdquo IEEE Transactions on WirelessCommunications vol 14 no 9 pp 4958ndash4971 2015

[6] Y Xiao K-C Chen C Yuen and L A DaSilva ldquoSpectrumsharing for device-to-device communications in cellular net-works a game theoretic approachrdquo in Proceedings of the IEEEInternational SymposiumonDynamic SpectrumAccessNetworks(DYSPAN rsquo14) pp 60ndash71 IEEE McLean Va USA April 2014

[7] M Dai S Zhang H Wang et al ldquoNetwork-coded relayingin multiuser multicast D2D networkrdquo International Journal ofAntennas and Propagation vol 2014 Article ID 589794 7 pages2014

[8] Z Zhou M Dong K Ota J Wu and T Sato ldquoDis-tributed interference-aware energy-efficient resource allocationfor device-to-device communications underlaying cellular net-worksrdquo in Proceedings of the Global Communications Conference(GLOBECOM rsquo14) pp 4454ndash4459 IEEE Austin Tex USADecember 2014

[9] S Wen X Zhu Z Lin X Zhang and D Yang ldquoDistributedresource management for device-to-device (D2D) communi-cation underlay cellular networksrdquo in Proceedings of the IEEE24th Annual International Symposium on Personal Indoor andMobile Radio Communications (PIMRC rsquo13) pp 1624ndash1628London UK September 2013

[10] F Wang C Xu L Song Q Zhao X Wang and Z HanldquoEnergy-aware resource allocation for device-to-device under-lay communicationrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC rsquo13) pp 6076ndash6080 IEEEBudapest Hungary June 2013

[11] S Wen X Zhu Y Lin Z Lin X Zhang and D YangldquoAchievable transmission capacity of relay-assisted device-to-device (D2D) communication underlay cellular networksrdquo inProceedings of the IEEE 78th Vehicular Technology Conference(VTC Fall rsquo13) pp 1ndash5 Las Vegas Nev USA September 2013

[12] H-S Kim J-H Na and E Cho ldquoResource allocation policyto avoid interference between cellular and D2D Links andD2D links in mobile networksrdquo in Proceedings of the 28th Inter-national Conference on Information Networking (ICOIN rsquo14)pp 588ndash591 IEEE Phuket Thailand February 2014

[13] G Fodor andNReider ldquoAdistributed power control scheme forcellular network assisted D2D communicationsrdquo in Proceedings


of the IEEE Global Telecommunications Conference (GLOBE-COM rsquo11) pp 1ndash6 Houston Tex USA December 2011

[14] H ElSawy E Hossain and M-S Alouini ldquoAnalytical mod-eling of mode selection and power control for underlay D2Dcommunication in cellular networksrdquo IEEE Transactions onCommunications vol 62 no 11 pp 4147ndash4161 2014

[15] MDai andCW Sung ldquoAchieving high diversity andmultiplex-ing gains in the asynchronous parallel relay networkrdquo EuropeanTransactions on Telecommunications vol 24 no 2 pp 232ndash2432013

[16] B Wang K J R Liu and T C Clancy ldquoEvolutionary coop-erative spectrum sensing game how to collaboraterdquo IEEETransactions on Communications vol 58 no 3 pp 890ndash9002010

[17] L Song D Niyato Z Han and E Hossain ldquoGame-theoreticresource allocation methods for device-to-device communica-tionrdquo IEEEWireless Communications vol 21 no 3 pp 136ndash1442014

[18] M Dai S Zhang B Chen X Lin and H Wang ldquoA refinedconvergence condition for iterative waterfilling algorithmrdquoIEEE Communications Letters vol 18 no 2 pp 269ndash272 2014

[19] J Bae Y S Choi J S Kim and M Y Chung ldquoArchitectureand performance evaluation of MmWave based 5G mobilecommunication systemrdquo in Proceedings of the 5th InternationalConference on Information and Communication TechnologyConvergence (ICTC rsquo14) pp 847ndash851 Busan Republic of KoreaOctober 2014

[20] Q Liang ldquoFault-tolerant and energy efficient wireless sensornetworks a cross-layer approachrdquo in Proceedings of the MilitaryCommunications Conference (MILCOM rsquo05) vol 3 pp 1862ndash1868 Atlantic City NJ USA October 2005

[21] Q Liang ldquoAd hoc wireless network trafficmdashself-similarity andforecastingrdquo IEEECommunications Letters vol 6 no 7 pp 297ndash299 2002

[22] Q Liang X Cheng S C Huang and D Chen ldquoOpportunisticsensing in wireless sensor networks theory and applicationrdquoIEEE Transactions on Computers vol 63 no 8 pp 2002ndash20102014

[23] D Tse and P Viswanath Fundamentals ofWireless Communica-tion Cambridage University Press 2014

[24] A Bhattarai C Charoenlarpnopparut P Suksompong andP Komolkiti ldquoDeveloping policies for channel allocation incognitive radio networks using game theoryrdquo in Proceedingsof the 11th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON rsquo14) pp 1ndash6 IEEENakhonRatchasimaThailand May 2014

[25] I H Hou Y Liu and A Sprintson ldquoA non-monetary protocolfor peer-to-peer content distribution in wireless broadcast net-works with network codingrdquo in Proceedings of the InternationalSymposium and Workshops on Modeling and Optimization inMobile Ad Hoc and Wireless Networks (WiOpt rsquo13) pp 170ndash177Tsukuba Science City Japan May 2013

[26] Z Han D Niyato W Saad T Basar and A Hjorungnes GameTheory in Wireless and Communication Networks CambridgeUniversity Press Cambridge UK 2012

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

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Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


RoboticsJournal of



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Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



In this work we let the transmitter of the D2D group helpthe cellular communication namely help the source to relayhis signal to the destination which provides another linkThetwo signals from these two links (one from BS and the otherfrom the D2D group) can be combined in a certain mannerfor example maximum ratio combining (MRC) to enhancethe received signal-to-noise ratio (SNR) which reduces theoutage probability and increases the achieved diversity [15]To implement the above conventional diversity techniqueAlamouti scheme is not compatible since BS needs toperform conjugation on one of the transmission signalsduring the collaboration process We propose a modifiedAlamouti scheme which does not modify the operation atBS namely the operation at the BS is identical to that intraditional cellular system This kind of cooperation canreduce the delivery time required for cellular communicationsystem and hence the saved time can be rewarded to D2Dcommunication

During the communication process free riding howeverexists in the D2D terminal In this paper the game theoreticalframework [16 17] can solve this problem and multi-D2Dgroups power can be controlled by Nash Equilibria [18] Thisscheme can be utilized into high communication efficiencydata collection in 5Gmobile communication system [19ndash22]for example

The organization of this paper is as follows In Section 2we first provide preliminaries and then describe the systemmodel In Section 3 we elaborate the proposed cooperationscheme that incorporates traditional cellular communicationandD2Dcommunication In Section 4we use game theoreti-cal framework to design the competition amongD2D groupsFinally in Section 5 we draw the conclusions

2 Preliminaries and System Model

21 Preliminaries We first describe the decode-and-forward(DF) relaying protocol and then illustrate the Alamoutischeme

211 Decode-and-Forward (DF) Refer to Figure 1 Transmit-ter119860 sends signal toward receiver 119861 via relay 119877 The link gainbetween 119860 and 119877 is 119906 and the link gain between 119877 and 119861 isV The channelrsquos input-output relationship of the two hops ischaracterized by

119910119877= 119906119909119860+ 119908119877

119910119861= V119909119877+ 119908119861

(1)

where 119909119877and 119910

119877denote the output signal and input signal

of relay 119877 respectively In the DF protocol the relay nodefirst tries to decode the message from the received signal Ifthe decoding is successful the relay reencodes the messageusing the same codebook as in source119860 Otherwise the relaysimply keeps silent

212 Alamouti Scheme Refer to Figure 2 Transmitters 1 and2 send signals simultaneously toward destination119863 The link

A B120583 v

R

Figure 1 Illustration of DF

h1D

h2D

D

1

2

Figure 2 Alamouti scheme

gain between transmitter 119894 isin 1 2 and destination 119863 is ℎ119894119863

The channelrsquos input-output relationship is characterized as

119910 [119898] = ℎ1119863 [119898] 1199091 [119898] + ℎ

2119863 [119898] 1199092 [119898] + 119908 [119898] (2)

where 119909119894[119898] denotes the transmitted signal by transmitter 119894

119910[119898] denotes the received signal at destination 119863 and 119908[119898]

denotes the thermal noise at destination119863 all at time slot119898In the Alamouti scheme [23] the two transmitters intend

to send two complex symbols1199061and1199062 respectively over two

consecutive symbol slots During slot 1 transmitter 1 sends 1199061

and transmitter 2 sends 1199062 namely 119909

1[1] = 119906

1 1199092[1] = 119906

2

During slot 2 transmitter 1 sendsminus119906lowast2and transmitter 2 sends

119906lowast

1 namely 119909

1[2] = minus119906

lowast

2 1199092[2] = 119906

lowast

1 If we assume that

the channel gain remains constant over these two consecutivesymbol times namely ℎ

1119863[1] = ℎ

1119863[2] ≜ ℎ

1 ℎ2119863

[1] =

ℎ2119863

[2] ≜ ℎ2 then we have two consecutive received signals

as

119910 [1] = ℎ11199061+ ℎ21199062+ 119908 [1]

119910 [2] = minusℎ1119906lowast

2+ ℎ2119906lowast

1+ 119908 [2]

(3)

Rewriting it into matrix form and performing the conju-gation operation on the lower half matrix we obtain

(

119910 [1]

119910 [2]lowast) = (

ℎ1

ℎ2

ℎlowast

2minusℎlowast

1

)(

1199061

1199062

) + (

119908 [1]

119908 [2]lowast) (4)

We observe that the two columns of the square matrix in(4) are orthogonal Hence the detection problem for 119906

1 1199062

decomposes into two separate orthogonal scalar problems

Remark Throughout this paper we use 119909lowast to denote the

conjugate of the complex number 119909 and 119867dagger to denote the

conjugate transpose of the complex matrix119867

22 System Model Refer to Figure 3 There are two subsys-tems One is the traditional cellular system and the otheris the D2D system Node 119878 communicates with node 119863

via 119861119878 as a relay which composes the traditional cellularsystem The users that are in a small circle form the D2Dcommunication group due to their closeness to each othernamely the communication within this group is one hop

The D2D group may help the source relay its transmittedsignal to the destination which provides another branch of


S

D2D group

D2D group

D2Dgroup

Communication line

Base stationBS

D


h1DhS1

hS2h2D

S D

1

2









119894(119898) be



BS D2DSlot 1 119906

11199062


2119906lowast

1


119910119894 (119898) = ℎ

119878119894radic119875119878119909119878 (119898) + 119908

119894 (119898)

119910119863 (119898) =

2

sum

119894=1

ℎ119894119863radic119875119894119909119894 (119898) + 119908

119863 (119898)

(5)

subject to Var119909119878(119898) le 119875

119878and Var119909

119894(119898) le 119875

119894for 119894 = 1 2

and 119908119894(119898) 119908

119863(119898) sim CN(0 119899)


119909119894 (119898) = 119909

119878 (119898) (6)


= 1198752

= 120581119875119878 Define signal-to-








119877119878 (ℎ) = log

2(1 + Γ

119863 (ℎ)) (7)













1and minus119906

lowast

2




BS D2DSlot 1 119906

1minus119906lowast

2

Slot 2 1199062

119906lowast

1


1and 119906

2in the block) For




119906119894119898

≜ 119909119894 (119898) = 119909

119878 (119898) (8)









119910119863 (1) = radic120581119875

119878(ℎ1119863

11990611

+ ℎ2119863

(minus119906lowast

22)) + 119908

119863 (1)

119910119863 (2) = radic120581119875

119878(ℎ1119863

11990612

+ ℎ2119863

(119906lowast

21)) + 119908

119863 (2)

(9)


(

119910119863 (1)

119910lowast

119863(2)

) = 119867radic120581119875119878(

119909119878 (1)

119909lowast

119878(2)

) + 119908119863 (10)

where

119867 ≜ (

ℎ1119863

minusℎ2119863

ℎlowast

2119863ℎlowast

1119863

)

119908119863≜ (

119908119863 (1)

119908lowast

2(2)

)

(11)


119867+(

119910119863 (1)

119910lowast

119863(2)

) = 119867+119867radic120581119875

119878(

119909119878 (1)

119909lowast

119878(2)

) + 119867dagger119908119863 (12)


|2+ |ℎ2119863

|2


ΓMADF119863

(ℎ) = Γ119863(Φ1 Φ2)

= (Φ1

1003816100381610038161003816ℎ11198631003816100381610038161003816

2+ Φ2

1003816100381610038161003816ℎ21198631003816100381610038161003816

2) 120581Γ

(13)

where for 119894 = 1 2

Φ119894≜


0 otherwise(14)





119863(1 0) = 120581|ℎ

1119863|2Γ


1119863|2+ |ℎ2119863

|2)120581Γ which



















is

U119892

119894lowast = 120572119892

119894lowast119901119892

119894lowast + 120573119892

119894lowast min (120591

1

1 120591

1

1198991

1205912

1 120591

2

1198992

) (15)

where 119901119892




119894lowast and 120573

119892





119892

119894lowast ≜

min(12059111 120591

1

1198991

1205912

1 120591

2

1198992


U119892

119894= 120573119892

119894min (120591

1

1 120591

1

1198991

1205912

1 120591

2

1198992

) 119894 = 119894lowast (16)


Uℎ

119895= 120573ℎ

119895min (120591

1

1 120591

1

1198991

1205912

1 120591

2

1198992

) ℎ = 119892 (17)


U119892=

119899119892

sum

119894=1

U119892

119894=

119899119892

sum

119894=1

120573119892

119894120591119892

119894lowast + 120572119892

119894lowast119901119892

119894lowast (18)


Uℎ=

119899ℎ

sum

119894=1

Uℎ

119894=

119899ℎ

sum

119894=1

120573ℎ

119894120591119892

119894lowast (19)





119892


119892

119894lowast = 120591 On one



119898119892

119894lowast user119898119892



119899119892

119894=1120573119892

119894120591 + 120572

119892

119894lowast119901119892

119894lowast where

120572119892

119894lowast119901119892


119899119892

119894=1120573119892

119894120591



119899119892

119894=1120573119892


min1205911 1205912 120591

119897 sim exp(Σ

119897120582119894) where 120591

119894sim exp(120582

119894) Therefore



119866

119892=1sum119899119892

119894=1120582119892

119894minus sum119899119892

119894=1120582119892

119894with

minusU119892 ≜ (cup119866

119896=1U119896) U119892


int

120591

119904=0

119899119892

sum

119894=1

120573119892


+ int

infin

119904=120591

(

119899119892

sum

119894=1

120573119892

119894120591 + 120572119892

119894lowast119901119892


=sum119899119892

119894=1120573119892

119894

120582minusU119892

+ (120572119892

119894lowast119901119892

119894lowast minus

sum119899119892

119894=1120573119892

119894

120582minusU119892

)119890minus120582minusU119892120591

(20)


Thus if 120572119892119894119901119892

119894= sum119899119892

119894=1120573119892



120582U =1

119866 minus 1

119866

sum

119892=1

119899119892

sum

119896=1

sum119899119892

119894=1120573119892

119894

120572119892

119896119901119892

119896


119894=1120573119892

119894

120572119892

119894119901119892

119894

(21)







119899119892

sum

119894=1

120582119892

119894= 120582U119892 (22)


119894rsquos


119894= 120582U119892119899119892 for all 119894 isin U119892

5 Conclusion




Acknowledgments



References




































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




S

D2D group

D2D group

D2Dgroup

Communication line

Base stationBS

D


h1DhS1

hS2h2D

S D

1

2









119894(119898) be



BS D2DSlot 1 119906

11199062


2119906lowast

1


119910119894 (119898) = ℎ

119878119894radic119875119878119909119878 (119898) + 119908

119894 (119898)

119910119863 (119898) =

2

sum

119894=1

ℎ119894119863radic119875119894119909119894 (119898) + 119908

119863 (119898)

(5)

subject to Var119909119878(119898) le 119875

119878and Var119909

119894(119898) le 119875

119894for 119894 = 1 2

and 119908119894(119898) 119908

119863(119898) sim CN(0 119899)


119909119894 (119898) = 119909

119878 (119898) (6)


= 1198752

= 120581119875119878 Define signal-to-








119877119878 (ℎ) = log

2(1 + Γ

119863 (ℎ)) (7)













1and minus119906

lowast

2




BS D2DSlot 1 119906

1minus119906lowast

2

Slot 2 1199062

119906lowast

1


1and 119906

2in the block) For




119906119894119898

≜ 119909119894 (119898) = 119909

119878 (119898) (8)









119910119863 (1) = radic120581119875

119878(ℎ1119863

11990611

+ ℎ2119863

(minus119906lowast

22)) + 119908

119863 (1)

119910119863 (2) = radic120581119875

119878(ℎ1119863

11990612

+ ℎ2119863

(119906lowast

21)) + 119908

119863 (2)

(9)


(

119910119863 (1)

119910lowast

119863(2)

) = 119867radic120581119875119878(

119909119878 (1)

119909lowast

119878(2)

) + 119908119863 (10)

where

119867 ≜ (

ℎ1119863

minusℎ2119863

ℎlowast

2119863ℎlowast

1119863

)

119908119863≜ (

119908119863 (1)

119908lowast

2(2)

)

(11)


119867+(

119910119863 (1)

119910lowast

119863(2)

) = 119867+119867radic120581119875

119878(

119909119878 (1)

119909lowast

119878(2)

) + 119867dagger119908119863 (12)


|2+ |ℎ2119863

|2


ΓMADF119863

(ℎ) = Γ119863(Φ1 Φ2)

= (Φ1

1003816100381610038161003816ℎ11198631003816100381610038161003816

2+ Φ2

1003816100381610038161003816ℎ21198631003816100381610038161003816

2) 120581Γ

(13)

where for 119894 = 1 2

Φ119894≜


0 otherwise(14)





119863(1 0) = 120581|ℎ

1119863|2Γ


1119863|2+ |ℎ2119863

|2)120581Γ which



















is

U119892

119894lowast = 120572119892

119894lowast119901119892

119894lowast + 120573119892

119894lowast min (120591

1

1 120591

1

1198991

1205912

1 120591

2

1198992

) (15)

where 119901119892




119894lowast and 120573

119892





119892

119894lowast ≜

min(12059111 120591

1

1198991

1205912

1 120591

2

1198992


U119892

119894= 120573119892

119894min (120591

1

1 120591

1

1198991

1205912

1 120591

2

1198992

) 119894 = 119894lowast (16)


Uℎ

119895= 120573ℎ

119895min (120591

1

1 120591

1

1198991

1205912

1 120591

2

1198992

) ℎ = 119892 (17)


U119892=

119899119892

sum

119894=1

U119892

119894=

119899119892

sum

119894=1

120573119892

119894120591119892

119894lowast + 120572119892

119894lowast119901119892

119894lowast (18)


Uℎ=

119899ℎ

sum

119894=1

Uℎ

119894=

119899ℎ

sum

119894=1

120573ℎ

119894120591119892

119894lowast (19)





119892


119892

119894lowast = 120591 On one



119898119892

119894lowast user119898119892



119899119892

119894=1120573119892

119894120591 + 120572

119892

119894lowast119901119892

119894lowast where

120572119892

119894lowast119901119892


119899119892

119894=1120573119892

119894120591



119899119892

119894=1120573119892


min1205911 1205912 120591

119897 sim exp(Σ

119897120582119894) where 120591

119894sim exp(120582

119894) Therefore



119866

119892=1sum119899119892

119894=1120582119892

119894minus sum119899119892

119894=1120582119892

119894with

minusU119892 ≜ (cup119866

119896=1U119896) U119892


int

120591

119904=0

119899119892

sum

119894=1

120573119892


+ int

infin

119904=120591

(

119899119892

sum

119894=1

120573119892

119894120591 + 120572119892

119894lowast119901119892


=sum119899119892

119894=1120573119892

119894

120582minusU119892

+ (120572119892

119894lowast119901119892

119894lowast minus

sum119899119892

119894=1120573119892

119894

120582minusU119892

)119890minus120582minusU119892120591

(20)


Thus if 120572119892119894119901119892

119894= sum119899119892

119894=1120573119892



120582U =1

119866 minus 1

119866

sum

119892=1

119899119892

sum

119896=1

sum119899119892

119894=1120573119892

119894

120572119892

119896119901119892

119896


119894=1120573119892

119894

120572119892

119894119901119892

119894

(21)







119899119892

sum

119894=1

120582119892

119894= 120582U119892 (22)


119894rsquos


119894= 120582U119892119899119892 for all 119894 isin U119892

5 Conclusion




Acknowledgments



References




































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





BS D2DSlot 1 119906

1minus119906lowast

2

Slot 2 1199062

119906lowast

1


1and 119906

2in the block) For




119906119894119898

≜ 119909119894 (119898) = 119909

119878 (119898) (8)









119910119863 (1) = radic120581119875

119878(ℎ1119863

11990611

+ ℎ2119863

(minus119906lowast

22)) + 119908

119863 (1)

119910119863 (2) = radic120581119875

119878(ℎ1119863

11990612

+ ℎ2119863

(119906lowast

21)) + 119908

119863 (2)

(9)


(

119910119863 (1)

119910lowast

119863(2)

) = 119867radic120581119875119878(

119909119878 (1)

119909lowast

119878(2)

) + 119908119863 (10)

where

119867 ≜ (

ℎ1119863

minusℎ2119863

ℎlowast

2119863ℎlowast

1119863

)

119908119863≜ (

119908119863 (1)

119908lowast

2(2)

)

(11)


119867+(

119910119863 (1)

119910lowast

119863(2)

) = 119867+119867radic120581119875

119878(

119909119878 (1)

119909lowast

119878(2)

) + 119867dagger119908119863 (12)


|2+ |ℎ2119863

|2


ΓMADF119863

(ℎ) = Γ119863(Φ1 Φ2)

= (Φ1

1003816100381610038161003816ℎ11198631003816100381610038161003816

2+ Φ2

1003816100381610038161003816ℎ21198631003816100381610038161003816

2) 120581Γ

(13)

where for 119894 = 1 2

Φ119894≜


0 otherwise(14)





119863(1 0) = 120581|ℎ

1119863|2Γ


1119863|2+ |ℎ2119863

|2)120581Γ which



















is

U119892

119894lowast = 120572119892

119894lowast119901119892

119894lowast + 120573119892

119894lowast min (120591

1

1 120591

1

1198991

1205912

1 120591

2

1198992

) (15)

where 119901119892




119894lowast and 120573

119892





119892

119894lowast ≜

min(12059111 120591

1

1198991

1205912

1 120591

2

1198992


U119892

119894= 120573119892

119894min (120591

1

1 120591

1

1198991

1205912

1 120591

2

1198992

) 119894 = 119894lowast (16)


Uℎ

119895= 120573ℎ

119895min (120591

1

1 120591

1

1198991

1205912

1 120591

2

1198992

) ℎ = 119892 (17)


U119892=

119899119892

sum

119894=1

U119892

119894=

119899119892

sum

119894=1

120573119892

119894120591119892

119894lowast + 120572119892

119894lowast119901119892

119894lowast (18)


Uℎ=

119899ℎ

sum

119894=1

Uℎ

119894=

119899ℎ

sum

119894=1

120573ℎ

119894120591119892

119894lowast (19)





119892


119892

119894lowast = 120591 On one



119898119892

119894lowast user119898119892



119899119892

119894=1120573119892

119894120591 + 120572

119892

119894lowast119901119892

119894lowast where

120572119892

119894lowast119901119892


119899119892

119894=1120573119892

119894120591



119899119892

119894=1120573119892


min1205911 1205912 120591

119897 sim exp(Σ

119897120582119894) where 120591

119894sim exp(120582

119894) Therefore



119866

119892=1sum119899119892

119894=1120582119892

119894minus sum119899119892

119894=1120582119892

119894with

minusU119892 ≜ (cup119866

119896=1U119896) U119892


int

120591

119904=0

119899119892

sum

119894=1

120573119892


+ int

infin

119904=120591

(

119899119892

sum

119894=1

120573119892

119894120591 + 120572119892

119894lowast119901119892


=sum119899119892

119894=1120573119892

119894

120582minusU119892

+ (120572119892

119894lowast119901119892

119894lowast minus

sum119899119892

119894=1120573119892

119894

120582minusU119892

)119890minus120582minusU119892120591

(20)


Thus if 120572119892119894119901119892

119894= sum119899119892

119894=1120573119892



120582U =1

119866 minus 1

119866

sum

119892=1

119899119892

sum

119896=1

sum119899119892

119894=1120573119892

119894

120572119892

119896119901119892

119896


119894=1120573119892

119894

120572119892

119894119901119892

119894

(21)







119899119892

sum

119894=1

120582119892

119894= 120582U119892 (22)


119894rsquos


119894= 120582U119892119899119892 for all 119894 isin U119892

5 Conclusion




Acknowledgments



References




































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in















is

U119892

119894lowast = 120572119892

119894lowast119901119892

119894lowast + 120573119892

119894lowast min (120591

1

1 120591

1

1198991

1205912

1 120591

2

1198992

) (15)

where 119901119892




119894lowast and 120573

119892





119892

119894lowast ≜

min(12059111 120591

1

1198991

1205912

1 120591

2

1198992


U119892

119894= 120573119892

119894min (120591

1

1 120591

1

1198991

1205912

1 120591

2

1198992

) 119894 = 119894lowast (16)


Uℎ

119895= 120573ℎ

119895min (120591

1

1 120591

1

1198991

1205912

1 120591

2

1198992

) ℎ = 119892 (17)


U119892=

119899119892

sum

119894=1

U119892

119894=

119899119892

sum

119894=1

120573119892

119894120591119892

119894lowast + 120572119892

119894lowast119901119892

119894lowast (18)


Uℎ=

119899ℎ

sum

119894=1

Uℎ

119894=

119899ℎ

sum

119894=1

120573ℎ

119894120591119892

119894lowast (19)





119892


119892

119894lowast = 120591 On one



119898119892

119894lowast user119898119892



119899119892

119894=1120573119892

119894120591 + 120572

119892

119894lowast119901119892

119894lowast where

120572119892

119894lowast119901119892


119899119892

119894=1120573119892

119894120591



119899119892

119894=1120573119892


min1205911 1205912 120591

119897 sim exp(Σ

119897120582119894) where 120591

119894sim exp(120582

119894) Therefore



119866

119892=1sum119899119892

119894=1120582119892

119894minus sum119899119892

119894=1120582119892

119894with

minusU119892 ≜ (cup119866

119896=1U119896) U119892


int

120591

119904=0

119899119892

sum

119894=1

120573119892


+ int

infin

119904=120591

(

119899119892

sum

119894=1

120573119892

119894120591 + 120572119892

119894lowast119901119892


=sum119899119892

119894=1120573119892

119894

120582minusU119892

+ (120572119892

119894lowast119901119892

119894lowast minus

sum119899119892

119894=1120573119892

119894

120582minusU119892

)119890minus120582minusU119892120591

(20)


Thus if 120572119892119894119901119892

119894= sum119899119892

119894=1120573119892



120582U =1

119866 minus 1

119866

sum

119892=1

119899119892

sum

119896=1

sum119899119892

119894=1120573119892

119894

120572119892

119896119901119892

119896


119894=1120573119892

119894

120572119892

119894119901119892

119894

(21)







119899119892

sum

119894=1

120582119892

119894= 120582U119892 (22)


119894rsquos


119894= 120582U119892119899119892 for all 119894 isin U119892

5 Conclusion




Acknowledgments



References




































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Thus if 120572119892119894119901119892

119894= sum119899119892

119894=1120573119892



120582U =1

119866 minus 1

119866

sum

119892=1

119899119892

sum

119896=1

sum119899119892

119894=1120573119892

119894

120572119892

119896119901119892

119896


119894=1120573119892

119894

120572119892

119894119901119892

119894

(21)







119899119892

sum

119894=1

120582119892

119894= 120582U119892 (22)


119894rsquos


119894= 120582U119892119899119892 for all 119894 isin U119892

5 Conclusion




Acknowledgments



References




































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in

























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Documents

Research Article Incorporating D2D to Current Cellular Communication Systemdownloads.hindawi.com/journals/misy/2016/2732917.pdf · 2019-07-30 · Research Article Incorporating D2D