A Performance Analysis Framework for … Heterogeneous Metropolitan Networks Based on Cross-Layer Design MarthaHernándezOchoa,1 MarioSiller,1 JohnWoods,2 andHectorAlejandroDuran-Limon3

Research ArticleA Performance Analysis Framework forWiFiWiMAX Heterogeneous MetropolitanNetworks Based on Cross-Layer Design

Martha Hernaacutendez Ochoa1 Mario Siller1

John Woods2 and Hector Alejandro Duran-Limon3

1 CINVESTAV Unidad Guadalajara Avenida del Bosque 1145 Col el bajıo 45019 Zapopan JAL Mexico2University of Essex Wivenhoe Park Colchester CO4 3SQ UK3 Information Systems Department CUCEA University of Guadalajara Periferico Norte No 799 Nucleo Belenes45100 Zapopan Jalisco Mexico

Correspondence should be addressed to Martha Hernandez Ochoa mhernandegdlcinvestavmx

Received 22 August 2013 Revised 30 November 2013 Accepted 14 December 2013 Published 3 March 2014

Academic Editor Jianhua He

Copyright copy 2014 Martha Hernandez Ochoa et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

The communication between network nodes within different protocol domains is often regarded simply as a black box withunknown configuration conditions in the path We address network heterogeneity using a white box approach and focus on itsinterconnection processes To achieve this purpose a Performance Analysis Framework (PAF) is proposed which is composed ofthe formalization of the latter using process algebra (PA) and the corresponding teletraffic performancemodels In this contributionwe target the IEEE 80216 and IEEE 80211 protocols For the teletraffic models we extend previous models for such scenario withthe inclusion of the following protocol operational parameters (metrics) bit error rate (BER) packet error ratio (PER) and packetlength (pl) From the framework teletraffic models the optimal packet length (OPL) end to end throughput delay and packetloss are obtained The PAF outperforms previous modeling solutions in terms of delay and throughput relative to NS3 simulationresults

1 Introduction

Recently the numbers of users and the quantity of infor-mation in heterogeneous networks have grown rapidly inmetropolitan areas The interconnection between nodeswithin different protocol domains is often regarded simplyas a black box with unknown configuration conditions inthe path With increased demand it has become necessaryto analyze and develop new models to understand theperformance of heterogeneous metropolitan area networks(HMAN) There are a number of factors that decrease thetransmission efficiency between networks such as (1) delay(2) jitter (3) medium access protocols (4) packet loss ratio(5) packet length (pl) (6) bandwidth (7) bit error rate (BER)and (8) packet error ratio (PER) These factors are key mea-sures reflecting the network performance but consideration

must also be given to scalability interoperability and securityto achieve the best network performance HMAN can beconsidered as a Machine-to-Machine (M2M) heterogeneousnetwork The process of autonomously communicating twoelectronic systems (ie without human intervention) suchas machines devices and actuators is called M2M com-munication M2M communicationrsquos characteristics are largenumber of heterogeneous nodes a gateway low power andlow cost [1ndash4] An M2M network is composed of five keyelements as defined by the European TelecommunicationsStandards Institute (ETSI) [3] (1) theM2Mcomponents (egelectrical devices smart nodes etc) (2) the M2M gatewaywhich is responsible for the connection among the devicesand the connection of the M2M communication network(3) the M2M applications which work as a middleware layerto pass data through various application services and are

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2014 Article ID 750971 16 pageshttpdxdoiorg1011552014750971

2 International Journal of Distributed Sensor Networks

(1) Identify the network heterogeneity This includesall the involved communication protocols acrossthe available communication paths and domainsUse an end to end communication perspective

(2) Define the metrics to models(3) Survey available teletraffic models for the

identified communication protocols from each domain(4) Extend and adapt the previous models according

to the network design and correspondingperformance metrics for each communicationprotocol or network domain Use the CLD approach

(5) Identify the gateway nodes and the correspondinginterconnection tasks defined in the protocolspecification and network design Base thisidentification process on the roles established on Section 41

(6) Derive the interconnection teletraffic modelsfor the gateway nodes

(7) Based on the processes defined in Section 41integrate all the involved teletraffic models acrossthe communication paths under an end to end perspective

(8) Validate the end to end performance modelsusing test bed implementations or network simulationImprove teletraffic models if necessary

Box 1 White box approach

used by specific business processing engines (4) the M2Marea network which enables connectivity between M2Mcomponents and M2M gateways and (5) the M2M commu-nication network (network domain) that provides connectionbetween M2M gateway(s) and M2M application(s) Alsothe M2M communication requires operational stability andsustainability [5]

The 80216 protocol supports M2M applications in the80216p version [5] This protocol enables a range of M2Mapplications in which the communication device requireswide-area wireless coverage in licensed bands and is auto-mated rather than human initiated or human-controlledThis is for purposes such as observation and control Therequirements that 80216 is intended to address includelow power consumption a large number of devices short-burst transmissions and device tampering detection andreporting The 80216 protocol acts as an aggregation pointfor 80216M2M devices and supports peer to peer (P2P)connectivity between these devices [5 8]

The 80211 protocol in the version of IEEE80211ah stan-dard has been found as an optimal candidate for M2Mcommunication in wireless communication systems Thisprotocol considers sensing applications and will addressrequired functions such as low power consumption largenumber of devices long-range and short-burst data transmis-sions [9]

The 80216 and 80211 protocols can be part of an M2Mnetwork whereM2Mdevices (communication enabled) forman M2M area network This M2M area network is based onthe IEEE80211 protocol whilst the access network that con-nects theM2Mgateway (nodeswith two interfaces 80211 and80216) to theM2Mcore (eg the 3rdGeneration Partnership

Project (3GPP) Initiative for mobile communication tech-nologies) is based on the IEEE80216 protocol In the M2Mservice platform the M2M gateway is connected to the M2Mmanagement server (through the communication network)whereby theM2Mapplications (smartmetering smart trans-port healthcare database etc) are reached [3]

Most network performance models consider only thehomogeneous specification (common part) of the protocolsthat build the network rather than also including the differ-ences among them We believe that end to end performanceanalysis of heterogeneous networks should consider (i) thedetailed specification (physical (PHY) and media accesscontrol (MAC) layers) and operational parameters of eachprotocol (BER PER and pl etc) and (ii) the interconnectionprocess that makes the heterogeneous network possibleMost research focuses on homogeneous behavior [10ndash17]therefore new and novel approaches are required to exploreheterogeneous network performance specifically based onthe IEEE80216 and IEEE80211 protocolsWe define a hetero-geneous network as interconnected networks with differentsoftware protocols hardware operational speed technologyand so forth but yet still capable of interoperability Weaddress network heterogeneity using white box approachand focus on its interconnection processes Box 1 For thispurpose a Performance Analysis Framework (PAF) is pro-posed which is composed of the formalization of the latterusing process algebra (PA) and the corresponding teletrafficperformance models In this contribution we target theIEEE80216 and IEEE80211 protocols

The main contribution of this paper is the evaluation ofend to end throughput and delay in a HMAN by consideringthe effect of different layers based on CLD (layer 2 and layer

International Journal of Distributed Sensor Networks 3

1 of OSI model) For this purpose a PAF is proposed AWiFiWiMAX HMAN is used as a case study The proposedPAF consists of the following key elements

(i) The first element is formalization of the end to endcommunication process of a HMAN using PA

(ii) The second element is teletraffic performancemodelsWe derived end to end performance models forheterogeneous environments which take into con-sideration the interconnection process of differentprotocol domain networks bit error rate packet errorratio and packet length In our proposed modelswe consider realistic error-prone channel conditionswhich have not been considered in previous relatedworks

The paper is structured as follows Section 2 presents therelated work In Section 3 we present the theoretical back-ground of the IEEE80211 and IEEE80216 protocolsThe PAF(the formalization of the end to end communication processof a HMAN using PA and teletraffic performance models)is presented in Section 4 In Section 5 the experimentalwork is presented The simulation results and discussions arepresented in Section 6 Finally some conclusions and futurework are drawn up in Section 7

2 Related Work

In this section we present a review of some relevant relatedwork The review is divided into two categories homoge-neous and heterogeneous approaches

21 Homogeneous Approaches Thehomogeneous approachesreviewed are described below

Bianchirsquos analytical model [10] is used to estimate thethroughput of an IEEE80211 network using the DistributedCoordination Function (DCF) under saturated conditionsThis assumes (i) any transmission queue that always has pack-ets to be sent (ii) an ideal channel and (iii) a finite numberof stations The model considers two DCF techniques basicand RTSCTS (request to sendclear to send) The approachadopted is to analyze a single stationmodeled using aMarkovChain The results demonstrate that better performance isachieved when the RTSCTS mechanism is used

Duffy et al in [11] present an extension of BianchirsquosmodelThey consider on-saturated network conditionsThey assumea perfect PHY layer so transmission errors are caused onlyby collisions and do not occur due to noise on the mediumThe analysis is focused on the throughput collision proba-bility delay total offered load and (the optimal) minimumcontention window They employ three load types Poissonconditional and uniform

In [12] Lin and Wongrsquos model (IEEE80211n) addresses aunidirectional and bidirectional RTSCTS access mechanismin the presence of collisions and channel errors in the systemThis model which is an extension of Bianchirsquos model con-siders BER probability minimum contention window lengthand a maximum back-off stage Their model also includes

the MAC Protocol Data Unit Aggregation (A-MPDU) andMAC Service Data Unit Aggregation (A-MSDU) techniquesto improve the MAC protocol performance Simulation andanalytical results are presented for throughput and delayThisis done for a different number of aggregation MPDUs andBER conditions

Hwang et al present in [13] a teletraffic mathemat-ical analysis for the delay of bandwidth requests basedon unicast multicast and broadcast IEEE80216de polling inIEEE80216de under error-freeerror-pronewireless channelconditions They derived the distribution for delays andthe truncated binary exponential back-off (adopted as acontention resolution) by means of analytical methods Theauthors study bandwidth efficiency and the utilization oftransmission opportunity which is defined as a ratio of suc-cessful transmission opportunities and total transmissionopportunities within a frame Based on numerical analysisthey obtained optimum values for parameters such as num-ber of transmission opportunities (or slots) the initial back-offwindow size andQuality of Service (QoS) requirement ondelay and loss

In [14] Tian et al propose a novel MAC scheme used forthe DCF named Scheduled RandomAccess protocol (SRAP)This scheme is dived in two parts schedule and contentionFor the former the protocol allows a throughput close to thetransmission capacity in a saturate case while for the lattera low delay is observed in low traffic load conditions Theanalysis of simulation results showed that SRAP can improvethe throughput with low delay The throughput analysis isbased on a teletrafficmodel and they state that SRAP achievesthroughput close to the theoretical upper bound

In [15] Calı et al develop as an analytical model forthe throughput a 119901-persistent IEEE80211 protocol whichdiffers from the standard protocol in terms of the selection ofthe back-off interval The standard protocol uses the binaryexponential back-off while in the 119901-persistent case the back-off is sampled from a geometric distributionwith a parameter119901 Also they demonstrated that (i) the standard protocolcan operate very far from the theoretical throughput limitdepending on the network conditions and (ii) the IEEE80211protocol is close to the theoretical throughput limit whenthe 119901-persistent (geometric distribution) back-off algorithmis employed

In [16] Liu et al proposed a scheduling algorithm basedon Cross-Layer Design (CLD) between the MAC layer andPHY layer Each connection employs adaptive modulationand coding (AMC) and considers the QoS requirementsThealgorithm operational parameters are derived from a series ofteletraffic models which consider performance metrics suchas bandwidth efficiency throughput delay PER and Signalto Noise Ratio (SNR) Simulations were implemented for theIEEE80216 standard

Chang et al in [17] analyze throughput using the Markovmodel of Vinel et al using different window sizes andSubscriber Station (SS) numbers The SS employs a pollingMAC instead of random access control based on the uplinksubframe of a (Worldwide Interoperability for MicrowaveAccess) WiMAX Network


22HeterogeneousApproaches Theheterogeneous approach-es reviewed are described below

In [18] El-Azouzi et al study an HMAN formed usingthe IEEE80211 and IEEE80216 protocols The aim is tostudy how to integrate different technologies cooperating toprovide universal connectivity and opportunity for the bestsuited services to users at anytime from anywhere This isenvisioned as a common scenario for fourth generation (4G)networks They believe that the integration of IEEE80211and IEEE80216 is one likely solution for distribution ofhigh data rate services for next generation wireless networks(NGWN)They study the stability of the nodes which extendthe WiMAX cell in particular gateway nodes The gatewaynodes have two interfaces IEEE80211 and IEEE80216 Theydevelop a CLD mathematical model for the throughput anddelay and assume stable conditions in the queues It considerslayers 2 and 3 In the latter two queues are employedforwarding and high layer traffic queues The Weighted FairQueueing (WFQ) [19] is used as the scheduling mechanismunder an assumption of saturation From the model theyconclude that WiMAX parameters do not impact the perfor-mance in terms of throughput of pure ad hoc nodes and viceversa We believe that the approach followed by the authorsfits well formodeling the integration of different technologiesallowing combining strengths and making up individuallimitationsThe solution from [18] has been applied in severalworks as follows (i) for studying stability-throughput trade-off in wireless ad hoc networks in [20] (ii) for performanceanalysis of delay throughput and energy consumption usinga comprehensive analytical model of the IEEE80211 [21] and(iii) for end to end delay performance analysis in wireless adhoc networks under CLD as presented in [22] In this paperthe work from [18] is referred to as the reference model

Yang et al in [23] consider an 80211 wireless local areanetwork (WLAN) which shares a common set of multiradiodevices with another network named CO-NETWORKwhichuses WiMAX They assume saturated network conditionsfor all WLAN radios They study how the throughput of aWLAN can be affected by scheduling the CO-NETWORKBased on teletrafficmodeling they show that this issue can beminimized using proposed scheduling optimization criteriafor the CO-NETWORK

A convergence-bridge is proposed in [24] It unifies theWiFiWiMAX Frequency Bands In other words by modi-fying the WiFi Orthogonal frequency-division multiplexing(OFDM) PHY layer WiFi devices are enabled to join theWiMAX-OFDM wireless network The convergence-bridgeis a thin layer in the WiFi OFDM PHY layer with 64carriers The WiMAX OFDM is fixed with 256 carriers Themain proposal for the convergence-bridge is to use multiplecarriers which fit both technologies

Different aspects of the interconnection process for bothhomogeneous and heterogeneous networks have been stud-ied in the literature There are many challenges to overcomebefore there is widespread adoption of heterogeneous tech-nologies of this kind into MAN scenarios [25] (eg embed-ded system anddevices) OPL andBER forWiFiWiMAX stillrequire further analysisThis is the focus of this work in termsof teletraffic modeling

Table 1 Three PHY layers specified by the IEEE80211 standard [6]

PHY Slot time CWmin CWmaxim

Frequency hopping spreadspectrum (FHSS) 50 120583s 16 1024

Direct sequence spreadspectrum (DSSS) 20 120583s 32 1024

Infrared (IR) 8 120583s 64 1024

3 IEEE80216 and IEEE80216 ProtocolsTheoretical Background

31 Overview of IEEE80216

MAC Layer We focused only on Time Division Duplexing(TDD) which is divided into two transmission periodsdownlink (DL) and uplink (UP) The DL is generally broad-cast TDD handles a duplex scheme where DL and UPtransmissions occur in different times but share the samefrequency The maximum transition time (round trip time)between transmitter and receiver is 2 120583s The TDD is builtfrom the base station (BS) and SS transmissions [7]

PHY Layer The physical layer is based on wireless MAN-OFDM interface according to the standard IEEE80216-2004[7] This interface uses 256 subcarriers of which 192 aredata subcarriers 8 are pilot subcarriers and 56 are null Thepilot subcarriers are used to minimize frequency and phaseshift The 56 null carriers are used for guard bands and DCfrequencies


MAC LayerThe DCF is employed in this research The DCFis the fundamental mechanism to access the medium basedon carrier sense multiple accesses with collision avoidance(CSMACA) The DCF employs a binary exponential back-off scheme When a station wants to transmit a new packetit monitors the channel activity If the channel is idle for aperiod equal to the distributed interframe space (DIFS) thestation transmits the packet On the other hand if the channelis busy (either during or immediately after the DIFS) thestation continues tomonitor the channel until it is sensed idlefor the DIFS

The station generates a random back-off interval beforeit transmits the packet After an idle DIFS a time slot isavailable and a station is allowed to transmit only at thestart of each time The time slot depends on the PHY layer(see Table 1) The back-off time is chosen in the interval 0to 119882-1 in each packet transmission The value 119882 repre-sents the contention window (CW) that is the amount oftime available for the slots [26] In the first attempt the 119882

is equal to CWmin (minimum CW) after each unsuccessfultransmission the 119882 is doubled subject to a maximum ofCWmaxim (maximum CW) CWmaxim = 2maxCWmin maxis the maximum backoff stage The values of CWmin andCWmaxim are shown in Table 1 The back-off time counter


decreases when the channel is sensed as being idle but stopswhen there is a transmission in the channel

The attempt rate is defined in [10] as the probability thata station transmits in a randomly chosen slot time

PHY Layer The PHY layer employed in this research isthe IEEE80211g protocol This protocol was finalized untilJune 2003 80211g is a relative late-comer to the wirelessmarketplace Despite the late start 80211g is now the defacto standard wireless networking protocol This standardis used on most laptops and handheld devices The 80211gprotocol uses the same industrial scientific and medical(ISM) frequency range as the 80211b protocol

This physical layer is based onDSSS according to the IEEEStandard 80211 [6] This PHY operates in the 24GHz ISMband and at a maximum raw data rate of 54Mbits (withusable throughput of about 22Mbps) Also this physical layercan consider OFDMmodulationThis makes it incompatiblewith 80211b and the higher frequency means shorter rangecompared to 80211bg at the same power

The frequency range is 2400ndash2495GHz which is usedby the 80211b and 80211g radio standards (correspondingto wavelengths of about 125 cm) A single 80211g link mayuse 54Mbps radios but it will only provide up to 22Mbps ofactual throughputThe remaining bandwidth is the overheadthat the radios need in order to coordinate their signals usingthe 80211g protocol

Since the 80211g wireless equipment is half duplex (ie itonly transmits or receives never both at once) the requiredthroughput must be doubled accordingly for a total of10Mbps The wireless links must provide that capacity everysecond or conversations will lag

4 The HMAN Performance AnalysisFramework (PAF)

In this section we propose the PAF which addresses thetransmission performance in an HMAN and is composedby (i) the formalization of the end to end communicationprocess of an HMAN using PA and (ii) teletraffic perfor-mance models In (i) PA is used to formally define thecommunication between the homogeneous (single protocoldomain) and the heterogeneous (multiprotocol domain) net-work sections whilst in (ii) several teletraffic performancemodels are defined and represent the networkrsquos behavioracross the transmission pathThe PAF is a general frameworkfor HMAN which will be deeply described on the followingsubsections based a case study for IEEE80211 and IEEE80216heterogeneous networks The PAF is depicted in Figure 1

41 The Formalization of the HMANModel Description

General Strategy The end to end communication process ofan HMAN can be modeled by PAThis formalism representsa mathematically rigorous framework for modelling systemprocesses

We define a HMAN as a septuple Φ = 119878 119879 rarr

119904 119889 119894 119873(119894) where 119878 = 119878dom 1 119878dom 2

119878119892 is a finite set whose

elements are the total number of nodes 119878dom 1and 119878dom 2

are a finite set whose elements can be any HMAN protocoland are defined as 119878dom 1

= 1198731 119873

2 119873

119909 119909 isin N and

119878dom 2= 119873

1 119873

2 119873

119910 119910 isin N respectively 119878

119892is a finite set

whose elements are gateway nodes which have two interfacesand is defined as 119878

119892= 119878dom 1

cap 119878dom 2= 119873

1 119873

2 119873

119911

119911 isin N 119904 is the traffic source which generates the packetsIn other words a node can have any of the following threeroles (1) source (transmitter) (2) destination (receiver) and(3) intermediate node which could also be a gateway

119879 = 120572119896 120572 is the transition label set the packet which

is sent from source to destination is labeled as 120572 while inthe opposite direction it is labeled as 120572

119901119896 The transition

relation is represented by rarr The destination is symbolizedby 119889 whilst 119894 is an intermediate node on path 119877

119904119889and 119873(119894)

is a finite set whose elements are the neighbors of node119894 |119878| = 119899 is the total number of nodes Each node hastwo queues the 119865⟨119890

1 119890bumax⟩ forwarding queue which

carries the packets from other nodes to their respectivedestinations and the 119876⟨119890

1 119890bumax⟩ queue that manages

the local node packets The sequence of packets in the bufferis represented by ⟨119890

1 119890bumax⟩ and bumax symbolizes its

maximum sizeThe local buffer can have any of the followingthree states (1) empty119876

120595⟨120576⟩ (2) full119876

120595⟨1198901 119890bumax⟩ and

(3) 119876120595

⟨1198901 119890

119896⟩ where (0 lt 119896 lt bumax)

Figure 2 shows the process graph that models the end toend communication flows in an HMAN The reception andtransmission flows set are represented by (120572

1 120572

120595) and

(1205721 120572

120595) respectively A nonsourcenode is symbolized as

119873120595 where 1 le 120595 lt 119899 A source node is represented as 119873 The

HMAN end to end communication process (CP) is definedas follows

CP1198902119890

def= sum 119873 sdot 119873

120595 1 le 120595 lt 119899 (1)

All plausible processes in the network can be representedusing the derivation tree graph from Figure 2

Any communication process 11987312057211205721

997888997888997888rarr sdot sdot sdot120572120595120572120595

997888997888997888997888rarr 119873120595where

(1205721sdot1205721 120572

120595sdot120572120595

119873120595) is a derivation of119873 and120572

1sdot1205721 120572

120595sdot

120572120595is a communication-sequence of so that 119873

120595is a 120572

1sdot

1205721 120572

120595sdot 120572

120595-derivative of 119873

When a packet is transmitted the source awaits anacknowledgment from the receiver This acknowledgementpacket is symbolized as 120585 when it leaves the receiver and as120585 when it reaches the source

The transmission process from the source is defined as

119873def= sum

119901119896isinPK1205721

sdot 1205851

sdot 119876 ⟨1198901 119890

119896minus1⟩ (2)

where PK is the packet set to be sent in the end to endcommunication process and 0 lt 119896 le bumax

The receiving process at the destination node is definedas

119873120595

def= 120572

120595(119901119896) sdot 120585

120595 (3)

where 120595 = 119899 minus 1


The PAF

Formalization of the end toend communication process

of a HMAN

Teletraffic performancemodels

A HMAN

Heterogeneouspart (80216 and80211 protocol)

Common part of80211 protocol

Figure 1 The PAF

N1205721

1205722

12057231205721 1205723

1205722

1205851

1205852

120585312058511205852

1205853

B

N1

N2

N3

Nnminus1

Figure 2 Process Graph

The communication process for any intermediate node isdefined as

119873120595

def= 120572

120595(119901119896) sdot 120585

120595sdot 119865

120595⟨1198901 119890

119896⟩ sdot 119873

120595

+ 120572120595+1

sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 119873

120595+1

+ 120572120595+1

sdot 120585120595+1

sdot 119876120595

⟨1198901 119890

119896minus1⟩ sdot 119873

120595+1

(4)

where 1 le 120595 lt 119899 and 0 lt 119896 le bumaxThe bridging process for a gateway node is defined as

119873120595

def= 120572

120595(119901119896) sdot 120585

120595sdot 119865

120595⟨1198901 119890

119896⟩ sdot 119873

120595

+ 120572120595+1

sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 119873

120595+1

(5)

where 1 le 120595 lt 119899 and 0 lt 119896 le bumaxAggregation occurs at bridge node when two or more

source packets are embedded into a single forwarding packet

This depends on the packet size source protocol and the for-warding payload size protocol This aggregation process isdefined as follows

119865120595

⟨1198901 119890

119896⟩

def= sum

119894isin119870

119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1(1198901 119890

119896) sdot 120585

120595+1sdot 119873

120595+1

(6)

where (0 lt 119896 lt bumax) and it represents the number ofembedded source packets that can fit into the forwardingpayload

The defined PA defines all the processes and entitiesinvolved in any HMAN A second aspect which is addressedby the PAF is the network behavior This is discussed next

42 Network Behavior Modeling

Methodology Teletraffic theory is considered as a tool tomodel and analyze the HMAN behavior We propose whitebox approach modeling methodology


43 Case StudyThe 80211 and 80216 HMAN Wemodel theend to end communication process for the HMAN study caseby PA as follows

CP1198902119890

def= sum 120572

1sdot 1205851

sdot 119876 ⟨1198901 119890

119896minus1⟩ sdot 120572

120595(119901119896)

sdot 120585120595

sdot 119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 120572

120595(119901119896) sdot 120585

120595

sdot sum119894isin119870

119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1(1198901 119890

119896)

sdot 120585120595+1

sdot 120572120595

(119901119896) sdot 120585120595

(7)

The previous equation (7) is derived from (1) (2) (3) (4) (5)and (6)

The teletraffic performance models are derived from anHMAN based on the IEEE80211 and IEEE80216 standardsconsidered as 119878dom 1

and 119878dom 2 respectively The PAF tele-

traffic performance models for the case study are related to(i) Bianchirsquos performance model for IEEE80211 DCF [10](ii) Lin and Wongrsquos analytical model which represents theperformance under unidirectional and bidirectional datatransfer 80211 [12] (iii) Fakhri et alrsquos mathematical modelwhich studies throughput optimization for OFDM modula-tion in a 80216 network [27] and (iv) Ci and Sharif rsquos modelfor an adaptive optimal frame length predictor for IEEE80211[28]

We extend the reference model with the inclusion ofthe following protocol operational parameters (metrics) biterror rate (BER) packet error ratio (PER) and packet length(pl) Thus our HMAN model considers BER PER and pltherefore we get end to end throughput and delay undererror-prone channel conditions

The CLD from [18] considers both network and MACparametersThe network layer handles two queues scheduledusing a WFQ scheme [19] we modify the CLD modelfrom [18] We now conceive that the WFQ is between thenetwork layer and the MAC Layer This is done in order toreduce network bandwidth usage Each node has the samenetwork layer andWFQThis design permits the exchange ofcommunication and information between layers and allowsgreater flexibility The queue controls two queues high layerpackets (hlp) and forward packets (fp) which have an infinitecapacity The fp is the forwarding queue which carries thepackets from other nodes to their destinations and the hlpwhich contains packets generated by node 119894 itself Each queuehas its own transmitted probability fp

119894is the probability to

transmit from fp whereas 1 minus fp119894is the probability to transmit

from hlpTheHMAN is considered a saturated systemwhichmeans that each node always transmits packets from hlpwhile fp could be empty The CLD for HMAN is shown inFigure 3

431 Mathematical Model for IEEE80216 Themathematicalmodel for IEEE80216 is based on Fakhri et alrsquos model [27]This model is focused on the optimization of throughputBER and OPL in a wireless system for OFDM modulation

Network layer

WFQ MACPHYWiMAX

WiFihlpfp

Figure 3 CLD for HMANModel

There are some assumptions made when developing thismathematical model The transmitter sends packets of 119871dom 2

bits in a continuous stream and the transmitter attaches a 119862

bit as the CRC The throughput is defined as the number ofpayload bits per second received correctly [27] (8)

119879dom 2=

119873

sum119897=1

119875dom 2 load119871dom 2

119877119897119891 (120574

119897) (8)

119875dom 2 load = 119871dom 2minus119874bytes 119871dom 2

is the total pl (bits) 119874bytes =

119867MAC + 119878FSH + 119862 119867MAC is the average MAC header size119878FSH is the fragmentation subheader size 119862 is the CRC bit119877119897is the symbol rate assigned to the subcarriers 119897 in bits per

second119891(120574119897) is the packet success rate (PSR) per user with119898-

Quadrature Amplitude Modulation (QAM) scheme and 120574119897is

the SNR in dB given by (9)

120574119897

=119875119897

1198730

lowast 119877119897

(9)

where 119875119897is the received power in watts 119873

0is the one-sided

noise power spectral density in wattsHzA symbol error in the packet automatically results in a

packet loss and the PSR is given in terms of symbol error rate(SER) 119875

119890by

119891 (120574119897) = (1 minus 119875

119890(120574))

119871dom 2119887 (10)

where 119887 is the number of bits per 119898-QAM symbol In (11) the119875119890of 119898-QAM in and additive white Gaussian noise (AWGN)

channel is (approximately) given by [29]

119875119890

(120574) = 4 (1 minus1

21198872) 119876 (119909) (11)

where 119909 = radic(3(2119887 minus 1))120574 and the 119876(119909) function is definedas

119876 (119909) =119890minus11990922

4mod+

1

2mod

mod minus1sum119895=1

exp(minus1199092

2sin2120579119895

) (12)

where 120579119895

= 1198951205872mod and mod is the modulation type

432 Mathematical Model for IEEE80211 In our researchwe consider the PER which is determined from the BERTheBER is defined as the number of bit errors divided by the totalnumber of bits transferred in a time interval and the pl [12]The PER is denoted by 119901

119890whilst the BER is 119875BER The PER is

defined as

119901119890

= 1 minus (1 minus 119875BER)119871119886 (13)


where 119871dom 1is WiFi pl in bits which includes the PHY

layer header (PHYH) the MAC layer header (MACH) andthe packet payload Let 120591dom 1 be the duration of WiFi slot(sec)The payload information (bits per second) is defined in

119875dom 1 load =119871dom 1

minus 119867total120591dom 1

(14)

where

119867total = (PHYH + MACH) (15)

The PHY layer header and MAC layer header are defined in[6]

433 HMAN End to EndThroughput Model The expressionfor throughput in [18] is

thp119904119861

= (119910119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891 lceil120591119898

119894119861

119871dom 1

119871dom 2

rceil 120601 ( 120574119894)

+119910119904119875119904119889

[1

120593119904

] )

minus1

(16)

where 119910119904

= 1 minus 120587119904119891119904is a value of a N-dimensional

row vector which contains stability values per node 120593 isthe transmission probability as defined in [10] 119873(119894) is thenumber ofWiFi neighbors and |(119894 119861)| represents the numberof intermediate nodes 119904 and 119861 which represents the basestation The throughput is defined as the payload (bits) persecond received successfully and is measured in packets persecond In (16) the dividend is the average service timeper packet at node 119894 Within the dividend 120587

119894represents the

probability that 119865119894has at least one packet to be forwarded

in the beginning of the start of each cycle (in [18] a cycle isreferred to as total number of slots to transmit one packetuntil itrsquos successful or dropped) 120587

119894119904119889is the probability that

119865119894has a packet ready in the first position of the queue to be

forwarded to path 119877119904119889

in the beginning of each cycle 120601( 120574119894) =

(1 minus 119890minus120574119894)119871dom 2119887 is the function of PSR 120591119898

119894119861= 119871dom 2

120588119898119894119861

is theWiMAX packet transmission time (sec) 120588

119898

119894119861= sum

119897isinL119894

120574119898

119894119861119897Δ119891

is the aggregation transmission rate (bps) when nodes use an119898-QAM modulation level 120574119898

119894119861119897Δ119891is the transmit rate (bits

per subcarrier) Δ119891is the bandwidth of one single subcarrier

119870 ismaximumnumber of transmissions allowed by a gateway119894 per packet for all paths and 119875

119904119889is the probability that a

node 119904 generates and transmits a packet to node 119889 Someassumptions are considered from [18] as follws (i) in theuplink transmission all nodes have the same destiny thus119875119904119861

= 1 (ii) the heterogeneous network is a symmetricmesh system hence each node has the same number ofWiFineighbors and (iii) the forwarding probability is 119891

119894equiv 119891 and

120593119894

equiv 120593

The throughput of the HMAN model is based on [1227 28] However they address only homogeneous networksIn our proposed model (see (17)) we introduce the PERas dividend and consider the heterogeneity of the network(80211 and 80216) The end to end throughput under error-prone channel conditions is then estimated as follows

thpHMAN119904119861

= (119884119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891119901119894

times lceil120591119898

119894119861

119871dom 1

(1 minus 119901119890) 119871dom 2

rceil 119891 (120574119897)

+119884119904

[1

120593119904

] )

minus1

(17)

where119891(120574119897) = (1 minus 119875

119890(120574))

119871dom 2119887 (13) and119901119890is taken from (13)

Now using (14) the throughput of the HMAN model isrewritten as follows

thpHMAN119904119861

= (119884119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891119901119894

times [[[

119873

sum119895=1

119875dom 2 load119871dom 2

119875dom 1 load120588119898119894119861

(1 minus 119901119890)

]]]

times119891 (120574119897) + 119884

119904[

1

120593119904

])

minus1

(18)

434 HMAN End to End Throughput Optimization Weemployed a variable change in the throughput equation (18)in order to differentiate this equation with respect to packetlength 119907 ℎ 119911(119871dom 1

119871dom 2) and 119906 The thpHMAN

119904119861is then

defined as follows

thpHMAN119904119861

=V

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906

(19)

where V = 119884119904(1 minus 120593)

119899 ℎ = 120587119894119904119889

119891(120593119894)minus1 119911(119871dom 1

119871dom 2) =

120587119892119904119889

119891119901119894119879lceil119875dom 1 load120588119898

119892119861(1 minus 119901

119890)rceil 119906 = 119884

119904[1120593

119904] and 119879 =

sum119873

119895=1(119875dom 2 load119871dom 2

)119891(120574119895)


435 Optimal WiMAX Packet Length We get the optimalWiMAXpl119871dom 2

by differentiating (19)with respect to119871dom 2

and using (8) (9) and (10) produces

119889thpHMAN119904119861

119889119871dom 2

= minusV [1199111015840 (119871dom 1

119871dom 2)]

[sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]2

(20)

where

119911 (119871dom 1 119871dom 2

)

= 120587119892119904119889

119891119901119894

119873

sum119895=1

119871dom 2minus 119874bytes

119871dom 2

times (1 minus 119875119890

(120574119895))

119871dom 2119887lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

(21)

The derivative of 119911(119871dom 1 119871dom 2

) is calculated with respectto 119871dom 2

as

119889119911 (119871dom 1 119871dom 2

)

119889119871dom 2

= 120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]

(22)

Setting this to zero produces an equation in 119871dom 2

minusV [1199111015840 (119871dom 1

119871dom 2)]

[sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

)]2

= 0

minus (V[120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]])

times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

)]

]

2

)

minus1

= 0

V[120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]] = 0

119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887= 0

(23)

We adopt the notation 119871dom 2= 119871lowastdom 2

for the optimalWiMAX pl that satisfies (23) then solving for 119871dom 2

119871lowast

dom 2

=119874bytes

2+

radic119874bytes2 minus (4119887119874bytes ln (1 minus 119875

119890(120574)))

2

(24)

Thus in a WiMAX system the OPL 119871dom 2depends on the

SNR per symbol 120574 symbol error probability 119875119890 and the

constellation size 2119887

436 Optimal Ad Hoc Packet Length We differentiate (18)with 119871dom 1

(using (13) and (14)) and set it to zero to obtainthe following condition

119889thpHMAN119904119861

119889119871dom 1

= minus (V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861

) (1 minus 119875BER)minus119871dom 1

times [1 minus ln (1 minus 119875BER) (119871dom 1minus 119867total)] )

times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]

]

2

)

minus1

(25)

Next we set the derivative to zero

(V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861



times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]

]

2

)

minus1

= 0


minus200

0

200

400

600

8000 500 1000 1500 2000

Figure 4 PyViz illustration on NS3

V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861


times [1 minus ln (1 minus 119875BER) (119871dom 1minus 119867total)] = 0

1 minus ln (1 minus 119875BER) (119871dom 1minus 119867total) = 0

(26)



119871lowast

dom 1= 119867total +

11003816100381610038161003816ln (1 minus 119875BER)

1003816100381610038161003816 (27)

Therefore in anWiFi system the OPL 119871dom 1depends on the

BER 119875BER

437 End to End Delay The mean end to end delay 119863119904119889

ofa packet on the path 119877

119904119889is the mean time taken from the

instant that a packet reaches the MAC layer of the source tothe time that is received in secondsThat delay time is for bothsuccessful and dropped packets The expression for delay isthe same as in [18]

119863119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882119901119905

119894+ 120591

succ119894119904119889

) (28)

where 119882119901119905

119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus 119891

119894)119891

119894))(1 minus thp

119904119861(120591119865119894

minus 120591119876

119894((1 minus

119891119894)119891

119894))) is the average waiting time in the forwarding queue

119865119894of a 119901119905 (WiMAX or WiFi protocols) arrival packet at node

119894 120591119865119894

= sum119904119889

(120587119894119904119889

120587119894)119879

119894119904119889represents the mean service time

of 119865119894 120591

119876

119894= sum

119889120593119894119879119894119894119889

is the average service time of 119876119894 and

the mean residual time of a packet for a (119904 119889) connection is119877119901119905

119894= sum

119904119889120587119894119904119889

119891119894119877119901119905

119894119904119889+ sum

119889119875119894119889

(1 minus 120587119894119891119894)119877

119901119905

119894119894119889 where

119877119901119905

119894119904119889=

119879(2)

119894119904119861

2119879119894119904119861

minus1

2 if 119894 isin 119878

119892and 119889 = 119861

119879(2)

119894119904119889

2119879119894119904119889

+1

2 otherwise

(29)

The second moment of 119879(2)

119894119904119861service time is given by

119879(2)

119894119904119861=

Ψ(2)

119894119904119889lceil

120591119898119894119861

120591119886rceil

2

if 119894 isin 119878119892and 119889 = 119861

Ψ(2)

119894119904119889+ Ψ

119894119904119889(1 minus 120593

119894)

1205932119894

otherwise

(30)

as 120591succ119894119904119889

is the mean service time of a successfully transmittedpacket on the same path 119877

119904119889 119901119905 is used for WiFi or WiMAX

120591succ119894119904119889

which has the same form as 120591119894119904119889

can be expressed asfollows

120591succ119894119904119889

=Ψsucc119894119904119889

120593119894

(31)

whereΨsucc119894119904119889

= sum119896119894119904119889

119896=1119896(1 minus 119875

119894119904119889)119896minus1

119875119894119904119889

is the average numberof attempts until it reaches a successful point

The delay of the HMAN Model is derived using (18) asfollows

119863HMAN119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882HMAN119901119905

119894+ 120591

succ119894119904119889

) (32)

Based on 119882119901119905

119894 the HMAN average waiting time in the

forwarding queue 119865119894is 119882HMAN119901119905

119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus

119891119901119894)119891

119901119894))(1 minus thpHMAN

119904119861(120591119865119894

minus 120591119876

119894((1 minus 119891119901

119894)119891

119901119894))) The

rest of the variables from (32) are defined above

5 The Experimental Work

BothWiMAX andWiFi networks are used in the simulationsThe objective is to evaluate the proposed HMAN modelagainst the reference model [18]The simulation experimentsare described as follows

The experimental work was carried out on the ns3 net-work simulator [30] The simulation scenario shown inFigure 4 is set for an M2M heterogeneous network of 9 SS ofwhich 5 are WiFi nodes 2 are gateways (multiple interfacesWiFi and WiMAX) and 2 are WiMAX nodes There is abase station (BS) WiMAX and each node has an ID from1 to 9 node IDs are sorted as follows 2 to 6 are the WiFinodes 8 and 9 are WiMAX nodes and 1 and 7 are thegateways node (IEEE80211 and IEEE80216) The nodes aredistributed based on Table 2 IEEE80211 PHY uses Direct-Sequence Spread Spectrum (DSSS) [12] IEEE80211 MAC


Common partof 80216 protocol



Flow a 6-5-1-B-9Flow b 4-2-7-B-8Flow c 3-5-1-B-9

Figure 5 HMAN topology

Table 2 Nodes coordinates

Node ID 1 2 3 4 5 6 7 8 9 B119883 (m) 190 160 60 0 135 0 230 2300 1400 1000119884 (m) 10 80 60 80 0 30 60 10 60 30

was used as the MAC protocol Some characteristics of themodel were based on IEEE80211 and IEEE80216 standardsThe simulation time was 500 s and the number of transmittedpackets was 500 (based on the central limit theorem)

We consider a Constant Speed Propagation Delay Modeland a Friss Propagation Loss Model which correspond wellto our Model The Friss propagation Loss Model considers afrequency of 55 GHz at 300 000 kms Optimized Link StateRouting (OLSR) [31] was used for instantaneous updates foreach routing table

There are three data flows a b and c shown in Figure 5Node 4 is considered as the source for all data flows Thedestination nodes are node 9 for flow a node 8 for flow b andnode 9 for flow c Nodes 9 and 8 are configured with Quadra-ture Phase Shift Keying (QPSK)modulationWe develop twoscenarios in which both have the same simulation parameters(from Section 51) In scenario (1) we configured gateway 1with one subcarrier and QPSK modulation (see Table 4) andgateway 7 with one subcarrier and 16-QAM (see Table 4) and

the cross-traffic average for flow b at gateway 7 was 475reception (Rx) and 525 transmission (Tx) In scenario (2)we configured gateway 1 with one subcarrier and 16-QAMmodulation (see Table 4) and gateway 7 with one subcarrierand QPSK modulation (see Table 4) the cross-traffic averagefor flow b at gateway 7 was 16 Rx and 265 Tx A totalof 12 subscenarios were conducted each with different plThe pl ranged from 100 to 1200 bytes with (increments)Δpl = 100 bytes Figure 4 shows the NS3 Python Visualizer(PyViz) representation of the HMAN topology from Figure 5(Cartesian plane)

The HMAN network topology is depicted in Figure 5

51 Simulation Parameters Some simulation parameters aresummarized in Tables 3 4 5 and 6The following parametersare used in both scenarios

Table 4 shows the spectral efficiencies (rate) usingIEEE80216 adaptive coding andmodulation (ACM) settings

6 Simulation Results and Discussions

To validate the HMAN Model we compare the obtainedresults with those obtained by the solution from [18] Weanalyzed the following metrics PSR end to end throughputend to end delay BER and OPL The main goal for theanalysis is to compare the HMAN performance against


010203040506070809

19

9535

102

475

104

108

105

2310

608

110

676

310

713

310

782

108

145

108

622

108

9610

916

6

PSR

SNR (dB)Flow a

010203040506070809

1

963

629

511

961

299

6354

951

819

7605

960

839

7273

972

629

9852

977

849

7103

PSR

SNR (dB)Flow b

010203040506070809

1

995

3510

247

510

410

810

523

106

081

106

763

107

333

107

8210

824

510

862

210

896

109

266

PSR

SNR (dB)Flow c

(a)

010203040506070809

1

873

188

8638

883

948

9012

900

648

998

898

519

0024

900

639

0196

901

968

9033

PSR

SNR (dB)

010203040506070809

19

3193

917

159

2438

920

59

2084

941

759

3481

940

59

3887

939

819

4537

938

33

PSR

SNR (dB)

010203040506070809

1

873

18

882

74

893

2

900

33

897

16

878

16

891

03

901

38

897

79

901

96

909

76

899

33

PSR

SNR (dB)Flow a Flow b Flow c

(b)

Figure 6 (a) QPSK PSR versus SNR in connection a (scenario 1) b (scenario 2) and c (scenario 1) respectively (b) 16-QAM PSR versus SNRin connection a (scenario 2) b (scenario 1) and c (scenario 2) respectively

Table 3 Simulation parameters

Parameter ValueSimulator NS-3-devSimulation length 500 sTransmission start 06 sPHYWiMAX layer OFDMPHYWiFi layer DSSSMACWiFi layer CSMACACode division multiplexing (CDMA) codes 256120591dom 2 and 120591dom 1 2msBandwidth 10MHzAutomatic repeat reQuest (ARQ) Selective Repeat

Table 4 ACM settings for IEEE80216 [7]

Modulationorder

TargetSINR (db)

Codingorder

Spectral efficiency(bitssymbol)

BPSK 64 12 05

QPSK 94 12 1

QPSK 112 34 15

16-QAM 164 12 2

16-QAM 182 34 3

64-QAM 223 23 4

64-QAM 244 34 45

Single carrierBPSK

16-QAM64-QAM

Symbol error rate (pe)

Pack

et su

cces

s rat

e

099

098

097

096

095

094

093

092

091

090 01 02 03 04 05 06 07 08 09 1

1

times10minus4

Figure 7 PSR versus SER

the solution from [18] and to verify that the HMAN modelagrees with the NS3 simulation

61 Packet Success Ratio (PSR) PSR was analyzed for rangedpl mentioned above in 12 subscenarios corresponding toscenarios 1 and 2 Figure 6(a) shows PSR versus SNR usingQPSK for flows a b and c Flows a and c employ the scenario1 configuration whilst flow b uses the scenario 2 Figure 6(b)shows PSR versus SNR using 16-QAM modulation resultsfor flows a b and c Flows a and c employ the scenario 2configuration whilst flow b uses the scenario 1 configuration


0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01

011

012

Packet length (bytes)

Nor

mal

ized

thro

ughp

ut

Reference modelHMAN modelNS3 simulation results

(a)

0 200 400 600 800 1000 1200006

0065

007

0075

008

0085

009

0095

01

0105


Nor

mal

ized

thro

ughp

ut


(b)

0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01


Nor

mal

ized

thro

ughp

ut


(c)

Figure 8 End to end throughput versus pl (bytes) in connections (a) (b) and (c) respectively

The SNR values are derived from the obtained PSR using120601( 120574

119894) = (1 minus 119890minus120574119894)

119871119887 and solving it for 120574119894(employing a

single subcarrier) It is observed from Figure 6(a) that whenthe same modulation scheme (equal baud rate) is employedfor both the source and destination nodes the PSR is higherthan the PSR using a different scheme as shown in Figure 6(b)(different baud rate) It is also observed that as the plincreases the SNR is changed

62 BER The BER and SER values are obtained from (10)(11) and (12) using the PSR simulation results Table 7

Table 5 Attempt rate probability (for each node 119894)

1198751 1198752 1198753 1198754 1198755 1198756 1198757 1198758 1198759

05 07 04 03 07 04 0 0 0

presents the average values for the 12 subscenarios corre-sponding to scenarios 1 and 2 We observed that when thesame modulation scheme is employed for both WiFi andWiMAX domains the BER value is lower than the BER valueusing a different scheme


0 200 400 600 800 1000 12000

10

20

30

40

50

60

70D

elay

(ms)

Absolute errorReference modelHMAN model

NS3 simulation results


(a)

0 200 400 600 800 1000 12000

20

40

60

80

100

Del

ay (m

s)




(b)

0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

Del

ay (m

s)




(c)

Figure 9 End to end delay (ms) versus pl (bytes) in connections (a) (b) and (c) respectively

Table 6 IEEE80216 MAC headers [7]

Header SizeGeneral mac header (GMH) 6 bytesGrant manager subheader (GMSH) 2 bytesPacking subheader (PSH) 3 bytesFragmentation subheader (FSH) 2 bytesCyclic redundancy check (CRC) 4 bytes

Table 7 BER values

Scenario Flow SER BER1 a c 13119890 minus 5 65119890 minus 6

1 b 186119890 minus 4 47119890 minus 5

2 a c 4119890 minus 4 95119890 minus 5

2 b 915119890 minus 5 46119890 minus 5

63 Symbol Error Rate (SER) Two important metrics for anHMAN end to end performance analysis are the PSR andSER In the case of the WiMAX domain these metrics are

derived from (10) (11) and (12) Figure 7 shows the PSRand SER relation under different modulation schemes It isobserved that as the number of bits increases per symbolfor a given SER value the PSR decreases significantly Notethat the corresponding BER and SER simulation result values(Table 7) are shown within the BER range of Figure 7

64 End to EndThroughput End to end throughput was ana-lyzed for both scenarios in an error-prone channel with dif-ferent BER values fromTable 7 for CSMACAwith RTSCTSFigure 8 shows the throughput versus variable pl results forflows a and c using scenario 2whilst flowbused scenario 1 Asshown in Table 7 the chosen BER values are representative ofthe protocols under test and have been selected to evaluate themodels under diverse network conditions Reference model[18] andHMANmodel results are obtained from (10) and (9)respectively

From the above experimental results we calculated themean square error (MSE) for both models in each communi-cation flow We can observe in Figure 8 that the throughputobtained by the HMAN model is 1146 more accurate inall the flows than the throughput obtained by the reference


Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

135

130

125

120

115

110

105

10001 015 02 025 03 035 04 045 05 055 06

(a)

Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

295

290

285

280

275

270

001

00102

00104

00106

00108

0011

00112

00114

00116

00118

0012

(b)

Figure 10 OPL versus PER in connection (a) and (b)

model Also the results of HMAN are closer to the results ofNS3 as can be seen in Figure 8

65 End to End Delay End to end delay was analyzed in bothscenarios Figure 9 shows end to end delay versus variable plin flows a b and c From Figure 9 it is predictably observedthat the delay increases as the pl is increased The averageabsolute error (AAE) is obtained between the HMANmodeland NS3 simulation results The AAE is 414 for flow a439 for flow c and 875 for flow c (100ndash1200 bytes)Flow b employs scenario 1 whilst flows a and c employscenario 2We consider an error-prone channel with the BERvalues of Table 7 in both scenarios It is observed that theHMAN model and reference model are smooth by contrastthe NS3 simulation results are undulating This is becauseNS3 is directly modeling the processing entities for examplenetwork interfacesTheHMANmodel outperforms previoussolutions in terms of delay and throughput relative to the NS3results and is largely indifferent to pl Reference model andthe HMAN model results are obtained from (28) and (32)respectively

From the above experimental results we calculated theMSE for both models in each flow communicationThe delayobtained by the HMAN model is 3421 more accurate inall the flows than the delay obtained by the reference modelAlso the results of HMAN are closer to the results of NS3 ascan be seen in Figure 9

66 OPL Efforts were made to find the OPL for bothscenarios there will be pl that maximizes the throughput inan error-prone channelWe used the PER obtained frombothscenarios as shown in Table 7 In Figure 10(a) it is observedthat for flow a from scenario 2 the OPL is 135 bytes for aPER of 01 and the OPL decreases as the PER is increasedFigure 10(b) shows flow b from scenario 1 where the OPL is

293 bytes for a PER of 001 Again the OPL decreases as thePER is increased These results are obtained from (16) (a) for119871lowast

dom 1and 17 for 119871lowastdom 2

(b)

7 Conclusions

We analyzed a heterogeneous network composed of aWiMAX cell and a WiFi network The WiMAX protocolshares many characteristics with cellular networks such asarchitectural support for billing mobility and QoS Themain contribution in this paper is the evaluation of endto end throughput and delay in a HMAN by consideringthe effect of different layers within the CLD (layer 2 andlayer 1 of OSI model) We extended previous models forsuch a scenario with the inclusion of the following protocoloperational parameters (metrics) BER PER pl and OPLFurther numerical and simulation results were performed tovalidate our HMAN model The HMAN model outperformsprevious modeling solutions in terms of delay and through-put relative to the NS3 results and is largely indifferent topl In a WiMAX system the OPL depends on the SNR persymbol error probability and the constellation size In aWiFi system the OPL depends on the BER By using ourHMAN expression we can compute the OPL for a given setof network conditions to improve network adaptability thiscould be applied dynamically The HMAN can be furtherextended to consider other network metrics such as jitterand frame segmentation and other protocols such as CANZigbee and Bluetooth The scenarios can also be applied to anumber of different modulation schemes and node densities

Conflict of Interests

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


References

[1] D Niyato L Xiao and PWang ldquoMachine-to-machine commu-nications for home energy management system in smart gridrdquoIEEE Communications Magazine vol 49 no 4 pp 53ndash59 2011

[2] Y Zhang R Yu S Xie W Yao Y Xiao and M GuizanildquoHome M2M networks architectures standards and QoSimprovementrdquo IEEE Communications Magazine vol 49 no 4pp 44ndash52 2011

[3] ETSI Etsi ts 102 690 v111 Machine-to-machine communica-tions (m2m) functional architecture 2011

[4] I Bojic G Jezic D Katusic S DesicM Kusek andDHuljenicldquoCommunication in machine-to-machine environmentsrdquo inProceedings of the 5th Balkan Conference in Informatics pp 283ndash286 ACM 2012

[5] J Kim J Lee J Kim and J Yun ldquoM2M service platforms sur-vey issues and enabling technologiesrdquo IEEE CommunicationsSurveys amp Tutorials 2013

[6] IEEE 80211 Standard for Information technology-Telecom-munications and information exchange between systems-Localand metropolitan area networks-Specific requirements Part 11Wireless LAN Medium Access Control (MAC) and PhysicalLayer (PHY) Specifications IEEE Computer Society Sponsoredby the LANMAN Standards Committee IEEE Standard 802112007

[7] IEEE Standard for Local and Metropolitan Area Networks Part16 Air Interface for Fixed Broadband Wireless Access SystemsIEEE Std 80216 2002

[8] K Chang A Soong M Tseng and Z Xiang ldquoGlobal wirelessmachine to machine standardizationrdquo IEEE Journals amp Maga-zines Internet Computing vol 15 no 2 pp 64ndash69 2011

[9] S Aust R V Prasad G M M Ignas and N NiemegeersldquoIEEE 80211ah advantages in standards and further challengesfor Sub 1 GHz Wi-Firdquo in Proceedings of the IEEE InternationalConference on Communications (ICC rsquo12) pp 6885ndash16889 2012

[10] G Bianchi ldquoPerformance analysis of the IEEE 80211 distributedcoordination functionrdquo IEEE Journal on Selected Areas inCommunications vol 18 no 3 pp 535ndash547 2000

[11] K Duffy D Malone and D J Leith ldquoModeling the 80211distributed coordination function in non-saturated conditionsrdquoIEEE Communications Letters vol 9 no 8 pp 715ndash717 2005

[12] Y Lin and V W S Wong ldquoFrame aggregation and optimalframe size adaptation for IEEE 80211nWLANsrdquo in Proceedingsof the Global Telecommunications Conference (IEEE GLOBE-COM rsquo06) pp 1ndash6 San Francisco Calif USA December 2006

[13] E Hwang K J Kim A Lyakhov and B D Choi ldquoPerformanceanalysis of bandwidth requests under unicast multicast andbroadcast pollings in IEEE 80216derdquo Telecommunication Sys-tems vol 50 pp 15ndash30 2012

[14] X Tian X Chen T Ideguchi and T Okuda ldquoImprovingprotocol capacity by scheduling random access on WLANsrdquoTelecommunication Systems vol 37 no 1-3 pp 19ndash28 2008

[15] F Calı M Conti and E Gregori ldquoDynamic tuning of theIEEE 80211 protocol to achieve a theoretical throughput limitrdquoIEEEACM Transactions on Networking vol 8 no 6 pp 785ndash799 2000

[16] Q Liu XWang and G B Giannakis ldquoA cross-layer schedulingalgorithm with QoS support in wireless networksrdquo IEEE Trans-actions onVehicular Technology vol 55 no 3 pp 839ndash847 2006

[17] B-J Chang C-M Chou and Y-H Liang ldquoMarkov chain anal-ysis of uplink subframe in polling-based WiMAX networksrdquoComputer Communications vol 31 no 10 pp 2381ndash2390 2008

[18] R El-Azouzi E Sabir S K Samanta R El-Khoury and E-H Bouyakhf ldquoAn end-to-end QoS framework for IEEE 80216and ad-hoc integrated networksrdquo in Proceedings of the 6thInternational Conference on Mobile Technology Application andSystems (Mobility rsquo09) ACM September 2009

[19] B Partridge Gigabit Networking Addison-Wesley Publishing1994

[20] A Kherani R El-Khoury R El-Azouzi and E AltmanldquoStability-throughput tradeoff and routing in multi-hop wire-less ad hoc networksrdquo Computer Networks vol 52 no 7 pp1365ndash1389 2008

[21] E Sabir R El-Azouzi and El-HoussinebouyakhfCross-LayeredQoS Framework for Next GenerationWireless Networks Univer-sitaires Europeennes (EUE) 2011

[22] R El-Azouzi E Sabir S K Samanta and R El-KhouryldquoAsymptotic delay analysis and timeout-based admission con-trol for ad hoc wireless networks with asymmetric usersrdquoComputer Communications vol 33 no 17 pp 2057ndash2069 2010

[23] X Yang J Zhu X Guo and TWang ldquoIntermittentWLAN andinteractions across heterogeneous wireless networksrdquo Telecom-munication Systems vol 43 no 1-2 pp 13ndash24 2010

[24] A Al-Sherbaz C Adams and S Jassim ldquoWiMAX-WiFi con-vergence with OFDM bridgerdquo in Mobile MultimediaImageProcessing Security and Applications S S Agaian and S AJassim Eds vol 7351 May 2009

[25] B Li Y Qin C P Low and C L Gwee ldquoA Survey on mobileWiMAX (Wireless broadband access)rdquo IEEE CommunicationsMagazine vol 45 no 12 pp 70ndash75 2007

[26] B A ForouzanData Communication andNetworking McGrawHill 3rd edition 2004

[27] Y Fakhri B Nsiri D Aboutajdine and L J Vidal ldquoThroughputoptimization Via the Packet length and transmission rate forwireless OFDM system in downlink transmissionrdquo Interna-tional Journal of Computer Science and Network Security B vol6 no 3 pp 41ndash46 2006

[28] S Ci andH Sharif ldquoAdaptive pptimal frame length predictor forIEEE 80211 wireless LANrdquo in Proceedings of the 6th IEE Interna-tional Symposium Digital Signal Processing for CommunicationSystems (IEE DSPCS rsquo02) Sydney Australia

[29] J G ProakisDigital Communications McGraw-Hill NewYorkNY USA 4th edition 2000

[30] ldquoThe ns-3 network simulatorrdquo ns-310 2011 httpwwwnsnamorg

[31] T Clausen and P Jacquet ldquoOptimized Link State Routing Pro-tocol (OLSR)rdquo Request for Comment 3626 Network WorkingGroup Project Hipercom INRIA 2003

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014


Shock and Vibration


Mechanical Engineering

Advances in


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of


Distributed Sensor Networks


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Active and Passive Electronic Components


Chemical EngineeringInternational Journal of

Control Scienceand Engineering

Journal of


Antennas andPropagation




Navigation and Observation


Advances inOptoElectronics


Volume 2014

RoboticsJournal of



(1) Identify the network heterogeneity This includesall the involved communication protocols acrossthe available communication paths and domainsUse an end to end communication perspective

(2) Define the metrics to models(3) Survey available teletraffic models for the

identified communication protocols from each domain(4) Extend and adapt the previous models according

to the network design and correspondingperformance metrics for each communicationprotocol or network domain Use the CLD approach

(5) Identify the gateway nodes and the correspondinginterconnection tasks defined in the protocolspecification and network design Base thisidentification process on the roles established on Section 41

(6) Derive the interconnection teletraffic modelsfor the gateway nodes

(7) Based on the processes defined in Section 41integrate all the involved teletraffic models acrossthe communication paths under an end to end perspective

(8) Validate the end to end performance modelsusing test bed implementations or network simulationImprove teletraffic models if necessary

Box 1 White box approach

used by specific business processing engines (4) the M2Marea network which enables connectivity between M2Mcomponents and M2M gateways and (5) the M2M commu-nication network (network domain) that provides connectionbetween M2M gateway(s) and M2M application(s) Alsothe M2M communication requires operational stability andsustainability [5]

The 80216 protocol supports M2M applications in the80216p version [5] This protocol enables a range of M2Mapplications in which the communication device requireswide-area wireless coverage in licensed bands and is auto-mated rather than human initiated or human-controlledThis is for purposes such as observation and control Therequirements that 80216 is intended to address includelow power consumption a large number of devices short-burst transmissions and device tampering detection andreporting The 80216 protocol acts as an aggregation pointfor 80216M2M devices and supports peer to peer (P2P)connectivity between these devices [5 8]

The 80211 protocol in the version of IEEE80211ah stan-dard has been found as an optimal candidate for M2Mcommunication in wireless communication systems Thisprotocol considers sensing applications and will addressrequired functions such as low power consumption largenumber of devices long-range and short-burst data transmis-sions [9]

The 80216 and 80211 protocols can be part of an M2Mnetwork whereM2Mdevices (communication enabled) forman M2M area network This M2M area network is based onthe IEEE80211 protocol whilst the access network that con-nects theM2Mgateway (nodeswith two interfaces 80211 and80216) to theM2Mcore (eg the 3rdGeneration Partnership

Project (3GPP) Initiative for mobile communication tech-nologies) is based on the IEEE80216 protocol In the M2Mservice platform the M2M gateway is connected to the M2Mmanagement server (through the communication network)whereby theM2Mapplications (smartmetering smart trans-port healthcare database etc) are reached [3]

Most network performance models consider only thehomogeneous specification (common part) of the protocolsthat build the network rather than also including the differ-ences among them We believe that end to end performanceanalysis of heterogeneous networks should consider (i) thedetailed specification (physical (PHY) and media accesscontrol (MAC) layers) and operational parameters of eachprotocol (BER PER and pl etc) and (ii) the interconnectionprocess that makes the heterogeneous network possibleMost research focuses on homogeneous behavior [10ndash17]therefore new and novel approaches are required to exploreheterogeneous network performance specifically based onthe IEEE80216 and IEEE80211 protocolsWe define a hetero-geneous network as interconnected networks with differentsoftware protocols hardware operational speed technologyand so forth but yet still capable of interoperability Weaddress network heterogeneity using white box approachand focus on its interconnection processes Box 1 For thispurpose a Performance Analysis Framework (PAF) is pro-posed which is composed of the formalization of the latterusing process algebra (PA) and the corresponding teletrafficperformance models In this contribution we target theIEEE80216 and IEEE80211 protocols

The main contribution of this paper is the evaluation ofend to end throughput and delay in a HMAN by consideringthe effect of different layers based on CLD (layer 2 and layer






2 Related Work






















Infrared (IR) 8 120583s 64 1024





















119904 119889 119894 119873(119894) where 119878 = 119878dom 1 119878dom 2




= 1198731 119873

2 119873

119909 119909 isin N and

119878dom 2= 119873

1 119873

2 119873




119892= 119878dom 1

cap 119878dom 2= 119873

1 119873

2 119873

119911






119904119889and 119873(119894)








120595⟨120576⟩ (2) full119876

120595⟨1198901 119890bumax⟩ and

(3) 119876120595

⟨1198901 119890

119896⟩ where (0 lt 119896 lt bumax)


1 120572

120595) and

(1205721 120572




CP1198902119890

def= sum 119873 sdot 119873

120595 1 le 120595 lt 119899 (1)




997888997888997888997888rarr 119873120595where

(1205721sdot1205721 120572

120595sdot120572120595


1sdot1205721 120572

120595sdot


120595is a 120572

1sdot

1205721 120572

120595sdot 120572




119873def= sum

119901119896isinPK1205721

sdot 1205851

sdot 119876 ⟨1198901 119890

119896minus1⟩ (2)



119873120595

def= 120572

120595(119901119896) sdot 120585

120595 (3)

where 120595 = 119899 minus 1


The PAF


of a HMAN


A HMAN



Figure 1 The PAF

N1205721

1205722

12057231205721 1205723

1205722

1205851

1205852

120585312058511205852

1205853

B

N1

N2

N3

Nnminus1



119873120595

def= 120572

120595(119901119896) sdot 120585

120595sdot 119865

120595⟨1198901 119890

119896⟩ sdot 119873

120595

+ 120572120595+1

sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 119873

120595+1

+ 120572120595+1

sdot 120585120595+1

sdot 119876120595

⟨1198901 119890

119896minus1⟩ sdot 119873

120595+1

(4)


119873120595

def= 120572

120595(119901119896) sdot 120585

120595sdot 119865

120595⟨1198901 119890

119896⟩ sdot 119873

120595

+ 120572120595+1

sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 119873

120595+1

(5)




119865120595

⟨1198901 119890

119896⟩

def= sum

119894isin119870

119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1(1198901 119890

119896) sdot 120585

120595+1sdot 119873

120595+1

(6)







CP1198902119890

def= sum 120572

1sdot 1205851

sdot 119876 ⟨1198901 119890

119896minus1⟩ sdot 120572

120595(119901119896)

sdot 120585120595

sdot 119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 120572

120595(119901119896) sdot 120585

120595


119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1(1198901 119890

119896)

sdot 120585120595+1

sdot 120572120595

(119901119896) sdot 120585120595

(7)











Network layer

WFQ MACPHYWiMAX

WiFihlpfp





119879dom 2=

119873

sum119897=1

119875dom 2 load119871dom 2

119877119897119891 (120574

119897) (8)







120574119897

=119875119897

1198730

lowast 119877119897

(9)


0is the one-sided



119890by

119891 (120574119897) = (1 minus 119875

119890(120574))

119871dom 2119887 (10)



119875119890

(120574) = 4 (1 minus1

21198872) 119876 (119909) (11)


119876 (119909) =119890minus11990922

4mod+

1

2mod


exp(minus1199092

2sin2120579119895

) (12)

where 120579119895




defined as

119901119890

= 1 minus (1 minus 119875BER)119871119886 (13)




119875dom 1 load =119871dom 1


(14)

where




thp119904119861

= (119910119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891 lceil120591119898

119894119861

119871dom 1

119871dom 2

rceil 120601 ( 120574119894)

+119910119904119875119904119889

[1

120593119904

] )

minus1

(16)

where 119910119904











119894119861= 119871dom 2

120588119898119894119861


119898

119894119861= sum

119897isinL119894

120574119898

119894119861119897Δ119891








119894equiv 119891 and

120593119894

equiv 120593


thpHMAN119904119861

= (119884119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891119901119894


119894119861

119871dom 1

(1 minus 119901119890) 119871dom 2

rceil 119891 (120574119897)

+119884119904

[1

120593119904

] )

minus1

(17)

where119891(120574119897) = (1 minus 119875

119890(120574))



thpHMAN119904119861

= (119884119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891119901119894

times [[[

119873

sum119895=1

119875dom 2 load119871dom 2

119875dom 1 load120588119898119894119861

(1 minus 119901119890)

]]]

times119891 (120574119897) + 119884

119904[

1

120593119904

])

minus1

(18)



119904119861is then

defined as follows

thpHMAN119904119861

=V

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906

(19)

where V = 119884119904(1 minus 120593)

119899 ℎ = 120587119894119904119889

119891(120593119894)minus1 119911(119871dom 1

119871dom 2) =

120587119892119904119889

119891119901119894119879lceil119875dom 1 load120588119898

119892119861(1 minus 119901

119890)rceil 119906 = 119884

119904[1120593

119904] and 119879 =

sum119873

119895=1(119875dom 2 load119871dom 2

)119891(120574119895)





119889thpHMAN119904119861

119889119871dom 2

= minusV [1199111015840 (119871dom 1

119871dom 2)]

[sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]2

(20)

where

119911 (119871dom 1 119871dom 2

)

= 120587119892119904119889

119891119901119894

119873

sum119895=1


119871dom 2

times (1 minus 119875119890

(120574119895))

119871dom 2119887lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

(21)



as

119889119911 (119871dom 1 119871dom 2

)

119889119871dom 2

= 120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]

(22)


minusV [1199111015840 (119871dom 1

119871dom 2)]

[sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

)]2

= 0

minus (V[120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]])

times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

)]

]

2

)

minus1

= 0

V[120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]] = 0

119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887= 0

(23)



119871lowast

dom 2

=119874bytes

2+


119890(120574)))

2

(24)






119889thpHMAN119904119861

119889119871dom 1

= minus (V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861



times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]

]

2

)

minus1

(25)


(V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861



times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]

]

2

)

minus1

= 0


minus200

0

200

400

600

8000 500 1000 1500 2000


V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861




(26)



119871lowast


11003816100381610038161003816ln (1 minus 119875BER)

1003816100381610038161003816 (27)


BER 119875BER





119863119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882119901119905

119894+ 120591

succ119894119904119889

) (28)

where 119882119901119905

119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus 119891

119894)119891


119904119861(120591119865119894

minus 120591119876

119894((1 minus

119891119894)119891



119894 120591119865119894

= sum119904119889

(120587119894119904119889

120587119894)119879


of 119865119894 120591

119876

119894= sum

119889120593119894119879119894119894119889



119894= sum

119904119889120587119894119904119889

119891119894119877119901119905

119894119904119889+ sum

119889119875119894119889

(1 minus 120587119894119891119894)119877

119901119905

119894119894119889 where

119877119901119905

119894119904119889=

119879(2)

119894119904119861

2119879119894119904119861

minus1

2 if 119894 isin 119878

119892and 119889 = 119861

119879(2)

119894119904119889

2119879119894119904119889

+1

2 otherwise

(29)



119879(2)

119894119904119861=

Ψ(2)

119894119904119889lceil

120591119898119894119861

120591119886rceil

2

if 119894 isin 119878119892and 119889 = 119861

Ψ(2)

119894119904119889+ Ψ

119894119904119889(1 minus 120593

119894)

1205932119894

otherwise

(30)

as 120591succ119894119904119889



120591succ119894119904119889



120591succ119894119904119889

=Ψsucc119894119904119889

120593119894

(31)

whereΨsucc119894119904119889

= sum119896119894119904119889

119896=1119896(1 minus 119875

119894119904119889)119896minus1

119875119894119904119889



119863HMAN119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882HMAN119901119905

119894+ 120591

succ119894119904119889

) (32)

Based on 119882119901119905



119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus

119891119901119894)119891


119904119861(120591119865119894

minus 120591119876

119894((1 minus 119891119901

119894)119891

119901119894))) The












Node ID 1 2 3 4 5 6 7 8 9 B119883 (m) 190 160 60 0 135 0 230 2300 1400 1000119884 (m) 10 80 60 80 0 30 60 10 60 30











010203040506070809

19

9535

102

475

104

108

105

2310

608

110

676

310

713

310

782

108

145

108

622

108

9610

916

6

PSR

SNR (dB)Flow a

010203040506070809

1

963

629

511

961

299

6354

951

819

7605

960

839

7273

972

629

9852

977

849

7103

PSR

SNR (dB)Flow b

010203040506070809

1

995

3510

247

510

410

810

523

106

081

106

763

107

333

107

8210

824

510

862

210

896

109

266

PSR

SNR (dB)Flow c

(a)

010203040506070809

1

873

188

8638

883

948

9012

900

648

998

898

519

0024

900

639

0196

901

968

9033

PSR

SNR (dB)

010203040506070809

19

3193

917

159

2438

920

59

2084

941

759

3481

940

59

3887

939

819

4537

938

33

PSR

SNR (dB)

010203040506070809

1

873

18

882

74

893

2

900

33

897

16

878

16

891

03

901

38

897

79

901

96

909

76

899

33

PSR


(b)





Modulationorder

TargetSINR (db)

Codingorder


BPSK 64 12 05

QPSK 94 12 1

QPSK 112 34 15

16-QAM 164 12 2

16-QAM 182 34 3

64-QAM 223 23 4

64-QAM 244 34 45

Single carrierBPSK

16-QAM64-QAM


Pack

et su

cces

s rat

e

099

098

097

096

095

094

093

092

091

090 01 02 03 04 05 06 07 08 09 1

1

times10minus4





0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01

011

012


Nor

mal

ized

thro

ughp

ut


(a)

0 200 400 600 800 1000 1200006

0065

007

0075

008

0085

009

0095

01

0105


Nor

mal

ized

thro

ughp

ut


(b)

0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01


Nor

mal

ized

thro

ughp

ut


(c)



119894) = (1 minus 119890minus120574119894)





1198751 1198752 1198753 1198754 1198755 1198756 1198757 1198758 1198759

05 07 04 03 07 04 0 0 0



0 200 400 600 800 1000 12000

10

20

30

40

50

60

70D

elay

(ms)




(a)

0 200 400 600 800 1000 12000

20

40

60

80

100

Del

ay (m

s)




(b)

0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

Del

ay (m

s)




(c)




Table 7 BER values


1 b 186119890 minus 4 47119890 minus 5

2 a c 4119890 minus 4 95119890 minus 5

2 b 915119890 minus 5 46119890 minus 5






Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

135

130

125

120

115

110

105

10001 015 02 025 03 035 04 045 05 055 06

(a)

Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

295

290

285

280

275

270

001

00102

00104

00106

00108

0011

00112

00114

00116

00118

0012

(b)








(b)

7 Conclusions





References

































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of







2 Related Work






















Infrared (IR) 8 120583s 64 1024





















119904 119889 119894 119873(119894) where 119878 = 119878dom 1 119878dom 2




= 1198731 119873

2 119873

119909 119909 isin N and

119878dom 2= 119873

1 119873

2 119873




119892= 119878dom 1

cap 119878dom 2= 119873

1 119873

2 119873

119911






119904119889and 119873(119894)








120595⟨120576⟩ (2) full119876

120595⟨1198901 119890bumax⟩ and

(3) 119876120595

⟨1198901 119890

119896⟩ where (0 lt 119896 lt bumax)


1 120572

120595) and

(1205721 120572




CP1198902119890

def= sum 119873 sdot 119873

120595 1 le 120595 lt 119899 (1)




997888997888997888997888rarr 119873120595where

(1205721sdot1205721 120572

120595sdot120572120595


1sdot1205721 120572

120595sdot


120595is a 120572

1sdot

1205721 120572

120595sdot 120572




119873def= sum

119901119896isinPK1205721

sdot 1205851

sdot 119876 ⟨1198901 119890

119896minus1⟩ (2)



119873120595

def= 120572

120595(119901119896) sdot 120585

120595 (3)

where 120595 = 119899 minus 1


The PAF


of a HMAN


A HMAN



Figure 1 The PAF

N1205721

1205722

12057231205721 1205723

1205722

1205851

1205852

120585312058511205852

1205853

B

N1

N2

N3

Nnminus1



119873120595

def= 120572

120595(119901119896) sdot 120585

120595sdot 119865

120595⟨1198901 119890

119896⟩ sdot 119873

120595

+ 120572120595+1

sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 119873

120595+1

+ 120572120595+1

sdot 120585120595+1

sdot 119876120595

⟨1198901 119890

119896minus1⟩ sdot 119873

120595+1

(4)


119873120595

def= 120572

120595(119901119896) sdot 120585

120595sdot 119865

120595⟨1198901 119890

119896⟩ sdot 119873

120595

+ 120572120595+1

sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 119873

120595+1

(5)




119865120595

⟨1198901 119890

119896⟩

def= sum

119894isin119870

119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1(1198901 119890

119896) sdot 120585

120595+1sdot 119873

120595+1

(6)







CP1198902119890

def= sum 120572

1sdot 1205851

sdot 119876 ⟨1198901 119890

119896minus1⟩ sdot 120572

120595(119901119896)

sdot 120585120595

sdot 119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 120572

120595(119901119896) sdot 120585

120595


119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1(1198901 119890

119896)

sdot 120585120595+1

sdot 120572120595

(119901119896) sdot 120585120595

(7)











Network layer

WFQ MACPHYWiMAX

WiFihlpfp





119879dom 2=

119873

sum119897=1

119875dom 2 load119871dom 2

119877119897119891 (120574

119897) (8)







120574119897

=119875119897

1198730

lowast 119877119897

(9)


0is the one-sided



119890by

119891 (120574119897) = (1 minus 119875

119890(120574))

119871dom 2119887 (10)



119875119890

(120574) = 4 (1 minus1

21198872) 119876 (119909) (11)


119876 (119909) =119890minus11990922

4mod+

1

2mod


exp(minus1199092

2sin2120579119895

) (12)

where 120579119895




defined as

119901119890

= 1 minus (1 minus 119875BER)119871119886 (13)




119875dom 1 load =119871dom 1


(14)

where




thp119904119861

= (119910119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891 lceil120591119898

119894119861

119871dom 1

119871dom 2

rceil 120601 ( 120574119894)

+119910119904119875119904119889

[1

120593119904

] )

minus1

(16)

where 119910119904











119894119861= 119871dom 2

120588119898119894119861


119898

119894119861= sum

119897isinL119894

120574119898

119894119861119897Δ119891








119894equiv 119891 and

120593119894

equiv 120593


thpHMAN119904119861

= (119884119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891119901119894


119894119861

119871dom 1

(1 minus 119901119890) 119871dom 2

rceil 119891 (120574119897)

+119884119904

[1

120593119904

] )

minus1

(17)

where119891(120574119897) = (1 minus 119875

119890(120574))



thpHMAN119904119861

= (119884119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891119901119894

times [[[

119873

sum119895=1

119875dom 2 load119871dom 2

119875dom 1 load120588119898119894119861

(1 minus 119901119890)

]]]

times119891 (120574119897) + 119884

119904[

1

120593119904

])

minus1

(18)



119904119861is then

defined as follows

thpHMAN119904119861

=V

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906

(19)

where V = 119884119904(1 minus 120593)

119899 ℎ = 120587119894119904119889

119891(120593119894)minus1 119911(119871dom 1

119871dom 2) =

120587119892119904119889

119891119901119894119879lceil119875dom 1 load120588119898

119892119861(1 minus 119901

119890)rceil 119906 = 119884

119904[1120593

119904] and 119879 =

sum119873

119895=1(119875dom 2 load119871dom 2

)119891(120574119895)





119889thpHMAN119904119861

119889119871dom 2

= minusV [1199111015840 (119871dom 1

119871dom 2)]

[sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]2

(20)

where

119911 (119871dom 1 119871dom 2

)

= 120587119892119904119889

119891119901119894

119873

sum119895=1


119871dom 2

times (1 minus 119875119890

(120574119895))

119871dom 2119887lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

(21)



as

119889119911 (119871dom 1 119871dom 2

)

119889119871dom 2

= 120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]

(22)


minusV [1199111015840 (119871dom 1

119871dom 2)]

[sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

)]2

= 0

minus (V[120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]])

times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

)]

]

2

)

minus1

= 0

V[120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]] = 0

119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887= 0

(23)



119871lowast

dom 2

=119874bytes

2+


119890(120574)))

2

(24)






119889thpHMAN119904119861

119889119871dom 1

= minus (V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861



times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]

]

2

)

minus1

(25)


(V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861



times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]

]

2

)

minus1

= 0


minus200

0

200

400

600

8000 500 1000 1500 2000


V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861




(26)



119871lowast


11003816100381610038161003816ln (1 minus 119875BER)

1003816100381610038161003816 (27)


BER 119875BER





119863119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882119901119905

119894+ 120591

succ119894119904119889

) (28)

where 119882119901119905

119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus 119891

119894)119891


119904119861(120591119865119894

minus 120591119876

119894((1 minus

119891119894)119891



119894 120591119865119894

= sum119904119889

(120587119894119904119889

120587119894)119879


of 119865119894 120591

119876

119894= sum

119889120593119894119879119894119894119889



119894= sum

119904119889120587119894119904119889

119891119894119877119901119905

119894119904119889+ sum

119889119875119894119889

(1 minus 120587119894119891119894)119877

119901119905

119894119894119889 where

119877119901119905

119894119904119889=

119879(2)

119894119904119861

2119879119894119904119861

minus1

2 if 119894 isin 119878

119892and 119889 = 119861

119879(2)

119894119904119889

2119879119894119904119889

+1

2 otherwise

(29)



119879(2)

119894119904119861=

Ψ(2)

119894119904119889lceil

120591119898119894119861

120591119886rceil

2

if 119894 isin 119878119892and 119889 = 119861

Ψ(2)

119894119904119889+ Ψ

119894119904119889(1 minus 120593

119894)

1205932119894

otherwise

(30)

as 120591succ119894119904119889



120591succ119894119904119889



120591succ119894119904119889

=Ψsucc119894119904119889

120593119894

(31)

whereΨsucc119894119904119889

= sum119896119894119904119889

119896=1119896(1 minus 119875

119894119904119889)119896minus1

119875119894119904119889



119863HMAN119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882HMAN119901119905

119894+ 120591

succ119894119904119889

) (32)

Based on 119882119901119905



119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus

119891119901119894)119891


119904119861(120591119865119894

minus 120591119876

119894((1 minus 119891119901

119894)119891

119901119894))) The












Node ID 1 2 3 4 5 6 7 8 9 B119883 (m) 190 160 60 0 135 0 230 2300 1400 1000119884 (m) 10 80 60 80 0 30 60 10 60 30











010203040506070809

19

9535

102

475

104

108

105

2310

608

110

676

310

713

310

782

108

145

108

622

108

9610

916

6

PSR

SNR (dB)Flow a

010203040506070809

1

963

629

511

961

299

6354

951

819

7605

960

839

7273

972

629

9852

977

849

7103

PSR

SNR (dB)Flow b

010203040506070809

1

995

3510

247

510

410

810

523

106

081

106

763

107

333

107

8210

824

510

862

210

896

109

266

PSR

SNR (dB)Flow c

(a)

010203040506070809

1

873

188

8638

883

948

9012

900

648

998

898

519

0024

900

639

0196

901

968

9033

PSR

SNR (dB)

010203040506070809

19

3193

917

159

2438

920

59

2084

941

759

3481

940

59

3887

939

819

4537

938

33

PSR

SNR (dB)

010203040506070809

1

873

18

882

74

893

2

900

33

897

16

878

16

891

03

901

38

897

79

901

96

909

76

899

33

PSR


(b)





Modulationorder

TargetSINR (db)

Codingorder


BPSK 64 12 05

QPSK 94 12 1

QPSK 112 34 15

16-QAM 164 12 2

16-QAM 182 34 3

64-QAM 223 23 4

64-QAM 244 34 45

Single carrierBPSK

16-QAM64-QAM


Pack

et su

cces

s rat

e

099

098

097

096

095

094

093

092

091

090 01 02 03 04 05 06 07 08 09 1

1

times10minus4





0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01

011

012


Nor

mal

ized

thro

ughp

ut


(a)

0 200 400 600 800 1000 1200006

0065

007

0075

008

0085

009

0095

01

0105


Nor

mal

ized

thro

ughp

ut


(b)

0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01


Nor

mal

ized

thro

ughp

ut


(c)



119894) = (1 minus 119890minus120574119894)





1198751 1198752 1198753 1198754 1198755 1198756 1198757 1198758 1198759

05 07 04 03 07 04 0 0 0



0 200 400 600 800 1000 12000

10

20

30

40

50

60

70D

elay

(ms)




(a)

0 200 400 600 800 1000 12000

20

40

60

80

100

Del

ay (m

s)




(b)

0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

Del

ay (m

s)




(c)




Table 7 BER values


1 b 186119890 minus 4 47119890 minus 5

2 a c 4119890 minus 4 95119890 minus 5

2 b 915119890 minus 5 46119890 minus 5






Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

135

130

125

120

115

110

105

10001 015 02 025 03 035 04 045 05 055 06

(a)

Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

295

290

285

280

275

270

001

00102

00104

00106

00108

0011

00112

00114

00116

00118

0012

(b)








(b)

7 Conclusions





References

































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of












Infrared (IR) 8 120583s 64 1024





















119904 119889 119894 119873(119894) where 119878 = 119878dom 1 119878dom 2




= 1198731 119873

2 119873

119909 119909 isin N and

119878dom 2= 119873

1 119873

2 119873




119892= 119878dom 1

cap 119878dom 2= 119873

1 119873

2 119873

119911






119904119889and 119873(119894)








120595⟨120576⟩ (2) full119876

120595⟨1198901 119890bumax⟩ and

(3) 119876120595

⟨1198901 119890

119896⟩ where (0 lt 119896 lt bumax)


1 120572

120595) and

(1205721 120572




CP1198902119890

def= sum 119873 sdot 119873

120595 1 le 120595 lt 119899 (1)




997888997888997888997888rarr 119873120595where

(1205721sdot1205721 120572

120595sdot120572120595


1sdot1205721 120572

120595sdot


120595is a 120572

1sdot

1205721 120572

120595sdot 120572




119873def= sum

119901119896isinPK1205721

sdot 1205851

sdot 119876 ⟨1198901 119890

119896minus1⟩ (2)



119873120595

def= 120572

120595(119901119896) sdot 120585

120595 (3)

where 120595 = 119899 minus 1


The PAF


of a HMAN


A HMAN



Figure 1 The PAF

N1205721

1205722

12057231205721 1205723

1205722

1205851

1205852

120585312058511205852

1205853

B

N1

N2

N3

Nnminus1



119873120595

def= 120572

120595(119901119896) sdot 120585

120595sdot 119865

120595⟨1198901 119890

119896⟩ sdot 119873

120595

+ 120572120595+1

sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 119873

120595+1

+ 120572120595+1

sdot 120585120595+1

sdot 119876120595

⟨1198901 119890

119896minus1⟩ sdot 119873

120595+1

(4)


119873120595

def= 120572

120595(119901119896) sdot 120585

120595sdot 119865

120595⟨1198901 119890

119896⟩ sdot 119873

120595

+ 120572120595+1

sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 119873

120595+1

(5)




119865120595

⟨1198901 119890

119896⟩

def= sum

119894isin119870

119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1(1198901 119890

119896) sdot 120585

120595+1sdot 119873

120595+1

(6)







CP1198902119890

def= sum 120572

1sdot 1205851

sdot 119876 ⟨1198901 119890

119896minus1⟩ sdot 120572

120595(119901119896)

sdot 120585120595

sdot 119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 120572

120595(119901119896) sdot 120585

120595


119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1(1198901 119890

119896)

sdot 120585120595+1

sdot 120572120595

(119901119896) sdot 120585120595

(7)











Network layer

WFQ MACPHYWiMAX

WiFihlpfp





119879dom 2=

119873

sum119897=1

119875dom 2 load119871dom 2

119877119897119891 (120574

119897) (8)







120574119897

=119875119897

1198730

lowast 119877119897

(9)


0is the one-sided



119890by

119891 (120574119897) = (1 minus 119875

119890(120574))

119871dom 2119887 (10)



119875119890

(120574) = 4 (1 minus1

21198872) 119876 (119909) (11)


119876 (119909) =119890minus11990922

4mod+

1

2mod


exp(minus1199092

2sin2120579119895

) (12)

where 120579119895




defined as

119901119890

= 1 minus (1 minus 119875BER)119871119886 (13)




119875dom 1 load =119871dom 1


(14)

where




thp119904119861

= (119910119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891 lceil120591119898

119894119861

119871dom 1

119871dom 2

rceil 120601 ( 120574119894)

+119910119904119875119904119889

[1

120593119904

] )

minus1

(16)

where 119910119904











119894119861= 119871dom 2

120588119898119894119861


119898

119894119861= sum

119897isinL119894

120574119898

119894119861119897Δ119891








119894equiv 119891 and

120593119894

equiv 120593


thpHMAN119904119861

= (119884119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891119901119894


119894119861

119871dom 1

(1 minus 119901119890) 119871dom 2

rceil 119891 (120574119897)

+119884119904

[1

120593119904

] )

minus1

(17)

where119891(120574119897) = (1 minus 119875

119890(120574))



thpHMAN119904119861

= (119884119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891119901119894

times [[[

119873

sum119895=1

119875dom 2 load119871dom 2

119875dom 1 load120588119898119894119861

(1 minus 119901119890)

]]]

times119891 (120574119897) + 119884

119904[

1

120593119904

])

minus1

(18)



119904119861is then

defined as follows

thpHMAN119904119861

=V

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906

(19)

where V = 119884119904(1 minus 120593)

119899 ℎ = 120587119894119904119889

119891(120593119894)minus1 119911(119871dom 1

119871dom 2) =

120587119892119904119889

119891119901119894119879lceil119875dom 1 load120588119898

119892119861(1 minus 119901

119890)rceil 119906 = 119884

119904[1120593

119904] and 119879 =

sum119873

119895=1(119875dom 2 load119871dom 2

)119891(120574119895)





119889thpHMAN119904119861

119889119871dom 2

= minusV [1199111015840 (119871dom 1

119871dom 2)]

[sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]2

(20)

where

119911 (119871dom 1 119871dom 2

)

= 120587119892119904119889

119891119901119894

119873

sum119895=1


119871dom 2

times (1 minus 119875119890

(120574119895))

119871dom 2119887lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

(21)



as

119889119911 (119871dom 1 119871dom 2

)

119889119871dom 2

= 120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]

(22)


minusV [1199111015840 (119871dom 1

119871dom 2)]

[sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

)]2

= 0

minus (V[120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]])

times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

)]

]

2

)

minus1

= 0

V[120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]] = 0

119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887= 0

(23)



119871lowast

dom 2

=119874bytes

2+


119890(120574)))

2

(24)






119889thpHMAN119904119861

119889119871dom 1

= minus (V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861



times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]

]

2

)

minus1

(25)


(V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861



times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]

]

2

)

minus1

= 0


minus200

0

200

400

600

8000 500 1000 1500 2000


V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861




(26)



119871lowast


11003816100381610038161003816ln (1 minus 119875BER)

1003816100381610038161003816 (27)


BER 119875BER





119863119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882119901119905

119894+ 120591

succ119894119904119889

) (28)

where 119882119901119905

119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus 119891

119894)119891


119904119861(120591119865119894

minus 120591119876

119894((1 minus

119891119894)119891



119894 120591119865119894

= sum119904119889

(120587119894119904119889

120587119894)119879


of 119865119894 120591

119876

119894= sum

119889120593119894119879119894119894119889



119894= sum

119904119889120587119894119904119889

119891119894119877119901119905

119894119904119889+ sum

119889119875119894119889

(1 minus 120587119894119891119894)119877

119901119905

119894119894119889 where

119877119901119905

119894119904119889=

119879(2)

119894119904119861

2119879119894119904119861

minus1

2 if 119894 isin 119878

119892and 119889 = 119861

119879(2)

119894119904119889

2119879119894119904119889

+1

2 otherwise

(29)



119879(2)

119894119904119861=

Ψ(2)

119894119904119889lceil

120591119898119894119861

120591119886rceil

2

if 119894 isin 119878119892and 119889 = 119861

Ψ(2)

119894119904119889+ Ψ

119894119904119889(1 minus 120593

119894)

1205932119894

otherwise

(30)

as 120591succ119894119904119889



120591succ119894119904119889



120591succ119894119904119889

=Ψsucc119894119904119889

120593119894

(31)

whereΨsucc119894119904119889

= sum119896119894119904119889

119896=1119896(1 minus 119875

119894119904119889)119896minus1

119875119894119904119889



119863HMAN119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882HMAN119901119905

119894+ 120591

succ119894119904119889

) (32)

Based on 119882119901119905



119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus

119891119901119894)119891


119904119861(120591119865119894

minus 120591119876

119894((1 minus 119891119901

119894)119891

119901119894))) The












Node ID 1 2 3 4 5 6 7 8 9 B119883 (m) 190 160 60 0 135 0 230 2300 1400 1000119884 (m) 10 80 60 80 0 30 60 10 60 30











010203040506070809

19

9535

102

475

104

108

105

2310

608

110

676

310

713

310

782

108

145

108

622

108

9610

916

6

PSR

SNR (dB)Flow a

010203040506070809

1

963

629

511

961

299

6354

951

819

7605

960

839

7273

972

629

9852

977

849

7103

PSR

SNR (dB)Flow b

010203040506070809

1

995

3510

247

510

410

810

523

106

081

106

763

107

333

107

8210

824

510

862

210

896

109

266

PSR

SNR (dB)Flow c

(a)

010203040506070809

1

873

188

8638

883

948

9012

900

648

998

898

519

0024

900

639

0196

901

968

9033

PSR

SNR (dB)

010203040506070809

19

3193

917

159

2438

920

59

2084

941

759

3481

940

59

3887

939

819

4537

938

33

PSR

SNR (dB)

010203040506070809

1

873

18

882

74

893

2

900

33

897

16

878

16

891

03

901

38

897

79

901

96

909

76

899

33

PSR


(b)





Modulationorder

TargetSINR (db)

Codingorder


BPSK 64 12 05

QPSK 94 12 1

QPSK 112 34 15

16-QAM 164 12 2

16-QAM 182 34 3

64-QAM 223 23 4

64-QAM 244 34 45

Single carrierBPSK

16-QAM64-QAM


Pack

et su

cces

s rat

e

099

098

097

096

095

094

093

092

091

090 01 02 03 04 05 06 07 08 09 1

1

times10minus4





0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01

011

012


Nor

mal

ized

thro

ughp

ut


(a)

0 200 400 600 800 1000 1200006

0065

007

0075

008

0085

009

0095

01

0105


Nor

mal

ized

thro

ughp

ut


(b)

0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01


Nor

mal

ized

thro

ughp

ut


(c)



119894) = (1 minus 119890minus120574119894)





1198751 1198752 1198753 1198754 1198755 1198756 1198757 1198758 1198759

05 07 04 03 07 04 0 0 0



0 200 400 600 800 1000 12000

10

20

30

40

50

60

70D

elay

(ms)




(a)

0 200 400 600 800 1000 12000

20

40

60

80

100

Del

ay (m

s)




(b)

0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

Del

ay (m

s)




(c)




Table 7 BER values


1 b 186119890 minus 4 47119890 minus 5

2 a c 4119890 minus 4 95119890 minus 5

2 b 915119890 minus 5 46119890 minus 5






Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

135

130

125

120

115

110

105

10001 015 02 025 03 035 04 045 05 055 06

(a)

Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

295

290

285

280

275

270

001

00102

00104

00106

00108

0011

00112

00114

00116

00118

0012

(b)








(b)

7 Conclusions





References

































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of














119904 119889 119894 119873(119894) where 119878 = 119878dom 1 119878dom 2




= 1198731 119873

2 119873

119909 119909 isin N and

119878dom 2= 119873

1 119873

2 119873




119892= 119878dom 1

cap 119878dom 2= 119873

1 119873

2 119873

119911






119904119889and 119873(119894)








120595⟨120576⟩ (2) full119876

120595⟨1198901 119890bumax⟩ and

(3) 119876120595

⟨1198901 119890

119896⟩ where (0 lt 119896 lt bumax)


1 120572

120595) and

(1205721 120572




CP1198902119890

def= sum 119873 sdot 119873

120595 1 le 120595 lt 119899 (1)




997888997888997888997888rarr 119873120595where

(1205721sdot1205721 120572

120595sdot120572120595


1sdot1205721 120572

120595sdot


120595is a 120572

1sdot

1205721 120572

120595sdot 120572




119873def= sum

119901119896isinPK1205721

sdot 1205851

sdot 119876 ⟨1198901 119890

119896minus1⟩ (2)



119873120595

def= 120572

120595(119901119896) sdot 120585

120595 (3)

where 120595 = 119899 minus 1


The PAF


of a HMAN


A HMAN



Figure 1 The PAF

N1205721

1205722

12057231205721 1205723

1205722

1205851

1205852

120585312058511205852

1205853

B

N1

N2

N3

Nnminus1



119873120595

def= 120572

120595(119901119896) sdot 120585

120595sdot 119865

120595⟨1198901 119890

119896⟩ sdot 119873

120595

+ 120572120595+1

sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 119873

120595+1

+ 120572120595+1

sdot 120585120595+1

sdot 119876120595

⟨1198901 119890

119896minus1⟩ sdot 119873

120595+1

(4)


119873120595

def= 120572

120595(119901119896) sdot 120585

120595sdot 119865

120595⟨1198901 119890

119896⟩ sdot 119873

120595

+ 120572120595+1

sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 119873

120595+1

(5)




119865120595

⟨1198901 119890

119896⟩

def= sum

119894isin119870

119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1(1198901 119890

119896) sdot 120585

120595+1sdot 119873

120595+1

(6)







CP1198902119890

def= sum 120572

1sdot 1205851

sdot 119876 ⟨1198901 119890

119896minus1⟩ sdot 120572

120595(119901119896)

sdot 120585120595

sdot 119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 120572

120595(119901119896) sdot 120585

120595


119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1(1198901 119890

119896)

sdot 120585120595+1

sdot 120572120595

(119901119896) sdot 120585120595

(7)











Network layer

WFQ MACPHYWiMAX

WiFihlpfp





119879dom 2=

119873

sum119897=1

119875dom 2 load119871dom 2

119877119897119891 (120574

119897) (8)







120574119897

=119875119897

1198730

lowast 119877119897

(9)


0is the one-sided



119890by

119891 (120574119897) = (1 minus 119875

119890(120574))

119871dom 2119887 (10)



119875119890

(120574) = 4 (1 minus1

21198872) 119876 (119909) (11)


119876 (119909) =119890minus11990922

4mod+

1

2mod


exp(minus1199092

2sin2120579119895

) (12)

where 120579119895




defined as

119901119890

= 1 minus (1 minus 119875BER)119871119886 (13)




119875dom 1 load =119871dom 1


(14)

where




thp119904119861

= (119910119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891 lceil120591119898

119894119861

119871dom 1

119871dom 2

rceil 120601 ( 120574119894)

+119910119904119875119904119889

[1

120593119904

] )

minus1

(16)

where 119910119904











119894119861= 119871dom 2

120588119898119894119861


119898

119894119861= sum

119897isinL119894

120574119898

119894119861119897Δ119891








119894equiv 119891 and

120593119894

equiv 120593


thpHMAN119904119861

= (119884119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891119901119894


119894119861

119871dom 1

(1 minus 119901119890) 119871dom 2

rceil 119891 (120574119897)

+119884119904

[1

120593119904

] )

minus1

(17)

where119891(120574119897) = (1 minus 119875

119890(120574))



thpHMAN119904119861

= (119884119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891119901119894

times [[[

119873

sum119895=1

119875dom 2 load119871dom 2

119875dom 1 load120588119898119894119861

(1 minus 119901119890)

]]]

times119891 (120574119897) + 119884

119904[

1

120593119904

])

minus1

(18)



119904119861is then

defined as follows

thpHMAN119904119861

=V

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906

(19)

where V = 119884119904(1 minus 120593)

119899 ℎ = 120587119894119904119889

119891(120593119894)minus1 119911(119871dom 1

119871dom 2) =

120587119892119904119889

119891119901119894119879lceil119875dom 1 load120588119898

119892119861(1 minus 119901

119890)rceil 119906 = 119884

119904[1120593

119904] and 119879 =

sum119873

119895=1(119875dom 2 load119871dom 2

)119891(120574119895)





119889thpHMAN119904119861

119889119871dom 2

= minusV [1199111015840 (119871dom 1

119871dom 2)]

[sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]2

(20)

where

119911 (119871dom 1 119871dom 2

)

= 120587119892119904119889

119891119901119894

119873

sum119895=1


119871dom 2

times (1 minus 119875119890

(120574119895))

119871dom 2119887lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

(21)



as

119889119911 (119871dom 1 119871dom 2

)

119889119871dom 2

= 120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]

(22)


minusV [1199111015840 (119871dom 1

119871dom 2)]

[sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

)]2

= 0

minus (V[120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]])

times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

)]

]

2

)

minus1

= 0

V[120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]] = 0

119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887= 0

(23)



119871lowast

dom 2

=119874bytes

2+


119890(120574)))

2

(24)






119889thpHMAN119904119861

119889119871dom 1

= minus (V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861



times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]

]

2

)

minus1

(25)


(V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861



times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]

]

2

)

minus1

= 0


minus200

0

200

400

600

8000 500 1000 1500 2000


V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861




(26)



119871lowast


11003816100381610038161003816ln (1 minus 119875BER)

1003816100381610038161003816 (27)


BER 119875BER





119863119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882119901119905

119894+ 120591

succ119894119904119889

) (28)

where 119882119901119905

119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus 119891

119894)119891


119904119861(120591119865119894

minus 120591119876

119894((1 minus

119891119894)119891



119894 120591119865119894

= sum119904119889

(120587119894119904119889

120587119894)119879


of 119865119894 120591

119876

119894= sum

119889120593119894119879119894119894119889



119894= sum

119904119889120587119894119904119889

119891119894119877119901119905

119894119904119889+ sum

119889119875119894119889

(1 minus 120587119894119891119894)119877

119901119905

119894119894119889 where

119877119901119905

119894119904119889=

119879(2)

119894119904119861

2119879119894119904119861

minus1

2 if 119894 isin 119878

119892and 119889 = 119861

119879(2)

119894119904119889

2119879119894119904119889

+1

2 otherwise

(29)



119879(2)

119894119904119861=

Ψ(2)

119894119904119889lceil

120591119898119894119861

120591119886rceil

2

if 119894 isin 119878119892and 119889 = 119861

Ψ(2)

119894119904119889+ Ψ

119894119904119889(1 minus 120593

119894)

1205932119894

otherwise

(30)

as 120591succ119894119904119889



120591succ119894119904119889



120591succ119894119904119889

=Ψsucc119894119904119889

120593119894

(31)

whereΨsucc119894119904119889

= sum119896119894119904119889

119896=1119896(1 minus 119875

119894119904119889)119896minus1

119875119894119904119889



119863HMAN119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882HMAN119901119905

119894+ 120591

succ119894119904119889

) (32)

Based on 119882119901119905



119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus

119891119901119894)119891


119904119861(120591119865119894

minus 120591119876

119894((1 minus 119891119901

119894)119891

119901119894))) The












Node ID 1 2 3 4 5 6 7 8 9 B119883 (m) 190 160 60 0 135 0 230 2300 1400 1000119884 (m) 10 80 60 80 0 30 60 10 60 30











010203040506070809

19

9535

102

475

104

108

105

2310

608

110

676

310

713

310

782

108

145

108

622

108

9610

916

6

PSR

SNR (dB)Flow a

010203040506070809

1

963

629

511

961

299

6354

951

819

7605

960

839

7273

972

629

9852

977

849

7103

PSR

SNR (dB)Flow b

010203040506070809

1

995

3510

247

510

410

810

523

106

081

106

763

107

333

107

8210

824

510

862

210

896

109

266

PSR

SNR (dB)Flow c

(a)

010203040506070809

1

873

188

8638

883

948

9012

900

648

998

898

519

0024

900

639

0196

901

968

9033

PSR

SNR (dB)

010203040506070809

19

3193

917

159

2438

920

59

2084

941

759

3481

940

59

3887

939

819

4537

938

33

PSR

SNR (dB)

010203040506070809

1

873

18

882

74

893

2

900

33

897

16

878

16

891

03

901

38

897

79

901

96

909

76

899

33

PSR


(b)





Modulationorder

TargetSINR (db)

Codingorder


BPSK 64 12 05

QPSK 94 12 1

QPSK 112 34 15

16-QAM 164 12 2

16-QAM 182 34 3

64-QAM 223 23 4

64-QAM 244 34 45

Single carrierBPSK

16-QAM64-QAM


Pack

et su

cces

s rat

e

099

098

097

096

095

094

093

092

091

090 01 02 03 04 05 06 07 08 09 1

1

times10minus4





0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01

011

012


Nor

mal

ized

thro

ughp

ut


(a)

0 200 400 600 800 1000 1200006

0065

007

0075

008

0085

009

0095

01

0105


Nor

mal

ized

thro

ughp

ut


(b)

0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01


Nor

mal

ized

thro

ughp

ut


(c)



119894) = (1 minus 119890minus120574119894)





1198751 1198752 1198753 1198754 1198755 1198756 1198757 1198758 1198759

05 07 04 03 07 04 0 0 0



0 200 400 600 800 1000 12000

10

20

30

40

50

60

70D

elay

(ms)




(a)

0 200 400 600 800 1000 12000

20

40

60

80

100

Del

ay (m

s)




(b)

0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

Del

ay (m

s)




(c)




Table 7 BER values


1 b 186119890 minus 4 47119890 minus 5

2 a c 4119890 minus 4 95119890 minus 5

2 b 915119890 minus 5 46119890 minus 5






Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

135

130

125

120

115

110

105

10001 015 02 025 03 035 04 045 05 055 06

(a)

Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

295

290

285

280

275

270

001

00102

00104

00106

00108

0011

00112

00114

00116

00118

0012

(b)








(b)

7 Conclusions





References

































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of



The PAF


of a HMAN


A HMAN



Figure 1 The PAF

N1205721

1205722

12057231205721 1205723

1205722

1205851

1205852

120585312058511205852

1205853

B

N1

N2

N3

Nnminus1



119873120595

def= 120572

120595(119901119896) sdot 120585

120595sdot 119865

120595⟨1198901 119890

119896⟩ sdot 119873

120595

+ 120572120595+1

sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 119873

120595+1

+ 120572120595+1

sdot 120585120595+1

sdot 119876120595

⟨1198901 119890

119896minus1⟩ sdot 119873

120595+1

(4)


119873120595

def= 120572

120595(119901119896) sdot 120585

120595sdot 119865

120595⟨1198901 119890

119896⟩ sdot 119873

120595

+ 120572120595+1

sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 119873

120595+1

(5)




119865120595

⟨1198901 119890

119896⟩

def= sum

119894isin119870

119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1(1198901 119890

119896) sdot 120585

120595+1sdot 119873

120595+1

(6)







CP1198902119890

def= sum 120572

1sdot 1205851

sdot 119876 ⟨1198901 119890

119896minus1⟩ sdot 120572

120595(119901119896)

sdot 120585120595

sdot 119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 120572

120595(119901119896) sdot 120585

120595


119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1(1198901 119890

119896)

sdot 120585120595+1

sdot 120572120595

(119901119896) sdot 120585120595

(7)











Network layer

WFQ MACPHYWiMAX

WiFihlpfp





119879dom 2=

119873

sum119897=1

119875dom 2 load119871dom 2

119877119897119891 (120574

119897) (8)







120574119897

=119875119897

1198730

lowast 119877119897

(9)


0is the one-sided



119890by

119891 (120574119897) = (1 minus 119875

119890(120574))

119871dom 2119887 (10)



119875119890

(120574) = 4 (1 minus1

21198872) 119876 (119909) (11)


119876 (119909) =119890minus11990922

4mod+

1

2mod


exp(minus1199092

2sin2120579119895

) (12)

where 120579119895




defined as

119901119890

= 1 minus (1 minus 119875BER)119871119886 (13)




119875dom 1 load =119871dom 1


(14)

where




thp119904119861

= (119910119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891 lceil120591119898

119894119861

119871dom 1

119871dom 2

rceil 120601 ( 120574119894)

+119910119904119875119904119889

[1

120593119904

] )

minus1

(16)

where 119910119904











119894119861= 119871dom 2

120588119898119894119861


119898

119894119861= sum

119897isinL119894

120574119898

119894119861119897Δ119891








119894equiv 119891 and

120593119894

equiv 120593


thpHMAN119904119861

= (119884119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891119901119894


119894119861

119871dom 1

(1 minus 119901119890) 119871dom 2

rceil 119891 (120574119897)

+119884119904

[1

120593119904

] )

minus1

(17)

where119891(120574119897) = (1 minus 119875

119890(120574))



thpHMAN119904119861

= (119884119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891119901119894

times [[[

119873

sum119895=1

119875dom 2 load119871dom 2

119875dom 1 load120588119898119894119861

(1 minus 119901119890)

]]]

times119891 (120574119897) + 119884

119904[

1

120593119904

])

minus1

(18)



119904119861is then

defined as follows

thpHMAN119904119861

=V

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906

(19)

where V = 119884119904(1 minus 120593)

119899 ℎ = 120587119894119904119889

119891(120593119894)minus1 119911(119871dom 1

119871dom 2) =

120587119892119904119889

119891119901119894119879lceil119875dom 1 load120588119898

119892119861(1 minus 119901

119890)rceil 119906 = 119884

119904[1120593

119904] and 119879 =

sum119873

119895=1(119875dom 2 load119871dom 2

)119891(120574119895)





119889thpHMAN119904119861

119889119871dom 2

= minusV [1199111015840 (119871dom 1

119871dom 2)]

[sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]2

(20)

where

119911 (119871dom 1 119871dom 2

)

= 120587119892119904119889

119891119901119894

119873

sum119895=1


119871dom 2

times (1 minus 119875119890

(120574119895))

119871dom 2119887lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

(21)



as

119889119911 (119871dom 1 119871dom 2

)

119889119871dom 2

= 120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]

(22)


minusV [1199111015840 (119871dom 1

119871dom 2)]

[sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

)]2

= 0

minus (V[120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]])

times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

)]

]

2

)

minus1

= 0

V[120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]] = 0

119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887= 0

(23)



119871lowast

dom 2

=119874bytes

2+


119890(120574)))

2

(24)






119889thpHMAN119904119861

119889119871dom 1

= minus (V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861



times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]

]

2

)

minus1

(25)


(V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861



times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]

]

2

)

minus1

= 0


minus200

0

200

400

600

8000 500 1000 1500 2000


V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861




(26)



119871lowast


11003816100381610038161003816ln (1 minus 119875BER)

1003816100381610038161003816 (27)


BER 119875BER





119863119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882119901119905

119894+ 120591

succ119894119904119889

) (28)

where 119882119901119905

119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus 119891

119894)119891


119904119861(120591119865119894

minus 120591119876

119894((1 minus

119891119894)119891



119894 120591119865119894

= sum119904119889

(120587119894119904119889

120587119894)119879


of 119865119894 120591

119876

119894= sum

119889120593119894119879119894119894119889



119894= sum

119904119889120587119894119904119889

119891119894119877119901119905

119894119904119889+ sum

119889119875119894119889

(1 minus 120587119894119891119894)119877

119901119905

119894119894119889 where

119877119901119905

119894119904119889=

119879(2)

119894119904119861

2119879119894119904119861

minus1

2 if 119894 isin 119878

119892and 119889 = 119861

119879(2)

119894119904119889

2119879119894119904119889

+1

2 otherwise

(29)



119879(2)

119894119904119861=

Ψ(2)

119894119904119889lceil

120591119898119894119861

120591119886rceil

2

if 119894 isin 119878119892and 119889 = 119861

Ψ(2)

119894119904119889+ Ψ

119894119904119889(1 minus 120593

119894)

1205932119894

otherwise

(30)

as 120591succ119894119904119889



120591succ119894119904119889



120591succ119894119904119889

=Ψsucc119894119904119889

120593119894

(31)

whereΨsucc119894119904119889

= sum119896119894119904119889

119896=1119896(1 minus 119875

119894119904119889)119896minus1

119875119894119904119889



119863HMAN119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882HMAN119901119905

119894+ 120591

succ119894119904119889

) (32)

Based on 119882119901119905



119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus

119891119901119894)119891


119904119861(120591119865119894

minus 120591119876

119894((1 minus 119891119901

119894)119891

119901119894))) The












Node ID 1 2 3 4 5 6 7 8 9 B119883 (m) 190 160 60 0 135 0 230 2300 1400 1000119884 (m) 10 80 60 80 0 30 60 10 60 30











010203040506070809

19

9535

102

475

104

108

105

2310

608

110

676

310

713

310

782

108

145

108

622

108

9610

916

6

PSR

SNR (dB)Flow a

010203040506070809

1

963

629

511

961

299

6354

951

819

7605

960

839

7273

972

629

9852

977

849

7103

PSR

SNR (dB)Flow b

010203040506070809

1

995

3510

247

510

410

810

523

106

081

106

763

107

333

107

8210

824

510

862

210

896

109

266

PSR

SNR (dB)Flow c

(a)

010203040506070809

1

873

188

8638

883

948

9012

900

648

998

898

519

0024

900

639

0196

901

968

9033

PSR

SNR (dB)

010203040506070809

19

3193

917

159

2438

920

59

2084

941

759

3481

940

59

3887

939

819

4537

938

33

PSR

SNR (dB)

010203040506070809

1

873

18

882

74

893

2

900

33

897

16

878

16

891

03

901

38

897

79

901

96

909

76

899

33

PSR


(b)





Modulationorder

TargetSINR (db)

Codingorder


BPSK 64 12 05

QPSK 94 12 1

QPSK 112 34 15

16-QAM 164 12 2

16-QAM 182 34 3

64-QAM 223 23 4

64-QAM 244 34 45

Single carrierBPSK

16-QAM64-QAM


Pack

et su

cces

s rat

e

099

098

097

096

095

094

093

092

091

090 01 02 03 04 05 06 07 08 09 1

1

times10minus4





0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01

011

012


Nor

mal

ized

thro

ughp

ut


(a)

0 200 400 600 800 1000 1200006

0065

007

0075

008

0085

009

0095

01

0105


Nor

mal

ized

thro

ughp

ut


(b)

0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01


Nor

mal

ized

thro

ughp

ut


(c)



119894) = (1 minus 119890minus120574119894)





1198751 1198752 1198753 1198754 1198755 1198756 1198757 1198758 1198759

05 07 04 03 07 04 0 0 0



0 200 400 600 800 1000 12000

10

20

30

40

50

60

70D

elay

(ms)




(a)

0 200 400 600 800 1000 12000

20

40

60

80

100

Del

ay (m

s)




(b)

0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

Del

ay (m

s)




(c)




Table 7 BER values


1 b 186119890 minus 4 47119890 minus 5

2 a c 4119890 minus 4 95119890 minus 5

2 b 915119890 minus 5 46119890 minus 5






Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

135

130

125

120

115

110

105

10001 015 02 025 03 035 04 045 05 055 06

(a)

Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

295

290

285

280

275

270

001

00102

00104

00106

00108

0011

00112

00114

00116

00118

0012

(b)








(b)

7 Conclusions





References

































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of




CP1198902119890

def= sum 120572

1sdot 1205851

sdot 119876 ⟨1198901 119890

119896minus1⟩ sdot 120572

120595(119901119896)

sdot 120585120595

sdot 119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1sdot 120585120595+1

sdot 119865120595

⟨1198901 119890

119896minus1⟩ sdot 120572

120595(119901119896) sdot 120585

120595


119865120595

⟨1198901 119890

119896⟩ sdot 120572

120595+1(1198901 119890

119896)

sdot 120585120595+1

sdot 120572120595

(119901119896) sdot 120585120595

(7)











Network layer

WFQ MACPHYWiMAX

WiFihlpfp





119879dom 2=

119873

sum119897=1

119875dom 2 load119871dom 2

119877119897119891 (120574

119897) (8)







120574119897

=119875119897

1198730

lowast 119877119897

(9)


0is the one-sided



119890by

119891 (120574119897) = (1 minus 119875

119890(120574))

119871dom 2119887 (10)



119875119890

(120574) = 4 (1 minus1

21198872) 119876 (119909) (11)


119876 (119909) =119890minus11990922

4mod+

1

2mod


exp(minus1199092

2sin2120579119895

) (12)

where 120579119895




defined as

119901119890

= 1 minus (1 minus 119875BER)119871119886 (13)




119875dom 1 load =119871dom 1


(14)

where




thp119904119861

= (119910119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891 lceil120591119898

119894119861

119871dom 1

119871dom 2

rceil 120601 ( 120574119894)

+119910119904119875119904119889

[1

120593119904

] )

minus1

(16)

where 119910119904











119894119861= 119871dom 2

120588119898119894119861


119898

119894119861= sum

119897isinL119894

120574119898

119894119861119897Δ119891








119894equiv 119891 and

120593119894

equiv 120593


thpHMAN119904119861

= (119884119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891119901119894


119894119861

119871dom 1

(1 minus 119901119890) 119871dom 2

rceil 119891 (120574119897)

+119884119904

[1

120593119904

] )

minus1

(17)

where119891(120574119897) = (1 minus 119875

119890(120574))



thpHMAN119904119861

= (119884119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891119901119894

times [[[

119873

sum119895=1

119875dom 2 load119871dom 2

119875dom 1 load120588119898119894119861

(1 minus 119901119890)

]]]

times119891 (120574119897) + 119884

119904[

1

120593119904

])

minus1

(18)



119904119861is then

defined as follows

thpHMAN119904119861

=V

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906

(19)

where V = 119884119904(1 minus 120593)

119899 ℎ = 120587119894119904119889

119891(120593119894)minus1 119911(119871dom 1

119871dom 2) =

120587119892119904119889

119891119901119894119879lceil119875dom 1 load120588119898

119892119861(1 minus 119901

119890)rceil 119906 = 119884

119904[1120593

119904] and 119879 =

sum119873

119895=1(119875dom 2 load119871dom 2

)119891(120574119895)





119889thpHMAN119904119861

119889119871dom 2

= minusV [1199111015840 (119871dom 1

119871dom 2)]

[sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]2

(20)

where

119911 (119871dom 1 119871dom 2

)

= 120587119892119904119889

119891119901119894

119873

sum119895=1


119871dom 2

times (1 minus 119875119890

(120574119895))

119871dom 2119887lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

(21)



as

119889119911 (119871dom 1 119871dom 2

)

119889119871dom 2

= 120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]

(22)


minusV [1199111015840 (119871dom 1

119871dom 2)]

[sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

)]2

= 0

minus (V[120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]])

times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

)]

]

2

)

minus1

= 0

V[120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]] = 0

119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887= 0

(23)



119871lowast

dom 2

=119874bytes

2+


119890(120574)))

2

(24)






119889thpHMAN119904119861

119889119871dom 1

= minus (V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861



times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]

]

2

)

minus1

(25)


(V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861



times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]

]

2

)

minus1

= 0


minus200

0

200

400

600

8000 500 1000 1500 2000


V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861




(26)



119871lowast


11003816100381610038161003816ln (1 minus 119875BER)

1003816100381610038161003816 (27)


BER 119875BER





119863119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882119901119905

119894+ 120591

succ119894119904119889

) (28)

where 119882119901119905

119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus 119891

119894)119891


119904119861(120591119865119894

minus 120591119876

119894((1 minus

119891119894)119891



119894 120591119865119894

= sum119904119889

(120587119894119904119889

120587119894)119879


of 119865119894 120591

119876

119894= sum

119889120593119894119879119894119894119889



119894= sum

119904119889120587119894119904119889

119891119894119877119901119905

119894119904119889+ sum

119889119875119894119889

(1 minus 120587119894119891119894)119877

119901119905

119894119894119889 where

119877119901119905

119894119904119889=

119879(2)

119894119904119861

2119879119894119904119861

minus1

2 if 119894 isin 119878

119892and 119889 = 119861

119879(2)

119894119904119889

2119879119894119904119889

+1

2 otherwise

(29)



119879(2)

119894119904119861=

Ψ(2)

119894119904119889lceil

120591119898119894119861

120591119886rceil

2

if 119894 isin 119878119892and 119889 = 119861

Ψ(2)

119894119904119889+ Ψ

119894119904119889(1 minus 120593

119894)

1205932119894

otherwise

(30)

as 120591succ119894119904119889



120591succ119894119904119889



120591succ119894119904119889

=Ψsucc119894119904119889

120593119894

(31)

whereΨsucc119894119904119889

= sum119896119894119904119889

119896=1119896(1 minus 119875

119894119904119889)119896minus1

119875119894119904119889



119863HMAN119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882HMAN119901119905

119894+ 120591

succ119894119904119889

) (32)

Based on 119882119901119905



119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus

119891119901119894)119891


119904119861(120591119865119894

minus 120591119876

119894((1 minus 119891119901

119894)119891

119901119894))) The












Node ID 1 2 3 4 5 6 7 8 9 B119883 (m) 190 160 60 0 135 0 230 2300 1400 1000119884 (m) 10 80 60 80 0 30 60 10 60 30











010203040506070809

19

9535

102

475

104

108

105

2310

608

110

676

310

713

310

782

108

145

108

622

108

9610

916

6

PSR

SNR (dB)Flow a

010203040506070809

1

963

629

511

961

299

6354

951

819

7605

960

839

7273

972

629

9852

977

849

7103

PSR

SNR (dB)Flow b

010203040506070809

1

995

3510

247

510

410

810

523

106

081

106

763

107

333

107

8210

824

510

862

210

896

109

266

PSR

SNR (dB)Flow c

(a)

010203040506070809

1

873

188

8638

883

948

9012

900

648

998

898

519

0024

900

639

0196

901

968

9033

PSR

SNR (dB)

010203040506070809

19

3193

917

159

2438

920

59

2084

941

759

3481

940

59

3887

939

819

4537

938

33

PSR

SNR (dB)

010203040506070809

1

873

18

882

74

893

2

900

33

897

16

878

16

891

03

901

38

897

79

901

96

909

76

899

33

PSR


(b)





Modulationorder

TargetSINR (db)

Codingorder


BPSK 64 12 05

QPSK 94 12 1

QPSK 112 34 15

16-QAM 164 12 2

16-QAM 182 34 3

64-QAM 223 23 4

64-QAM 244 34 45

Single carrierBPSK

16-QAM64-QAM


Pack

et su

cces

s rat

e

099

098

097

096

095

094

093

092

091

090 01 02 03 04 05 06 07 08 09 1

1

times10minus4





0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01

011

012


Nor

mal

ized

thro

ughp

ut


(a)

0 200 400 600 800 1000 1200006

0065

007

0075

008

0085

009

0095

01

0105


Nor

mal

ized

thro

ughp

ut


(b)

0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01


Nor

mal

ized

thro

ughp

ut


(c)



119894) = (1 minus 119890minus120574119894)





1198751 1198752 1198753 1198754 1198755 1198756 1198757 1198758 1198759

05 07 04 03 07 04 0 0 0



0 200 400 600 800 1000 12000

10

20

30

40

50

60

70D

elay

(ms)




(a)

0 200 400 600 800 1000 12000

20

40

60

80

100

Del

ay (m

s)




(b)

0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

Del

ay (m

s)




(c)




Table 7 BER values


1 b 186119890 minus 4 47119890 minus 5

2 a c 4119890 minus 4 95119890 minus 5

2 b 915119890 minus 5 46119890 minus 5






Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

135

130

125

120

115

110

105

10001 015 02 025 03 035 04 045 05 055 06

(a)

Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

295

290

285

280

275

270

001

00102

00104

00106

00108

0011

00112

00114

00116

00118

0012

(b)








(b)

7 Conclusions





References

































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of





119875dom 1 load =119871dom 1


(14)

where




thp119904119861

= (119910119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891 lceil120591119898

119894119861

119871dom 1

119871dom 2

rceil 120601 ( 120574119894)

+119910119904119875119904119889

[1

120593119904

] )

minus1

(16)

where 119910119904











119894119861= 119871dom 2

120588119898119894119861


119898

119894119861= sum

119897isinL119894

120574119898

119894119861119897Δ119891








119894equiv 119891 and

120593119894

equiv 120593


thpHMAN119904119861

= (119884119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891119901119894


119894119861

119871dom 1

(1 minus 119901119890) 119871dom 2

rceil 119891 (120574119897)

+119884119904

[1

120593119904

] )

minus1

(17)

where119891(120574119897) = (1 minus 119875

119890(120574))



thpHMAN119904119861

= (119884119904(1 minus 120593)

119899(|119894119861|+1))

times ( sum119904119889119894isin119877

119904119889119894isin119878119892

120587119894119904119889

119891(120593119894)minus1

+ 120587119892119904119889

119891119901119894

times [[[

119873

sum119895=1

119875dom 2 load119871dom 2

119875dom 1 load120588119898119894119861

(1 minus 119901119890)

]]]

times119891 (120574119897) + 119884

119904[

1

120593119904

])

minus1

(18)



119904119861is then

defined as follows

thpHMAN119904119861

=V

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906

(19)

where V = 119884119904(1 minus 120593)

119899 ℎ = 120587119894119904119889

119891(120593119894)minus1 119911(119871dom 1

119871dom 2) =

120587119892119904119889

119891119901119894119879lceil119875dom 1 load120588119898

119892119861(1 minus 119901

119890)rceil 119906 = 119884

119904[1120593

119904] and 119879 =

sum119873

119895=1(119875dom 2 load119871dom 2

)119891(120574119895)





119889thpHMAN119904119861

119889119871dom 2

= minusV [1199111015840 (119871dom 1

119871dom 2)]

[sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]2

(20)

where

119911 (119871dom 1 119871dom 2

)

= 120587119892119904119889

119891119901119894

119873

sum119895=1


119871dom 2

times (1 minus 119875119890

(120574119895))

119871dom 2119887lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

(21)



as

119889119911 (119871dom 1 119871dom 2

)

119889119871dom 2

= 120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]

(22)


minusV [1199111015840 (119871dom 1

119871dom 2)]

[sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

)]2

= 0

minus (V[120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]])

times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

)]

]

2

)

minus1

= 0

V[120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]] = 0

119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887= 0

(23)



119871lowast

dom 2

=119874bytes

2+


119890(120574)))

2

(24)






119889thpHMAN119904119861

119889119871dom 1

= minus (V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861



times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]

]

2

)

minus1

(25)


(V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861



times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]

]

2

)

minus1

= 0


minus200

0

200

400

600

8000 500 1000 1500 2000


V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861




(26)



119871lowast


11003816100381610038161003816ln (1 minus 119875BER)

1003816100381610038161003816 (27)


BER 119875BER





119863119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882119901119905

119894+ 120591

succ119894119904119889

) (28)

where 119882119901119905

119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus 119891

119894)119891


119904119861(120591119865119894

minus 120591119876

119894((1 minus

119891119894)119891



119894 120591119865119894

= sum119904119889

(120587119894119904119889

120587119894)119879


of 119865119894 120591

119876

119894= sum

119889120593119894119879119894119894119889



119894= sum

119904119889120587119894119904119889

119891119894119877119901119905

119894119904119889+ sum

119889119875119894119889

(1 minus 120587119894119891119894)119877

119901119905

119894119894119889 where

119877119901119905

119894119904119889=

119879(2)

119894119904119861

2119879119894119904119861

minus1

2 if 119894 isin 119878

119892and 119889 = 119861

119879(2)

119894119904119889

2119879119894119904119889

+1

2 otherwise

(29)



119879(2)

119894119904119861=

Ψ(2)

119894119904119889lceil

120591119898119894119861

120591119886rceil

2

if 119894 isin 119878119892and 119889 = 119861

Ψ(2)

119894119904119889+ Ψ

119894119904119889(1 minus 120593

119894)

1205932119894

otherwise

(30)

as 120591succ119894119904119889



120591succ119894119904119889



120591succ119894119904119889

=Ψsucc119894119904119889

120593119894

(31)

whereΨsucc119894119904119889

= sum119896119894119904119889

119896=1119896(1 minus 119875

119894119904119889)119896minus1

119875119894119904119889



119863HMAN119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882HMAN119901119905

119894+ 120591

succ119894119904119889

) (32)

Based on 119882119901119905



119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus

119891119901119894)119891


119904119861(120591119865119894

minus 120591119876

119894((1 minus 119891119901

119894)119891

119901119894))) The












Node ID 1 2 3 4 5 6 7 8 9 B119883 (m) 190 160 60 0 135 0 230 2300 1400 1000119884 (m) 10 80 60 80 0 30 60 10 60 30











010203040506070809

19

9535

102

475

104

108

105

2310

608

110

676

310

713

310

782

108

145

108

622

108

9610

916

6

PSR

SNR (dB)Flow a

010203040506070809

1

963

629

511

961

299

6354

951

819

7605

960

839

7273

972

629

9852

977

849

7103

PSR

SNR (dB)Flow b

010203040506070809

1

995

3510

247

510

410

810

523

106

081

106

763

107

333

107

8210

824

510

862

210

896

109

266

PSR

SNR (dB)Flow c

(a)

010203040506070809

1

873

188

8638

883

948

9012

900

648

998

898

519

0024

900

639

0196

901

968

9033

PSR

SNR (dB)

010203040506070809

19

3193

917

159

2438

920

59

2084

941

759

3481

940

59

3887

939

819

4537

938

33

PSR

SNR (dB)

010203040506070809

1

873

18

882

74

893

2

900

33

897

16

878

16

891

03

901

38

897

79

901

96

909

76

899

33

PSR


(b)





Modulationorder

TargetSINR (db)

Codingorder


BPSK 64 12 05

QPSK 94 12 1

QPSK 112 34 15

16-QAM 164 12 2

16-QAM 182 34 3

64-QAM 223 23 4

64-QAM 244 34 45

Single carrierBPSK

16-QAM64-QAM


Pack

et su

cces

s rat

e

099

098

097

096

095

094

093

092

091

090 01 02 03 04 05 06 07 08 09 1

1

times10minus4





0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01

011

012


Nor

mal

ized

thro

ughp

ut


(a)

0 200 400 600 800 1000 1200006

0065

007

0075

008

0085

009

0095

01

0105


Nor

mal

ized

thro

ughp

ut


(b)

0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01


Nor

mal

ized

thro

ughp

ut


(c)



119894) = (1 minus 119890minus120574119894)





1198751 1198752 1198753 1198754 1198755 1198756 1198757 1198758 1198759

05 07 04 03 07 04 0 0 0



0 200 400 600 800 1000 12000

10

20

30

40

50

60

70D

elay

(ms)




(a)

0 200 400 600 800 1000 12000

20

40

60

80

100

Del

ay (m

s)




(b)

0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

Del

ay (m

s)




(c)




Table 7 BER values


1 b 186119890 minus 4 47119890 minus 5

2 a c 4119890 minus 4 95119890 minus 5

2 b 915119890 minus 5 46119890 minus 5






Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

135

130

125

120

115

110

105

10001 015 02 025 03 035 04 045 05 055 06

(a)

Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

295

290

285

280

275

270

001

00102

00104

00106

00108

0011

00112

00114

00116

00118

0012

(b)








(b)

7 Conclusions





References

































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of






119889thpHMAN119904119861

119889119871dom 2

= minusV [1199111015840 (119871dom 1

119871dom 2)]

[sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]2

(20)

where

119911 (119871dom 1 119871dom 2

)

= 120587119892119904119889

119891119901119894

119873

sum119895=1


119871dom 2

times (1 minus 119875119890

(120574119895))

119871dom 2119887lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

(21)



as

119889119911 (119871dom 1 119871dom 2

)

119889119871dom 2

= 120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]

(22)


minusV [1199111015840 (119871dom 1

119871dom 2)]

[sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

)]2

= 0

minus (V[120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]])

times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

)]

]

2

)

minus1

= 0

V[120587119892119904119889

119891119901119894lceil

119875dom 1 load120588119898119892119861

(1 minus 119901119890)

rceil

times [119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)

times119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887]] = 0

119874bytes

1198712dom 2

119891 (120574119895) + (1 minus

119874bytes

119871dom 2

)119891 (120574

119895) ln (1 minus 119875

119890(120574119895))

119887= 0

(23)



119871lowast

dom 2

=119874bytes

2+


119890(120574)))

2

(24)






119889thpHMAN119904119861

119889119871dom 1

= minus (V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861



times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]

]

2

)

minus1

(25)


(V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861



times ([

[

sum119904119889119894isin119877

119904119889119894isin119878119892

ℎ + 119911 (119871dom 1 119871dom 2

) + 119906]

]

2

)

minus1

= 0


minus200

0

200

400

600

8000 500 1000 1500 2000


V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861




(26)



119871lowast


11003816100381610038161003816ln (1 minus 119875BER)

1003816100381610038161003816 (27)


BER 119875BER





119863119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882119901119905

119894+ 120591

succ119894119904119889

) (28)

where 119882119901119905

119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus 119891

119894)119891


119904119861(120591119865119894

minus 120591119876

119894((1 minus

119891119894)119891



119894 120591119865119894

= sum119904119889

(120587119894119904119889

120587119894)119879


of 119865119894 120591

119876

119894= sum

119889120593119894119879119894119894119889



119894= sum

119904119889120587119894119904119889

119891119894119877119901119905

119894119904119889+ sum

119889119875119894119889

(1 minus 120587119894119891119894)119877

119901119905

119894119894119889 where

119877119901119905

119894119904119889=

119879(2)

119894119904119861

2119879119894119904119861

minus1

2 if 119894 isin 119878

119892and 119889 = 119861

119879(2)

119894119904119889

2119879119894119904119889

+1

2 otherwise

(29)



119879(2)

119894119904119861=

Ψ(2)

119894119904119889lceil

120591119898119894119861

120591119886rceil

2

if 119894 isin 119878119892and 119889 = 119861

Ψ(2)

119894119904119889+ Ψ

119894119904119889(1 minus 120593

119894)

1205932119894

otherwise

(30)

as 120591succ119894119904119889



120591succ119894119904119889



120591succ119894119904119889

=Ψsucc119894119904119889

120593119894

(31)

whereΨsucc119894119904119889

= sum119896119894119904119889

119896=1119896(1 minus 119875

119894119904119889)119896minus1

119875119894119904119889



119863HMAN119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882HMAN119901119905

119894+ 120591

succ119894119904119889

) (32)

Based on 119882119901119905



119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus

119891119901119894)119891


119904119861(120591119865119894

minus 120591119876

119894((1 minus 119891119901

119894)119891

119901119894))) The












Node ID 1 2 3 4 5 6 7 8 9 B119883 (m) 190 160 60 0 135 0 230 2300 1400 1000119884 (m) 10 80 60 80 0 30 60 10 60 30











010203040506070809

19

9535

102

475

104

108

105

2310

608

110

676

310

713

310

782

108

145

108

622

108

9610

916

6

PSR

SNR (dB)Flow a

010203040506070809

1

963

629

511

961

299

6354

951

819

7605

960

839

7273

972

629

9852

977

849

7103

PSR

SNR (dB)Flow b

010203040506070809

1

995

3510

247

510

410

810

523

106

081

106

763

107

333

107

8210

824

510

862

210

896

109

266

PSR

SNR (dB)Flow c

(a)

010203040506070809

1

873

188

8638

883

948

9012

900

648

998

898

519

0024

900

639

0196

901

968

9033

PSR

SNR (dB)

010203040506070809

19

3193

917

159

2438

920

59

2084

941

759

3481

940

59

3887

939

819

4537

938

33

PSR

SNR (dB)

010203040506070809

1

873

18

882

74

893

2

900

33

897

16

878

16

891

03

901

38

897

79

901

96

909

76

899

33

PSR


(b)





Modulationorder

TargetSINR (db)

Codingorder


BPSK 64 12 05

QPSK 94 12 1

QPSK 112 34 15

16-QAM 164 12 2

16-QAM 182 34 3

64-QAM 223 23 4

64-QAM 244 34 45

Single carrierBPSK

16-QAM64-QAM


Pack

et su

cces

s rat

e

099

098

097

096

095

094

093

092

091

090 01 02 03 04 05 06 07 08 09 1

1

times10minus4





0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01

011

012


Nor

mal

ized

thro

ughp

ut


(a)

0 200 400 600 800 1000 1200006

0065

007

0075

008

0085

009

0095

01

0105


Nor

mal

ized

thro

ughp

ut


(b)

0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01


Nor

mal

ized

thro

ughp

ut


(c)



119894) = (1 minus 119890minus120574119894)





1198751 1198752 1198753 1198754 1198755 1198756 1198757 1198758 1198759

05 07 04 03 07 04 0 0 0



0 200 400 600 800 1000 12000

10

20

30

40

50

60

70D

elay

(ms)




(a)

0 200 400 600 800 1000 12000

20

40

60

80

100

Del

ay (m

s)




(b)

0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

Del

ay (m

s)




(c)




Table 7 BER values


1 b 186119890 minus 4 47119890 minus 5

2 a c 4119890 minus 4 95119890 minus 5

2 b 915119890 minus 5 46119890 minus 5






Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

135

130

125

120

115

110

105

10001 015 02 025 03 035 04 045 05 055 06

(a)

Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

295

290

285

280

275

270

001

00102

00104

00106

00108

0011

00112

00114

00116

00118

0012

(b)








(b)

7 Conclusions





References

































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of



minus200

0

200

400

600

8000 500 1000 1500 2000


V(120587119892119904119889

119891119901119894

119879

120591dom 1120588119898119892119861




(26)



119871lowast


11003816100381610038161003816ln (1 minus 119875BER)

1003816100381610038161003816 (27)


BER 119875BER





119863119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882119901119905

119894+ 120591

succ119894119904119889

) (28)

where 119882119901119905

119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus 119891

119894)119891


119904119861(120591119865119894

minus 120591119876

119894((1 minus

119891119894)119891



119894 120591119865119894

= sum119904119889

(120587119894119904119889

120587119894)119879


of 119865119894 120591

119876

119894= sum

119889120593119894119879119894119894119889



119894= sum

119904119889120587119894119904119889

119891119894119877119901119905

119894119904119889+ sum

119889119875119894119889

(1 minus 120587119894119891119894)119877

119901119905

119894119894119889 where

119877119901119905

119894119904119889=

119879(2)

119894119904119861

2119879119894119904119861

minus1

2 if 119894 isin 119878

119892and 119889 = 119861

119879(2)

119894119904119889

2119879119894119904119889

+1

2 otherwise

(29)



119879(2)

119894119904119861=

Ψ(2)

119894119904119889lceil

120591119898119894119861

120591119886rceil

2

if 119894 isin 119878119892and 119889 = 119861

Ψ(2)

119894119904119889+ Ψ

119894119904119889(1 minus 120593

119894)

1205932119894

otherwise

(30)

as 120591succ119894119904119889



120591succ119894119904119889



120591succ119894119904119889

=Ψsucc119894119904119889

120593119894

(31)

whereΨsucc119894119904119889

= sum119896119894119904119889

119896=1119896(1 minus 119875

119894119904119889)119896minus1

119875119894119904119889



119863HMAN119904119889

=Ψsucc119904119904119889

120593119904

+

|119877119904119889|

sum119894=1

(119882HMAN119901119905

119894+ 120591

succ119894119904119889

) (32)

Based on 119882119901119905



119894= (119877

119901119905

119894+ 120591

119876

119894((1 minus

119891119901119894)119891


119904119861(120591119865119894

minus 120591119876

119894((1 minus 119891119901

119894)119891

119901119894))) The












Node ID 1 2 3 4 5 6 7 8 9 B119883 (m) 190 160 60 0 135 0 230 2300 1400 1000119884 (m) 10 80 60 80 0 30 60 10 60 30











010203040506070809

19

9535

102

475

104

108

105

2310

608

110

676

310

713

310

782

108

145

108

622

108

9610

916

6

PSR

SNR (dB)Flow a

010203040506070809

1

963

629

511

961

299

6354

951

819

7605

960

839

7273

972

629

9852

977

849

7103

PSR

SNR (dB)Flow b

010203040506070809

1

995

3510

247

510

410

810

523

106

081

106

763

107

333

107

8210

824

510

862

210

896

109

266

PSR

SNR (dB)Flow c

(a)

010203040506070809

1

873

188

8638

883

948

9012

900

648

998

898

519

0024

900

639

0196

901

968

9033

PSR

SNR (dB)

010203040506070809

19

3193

917

159

2438

920

59

2084

941

759

3481

940

59

3887

939

819

4537

938

33

PSR

SNR (dB)

010203040506070809

1

873

18

882

74

893

2

900

33

897

16

878

16

891

03

901

38

897

79

901

96

909

76

899

33

PSR


(b)





Modulationorder

TargetSINR (db)

Codingorder


BPSK 64 12 05

QPSK 94 12 1

QPSK 112 34 15

16-QAM 164 12 2

16-QAM 182 34 3

64-QAM 223 23 4

64-QAM 244 34 45

Single carrierBPSK

16-QAM64-QAM


Pack

et su

cces

s rat

e

099

098

097

096

095

094

093

092

091

090 01 02 03 04 05 06 07 08 09 1

1

times10minus4





0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01

011

012


Nor

mal

ized

thro

ughp

ut


(a)

0 200 400 600 800 1000 1200006

0065

007

0075

008

0085

009

0095

01

0105


Nor

mal

ized

thro

ughp

ut


(b)

0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01


Nor

mal

ized

thro

ughp

ut


(c)



119894) = (1 minus 119890minus120574119894)





1198751 1198752 1198753 1198754 1198755 1198756 1198757 1198758 1198759

05 07 04 03 07 04 0 0 0



0 200 400 600 800 1000 12000

10

20

30

40

50

60

70D

elay

(ms)




(a)

0 200 400 600 800 1000 12000

20

40

60

80

100

Del

ay (m

s)




(b)

0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

Del

ay (m

s)




(c)




Table 7 BER values


1 b 186119890 minus 4 47119890 minus 5

2 a c 4119890 minus 4 95119890 minus 5

2 b 915119890 minus 5 46119890 minus 5






Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

135

130

125

120

115

110

105

10001 015 02 025 03 035 04 045 05 055 06

(a)

Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

295

290

285

280

275

270

001

00102

00104

00106

00108

0011

00112

00114

00116

00118

0012

(b)








(b)

7 Conclusions





References

































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of









Node ID 1 2 3 4 5 6 7 8 9 B119883 (m) 190 160 60 0 135 0 230 2300 1400 1000119884 (m) 10 80 60 80 0 30 60 10 60 30











010203040506070809

19

9535

102

475

104

108

105

2310

608

110

676

310

713

310

782

108

145

108

622

108

9610

916

6

PSR

SNR (dB)Flow a

010203040506070809

1

963

629

511

961

299

6354

951

819

7605

960

839

7273

972

629

9852

977

849

7103

PSR

SNR (dB)Flow b

010203040506070809

1

995

3510

247

510

410

810

523

106

081

106

763

107

333

107

8210

824

510

862

210

896

109

266

PSR

SNR (dB)Flow c

(a)

010203040506070809

1

873

188

8638

883

948

9012

900

648

998

898

519

0024

900

639

0196

901

968

9033

PSR

SNR (dB)

010203040506070809

19

3193

917

159

2438

920

59

2084

941

759

3481

940

59

3887

939

819

4537

938

33

PSR

SNR (dB)

010203040506070809

1

873

18

882

74

893

2

900

33

897

16

878

16

891

03

901

38

897

79

901

96

909

76

899

33

PSR


(b)





Modulationorder

TargetSINR (db)

Codingorder


BPSK 64 12 05

QPSK 94 12 1

QPSK 112 34 15

16-QAM 164 12 2

16-QAM 182 34 3

64-QAM 223 23 4

64-QAM 244 34 45

Single carrierBPSK

16-QAM64-QAM


Pack

et su

cces

s rat

e

099

098

097

096

095

094

093

092

091

090 01 02 03 04 05 06 07 08 09 1

1

times10minus4





0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01

011

012


Nor

mal

ized

thro

ughp

ut


(a)

0 200 400 600 800 1000 1200006

0065

007

0075

008

0085

009

0095

01

0105


Nor

mal

ized

thro

ughp

ut


(b)

0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01


Nor

mal

ized

thro

ughp

ut


(c)



119894) = (1 minus 119890minus120574119894)





1198751 1198752 1198753 1198754 1198755 1198756 1198757 1198758 1198759

05 07 04 03 07 04 0 0 0



0 200 400 600 800 1000 12000

10

20

30

40

50

60

70D

elay

(ms)




(a)

0 200 400 600 800 1000 12000

20

40

60

80

100

Del

ay (m

s)




(b)

0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

Del

ay (m

s)




(c)




Table 7 BER values


1 b 186119890 minus 4 47119890 minus 5

2 a c 4119890 minus 4 95119890 minus 5

2 b 915119890 minus 5 46119890 minus 5






Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

135

130

125

120

115

110

105

10001 015 02 025 03 035 04 045 05 055 06

(a)

Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

295

290

285

280

275

270

001

00102

00104

00106

00108

0011

00112

00114

00116

00118

0012

(b)








(b)

7 Conclusions





References

































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of



010203040506070809

19

9535

102

475

104

108

105

2310

608

110

676

310

713

310

782

108

145

108

622

108

9610

916

6

PSR

SNR (dB)Flow a

010203040506070809

1

963

629

511

961

299

6354

951

819

7605

960

839

7273

972

629

9852

977

849

7103

PSR

SNR (dB)Flow b

010203040506070809

1

995

3510

247

510

410

810

523

106

081

106

763

107

333

107

8210

824

510

862

210

896

109

266

PSR

SNR (dB)Flow c

(a)

010203040506070809

1

873

188

8638

883

948

9012

900

648

998

898

519

0024

900

639

0196

901

968

9033

PSR

SNR (dB)

010203040506070809

19

3193

917

159

2438

920

59

2084

941

759

3481

940

59

3887

939

819

4537

938

33

PSR

SNR (dB)

010203040506070809

1

873

18

882

74

893

2

900

33

897

16

878

16

891

03

901

38

897

79

901

96

909

76

899

33

PSR


(b)





Modulationorder

TargetSINR (db)

Codingorder


BPSK 64 12 05

QPSK 94 12 1

QPSK 112 34 15

16-QAM 164 12 2

16-QAM 182 34 3

64-QAM 223 23 4

64-QAM 244 34 45

Single carrierBPSK

16-QAM64-QAM


Pack

et su

cces

s rat

e

099

098

097

096

095

094

093

092

091

090 01 02 03 04 05 06 07 08 09 1

1

times10minus4





0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01

011

012


Nor

mal

ized

thro

ughp

ut


(a)

0 200 400 600 800 1000 1200006

0065

007

0075

008

0085

009

0095

01

0105


Nor

mal

ized

thro

ughp

ut


(b)

0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01


Nor

mal

ized

thro

ughp

ut


(c)



119894) = (1 minus 119890minus120574119894)





1198751 1198752 1198753 1198754 1198755 1198756 1198757 1198758 1198759

05 07 04 03 07 04 0 0 0



0 200 400 600 800 1000 12000

10

20

30

40

50

60

70D

elay

(ms)




(a)

0 200 400 600 800 1000 12000

20

40

60

80

100

Del

ay (m

s)




(b)

0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

Del

ay (m

s)




(c)




Table 7 BER values


1 b 186119890 minus 4 47119890 minus 5

2 a c 4119890 minus 4 95119890 minus 5

2 b 915119890 minus 5 46119890 minus 5






Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

135

130

125

120

115

110

105

10001 015 02 025 03 035 04 045 05 055 06

(a)

Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

295

290

285

280

275

270

001

00102

00104

00106

00108

0011

00112

00114

00116

00118

0012

(b)








(b)

7 Conclusions





References

































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of



0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01

011

012


Nor

mal

ized

thro

ughp

ut


(a)

0 200 400 600 800 1000 1200006

0065

007

0075

008

0085

009

0095

01

0105


Nor

mal

ized

thro

ughp

ut


(b)

0 200 400 600 800 1000 1200003

004

005

006

007

008

009

01


Nor

mal

ized

thro

ughp

ut


(c)



119894) = (1 minus 119890minus120574119894)





1198751 1198752 1198753 1198754 1198755 1198756 1198757 1198758 1198759

05 07 04 03 07 04 0 0 0



0 200 400 600 800 1000 12000

10

20

30

40

50

60

70D

elay

(ms)




(a)

0 200 400 600 800 1000 12000

20

40

60

80

100

Del

ay (m

s)




(b)

0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

Del

ay (m

s)




(c)




Table 7 BER values


1 b 186119890 minus 4 47119890 minus 5

2 a c 4119890 minus 4 95119890 minus 5

2 b 915119890 minus 5 46119890 minus 5






Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

135

130

125

120

115

110

105

10001 015 02 025 03 035 04 045 05 055 06

(a)

Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

295

290

285

280

275

270

001

00102

00104

00106

00108

0011

00112

00114

00116

00118

0012

(b)








(b)

7 Conclusions





References

































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of



0 200 400 600 800 1000 12000

10

20

30

40

50

60

70D

elay

(ms)




(a)

0 200 400 600 800 1000 12000

20

40

60

80

100

Del

ay (m

s)




(b)

0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

Del

ay (m

s)




(c)




Table 7 BER values


1 b 186119890 minus 4 47119890 minus 5

2 a c 4119890 minus 4 95119890 minus 5

2 b 915119890 minus 5 46119890 minus 5






Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

135

130

125

120

115

110

105

10001 015 02 025 03 035 04 045 05 055 06

(a)

Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

295

290

285

280

275

270

001

00102

00104

00106

00108

0011

00112

00114

00116

00118

0012

(b)








(b)

7 Conclusions





References

































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of



Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

135

130

125

120

115

110

105

10001 015 02 025 03 035 04 045 05 055 06

(a)

Opt

imal

pac

ket l

engt

h (b

ytes

)

Packet error rate

295

290

285

280

275

270

001

00102

00104

00106

00108

0011

00112

00114

00116

00118

0012

(b)








(b)

7 Conclusions





References

































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of



References

































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of



VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of


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