research article capacity enhancement in 60ghz based d2d...

Research ArticleCapacity Enhancement in 60 GHz Based D2D Networks by RelaySelection and Scheduling

Waheed ur Rehman Tabinda Salam Jin Xu and Xiaofeng Tao

National Engineering Laboratory for Mobile Network Security Key Laboratory of Universal Wireless CommunicationsMinistry of Education Beijing University of Posts and Telecommunications Beijing 100876 China

Correspondence should be addressed to Xiaofeng Tao taoxfbupteducn

Received 27 June 2014 Revised 26 August 2014 Accepted 26 August 2014

Academic Editor Lingyang Song

Copyright copy 2015 Waheed ur Rehman et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Millimeter-wave or 60GHz communication is a promising technology that enables data rates in multigigabits However itstremendous propagation loss and signal blockage may severely affect the network throughput In current data-centric device-to-device (D2D) communication networks the devices with intended data communications usually lay in close proximity unlikethe case in voice-centric networks So the network can be visualized as a naturally formed groups of devices In this paper wejointly consider resource scheduling and relay selection to improve network capacity in 60GHz based D2D networks Two typesof transmission scenarios are considered in wireless personal area networks (WPANs) intra and intergroup A distributed receiverbased relay selection scheme is proposed for intragroup transmission while a distance based relay selection scheme is proposed forintergroup transmission The outage analysis of our proposed relay selection scheme is provided along with the numerical resultsWe then propose a concurrent transmission scheduling algorithm based on vertex coloring technique The proposed schedulingalgorithm employs time and space division inmmWaveWPANs Using vertexmulticoloring we allow transmitter-receiver (119879119909-119877119909)communication pairs to span overmore colors enabling better time slot utilizationWe evaluate our scheduling algorithm in single-hop and multihop scenarios and discover that it outperforms other schemes by significantly improving network throughput

1 Introduction

The demand for high-bandwidth applications in the recentyears has been growing exponentially The high-speed Inter-net has raised users expectations to a level where they areimpatient to wait for their data communication requests60GHz communication network promises data rate in giga-bits and can be used in both indoor [1] and outdoor scenarios[2] Device-to-device (D2D) being an emerging technologyhelps offload the data from the central node by encouragingdirect communication between transceivers Both 60GHzand D2D are also seen as enablers for 5G networks [3 4]The confluence of 60GHz with D2D communication can beseen as paragon that satisfies users quality of experience [5]by enhancing network capacity

One of the unique characteristics of 60GHz networks isits tremendous propagation loss which severely affects thedata rates However unlike traditional networks [6] this

characteristic reduces the impact of interference in 60GHzPropagation loss coupled with shortage of multipath signalsentails the use of line-of-sight (LOS) communication toachieve higher data rates Directive antennas are employedto cater for propagation loss and attaining data rates inmultigigabits However directive antennas result in anothernuisance a signal blockage which may result in signalattenuation up to 40 dB [7] The network capacity in 60GHznetworks is severely affected by signal blockage and prop-agation loss Beamforming (BF) [8ndash10] can partially rectifythe signal blockage problem by steering the signal around theobstacle rather than burning through them However in BFneighbor discovery procedure normally requires significanttime for signaling Thus system throughput is significantlyaffected in dense deployment

The use of relays in 60GHz basedD2Dnetworks providesan alternative for signal blockage Relays not only help in sig-nal blockage but also reduce the tremendous propagation loss

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2015 Article ID 205163 15 pageshttpdxdoiorg1011552015205163

2 International Journal of Antennas and Propagation

[11] The effect of distance in 60GHz networks is detrimentalas compared to networks operating at lower frequenciesRelays partition a communication link into shorter distancesand help achieve the so-called ldquodistance gainrdquo

In short-ranged data-centric communication networkthe premise that two parties initiate communication to bein close proximity is acceptable contrary to voice-centricnetworks Rather it would be common to have a situa-tion where several co-located devices (DEVs) would liketo share contents such as digital pictures or interact forapplications such as video gaming and social networking[12] As a result the network can be visualized as naturallyformed groups rather than DEVs scattered randomly Insuch scenario usually the transmitter and receiver (119879119909 119877119909)pair stays for the duration of their transmission Examplesmay include file transfer kiosk home entertainment systemwhere sound system HDTV and gaming devices are in closeproximity along with the people intending to communicatewith them Two types of communication may be seen insuch scenario intra and intergroup transmission Due to therationale behind such grouping it can safely be assumedthat most of the times nearby devices would be involvedin data communications with occasional distant devicesWe devised two algorithms each for intra and intergroupcommunication respectively A receiver based distributedalgorithm is proposed for intragroup communication whilea centralized algorithm is proposed for intergroup transmis-sion In order to further improve network throughput wehave also proposed a concurrent transmission schedulingalgorithm that works jointly with relay selection schemes Itis also argued that network throughput in such short-rangednetworks mainly depends on scheduling scheme rather thantransmission power control [13] which makes it imperativeto have an efficient resource allocation scheme

The main contributions of this paper include the fol-lowing (1) To enhance network capacity in order to meetdemands of bandwidth craving applications we have pro-posed two relay selection algorithms a novel distributed relayselection scheme for intragroup transmission where DEVscan effectively select a relay by exploiting the directionalnature of 60GHz based D2D networks and also simple butan effective intergroup relay algorithm Both algorithms try tofind themidmost relay and try to select the relay to maximizedistance gain (2) Capacity analysis is provided by utilizingour proposed relay selection algorithms in conjunction withour proposed concurrent transmission scheduling algorithmin [5]The scheduling algorithm ismodified to catermultihopscenario The simulation results show that our proposedalgorithms significantly improve the network capacity insingle- and multihop scenarios Multihopping in 60GHzbased D2D networks helps increase the network throughputby encouraging concurrent transmissions However inducedcomplexity and varying relay distances may seriously affectthe end-to-end data rate of an individual flow Applicationswith higher throughput requirement such as uncompressedhigh-definition videos and real-time audiovideo applica-tions have stringent quality of service requirements Sincelinks in mmWave require high data rate too many hopsthat exhibit uniform characteristics are very challenging

and can seriously affect the individual flows Therefore weare considering a two-hop scenario Furthermore we areconsidering an indoor scenario such as home or office wheremultiple hops may not be feasible In this paper two-hop andmultihop are interchangeably used

The rest of the paper is organized as follows Section 2provides an overview of related relay selection and schedulingalgorithm research work in 60GHz networks followed bysystem model in Section 3 The detailed discussion of ourproposed relay selection schemes and scheduling algorithmis provided in Section 4 Numerical results to compareour proposed schemes are given in Section 5 followed byconclusion in Section 6

2 Related Work

Relay selection and scheduling algorithm for 60GHz havegenerated sizable literature [7 11 14ndash22] in recent years Bothefforts are made to achieve one goal capacity enhancementeither directly or indirectlyThe first analytical and simulatedstudy on the use of relays in 60GHz is provided in [11] Thepaper shows that at least 33 of free space path loss can beimproved by using relays The paper also signifies the properpositioning of the relay However the simulation results areprovided on the basis of grid topology and fixed relaysmostlypositioned on ceiling Centralized relay selection approach isproposed in [7] where each sender DEV knows two pathsto the destination direct and relay path The relay path isdiscovered in advance and in case of blockage the datawould ldquodeflectrdquo through relay node Minimum cochannelinterference is considered as selection metric In [15] a relayselection scheme is proposed based on distance and trafficload The authors propose to replace a long direct path withseveral multihop paths to improve the network throughputA diffraction based model to determine network link con-nectivity is also studied in [16] It is shown that the proposedmultihop protocol works with highly directional antennaarrays and is able to maintain high network utilization withlow overhead Use of beam sectors is proposed in [17] todiscover an effective relay However the proposed scheme iscentralized and involves higher overhead and complexity Ajoint relay selection and analog network coding over two-way relay channels are proposed in [23] In the proposedrelay selection amplify-and-forward (RS-AF) scheme twosource nodes first transmit to all the relays at the same timeThe selected relay then broadcasts the signal back to bothsources to achieve a minimum sum symbol error rate (SER)A suboptimal Max-Min criterion is proposed to facilitate theselection process where a single relay which minimizes themaximum SER of two source nodes will be selected

Apart from relay selection scheduling algorithms arealso proposed for capacity enhancement in conjunctionwithwithout relay selection More recently in 60GHz net-works concurrent transmission is encouraged due to itshighly directional nature The concept of concurrent trans-mission is not new but coupled with the directional antennaand short-range nature of 60GHz networks its effective-ness can be multifolded The case of concurrent trans-mission scheduling has been investigated extensively in the

International Journal of Antennas and Propagation 3

Relay

Relay

RX3

Idle

Idle

RelayPNC

Idle

Idle

Relay

Relay

Tx1

Tx3

Tx7

Tx6

Tx5

Tx4

Tx

Tx3

TxRx2

Rx7 Rx6

Rx5

Rx4

RxRx

Rx1

Figure 1 System Model for Typical D2DWPAN

literature [18ndash22] The authors in [18] propose a hybridSDMATDMA scalable heuristic scheduling scheme forthroughput enhancement in practical mmWave systemsThe authors in [19] propose an opportunistic spatial reusealgorithm to allow concurrent transmission in 802153cnetworks In [20] the authors define an exclusive region(ER) condition to support concurrent transmission Theyfurther propose a randomized exclusive region (REX) basedscheduling scheme for resource allocation However REX is arandomized scheduling scheme with unpredictable iterationtimes based on greedy algorithm (GA) Qiao et al presenta multihop concurrent transmission algorithm in mmWaveWPAN [21] The proposed multihop algorithm improved thenetwork throughput as compared to single-hop concurrenttransmission The authors in [22] propose a concurrenttransmission algorithm based on DEVs locations Uponcollecting coordinates and transmission requests of DEVspiconet network controller (PNC) schedules noninterferedflows in the same time slot

3 System Model

A network based on 802153c with dense deployment ofDEVs is considered with one central DEV called PNCInitially DEVs are distributed randomly with a PNC in thecenter with quasi-omni transmission Over time due to thetendency of (119879119909 119877119909) pair to come closeWPAN has naturallyformed groups as shown in Figure 1 It is observed that insuch scenarios the communicating DEVs usually stay forthe duration of their transmission Direct transmission ispreferred for intragroup transmission However if the signalis blocked or the interference at certain antenna element getsgreater than a defined threshold an appropriate relay wouldbe selected distributively A DEVmay choose to send data toa distant DEV(s) in which case an intergroup relay selectionscheme would be initiated by PNC selecting an appropriaterelay to facilitate the transmission

31 Quasi-Omni Transmission for PNC Devices in 802153csuffer from high path loss at 60GHz frequency bandTherefore they should focus radiant energy for the datatransmissions in the intended direction Similarly they mayconcentrate on the energy for data receptions at a spe-cific direction to gather more power making it necessaryto employ directional communication technologies at the60GHz frequency bandThe PNC in 802153c should broad-cast beacons in all directions since every device connectedwith the PNC should receive the beacons for proper opera-tions Quasi-omni is a directional transmission but it mimicsomnidirectional transmission by consecutively rotating itstransmission direction through 360∘ [24] In the 802153cWPANs the PNC can adopt quasi-omni transmissions forbroadcast message transmissions

32 Antenna Model Highly directional antenna is consid-ered for ourmodel Directional antennas fall in two categories[25] sectoredswitched antenna array and adaptive antennaarrayWe are considering the former that can intelligently putamain beam in the direction of the desired signal andnullifiesin the directions of the interference In [26] Mudumbai etal also concluded that a mmWave link can be abstracted asa pesudowired link which shows support for our flat-topantenna model

Every DEV employs an antenna with 119873 beams each ofwhich spans an angle of 2120587119873 radians The transmitters andreceivers will always steer beams to each other Directionalantennas are characterized by their pattern functions thatmeasure the power gain 119866(120601) over the angle 120601 The normal-ized pattern function is defined as

119892 (120601) =119866 (120601)

119866max (1)

where 119866max = max120601119866(120601) In a flat-top antenna model the

antenna gain is constant that is 119892(120601) = 1 when |120601| le Δ1206012and 0 otherwise HereΔ120601 = 2120587119873 is the antenna beamwidth


Thus the antenna gains for (119879119909 119877119909) pair will be 119866119905= 119866119903= 1

within the antenna beamwidth and 119866119905= 119866119903= 0 outside

33 mmWave Transmission Model The capacity of an addi-tive white Gaussian noise (AWGN) channel with broadbandinterference assumed as Gaussian distribution is given by

119862 = 119882 log2

[1 +119875119903

(1198730+ 119868)119882

] (2)

where 119875119903is the received signal power 119882 is the system

bandwidth and1198730and 119868 are the one-side power spectral den-

sities of white Gaussian noise and broadband interferencerespectively The received signal power can be calculatedusing Friis transmission equation as

119875119903(119889) = 119875

119905119866119903119866119905(120582

4120587)

2

(1

119889)

119899

(3)

where 119875119905is the transmit power 119866

119903and 119866

119905are the antenna

gains of receiver and transmitter respectively 120582 is the wave-length (usually taken as 5mm) 119889 is the transmission distancebetween (119879119909 119877119909) pair and 119899 is the path loss exponent(usually in the range of 2 to 6 for indoor scenarios) Bycombining (3) and (4) the data rate can be obtained as

119877 le 119862 = 119882120573 log2

[1 +1198751199051198661199031198661199051205822

161205872 (1198730+ 119868)119882119889119899

] (4)

Here 120573 is the data rate loss due to the noncontinuity of time-slot resource and 0 le 120573 le 1 We can observe from (4) thatthe flow throughput reduction over distance is more seriousin 60GHz network due to its large bandwidth and smallwavelength

34 Two-Hop Relay Model We are considering a typicalindoor environment with possibility of concurrent transmis-sions as shown in Figure 1We can see that flows are scheduledin the same time slot possibly interfering with one anotherAll 119879119909DEVs are transmitting at fixed average power withoutany power control schemesWe are also considering obstaclesthat block the direct path and hence no direct path existsbetween 119879119909 and 119877119909 In order to improve the DEVrsquos signal-to-noise ratio (SNR) a relay can be selected using our proposedalgorithm Decode-and-forward (DAF) relays are consideredwith half-duplex communication that is in the first hop 119879119909transmits data to relay which is decoded by the relay whichthen transmits to 119877119909 in the second hop

As we can see in Figures 2 and 3119862 and119860 are transmittingdata to 119863 and 119861 respectively in both inter- and intragrouptransmission scenarios In case of blockage of LOS pathbetween (119862119863) flow data may be relayed through 119877 If 119875119862

119905

is the transmit power of 119862 the received SNR at 119877 can beexpressed as

120574119862119877=

119875119862

119905

119870119862119877(1198890radic1198672 + 119889

2

1

)

119899

120576119862119877

1003816100381610038161003816ℎ1198621198771003816100381610038161003816

2

1198730

(5)

R

d1

d2

Relay pathDirect path

A4 A5

A12

A6

A10

A7

A1

A2

A3

A9

A11A13A14

C

D

A

B

Figure 2 Intergroup multihop scenario

32

14

5

6 78

R

d1

d2


C

D

A

B

Figure 3 Intragroup multihop scenario

where119870119862119877

is free space path loss at11988901198890is reference distance

(1m) 119899 is path loss exponent119867 is the height of transmittingDEV (taken as constant for all DEVs except PNC) 119889

1is

the transmitter-relay distance 120576119862119877= 10minus(12060111988911986110) denotes the

shadow fading 120601119889119861

is zero mean Gaussian random variableℎ119862119877

is channel coefficient of the (119862 119877) link and 1198730is the

average background white Gaussian noise powerAssume that relay 119877 has transmit power 119875119877

119905

and theinterfering flow has an average transmit power 119901119868

119905

then the


received signal-to-interference-plus-noise ratio (SINR) canbe expressed as

120574119877119863=

119875119903(119910)

119875119903(119910119868) + 1198730

=119875119877

119905

119870119877119863(11988901198892)119899

120576119877119863

1003816100381610038161003816ℎ1198771198631003816100381610038161003816

2

119875119868

119905

119870119868(1198890119889119868)119899

120576119868

1003816100381610038161003816ℎ1198681003816100381610038161003816

2

+ 1198730

(6)

where 119875119903(119910) is the received desired signal power and 119875

119903(119910119868) is

the interference power at receiver

4 Capacity Enhancement Using Relay andScheduling Schemes

In this section we are focusing on relay selection andscheduling mechanism to enhance D2D networks based on60GHz to successfully achieve the data rates it promises

41 Relay Selection Schemes We first define the relay selec-tion problem as follows Let 119876 be the set of all DEVs in anetwork For any pair of DEVs 119909 119910 isin 119876 and a subset 119875 sub 119876we find another DEV 119901 belonging to 119875 that minimizes thesum of delays in the overlay link of 119909 minus 119901 and 119901 minus 119910 In ageneral selection scheme a subset 119875 of DEVs of 119876 is chosenand the twoDEVs119909 and119910measure the network distance to allthe DEVs in 119875 Finally 119909 and 119910 select the DEV that results inthe smallest one-hop network distanceThe size of the chosensubset 119875 determines the amount of measurement traffic

As mentioned earlier two types of transmissions areconsidered inter- and intragroup It is observed that in high-speed short-ranged WPANs (119879119909 119877119909) pair come close fortheir transmission [12] and then stay for several minutesduring their data transmission Sowe can assume thatmost ofthe transmission will be based on intragroup with occasionalintergroup transmissions Therefore we have proposed anovel low complexity distributed relay algorithm for intra-group and a simple but effective centralized distance basedrelay algorithm for intergroup transmissions

411 Intergroup Relay Selection In this subsection we pro-pose a relay selection algorithm for intergroup multihoptransmission in mmWave WPANs Midmost relay position-ing distance and traffic load are considered to take the relaydecision as mentioned in Algorithm 1 Our emphasis lies onmidmost relay positioning and distance Traffic flow metriccan be considered useful in case that multiple potential relayDEVs yield the same value at step (7) of Algorithm 1 Weare considering a two-hop scenario as shown in Figure 2Suppose that the total number of groups in a network is119872 Then each 119866

119894for 119894 = 1 119872 contains DEVs which

mostly communicate with one another (rationale behind thegrouping) The PNC would assign weights to all potentialDEVs to evaluate the best relay DEV Suppose that 119875relayis the total number of potential relay DEVs (119875

119896forall119896 =

(1 2 119875relay)) Weights are assigned on the basis of linklengths and traffic load (Algorithm 1 lines 6ndash8) The terms119865(119875119896) and119864 [119866

119892] represent traffic load at DEV119875

119896and average

traffic load on all DEVs in group119866119892 respectively Traffic load

is calculated as a ratio of traffic load on a DEV 119875119896and sum

of traffic load on all DEVs in that group In (4) data rate is a

Table 1 Table maintained by 119877119909

Beams SNR levels Potential relay DEVs1 120574

1

DEV1

2 1205742

DEV2

3 1205743

DEV3 DEV4

4 1205744

DEV5 DEV6

5 1205745

DEV7

6 1205746

DEV8

7 1205747

DEV9

8 1205748

DEV10

function of 119889119899 which is also introduced in Algorithm 1 (line7) where119863 refers to distance of corresponding pair The bestrelay would be the DEV with the smallest weight

412 Intragroup Distributed Relay Selection In this subsec-tion we propose a receiver based distributed relay selectionfor intragroup transmission We are considering an antennawith 119873 = 8 beams at each DEV covering 360 degreesas shown in Figure 3 All DEVs are assumed to be capableof measuring SINR levels on their antenna elements andare aware of the neighboring DEV(s) within their beamsrsquocoverage areas Discovery of neighboring DEVs can beaccomplished either by using some discovery techniques [27]or through learning by successful transmissions and othersignaling with the DEVs for some threshold amount of timeDuring transmission each119877119909DEV ismaintaining a table thatcontains SINR levels andDEVs information on the respectiveantenna elements as shown in Table 1 The frequency of tableupdates at119877119909 depends on its mobility along with themobilityand recurrence of mutual transmissions among neighboringDEVs

The first column in Table 1 represents the total number ofantenna elements followed by SINR levels on the respectiveantenna elements in the second column The third columnrepresents the location(s) of DEV(s) lying in the area ofthe corresponding beams Our algorithm tries to find theminimum distance by exploiting the directional nature of60GHz based D2D networks The rationale behind ourbest relay is the least distance along with midmost relayplacement As shown in (4) and Figure 4 data rate is severelyaffected by distance especially for 119899 gt 2 in 60GHz networksAs we can see in Figure 4 those relays lying close to midmostbetween receiver and transmitter result in higher capacitygain An inequality of both hops of even 5 difference wouldresult in lower capacity Therefore relay with least distancealong (119879119909 119889relay 119877119909)withmidmost placement is encouragedThe intuition of finding the least distance relay for beamsector 119894 is to search the neighboring sectors Our proposedalgorithm tries to search 4 beam sectors (119894minus2 119894minus1 119894+1 119894+2)(for 119894 = 1 119894 minus 1 119894 minus 2 correspond to beams 8 and 7respectively) with the assumption of the same SINR levelson each antenna element Other beam sectors being almostin the opposite direction would result in a longer relay pathand would not be cost effective Our proposed relay selectionscheme is given in Algorithm 2 For an active transmission


(1) Inputs link lengths and traffic load(2)Output Best relay DEV for (119879119909 119877119909) pair based on distance and traffic load

(3) With (119879119909 119877119909) pair(4) if 119879119909 and 119877119909 belongs to different groups then(5) say 119879119909 isin 119866

119894

and 119877119909 isin 119866119895

forall119894 119895 larr (1 2 119872) and 119894 = 119895

119872 is maximum number of groups in WPAN(6) for 119896 larr 1 to 119875relay do

(7) 119908 (119879119909 119877119909) larr119863119899

(119879119909 119875119896

) + 119863119899

(119875119896

119877119909)

119863119899 (119879119909 119877119909)+119865 (119875119896

)

119864 [119866119892

]

where 119892 larr group 119894 or group 119895119908(119879119909 119877119909) is a set of all weights assigned to potential DEVs for (119879119909 119877119909) pair

(8) end for(9) Select 119889relay isin 119875119896 with weight Min[119908(119879119909 119877119909)] and forall119896 larr (1 2 119875relay)

(10) end if

Algorithm 1 Distance based intergroup relay selection

(1) Input Table maintained by 119877119909(2)Output Best Relay 119889relay for (119879119909 119877119909) pair

(3) With active reception of signal at sector 119894(4) if 120574

119894

le 120574th or Signal Blockage then(5) Search table for (119894 minus 2 119894 minus 1 119894 + 1 119894 + 2) rows for potential relays Let 119875relay be total

potential relay DEVs found(6) Calculate Distance (119879119909 119903

119895

119877119909) forall119895 larr (1 2 119875relay) that is end-to-end distance of relaypaths for all 119875relay

(7) 119889relay larr Min(119879119909 119903119895

119877119909) forall119895 larr (1 2 119875relay) where 119889relay is a set containing one ormore relays with minimum distance119863min

(8) if |119889relay| gt 1 that is more than one relays (say 119875min sub 119875relay) with same minimumdistance119863min then

(9) for 119895 larr 1 to 119875min do

(10) Mid (119895) larr (

10038161003816100381610038161003816100381610038161003816100381610038161003816

1

2minus

119889 (119879119909 119903119895

)

119863min

10038161003816100381610038161003816100381610038161003816100381610038161003816

) + (

10038161003816100381610038161003816100381610038161003816100381610038161003816

1

2minus

119889 (119903119895

119877119909)

119863min

10038161003816100381610038161003816100381610038161003816100381610038161003816

)

(11) end for(12) 119889relay larr Min(119872119894119889)(13) end if(14) end if

Algorithm 2 Distributed receiver based intragroup relay selection

at sector 119894 119877119909 will continuously calculate SINR at all theantenna elements (119873 = 8) If the SINR at 119894th element (120574

119894)

is less than or equal to the threshold SINR (120574th) or in caseof blockage of LOS path 119877119909 DEV can check the table for theneighboring four beams The intuition is that these regionswill have the relay DEV with the least distance Possiblerelay DEVs on other beams (other than four neighboringbeams) will be too far away to be effective The relay withminimum relay path (119863min) is considered as the best relay(119889relay) In case of more than one such DEV distance of 119889relayto 119879119909 and 119877119909 is checked A DEV which lies at midmostposition ((119879119909 119889relay 119877119909)2) of the link is selected as relay forthe corresponding (119879119909 119877119909) pair

Example We try to explain the algorithm using an exampleAs mentioned earlier distance plays a major role in mmWavenetworks especially for 119899 gt 2 It is very important to selecta relay at the midmost position between 119879119909 and 119877119909 InFigure 5 we can see that there are different relays placed forthe (119879119909 119877119909) pair at various distances The distance between119879119909 and 119877119909 is 6m The distance of 119879119909 and 119877119909 from relaysvaries However the sum of their distances from 119879119909 and 119877119909is the same that is 8m

For 1198771 1198772 and 1198773 Algorithms 1 and 2 will respectivelycalculate |(22 +62)62| = 111 |(52 +32)62| = 0944 |(352 +452

)62

| = 0902 and |(12) minus (28)| + |(12) minus (68)| = 05|(12) minus (58)| + |(12) minus (38)| = 025 |(12) minus (358)| +


25

20

15

10

5

00 5 10 15 20

Distance (m)

Capa

city

(Gbp

s)

n = 3n = 2

Near equal relay-(Tx Rx) paths5 relay-(Tx Rx) path dierence25 relay-(Tx Rx) path dierence40 relay-(Tx Rx) path dierence

Figure 4 Relay to (119879119909 119877119909) distance analysis

Tx Rx

R2

R3

R1

2m 3m5m

45m35m

6m

6m

Figure 5 Relay selection example

B

C

A

D

120579

120579

Figure 6 Concurrent transmission scenario

|(12) minus (458)| = 0125 1198773 will be selected as relay byboth Algorithms 1 and 2 (119889relay) depending upon inter- orintragroup transmission

42 Vertex Multicoloring Scheduling Algorithm In this sec-tion we propose an algorithm for concurrent transmissionin 60GHz based D2D networks employing the principleof vertex coloring (VC) Our proposed vertex multicolor-ing concurrent transmission (VMCCT) algorithm schedules(119879119909 119877119909) flows in the same time resource The consideredflows have all the distinct transmitters and receivers with noshared transceiver

421 Concurrent Transmission Conditions In this subsec-tion we discuss the conditions for concurrent transmissionFigure 6 shows two concurrent flows scenario in 60GHzbased D2D networksWe can see that two transmitters (119860 119862)try to send data to two receivers (119861 119863) in the same time slotHence the sufficient condition 1 for concurrent transmissionbetween pair (119860 119861) and pair (119862119863)with beamwidth 120579 can beobtained as follows

Concurrent Transmission Sufficient Condition 1 Here weassess whether the flows (119860 119861) and (119862119863) are within thesignal beams of each other by using the following condition

ang119863119860119861 gt120579

2 ang119861119862119863 gt

120579

2 (7)

where ang119863119860119861 and ang119861119862119863 could be obtained from the cosinelaw

ang119863119860119861 = arccos(1198601198632

+ 1198601198612

minus 1198611198632

2119860119863 times 119860119861)

ang119861119862119863 = arccos(1198611198622

+ 1198621198632

minus 1198611198632

2119861119862 times 119862119863)

(8)

Concurrent flows with mutual interference can beallowed as long as they are apart by a certain thresholddistance The threshold distance is defined as an area wherethe mutual interference can be seen as background noise Toaccomplish this an exclusive region (ER) around the receiveris defined in [20] which allows concurrent transmission ofmutually interfering flowsHencewe can obtain the sufficientcondition 2 for concurrent transmission between pair (119860 119861)and pair (119862119863) as follows

Concurrent Transmission Sufficient Condition 2 If the flowsare in conflict with each other then the transmitter-receiverdistances of the conflicting flows are checked to see if they areapart a threshold distance by using the following condition

119860119863 gt 119877ER (ang119863119860119861 lt120579

2)

119861119862 gt 119877ER (ang119861119862119863 lt120579

2)

(9)


2

1

4

6

3

5

(c) Optimized algorithm

(b) Vertex coloring algorithm

(a) Simple graph based on conflict matrix

Time slots allocated

Tim

e slo

ts al

loca

ted

g1

g3

4

2

1

6

3

5

g3

2

1 3

3

5

6 4

GreenRed

Yellow

50

50

40

40

36

36

200

200

66

66

133133

2 4 6 1 4 5

1 4 5

3 6

2 6

50

40

36

200

66

133

Figure 7 Conflict graph representation of VC and VMCCT

using the ER definition in [20]

119877ER = (1198961119866119905119866119903119875119905

1198730119882

)

1119899

(10)

where 119877ER is the radius of ER as shown in Figure 6 (aroundDEV 119863) 119896

1prop (1205824120587)

2 is a constant coefficient dependenton the wavelength 120582 119866

119905and 119866

119903are the antenna gains for

the transmitter and receiver respectively 119875119905is the transmit

power and 119899 is the pathloss exponent Here condition 2 willkeep the accumulative interference in the network below anacceptable threshold

Both concurrent transmission conditions 1 and 2 realizethe possibility of concurrent transmission for different flowsFor illustration as in Figure 6 receiver 119863 is inside thebeamwidth of transmitter 119860 but the distance between 119860 and119863 is larger than 119877ER Therefore concurrent transmission ofpairs (119860 119861) and (119862119863) would be allowed

422 Construction of Conflict Matrix A conflict matrix(CM) represents the relationship between different flowsThe

relationship is represented by 1 (conflict) and 0 (no conflict)as shown below

CM(6times6)

=

[[[[[[[

[

0 1 0 0 0 1

0 0 1 0 0 0

1 1 0 0 0 0

0 0 1 0 0 0

0 0 0 0 0 0

1 0 0 0 1 0

]]]]]]]

]

(11)

Equation (11) shows a conflictmatrix of 6flows Element 1results when the corresponding flows fail to meet concurrentconditions 1 and 2 Therefore they cannot be allowed totransmit their data concurrently The rows of the conflictmatrix represent the conflict relationship among flows Eachrow is constructed by considering the conflict relationshipfrom the corresponding flow to all the other flows unilaterallyTherefore if some flow 119894 has no conflict with flow 119895 it does notnecessarily mean that flow 119895 also has no conflict with flow 119894This situation can be seen inmatrix as shown in (11) at indices(12) and (21) The conflict matrix can also be representedas an undirected graph called conflict graph The conflictmatrix in (11) is converted into conflict graph as shown inFigure 7(a) The flows are represented as vertices and their


mutual conflicts are represented as edges between them Itshould be noted that values in the conflict matrix for flow1 and 2 at indices (12) and (21) are not same but they haveresulted in a conflict (an edge) in conflict graph

423 Time-Slot Allocation Based on VC Time slot beingscarce resource requires efficient allocation We employ VCalgorithm to effectively resolve conflict among flows andefficiently assign time resource VC algorithm has beenused for resource allocation in different types of networks[28ndash31] including mmWave cognitive radios and ad hocnetworks VC will color all vertices (flows) in conflict graphwith minimum number of colors (time slots) Two directlyconnected vertices cannot have the same color We can seein Figure 7(b) that VC colors all the six vertices using threecolors With green red and yellow representing first secondand third time slots respectively we can transmit flows 2 and6 in first time slot flows 1 4 and 5 in second time slot andflow 3 in the third time slot

424 Time-Slot Allocation Based on VMCCT The conser-vative time-slot allocation based on VC is not efficient Ourproposed multicoloring algorithm allocates time slots moreaggressively to improve network throughput Algorithm 3shows the details of our proposed scheme Our scheme startsby constructing a conflict matrix (Algorithm 2 lines 3ndash16)The conflict matrix is then used to resolve conflict and assigntime slots based on VC and VMCCT

The proposed algorithm can be explained with the helpof Figure 7 Time-slot allocation based on VC and VMCCTis shown in Figures 7(b) and 7(c) respectively The basicprinciple with multiple colors for a vertex is the same as thetraditional VC that is the color between connected verticesshould be different Hence the possible colors for a specificvertex should not include matching colors of its neighborswhich can be shown as follows

Color 119881 (119894) = Color All minus Color 119873(119894) (12)

where Color 119881(119894) represents the color assigned to flow 119894Color All holds the set of all colors and Color 119873(119894) repre-sents the color of the neighboring vertex

With (12) we can obtain the final multicoloring resultsfor all the vertices Vertex selection for multicoloring cansignificantly affect the network throughput because differentflows can exhibit different data rates In order to improve thenetwork throughput we give each of the vertices a weightbased on its intended data rate Since mutual interferenceis below the background noise because of the distance andhigh propagation loss it is appropriate to use the transmissiondistance as a metric for color selection

119908 (119894) =sum119881

119894=1

119889 (119894)

119889 (119894) (13)

where 119881 is the number of vertices and 119889(119894) donates thedistance between the transmitter and receiver in a flow 119894Using (13) flow 119894 with shorter transmission distance will gethigher weight In order tomulticolor the vertices as proposed

Table 2 Simulation parameters

Parameters ValuesSystem bandwidth (119882) 1800MHzTransmission power (119875

119905

) 01mWBackground noise (119873

119900

) minus134 dBmMHzPath loss exponent (119899) 3

Reference distance (119889ref) 15mPath loss at 119889ref (PL119900) 715 dBSlot time Δ119905 18120583secNumber of slots in superframe 1000

in VMCCT we will sort the vertices in descending order oftheir weights

In Figure 7(b) weights are shown on the top of eachvertex we can get the Color All and sorted weights sets fromthe graph

Color All = (REDGREENYELLOW) (14)

Weight=200 (4) 133 (6) 66 (5) 50 (1) 40 (2) 36 (3) (15)

Hence vertex 4 with the largest weight will be consideredfirst By using (15) we can assign color to vertex 4 as follows

Color 119881 (4) = (REDGREENYELLOW) minus (YELLOW)

= (REDGREEN) (16)

This will yield red and green color to vertex 4 Similarlyvertex 6 will be assigned both green and yellow colors Thenthe Color 119873(6) will be refreshed to (GREEN YELLOW) sovertex 5 can only be assigned a red color Similarly we can getthe final results for flows 1 2 and 3 as shown in Figure 7(c)

5 Performance Evaluations

In order to evaluate our proposed relay selection schemesand scheduling algorithm we consider 15 times 15metersrsquo roomwith random distribution of 30 DEVs All the DEVs areplaced using polar coordinates hence information abouttheir locations and distances from the PNC is known Datatransmission is based on IEEE 802153c standard We haveevaluated our proposed schemes under single- and multi-hop scenarios We assume static locations of DEVs for theduration of superframeThemobility in IEEE 802153c basedWPAN is very low (1metersec) In such a scenario ignoringmobility for the duration of superframe is not impracticalThe simulation parameters are shown in Table 2

51 Single-Hop Scenario We compare our proposedVMCCTscheme [5] for single-hop scenariowith the traditional single-hop GA scheme presented in [20] as well as with the well-known TDMA method under the same assumptions andsystem model The reader is referred to [5] for further detailswhile we provide some details for completeness


(1) Inputs Set of all flows that is 119865119897119900119908(1) to 119865119897119900119908(119881)(2)Output vertex multi-color graph for scheduling concurrent transmission

(3) for 119877119900119908 = 1 119877119900119908 lt 119881 119877119900119908 + + do(4) for 119862119900119897119906119898119899 = 1 119862119900119897119906119898119899 lt 119881 119862119900119897119906119898119899 + + do(5) if 119877119900119908 = 119862119900119897119906119898119899 then(6) 120572 = 119860119899119892119897119890(119877119900119908 119862119900119897119906119898119899)

(7) 119863 = 119863119894119904119905119886119899119888119890(119877119900119908 119862119900119897119906119898119899)

(8) if 120572 lt 1205792 and119863 lt ER then(9) Use relay selection algorithms go back and calculate 120572 and119863(10) if no relay found Conflict Matrix(Row Column) = 1(11) else(12) Conflict Matrix(Row Column) = 0(13) end if(14) end if(15) end for(16) end for(17) 119862119900119897119900119903 119866119903119886119901ℎ = 119865119906119899119888119905119894119900119899 VC(119862119900119899119891119897119894119888119905119872119886119905119903119894119909)(18) for 119862119899119905 = 1 119862119899119905 lt 119881 119862119899119905 + + do(19) 119863(119862119899119905) = 119865119906119899119888119905119894119900119899 119863119894119904119905119886119899119888119890(119865119897119900119908(119862119899119905))

(20) end for(21) for 119862119899119905 = 1 119862119899119905 lt 119881 119862119899119905 + + do(22) 119908(119862119899119905) = 119865119906119899119888119905119894119900119899 119882119890119894119892ℎ119905(119863(119862119899119905))

(23) end for(24) for 119862119899119905 = 1 119862119899119905 lt 119881 119862119899119905 + + do(25) 119909 = Max(119908)(26) 119862119900119897119900119903 119881(119909) = 119862119900119897119900119903 119860119897119897 minus 119862119900119897119900119903 119873(119909)

(27) 119908(119909) = 0

(28) end for

Algorithm 3 Vertex multicoloring concurrent transmission algorithm

10

9

8

7

6

5

4

3

2

1

04 6 8 10 12 14

Number of flows

Flow

s per

slot

TDMAVMCCT (30deg)Greedy (30deg)

VMCCT (60deg)Greedy (60deg)

Figure 8 Improved average flows throughput versus flow density

Figures 8 and 9 show the performance of VMCCTaverage flow rate with respect to increasing flow densityand beamwidths respectively Beamwidths of 30 and 60degrees are considered in Figure 8 We can see that the

10

20 30 40 50 60 70 80

9

8

7

6

5

4

3

2

1

0

Flow

s per

slot

TDMAVMCCT (14 flows)Greedy (14 flows)

VMCCT (8 flows)Greedy (8 flows)

Beamwidth (deg)

Figure 9 Improved average flow throughput versus increasingbeamwidth

traditional TDMA scheme can only transmit one flow pertime slot While compared to GA we can see that averageflows per slot using VMCCT are better than GAThe average


10

15

5

04 6 8 10 12 14

Number of flows

Net

wor

k th

roug

hput

(Gbp

s)



Figure 10 Improved network throughput versus flow density

20

20 30 40 50 60 70 80

18

16

14

12

10

8

6

4

2

0

Beamwidth (deg)

Net

wor

k th

roug

hput

(Gbp

s)



Figure 11 Network throughput versus increasing beamwidth

flow per slot is improved by almost one for both 30 and60 degreesrsquo beamwidths VMCCT scheme is also evaluatedagainst increasing beamwidths as shown in Figure 9 Byincreasing the beamwidth the signal can span larger arearesulting in more interference Hence the chances of con-current transmission will also be reduced We have used flowdensities of 8 and 14 for evaluating the effects of increasedbeamwidth on flow rate It can be seen that almost anadditional flow can be transmitted per slot withVMCCT thanthat of the GA scheme

Figures 10 and 11 show the VMCCT performance byenhancing network throughput with respect to increasingflow density and beamwidth respectively It can be seen in

Figure 10 that VMCCT improved network throughput ascompared to GA and hence can support applications suchas HD TV online gaming and uncompressed video withstringent bandwidth and quality requirements On the otherhand TDMA provides a constant data rate as it supports onetransmission at any particular time Similar results can beseen in Figure 11 where VMCCT decreases more gracefullydue to increasing beamwidths as compared to other schemesOn average our scheme provides throughput improvementof 2Gbps (60-degree beamwidth) and 3Gbps (30-degreebeamwidth) as compared to GAThe rationale behind betterperformance gain is the limited interference at 30-degreebeamwidth as compared to 60 degrees In terms of percent-age on average VMCCT improves network throughput by19 and average flows per slot by 12 as compared to the GAscheme

52 Multihop Scenario In this section we will evaluate ourproposed relay selection schemes We also have evaluatedour proposed VMCCT scheme in multihop scenario usingthe proposed relay selection schemes We are considering atypicalWPANs scenario wheremost of the transmissions arewithin intragroup with occasional intergroup transmissionsWefirst evaluate our relay selection schemes and then providesimulation results to show their effectiveness in conjunctionwith our proposed VMCCT scheme

521 Outage Analysis In order to evaluate our proposedrelay selection schemes we use outage probability (OP) asmetric OP is an important performance indicator in wirelesssystems OP can be defined as the probability that the end-to-end SNR falls below a predefined threshold 120574th Thetype of threshold 120574th varies according to different quality ofservice requirements For example the valuemay be based onminimum error rate or a minimum data rate Since 60GHzpromises data rate in Gbps therefore we choose achievabletransmission rate as a threshold which can be calculated as

119877 = 119882119891120578 log2

(1 +120574th120574119891

) (17)

where 119882119891denotes adjustments to the system bandwidth

efficiency 120574119891is the system SINR implementation efficiency

and 120578 is a correction factor to facilitate the derivation It ischosen to be 1

Since we are considering two-hop scenario according to(17) in half-duplex relay system to meet a required end-to-end data rate 119877 both hops should support a rate greater orequal to 2119877 Thus 120574th becomes

120574th = 120574119891 (2(2119877119882119891120578) minus 1) (18)

In relay assisted transmission in two-hop scenario the outageis decided by either of the weaker hops Thus OP can beexpressed as

119875out = 119875119903 (min (120574119862119877 120574119877119863)) lt 120574th (19)


Thus we have

119875out (1198891 1198892 119889119868 120574th)

= 119875119903 (min (120574119862119877(1198891) 120574

119877119863(119889119868 1198892)) lt 120574th)

= 1 minus (1 minus 119865119862119877(1198891 120574th)) (1 minus 119865119877119863 (1198891 119889119868 120574th))

= 119865119862119877(1198891 120574th) + 119865119877119863 (1198891 119889119868 120574th)

minus 119865119862119877(1198891 120574th) 119865119877119863 (119889119868 1198892 120574th)

(20)

where 119865119862119877(1198891 120574th) and 119865119877119863(119889119868 1198892 120574th) are the cumulative

distribution functions of the received SINR of both hopsthat is 119862

119877and 119877 minus 119863 respectively Rayleigh distribution

is considered in [32] to model non-line-of-sight (NLOS)scenario for office home and library environment Hencethe instantaneous received power of the desired signal followsan exponential distribution with probability density function(pdf) expressed as

119875120574119862119877(119909) =

1

119875119903

exp(minus 119909119875119903

) (21)

The OP of 119862 minus 119877 hop can be calculated as

119865119862119877= 119875119903 (119909 lt 120574th1198730)

= 1 minus 119875119903 (119909 gt 120574th1198730)

= 1 minus int

infin

120574th1198730

1

119875119903

exp(minus 119909119875119903) 119889119909

= 1 minus exp(minus120574th1198730

119875119903

)

(22)

where 119875119903(119909) = 119875

119862

119905

119870119862119877(1198890radic1198672 + 119889

2

1

)

119899

120576119862119877

For 119877 minus 119863 hop the desired and interfering channel coef-ficients are considered to be independent and not identicallydistributed (INID) Both follow Rayleigh distribution Thusthe OP of the 119877 minus 119863 hop can be approximated as

119865119877119863= 119875119903 (119909 lt 120574th (119910 + 1198730))

= 1 minus 119875119903 (119909 gt 120574th (119910 + 1198730))

= 1 minus int

infin

0

119891 (119910)int

infin

120574th(119910+1198730)119891 (119909) 119889119909119889119910

= 1 minus int

infin

0

1

119875119903119868(119877119863)

exp(minus119910

119875119903119868(119877119863)

)

times int

infin

120574th(119910+1198730)

1

119875119903119877119863

exp(minus 119909

119875119903119877119863

)119889119909119889119910

= 1 minus119875119903119877119863

119875119903119877119863+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903119877119863

)

(23)

Out

age p

roba

bilit

y

Varying relay distance

Direct transmissionFixed relay selectionProposed relay selection

10minus1

10minus2

10minus3

10minus4

100

2 4 6 8 10 12 14 16 18 20

Figure 12 Outage probability with varying relay distance

Hence OP at a given DEV position can be obtained byinserting (21) and (22) in (19) as follows

119875out (1198891 1198892 120574th)

= 1 minus exp(minus120574th119875119903(119862119877)

)

+ 1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

)

minus (1 minus exp(minus120574th119875119903(119862119863)

))

times (1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

))

(24)

522 Simulation Results In this subsection numericalresults are employed to evaluate our proposed relay selec-tion and VMCCT schemes Ergodic capacity and OP arecompared for direct transmission fixed relay and our pro-posed relay selection schemes The simulation parametersare shown in Table 2 In Figure 12 OP of our proposedrelay schemes is compared with direct transmission and fixedrelay selection schemes The 119877119909 position is fixed at 119863 whiledifferent relays are selected with varying distances We cansee that there is a point where OP is the minimumWhen thedistance increases relays help reduce the OP Our proposedschemes select the minimum relay path with the efforts offinding relay in the midmost position This helps reducethe OP of our proposed schemes Figure 13 compares theOP of fixed relay node and direct transmission with ourproposed relay selection schemes We can see that as thedistance between 119879119909 and 119877119909 increases fixed relay nodersquosperformance degrades significantly as compared to our relayselection schemes Distance plays a major role in 60GHz

International Journal of Antennas and Propagation 13O

utag

e pro

babi

lity

Transmitter-receiver distance

Direct transmission

Fixed relay selectionProposed relay selection

10minus1

10minus2

10minus3

10minus4

100

5 10 15 20

Figure 13 Outage probability with varying 119879119909-119877119909 distance


Direct transmission

Ergo

dic c

apac

ity (b

itss

Hz)

Fixed relay selectionDistributed relay selection

15 2054

6

8

10

12

14

16

18

10

Figure 14 Ergodic capacity with varying 119879119909-119877119909 distances

based D2D network and the tremendous propagation lossrequires careful relay selection in such system Our proposedscheme outperforms both direct and fixed relay nodes bysignificantly improving OP Ergodic capacity is analyzed inFigure 14 We can see that ergodic capacity is very lowin direct transmission As the distances increases ergodiccapacity decreases rapidly However our proposed relayselection schemes degrades gracefully as compared to otherschemesThefixed relay node and our relay selection schemesare equal only on the condition that the fixed relay nodebe located at the optimal position Overall our proposedrelay selection schemes perform better as compared to otherschemes by improving OP and ergodic capacity significantly

We used our proposed VMCCT algorithm in multihopscenario Our proposed algorithms try to find a suitable

3

25

2

15

1

05

05 10 15 20 25 30 35 40 45 50

Number of traffic flows

Aver

age fl

ow th

roug

hput

(Gbp

s)

TDMAMultihop-60 (greedy)Multihop-60 (VMCCT)

Multihop-30 (greedy)Multihop-30 (VMCCT)

Figure 15 Average flow throughput in multihop scenario

0

4

2

6

8

10

12

14

16

18

20

5 10 15 20 25 30 35 40 45 50


Net

wor

k th

roug

hput

(Gbp

s)



Figure 16 Network throughput in multihop scenario

relay placed at near-equal distance from 119879119909 and 119877119909 Ouralgorithm works equally well in multihop scenario and bothGA and TDMA Figures 15 and 16 show performance ofVMCCT in single- and multihop scenarios respectivelyImprovement in average flow throughput against traffic flowdensity can be seen in Figure 15 We evaluated our systemwith up to 50 flows under the very dense deployment Wecan see that the proposedVMCCT algorithm in themultihopscenario performs better as compared to other schemes bysignificantly increasing average flow throughput The use ofrelays helps alleviate network interference and encouragesmore concurrent transmissions Similarly in Figure 16 we


can see that the network throughput is significantly improvedusing VMCCT in multihop scenario Overall the perfor-mance of our proposed VMCCT scheme outperforms GA byimproving the network throughput

6 Conclusion

In order to improve the network capacity in 60GHz basedD2D networks we jointly consider relay selection andscheduling algorithm Owing to tremendous propagationloss distance is used as a main metric for relay selectionApart from distance a relay with midmost positioningis encouraged for both inter and intragroup transmissionscenarios A novel distributed relay selection algorithm isproposed for intragroup transmission scenario The outageprobability analysis is provided to compare our relay selectionschemes with fixed relay selection schemes Furthermore weevaluated our proposed relay selection schemes jointly withscheduling algorithm in single- and multihop scenarios Wehave compared our results with GA and TDMA under thesame systemmodel Our proposed scheme outperforms bothGA and TDMA in terms of network throughput and averageflows per slot Network throughput and average number offlows per slot are improved by 19 and 12 respectively

Conflict of Interests

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

Acknowledgments

This paper is supported by the State Key Program of NationalNatural Science of China (Grant no 61231009) BeijingHigher Education Young Elite Teacher Project under GrantYETP0429 and National High-tech Research and Develop-ment Program of China (no 2014AA01A701)

References

[1] S K Yong P Xia and A V Garcia 60 GHz Technology ForGbps WLAN and WPAN FromTheory to Practice JohnWileyamp Sons 2011

[2] T S Rappaport F Gutierrez E Ben-Dor J N Murdock YQiao and J I Tamir ldquoBroadband millimeter-wave propagationmeasurements and models using adaptive-beam antennas foroutdoor Urban cellular communicationsrdquo IEEE Transactions onAntennas and Propagation vol 61 no 4 pp 1850ndash1859 2013

[3] X Xu H Zhang X Dai Y Hou X Tao and P Zhang ldquoSDNbased next generation mobile network with service slicing andtrialsrdquo China Communications vol 11 no 2 pp 65ndash77 2014

[4] S Chen and J Zhao ldquoThe requirements challenges andtechnologies for 5G of terrestrial mobile telecommunicationrdquoIEEE Communications Magazine vol 52 no 5 pp 36ndash43 2014

[5] W Ur Rehman J Han C Yang and M Ahmed ldquoOn schedul-ing algorithm for device-to-device communication in 60GHznetworksrdquo in Proceedings of the Wireless Communications andNetworking Conference (WCNC rsquo14) April 2014

[6] X Ge K Huang C-X Wang X Hong and X Yang ldquoCapac-ity analysis of a multi-cell multi-antenna cooperative cellularnetwork with co-channel interferencerdquo IEEE Transactions onWireless Communications vol 10 no 10 pp 3298ndash3309 2011

[7] Z Lan C-S Sum J Wang et al ldquoRelay with deflection routingfor effective throughput improvement in Gbps millimeter-waveWPAN systemsrdquo IEEE Journal on Selected Areas in Communi-cations vol 27 no 8 pp 1453ndash1465 2009

[8] W Roh J-Y Seol J Park et al ldquoMillimeter-wave beamformingas an enabling technology for 5G cellular communications the-oretical feasibility and prototype resultsrdquo IEEECommunicationsMagazine vol 52 no 2 pp 106ndash113 2014

[9] B Li Z Zhou H Zhang and A Nallanathan ldquoEfficientbeamforming training for 60-GHz millimeter-wave commu-nications a novel numerical optimization frameworkrdquo IEEETransactions on Vehicular Technology vol 63 no 2 pp 703ndash7172014

[10] SWyne K Haneda S Ranvier F Tufvesson and A F MolischldquoBeamforming effects on measured mm-wave channel charac-teristicsrdquo IEEE Transactions on Wireless Communications vol10 no 11 pp 3553ndash3559 2011

[11] Z Genc G M Olcer E Onur and I Niemegeers ldquoImproving60GHz indoor connectivity with relayingrdquo in Proceedings of theIEEE International Conference onCommunications (ICC 10) pp1ndash6 Cape Town South Africa May 2010

[12] F Boccardi R Heath Jr A Lozano T L Marzetta and PPopovski ldquoFive disruptive technology directions for 5Grdquo IEEECommunications Magazine vol 52 no 2 pp 74ndash80 2014

[13] Z Yang L Cai and W-S Lu ldquoPractical scheduling algo-rithms for concurrent transmissions in rate-adaptive wirelessnetworksrdquo inProceedings of the IEEE INFOCOM pp 1ndash9March2010

[14] Q Cui X Yang J Hamalainen X Tao and P Zhang ldquoOptimalenergy-efficient relay deployment for the bidirectional relaytransmission schemesrdquo IEEETransactions onVehicular Technol-ogy vol 63 no 6 pp 2625ndash2641 2014

[15] J Qiao L X Cai X Shen and J W Mark ldquoEnabling multi-hop concurrent transmissions in 60 GHz wireless personal areanetworksrdquo IEEE Transactions on Wireless Communications vol10 no 11 pp 3824ndash3833 2011

[16] S Singh F Ziliotto UMadhow EM Belding andM RodwellldquoBlockage and directivity in 60GHz wireless personal areanetworks from cross-layer model to multihop MAC designrdquoIEEE Journal on Selected Areas in Communications vol 27 no8 pp 1400ndash1413 2009

[17] S Singh F Ziliotto U Madhow E M Belding and M JW Rodwell ldquoMillimeter wave WPAN cross-layer modelingand multihop architecturerdquo in Proceedings of the 26th IEEEInternational Conference on Computer Communications (IEEEINFOCOM rdquo07) pp 2336ndash2340 IEEE May 2007

[18] C-S Sum and H Harada ldquoScalable heuristic STDMA schedul-ing scheme for practical multi-Gbps millimeter-wave WPANand WLAN systemsrdquo IEEE Transactions on Wireless Commu-nications vol 11 no 7 pp 2658ndash2669 2012

[19] S Jin M Choi K Kim and S Choi ldquoOpportunistic spatialreuse in IEEE 802153c wireless personal area networksrdquo IEEETransactions on Vehicular Technology vol 62 no 2 pp 824ndash834 2013

[20] L X Cai L Caai X Shen and J W Mark ldquoRex a random-ized Exclusive region based scheduling scheme for mmWaveWPANs with directional antennardquo IEEE Transactions on Wire-less Communications vol 9 no 1 pp 113ndash121 2010


[21] J Qiao L X Cai X Shen and J W Mark ldquoSTDMA-based scheduling algorithm for concurrent transmissions indirectional millimeter wave networksrdquo in Proceedings of theIEEE International Conference onCommunications (ICC 12) pp5221ndash5225 Ottawa Canada June 2012

[22] SMHur SMao Y THou KNam and J H Reed ldquoExploitinglocation information for concurrent transmissions in multihopwireless networksrdquo IEEE Transactions on Vehicular Technologyvol 58 no 1 pp 314ndash323 2009

[23] L Song ldquoRelay selection for bi-directional amplify-and-forward wireless networksrdquo in Proceedings of the IEEE Interna-tional Conference on Communications (ICC 11) pp 1ndash5 KyotoJapan June 2011

[24] L Goratti T Wysocki M-R Akhavan J Lei H Nakase andS Kato ldquoOptimal beamwidth for beacon and contention accessperiods in IEEE 802153c WPANrdquo in Proceedings of the IEEE21st International Symposium on Personal Indoor and MobileRadio Communications (PIMRC rsquo10) pp 1395ndash1400 September2010

[25] C Balanis Antenna Theory Analysis and Design John Wiley ampSons Hoboken NJ USA 1997

[26] R Mudumbai S Singh and U Madhow ldquoMedium accesscontrol for 60 GHz outdoor mesh networks with highly direc-tional linksrdquo in Proceedings of the 28th Conference on ComputerCommunications (INFOCOM rsquo09) pp 2871ndash2875 IEEE April2009

[27] G Sun F Wu X Gao G Chen and W Wang ldquoTime-efficientprotocols for neighbor discovery in wireless Ad Hoc networksrdquoIEEE Transactions on Vehicular Technology vol 62 no 6 pp2780ndash2791 2013

[28] L Xiaoyang D Enqing Q Fulong and C Bo ldquoVertex coloringbased distributed link scheduling for wireless sensor networksrdquoin Proceedings of the 18th Asia-Pacific Conference on Communi-cations (APCC 12) pp 754ndash759 Jeju Island Republic of KoreaOctober 2012

[29] M Cheng and L Yin ldquoTransmission scheduling in sensornetworks via directed edge coloringrdquo in Proceedings of theIEEE International Conference on Communications (ICC rsquo07)pp 3710ndash3715 June 2007

[30] E Driouch W Ajib and A Ben Dhaou ldquoA greedy spectrumsharing algorithm for cognitive radio networksrdquo in Proceedingsof the International Conference on Computing Networking andCommunications (ICNC rsquo12) pp 1010ndash1014 February 2012

[31] I K Son S Mao M X Gong and Y Li ldquoOn frame-basedscheduling for directional mmWave WPANsrdquo in Proceedings ofthe IEEEConference on Computer Communications (INFOCOMrsquo12) pp 2149ndash2157 March 2012

[32] S-K Yong ldquoChannel modeling sub committee final reportrdquoIEEE 80215-07-0584-01-003c-tg3c 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



[11] The effect of distance in 60GHz networks is detrimentalas compared to networks operating at lower frequenciesRelays partition a communication link into shorter distancesand help achieve the so-called ldquodistance gainrdquo

In short-ranged data-centric communication networkthe premise that two parties initiate communication to bein close proximity is acceptable contrary to voice-centricnetworks Rather it would be common to have a situa-tion where several co-located devices (DEVs) would liketo share contents such as digital pictures or interact forapplications such as video gaming and social networking[12] As a result the network can be visualized as naturallyformed groups rather than DEVs scattered randomly Insuch scenario usually the transmitter and receiver (119879119909 119877119909)pair stays for the duration of their transmission Examplesmay include file transfer kiosk home entertainment systemwhere sound system HDTV and gaming devices are in closeproximity along with the people intending to communicatewith them Two types of communication may be seen insuch scenario intra and intergroup transmission Due to therationale behind such grouping it can safely be assumedthat most of the times nearby devices would be involvedin data communications with occasional distant devicesWe devised two algorithms each for intra and intergroupcommunication respectively A receiver based distributedalgorithm is proposed for intragroup communication whilea centralized algorithm is proposed for intergroup transmis-sion In order to further improve network throughput wehave also proposed a concurrent transmission schedulingalgorithm that works jointly with relay selection schemes Itis also argued that network throughput in such short-rangednetworks mainly depends on scheduling scheme rather thantransmission power control [13] which makes it imperativeto have an efficient resource allocation scheme

The main contributions of this paper include the fol-lowing (1) To enhance network capacity in order to meetdemands of bandwidth craving applications we have pro-posed two relay selection algorithms a novel distributed relayselection scheme for intragroup transmission where DEVscan effectively select a relay by exploiting the directionalnature of 60GHz based D2D networks and also simple butan effective intergroup relay algorithm Both algorithms try tofind themidmost relay and try to select the relay to maximizedistance gain (2) Capacity analysis is provided by utilizingour proposed relay selection algorithms in conjunction withour proposed concurrent transmission scheduling algorithmin [5]The scheduling algorithm ismodified to catermultihopscenario The simulation results show that our proposedalgorithms significantly improve the network capacity insingle- and multihop scenarios Multihopping in 60GHzbased D2D networks helps increase the network throughputby encouraging concurrent transmissions However inducedcomplexity and varying relay distances may seriously affectthe end-to-end data rate of an individual flow Applicationswith higher throughput requirement such as uncompressedhigh-definition videos and real-time audiovideo applica-tions have stringent quality of service requirements Sincelinks in mmWave require high data rate too many hopsthat exhibit uniform characteristics are very challenging

and can seriously affect the individual flows Therefore weare considering a two-hop scenario Furthermore we areconsidering an indoor scenario such as home or office wheremultiple hops may not be feasible In this paper two-hop andmultihop are interchangeably used

The rest of the paper is organized as follows Section 2provides an overview of related relay selection and schedulingalgorithm research work in 60GHz networks followed bysystem model in Section 3 The detailed discussion of ourproposed relay selection schemes and scheduling algorithmis provided in Section 4 Numerical results to compareour proposed schemes are given in Section 5 followed byconclusion in Section 6

2 Related Work

Relay selection and scheduling algorithm for 60GHz havegenerated sizable literature [7 11 14ndash22] in recent years Bothefforts are made to achieve one goal capacity enhancementeither directly or indirectlyThe first analytical and simulatedstudy on the use of relays in 60GHz is provided in [11] Thepaper shows that at least 33 of free space path loss can beimproved by using relays The paper also signifies the properpositioning of the relay However the simulation results areprovided on the basis of grid topology and fixed relaysmostlypositioned on ceiling Centralized relay selection approach isproposed in [7] where each sender DEV knows two pathsto the destination direct and relay path The relay path isdiscovered in advance and in case of blockage the datawould ldquodeflectrdquo through relay node Minimum cochannelinterference is considered as selection metric In [15] a relayselection scheme is proposed based on distance and trafficload The authors propose to replace a long direct path withseveral multihop paths to improve the network throughputA diffraction based model to determine network link con-nectivity is also studied in [16] It is shown that the proposedmultihop protocol works with highly directional antennaarrays and is able to maintain high network utilization withlow overhead Use of beam sectors is proposed in [17] todiscover an effective relay However the proposed scheme iscentralized and involves higher overhead and complexity Ajoint relay selection and analog network coding over two-way relay channels are proposed in [23] In the proposedrelay selection amplify-and-forward (RS-AF) scheme twosource nodes first transmit to all the relays at the same timeThe selected relay then broadcasts the signal back to bothsources to achieve a minimum sum symbol error rate (SER)A suboptimal Max-Min criterion is proposed to facilitate theselection process where a single relay which minimizes themaximum SER of two source nodes will be selected

Apart from relay selection scheduling algorithms arealso proposed for capacity enhancement in conjunctionwithwithout relay selection More recently in 60GHz net-works concurrent transmission is encouraged due to itshighly directional nature The concept of concurrent trans-mission is not new but coupled with the directional antennaand short-range nature of 60GHz networks its effective-ness can be multifolded The case of concurrent trans-mission scheduling has been investigated extensively in the


Relay

Relay

RX3

Idle

Idle

RelayPNC

Idle

Idle

Relay

Relay

Tx1

Tx3

Tx7

Tx6

Tx5

Tx4

Tx

Tx3

TxRx2

Rx7 Rx6

Rx5

Rx4

RxRx

Rx1



3 System Model





119892 (120601) =119866 (120601)

119866max (1)







119862 = 119882 log2

[1 +119875119903

(1198730+ 119868)119882

] (2)




119875119903(119889) = 119875

119905119866119903119866119905(120582

4120587)

2

(1

119889)

119899

(3)


119903and 119866



119877 le 119862 = 119882120573 log2

[1 +1198751199051198661199031198661199051205822

161205872 (1198730+ 119868)119882119889119899

] (4)




119905


120574119862119877=

119875119862

119905

119870119862119877(1198890radic1198672 + 119889

2

1

)

119899

120576119862119877

1003816100381610038161003816ℎ1198621198771003816100381610038161003816

2

1198730

(5)

R

d1

d2


A4 A5

A12

A6

A10

A7

A1

A2

A3

A9

A11A13A14

C

D

A

B


32

14

5

6 78

R

d1

d2


C

D

A

B


where119870119862119877



1is


shadow fading 120601119889119861




119905


119905

then the



120574119877119863=

119875119903(119910)

119875119903(119910119868) + 1198730

=119875119877

119905

119870119877119863(11988901198892)119899

120576119877119863

1003816100381610038161003816ℎ1198771198631003816100381610038161003816

2

119875119868

119905

119870119868(1198890119889119868)119899

120576119868

1003816100381610038161003816ℎ1198681003816100381610038161003816

2

+ 1198730

(6)


119903(119910119868) is









119896forall119896 =



119896and average






1

DEV1

2 1205742

DEV2

3 1205743

DEV3 DEV4

4 1205744

DEV5 DEV6

5 1205745

DEV7

6 1205746

DEV8

7 1205747

DEV9

8 1205748

DEV10







119894

and 119877119909 isin 119866119895

forall119894 119895 larr (1 2 119872) and 119894 = 119895


(7) 119908 (119879119909 119877119909) larr119863119899

(119879119909 119875119896

) + 119863119899

(119875119896

119877119909)

119863119899 (119879119909 119877119909)+119865 (119875119896

)

119864 [119866119892

]



(10) end if




119894



119895


(7) 119889relay larr Min(119879119909 119903119895



(9) for 119895 larr 1 to 119875min do

(10) Mid (119895) larr (

10038161003816100381610038161003816100381610038161003816100381610038161003816

1

2minus

119889 (119879119909 119903119895

)

119863min

10038161003816100381610038161003816100381610038161003816100381610038161003816

) + (

10038161003816100381610038161003816100381610038161003816100381610038161003816

1

2minus

119889 (119903119895

119877119909)

119863min

10038161003816100381610038161003816100381610038161003816100381610038161003816

)




119894)




)62



25

20

15

10

5

00 5 10 15 20

Distance (m)

Capa

city

(Gbp

s)

n = 3n = 2



Tx Rx

R2

R3

R1

2m 3m5m

45m35m

6m

6m


B

C

A

D

120579

120579






ang119863119860119861 gt120579

2 ang119861119862119863 gt

120579

2 (7)


ang119863119860119861 = arccos(1198601198632

+ 1198601198612

minus 1198611198632

2119860119863 times 119860119861)

ang119861119862119863 = arccos(1198611198622

+ 1198621198632

minus 1198611198632

2119861119862 times 119862119863)

(8)



119860119863 gt 119877ER (ang119863119860119861 lt120579

2)

119861119862 gt 119877ER (ang119861119862119863 lt120579

2)

(9)


2

1

4

6

3

5





Tim

e slo

ts al

loca

ted

g1

g3

4

2

1

6

3

5

g3

2

1 3

3

5

6 4

GreenRed

Yellow

50

50

40

40

36

36

200

200

66

66

133133

2 4 6 1 4 5

1 4 5

3 6

2 6

50

40

36

200

66

133



119877ER = (1198961119866119905119866119903119875119905

1198730119882

)

1119899

(10)


1prop (1205824120587)


119905and 119866







CM(6times6)

=

[[[[[[[

[

0 1 0 0 0 1

0 0 1 0 0 0

1 1 0 0 0 0

0 0 1 0 0 0

0 0 0 0 0 0

1 0 0 0 1 0

]]]]]]]

]

(11)










119908 (119894) =sum119881

119894=1

119889 (119894)

119889 (119894) (13)




119905


119900






Weight=200 (4) 133 (6) 66 (5) 50 (1) 40 (2) 36 (3) (15)



= (REDGREEN) (16)








(7) 119863 = 119863119894119904119905119886119899119888119890(119877119900119908 119862119900119897119906119898119899)


(20) end for(21) for 119862119899119905 = 1 119862119899119905 lt 119881 119862119899119905 + + do(22) 119908(119862119899119905) = 119865119906119899119888119905119894119900119899 119882119890119894119892ℎ119905(119863(119862119899119905))


(27) 119908(119909) = 0

(28) end for


10

9

8

7

6

5

4

3

2

1

04 6 8 10 12 14

Number of flows

Flow

s per

slot





10

20 30 40 50 60 70 80

9

8

7

6

5

4

3

2

1

0

Flow

s per

slot



Beamwidth (deg)




10

15

5

04 6 8 10 12 14

Number of flows

Net

wor

k th

roug

hput

(Gbp

s)




20

20 30 40 50 60 70 80

18

16

14

12

10

8

6

4

2

0

Beamwidth (deg)

Net

wor

k th

roug

hput

(Gbp

s)









119877 = 119882119891120578 log2

(1 +120574th120574119891

) (17)





120574th = 120574119891 (2(2119877119882119891120578) minus 1) (18)


119875out = 119875119903 (min (120574119862119877 120574119877119863)) lt 120574th (19)


Thus we have

119875out (1198891 1198892 119889119868 120574th)

= 119875119903 (min (120574119862119877(1198891) 120574

119877119863(119889119868 1198892)) lt 120574th)


= 119865119862119877(1198891 120574th) + 119865119877119863 (1198891 119889119868 120574th)

minus 119865119862119877(1198891 120574th) 119865119877119863 (119889119868 1198892 120574th)

(20)





119875120574119862119877(119909) =

1

119875119903

exp(minus 119909119875119903

) (21)


119865119862119877= 119875119903 (119909 lt 120574th1198730)

= 1 minus 119875119903 (119909 gt 120574th1198730)

= 1 minus int

infin

120574th1198730

1

119875119903

exp(minus 119909119875119903) 119889119909


119875119903

)

(22)

where 119875119903(119909) = 119875

119862

119905

119870119862119877(1198890radic1198672 + 119889

2

1

)

119899

120576119862119877


119865119877119863= 119875119903 (119909 lt 120574th (119910 + 1198730))

= 1 minus 119875119903 (119909 gt 120574th (119910 + 1198730))

= 1 minus int

infin

0

119891 (119910)int

infin

120574th(119910+1198730)119891 (119909) 119889119909119889119910

= 1 minus int

infin

0

1

119875119903119868(119877119863)

exp(minus119910

119875119903119868(119877119863)

)

times int

infin

120574th(119910+1198730)

1

119875119903119877119863

exp(minus 119909

119875119903119877119863

)119889119909119889119910

= 1 minus119875119903119877119863

119875119903119877119863+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903119877119863

)

(23)

Out

age p

roba

bilit

y



10minus1

10minus2

10minus3

10minus4

100

2 4 6 8 10 12 14 16 18 20



119875out (1198891 1198892 120574th)


)

+ 1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

)


))

times (1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

))

(24)



utag

e pro

babi

lity


Direct transmission


10minus1

10minus2

10minus3

10minus4

100

5 10 15 20



Direct transmission

Ergo

dic c

apac

ity (b

itss

Hz)


15 2054

6

8

10

12

14

16

18

10




3

25

2

15

1

05

05 10 15 20 25 30 35 40 45 50


Aver

age fl

ow th

roug

hput

(Gbp

s)




0

4

2

6

8

10

12

14

16

18

20

5 10 15 20 25 30 35 40 45 50


Net

wor

k th

roug

hput

(Gbp

s)







6 Conclusion




Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Relay

Relay

RX3

Idle

Idle

RelayPNC

Idle

Idle

Relay

Relay

Tx1

Tx3

Tx7

Tx6

Tx5

Tx4

Tx

Tx3

TxRx2

Rx7 Rx6

Rx5

Rx4

RxRx

Rx1



3 System Model





119892 (120601) =119866 (120601)

119866max (1)







119862 = 119882 log2

[1 +119875119903

(1198730+ 119868)119882

] (2)




119875119903(119889) = 119875

119905119866119903119866119905(120582

4120587)

2

(1

119889)

119899

(3)


119903and 119866



119877 le 119862 = 119882120573 log2

[1 +1198751199051198661199031198661199051205822

161205872 (1198730+ 119868)119882119889119899

] (4)




119905


120574119862119877=

119875119862

119905

119870119862119877(1198890radic1198672 + 119889

2

1

)

119899

120576119862119877

1003816100381610038161003816ℎ1198621198771003816100381610038161003816

2

1198730

(5)

R

d1

d2


A4 A5

A12

A6

A10

A7

A1

A2

A3

A9

A11A13A14

C

D

A

B


32

14

5

6 78

R

d1

d2


C

D

A

B


where119870119862119877



1is


shadow fading 120601119889119861




119905


119905

then the



120574119877119863=

119875119903(119910)

119875119903(119910119868) + 1198730

=119875119877

119905

119870119877119863(11988901198892)119899

120576119877119863

1003816100381610038161003816ℎ1198771198631003816100381610038161003816

2

119875119868

119905

119870119868(1198890119889119868)119899

120576119868

1003816100381610038161003816ℎ1198681003816100381610038161003816

2

+ 1198730

(6)


119903(119910119868) is









119896forall119896 =



119896and average






1

DEV1

2 1205742

DEV2

3 1205743

DEV3 DEV4

4 1205744

DEV5 DEV6

5 1205745

DEV7

6 1205746

DEV8

7 1205747

DEV9

8 1205748

DEV10







119894

and 119877119909 isin 119866119895

forall119894 119895 larr (1 2 119872) and 119894 = 119895


(7) 119908 (119879119909 119877119909) larr119863119899

(119879119909 119875119896

) + 119863119899

(119875119896

119877119909)

119863119899 (119879119909 119877119909)+119865 (119875119896

)

119864 [119866119892

]



(10) end if




119894



119895


(7) 119889relay larr Min(119879119909 119903119895



(9) for 119895 larr 1 to 119875min do

(10) Mid (119895) larr (

10038161003816100381610038161003816100381610038161003816100381610038161003816

1

2minus

119889 (119879119909 119903119895

)

119863min

10038161003816100381610038161003816100381610038161003816100381610038161003816

) + (

10038161003816100381610038161003816100381610038161003816100381610038161003816

1

2minus

119889 (119903119895

119877119909)

119863min

10038161003816100381610038161003816100381610038161003816100381610038161003816

)




119894)




)62



25

20

15

10

5

00 5 10 15 20

Distance (m)

Capa

city

(Gbp

s)

n = 3n = 2



Tx Rx

R2

R3

R1

2m 3m5m

45m35m

6m

6m


B

C

A

D

120579

120579






ang119863119860119861 gt120579

2 ang119861119862119863 gt

120579

2 (7)


ang119863119860119861 = arccos(1198601198632

+ 1198601198612

minus 1198611198632

2119860119863 times 119860119861)

ang119861119862119863 = arccos(1198611198622

+ 1198621198632

minus 1198611198632

2119861119862 times 119862119863)

(8)



119860119863 gt 119877ER (ang119863119860119861 lt120579

2)

119861119862 gt 119877ER (ang119861119862119863 lt120579

2)

(9)


2

1

4

6

3

5





Tim

e slo

ts al

loca

ted

g1

g3

4

2

1

6

3

5

g3

2

1 3

3

5

6 4

GreenRed

Yellow

50

50

40

40

36

36

200

200

66

66

133133

2 4 6 1 4 5

1 4 5

3 6

2 6

50

40

36

200

66

133



119877ER = (1198961119866119905119866119903119875119905

1198730119882

)

1119899

(10)


1prop (1205824120587)


119905and 119866







CM(6times6)

=

[[[[[[[

[

0 1 0 0 0 1

0 0 1 0 0 0

1 1 0 0 0 0

0 0 1 0 0 0

0 0 0 0 0 0

1 0 0 0 1 0

]]]]]]]

]

(11)










119908 (119894) =sum119881

119894=1

119889 (119894)

119889 (119894) (13)




119905


119900






Weight=200 (4) 133 (6) 66 (5) 50 (1) 40 (2) 36 (3) (15)



= (REDGREEN) (16)








(7) 119863 = 119863119894119904119905119886119899119888119890(119877119900119908 119862119900119897119906119898119899)


(20) end for(21) for 119862119899119905 = 1 119862119899119905 lt 119881 119862119899119905 + + do(22) 119908(119862119899119905) = 119865119906119899119888119905119894119900119899 119882119890119894119892ℎ119905(119863(119862119899119905))


(27) 119908(119909) = 0

(28) end for


10

9

8

7

6

5

4

3

2

1

04 6 8 10 12 14

Number of flows

Flow

s per

slot





10

20 30 40 50 60 70 80

9

8

7

6

5

4

3

2

1

0

Flow

s per

slot



Beamwidth (deg)




10

15

5

04 6 8 10 12 14

Number of flows

Net

wor

k th

roug

hput

(Gbp

s)




20

20 30 40 50 60 70 80

18

16

14

12

10

8

6

4

2

0

Beamwidth (deg)

Net

wor

k th

roug

hput

(Gbp

s)









119877 = 119882119891120578 log2

(1 +120574th120574119891

) (17)





120574th = 120574119891 (2(2119877119882119891120578) minus 1) (18)


119875out = 119875119903 (min (120574119862119877 120574119877119863)) lt 120574th (19)


Thus we have

119875out (1198891 1198892 119889119868 120574th)

= 119875119903 (min (120574119862119877(1198891) 120574

119877119863(119889119868 1198892)) lt 120574th)


= 119865119862119877(1198891 120574th) + 119865119877119863 (1198891 119889119868 120574th)

minus 119865119862119877(1198891 120574th) 119865119877119863 (119889119868 1198892 120574th)

(20)





119875120574119862119877(119909) =

1

119875119903

exp(minus 119909119875119903

) (21)


119865119862119877= 119875119903 (119909 lt 120574th1198730)

= 1 minus 119875119903 (119909 gt 120574th1198730)

= 1 minus int

infin

120574th1198730

1

119875119903

exp(minus 119909119875119903) 119889119909


119875119903

)

(22)

where 119875119903(119909) = 119875

119862

119905

119870119862119877(1198890radic1198672 + 119889

2

1

)

119899

120576119862119877


119865119877119863= 119875119903 (119909 lt 120574th (119910 + 1198730))

= 1 minus 119875119903 (119909 gt 120574th (119910 + 1198730))

= 1 minus int

infin

0

119891 (119910)int

infin

120574th(119910+1198730)119891 (119909) 119889119909119889119910

= 1 minus int

infin

0

1

119875119903119868(119877119863)

exp(minus119910

119875119903119868(119877119863)

)

times int

infin

120574th(119910+1198730)

1

119875119903119877119863

exp(minus 119909

119875119903119877119863

)119889119909119889119910

= 1 minus119875119903119877119863

119875119903119877119863+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903119877119863

)

(23)

Out

age p

roba

bilit

y



10minus1

10minus2

10minus3

10minus4

100

2 4 6 8 10 12 14 16 18 20



119875out (1198891 1198892 120574th)


)

+ 1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

)


))

times (1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

))

(24)



utag

e pro

babi

lity


Direct transmission


10minus1

10minus2

10minus3

10minus4

100

5 10 15 20



Direct transmission

Ergo

dic c

apac

ity (b

itss

Hz)


15 2054

6

8

10

12

14

16

18

10




3

25

2

15

1

05

05 10 15 20 25 30 35 40 45 50


Aver

age fl

ow th

roug

hput

(Gbp

s)




0

4

2

6

8

10

12

14

16

18

20

5 10 15 20 25 30 35 40 45 50


Net

wor

k th

roug

hput

(Gbp

s)







6 Conclusion




Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119862 = 119882 log2

[1 +119875119903

(1198730+ 119868)119882

] (2)




119875119903(119889) = 119875

119905119866119903119866119905(120582

4120587)

2

(1

119889)

119899

(3)


119903and 119866



119877 le 119862 = 119882120573 log2

[1 +1198751199051198661199031198661199051205822

161205872 (1198730+ 119868)119882119889119899

] (4)




119905


120574119862119877=

119875119862

119905

119870119862119877(1198890radic1198672 + 119889

2

1

)

119899

120576119862119877

1003816100381610038161003816ℎ1198621198771003816100381610038161003816

2

1198730

(5)

R

d1

d2


A4 A5

A12

A6

A10

A7

A1

A2

A3

A9

A11A13A14

C

D

A

B


32

14

5

6 78

R

d1

d2


C

D

A

B


where119870119862119877



1is


shadow fading 120601119889119861




119905


119905

then the



120574119877119863=

119875119903(119910)

119875119903(119910119868) + 1198730

=119875119877

119905

119870119877119863(11988901198892)119899

120576119877119863

1003816100381610038161003816ℎ1198771198631003816100381610038161003816

2

119875119868

119905

119870119868(1198890119889119868)119899

120576119868

1003816100381610038161003816ℎ1198681003816100381610038161003816

2

+ 1198730

(6)


119903(119910119868) is









119896forall119896 =



119896and average






1

DEV1

2 1205742

DEV2

3 1205743

DEV3 DEV4

4 1205744

DEV5 DEV6

5 1205745

DEV7

6 1205746

DEV8

7 1205747

DEV9

8 1205748

DEV10







119894

and 119877119909 isin 119866119895

forall119894 119895 larr (1 2 119872) and 119894 = 119895


(7) 119908 (119879119909 119877119909) larr119863119899

(119879119909 119875119896

) + 119863119899

(119875119896

119877119909)

119863119899 (119879119909 119877119909)+119865 (119875119896

)

119864 [119866119892

]



(10) end if




119894



119895


(7) 119889relay larr Min(119879119909 119903119895



(9) for 119895 larr 1 to 119875min do

(10) Mid (119895) larr (

10038161003816100381610038161003816100381610038161003816100381610038161003816

1

2minus

119889 (119879119909 119903119895

)

119863min

10038161003816100381610038161003816100381610038161003816100381610038161003816

) + (

10038161003816100381610038161003816100381610038161003816100381610038161003816

1

2minus

119889 (119903119895

119877119909)

119863min

10038161003816100381610038161003816100381610038161003816100381610038161003816

)




119894)




)62



25

20

15

10

5

00 5 10 15 20

Distance (m)

Capa

city

(Gbp

s)

n = 3n = 2



Tx Rx

R2

R3

R1

2m 3m5m

45m35m

6m

6m


B

C

A

D

120579

120579






ang119863119860119861 gt120579

2 ang119861119862119863 gt

120579

2 (7)


ang119863119860119861 = arccos(1198601198632

+ 1198601198612

minus 1198611198632

2119860119863 times 119860119861)

ang119861119862119863 = arccos(1198611198622

+ 1198621198632

minus 1198611198632

2119861119862 times 119862119863)

(8)



119860119863 gt 119877ER (ang119863119860119861 lt120579

2)

119861119862 gt 119877ER (ang119861119862119863 lt120579

2)

(9)


2

1

4

6

3

5





Tim

e slo

ts al

loca

ted

g1

g3

4

2

1

6

3

5

g3

2

1 3

3

5

6 4

GreenRed

Yellow

50

50

40

40

36

36

200

200

66

66

133133

2 4 6 1 4 5

1 4 5

3 6

2 6

50

40

36

200

66

133



119877ER = (1198961119866119905119866119903119875119905

1198730119882

)

1119899

(10)


1prop (1205824120587)


119905and 119866







CM(6times6)

=

[[[[[[[

[

0 1 0 0 0 1

0 0 1 0 0 0

1 1 0 0 0 0

0 0 1 0 0 0

0 0 0 0 0 0

1 0 0 0 1 0

]]]]]]]

]

(11)










119908 (119894) =sum119881

119894=1

119889 (119894)

119889 (119894) (13)




119905


119900






Weight=200 (4) 133 (6) 66 (5) 50 (1) 40 (2) 36 (3) (15)



= (REDGREEN) (16)








(7) 119863 = 119863119894119904119905119886119899119888119890(119877119900119908 119862119900119897119906119898119899)


(20) end for(21) for 119862119899119905 = 1 119862119899119905 lt 119881 119862119899119905 + + do(22) 119908(119862119899119905) = 119865119906119899119888119905119894119900119899 119882119890119894119892ℎ119905(119863(119862119899119905))


(27) 119908(119909) = 0

(28) end for


10

9

8

7

6

5

4

3

2

1

04 6 8 10 12 14

Number of flows

Flow

s per

slot





10

20 30 40 50 60 70 80

9

8

7

6

5

4

3

2

1

0

Flow

s per

slot



Beamwidth (deg)




10

15

5

04 6 8 10 12 14

Number of flows

Net

wor

k th

roug

hput

(Gbp

s)




20

20 30 40 50 60 70 80

18

16

14

12

10

8

6

4

2

0

Beamwidth (deg)

Net

wor

k th

roug

hput

(Gbp

s)









119877 = 119882119891120578 log2

(1 +120574th120574119891

) (17)





120574th = 120574119891 (2(2119877119882119891120578) minus 1) (18)


119875out = 119875119903 (min (120574119862119877 120574119877119863)) lt 120574th (19)


Thus we have

119875out (1198891 1198892 119889119868 120574th)

= 119875119903 (min (120574119862119877(1198891) 120574

119877119863(119889119868 1198892)) lt 120574th)


= 119865119862119877(1198891 120574th) + 119865119877119863 (1198891 119889119868 120574th)

minus 119865119862119877(1198891 120574th) 119865119877119863 (119889119868 1198892 120574th)

(20)





119875120574119862119877(119909) =

1

119875119903

exp(minus 119909119875119903

) (21)


119865119862119877= 119875119903 (119909 lt 120574th1198730)

= 1 minus 119875119903 (119909 gt 120574th1198730)

= 1 minus int

infin

120574th1198730

1

119875119903

exp(minus 119909119875119903) 119889119909


119875119903

)

(22)

where 119875119903(119909) = 119875

119862

119905

119870119862119877(1198890radic1198672 + 119889

2

1

)

119899

120576119862119877


119865119877119863= 119875119903 (119909 lt 120574th (119910 + 1198730))

= 1 minus 119875119903 (119909 gt 120574th (119910 + 1198730))

= 1 minus int

infin

0

119891 (119910)int

infin

120574th(119910+1198730)119891 (119909) 119889119909119889119910

= 1 minus int

infin

0

1

119875119903119868(119877119863)

exp(minus119910

119875119903119868(119877119863)

)

times int

infin

120574th(119910+1198730)

1

119875119903119877119863

exp(minus 119909

119875119903119877119863

)119889119909119889119910

= 1 minus119875119903119877119863

119875119903119877119863+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903119877119863

)

(23)

Out

age p

roba

bilit

y



10minus1

10minus2

10minus3

10minus4

100

2 4 6 8 10 12 14 16 18 20



119875out (1198891 1198892 120574th)


)

+ 1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

)


))

times (1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

))

(24)



utag

e pro

babi

lity


Direct transmission


10minus1

10minus2

10minus3

10minus4

100

5 10 15 20



Direct transmission

Ergo

dic c

apac

ity (b

itss

Hz)


15 2054

6

8

10

12

14

16

18

10




3

25

2

15

1

05

05 10 15 20 25 30 35 40 45 50


Aver

age fl

ow th

roug

hput

(Gbp

s)




0

4

2

6

8

10

12

14

16

18

20

5 10 15 20 25 30 35 40 45 50


Net

wor

k th

roug

hput

(Gbp

s)







6 Conclusion




Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











120574119877119863=

119875119903(119910)

119875119903(119910119868) + 1198730

=119875119877

119905

119870119877119863(11988901198892)119899

120576119877119863

1003816100381610038161003816ℎ1198771198631003816100381610038161003816

2

119875119868

119905

119870119868(1198890119889119868)119899

120576119868

1003816100381610038161003816ℎ1198681003816100381610038161003816

2

+ 1198730

(6)


119903(119910119868) is









119896forall119896 =



119896and average






1

DEV1

2 1205742

DEV2

3 1205743

DEV3 DEV4

4 1205744

DEV5 DEV6

5 1205745

DEV7

6 1205746

DEV8

7 1205747

DEV9

8 1205748

DEV10







119894

and 119877119909 isin 119866119895

forall119894 119895 larr (1 2 119872) and 119894 = 119895


(7) 119908 (119879119909 119877119909) larr119863119899

(119879119909 119875119896

) + 119863119899

(119875119896

119877119909)

119863119899 (119879119909 119877119909)+119865 (119875119896

)

119864 [119866119892

]



(10) end if




119894



119895


(7) 119889relay larr Min(119879119909 119903119895



(9) for 119895 larr 1 to 119875min do

(10) Mid (119895) larr (

10038161003816100381610038161003816100381610038161003816100381610038161003816

1

2minus

119889 (119879119909 119903119895

)

119863min

10038161003816100381610038161003816100381610038161003816100381610038161003816

) + (

10038161003816100381610038161003816100381610038161003816100381610038161003816

1

2minus

119889 (119903119895

119877119909)

119863min

10038161003816100381610038161003816100381610038161003816100381610038161003816

)




119894)




)62



25

20

15

10

5

00 5 10 15 20

Distance (m)

Capa

city

(Gbp

s)

n = 3n = 2



Tx Rx

R2

R3

R1

2m 3m5m

45m35m

6m

6m


B

C

A

D

120579

120579






ang119863119860119861 gt120579

2 ang119861119862119863 gt

120579

2 (7)


ang119863119860119861 = arccos(1198601198632

+ 1198601198612

minus 1198611198632

2119860119863 times 119860119861)

ang119861119862119863 = arccos(1198611198622

+ 1198621198632

minus 1198611198632

2119861119862 times 119862119863)

(8)



119860119863 gt 119877ER (ang119863119860119861 lt120579

2)

119861119862 gt 119877ER (ang119861119862119863 lt120579

2)

(9)


2

1

4

6

3

5





Tim

e slo

ts al

loca

ted

g1

g3

4

2

1

6

3

5

g3

2

1 3

3

5

6 4

GreenRed

Yellow

50

50

40

40

36

36

200

200

66

66

133133

2 4 6 1 4 5

1 4 5

3 6

2 6

50

40

36

200

66

133



119877ER = (1198961119866119905119866119903119875119905

1198730119882

)

1119899

(10)


1prop (1205824120587)


119905and 119866







CM(6times6)

=

[[[[[[[

[

0 1 0 0 0 1

0 0 1 0 0 0

1 1 0 0 0 0

0 0 1 0 0 0

0 0 0 0 0 0

1 0 0 0 1 0

]]]]]]]

]

(11)










119908 (119894) =sum119881

119894=1

119889 (119894)

119889 (119894) (13)




119905


119900






Weight=200 (4) 133 (6) 66 (5) 50 (1) 40 (2) 36 (3) (15)



= (REDGREEN) (16)








(7) 119863 = 119863119894119904119905119886119899119888119890(119877119900119908 119862119900119897119906119898119899)


(20) end for(21) for 119862119899119905 = 1 119862119899119905 lt 119881 119862119899119905 + + do(22) 119908(119862119899119905) = 119865119906119899119888119905119894119900119899 119882119890119894119892ℎ119905(119863(119862119899119905))


(27) 119908(119909) = 0

(28) end for


10

9

8

7

6

5

4

3

2

1

04 6 8 10 12 14

Number of flows

Flow

s per

slot





10

20 30 40 50 60 70 80

9

8

7

6

5

4

3

2

1

0

Flow

s per

slot



Beamwidth (deg)




10

15

5

04 6 8 10 12 14

Number of flows

Net

wor

k th

roug

hput

(Gbp

s)




20

20 30 40 50 60 70 80

18

16

14

12

10

8

6

4

2

0

Beamwidth (deg)

Net

wor

k th

roug

hput

(Gbp

s)









119877 = 119882119891120578 log2

(1 +120574th120574119891

) (17)





120574th = 120574119891 (2(2119877119882119891120578) minus 1) (18)


119875out = 119875119903 (min (120574119862119877 120574119877119863)) lt 120574th (19)


Thus we have

119875out (1198891 1198892 119889119868 120574th)

= 119875119903 (min (120574119862119877(1198891) 120574

119877119863(119889119868 1198892)) lt 120574th)


= 119865119862119877(1198891 120574th) + 119865119877119863 (1198891 119889119868 120574th)

minus 119865119862119877(1198891 120574th) 119865119877119863 (119889119868 1198892 120574th)

(20)





119875120574119862119877(119909) =

1

119875119903

exp(minus 119909119875119903

) (21)


119865119862119877= 119875119903 (119909 lt 120574th1198730)

= 1 minus 119875119903 (119909 gt 120574th1198730)

= 1 minus int

infin

120574th1198730

1

119875119903

exp(minus 119909119875119903) 119889119909


119875119903

)

(22)

where 119875119903(119909) = 119875

119862

119905

119870119862119877(1198890radic1198672 + 119889

2

1

)

119899

120576119862119877


119865119877119863= 119875119903 (119909 lt 120574th (119910 + 1198730))

= 1 minus 119875119903 (119909 gt 120574th (119910 + 1198730))

= 1 minus int

infin

0

119891 (119910)int

infin

120574th(119910+1198730)119891 (119909) 119889119909119889119910

= 1 minus int

infin

0

1

119875119903119868(119877119863)

exp(minus119910

119875119903119868(119877119863)

)

times int

infin

120574th(119910+1198730)

1

119875119903119877119863

exp(minus 119909

119875119903119877119863

)119889119909119889119910

= 1 minus119875119903119877119863

119875119903119877119863+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903119877119863

)

(23)

Out

age p

roba

bilit

y



10minus1

10minus2

10minus3

10minus4

100

2 4 6 8 10 12 14 16 18 20



119875out (1198891 1198892 120574th)


)

+ 1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

)


))

times (1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

))

(24)



utag

e pro

babi

lity


Direct transmission


10minus1

10minus2

10minus3

10minus4

100

5 10 15 20



Direct transmission

Ergo

dic c

apac

ity (b

itss

Hz)


15 2054

6

8

10

12

14

16

18

10




3

25

2

15

1

05

05 10 15 20 25 30 35 40 45 50


Aver

age fl

ow th

roug

hput

(Gbp

s)




0

4

2

6

8

10

12

14

16

18

20

5 10 15 20 25 30 35 40 45 50


Net

wor

k th

roug

hput

(Gbp

s)







6 Conclusion




Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119894

and 119877119909 isin 119866119895

forall119894 119895 larr (1 2 119872) and 119894 = 119895


(7) 119908 (119879119909 119877119909) larr119863119899

(119879119909 119875119896

) + 119863119899

(119875119896

119877119909)

119863119899 (119879119909 119877119909)+119865 (119875119896

)

119864 [119866119892

]



(10) end if




119894



119895


(7) 119889relay larr Min(119879119909 119903119895



(9) for 119895 larr 1 to 119875min do

(10) Mid (119895) larr (

10038161003816100381610038161003816100381610038161003816100381610038161003816

1

2minus

119889 (119879119909 119903119895

)

119863min

10038161003816100381610038161003816100381610038161003816100381610038161003816

) + (

10038161003816100381610038161003816100381610038161003816100381610038161003816

1

2minus

119889 (119903119895

119877119909)

119863min

10038161003816100381610038161003816100381610038161003816100381610038161003816

)




119894)




)62



25

20

15

10

5

00 5 10 15 20

Distance (m)

Capa

city

(Gbp

s)

n = 3n = 2



Tx Rx

R2

R3

R1

2m 3m5m

45m35m

6m

6m


B

C

A

D

120579

120579






ang119863119860119861 gt120579

2 ang119861119862119863 gt

120579

2 (7)


ang119863119860119861 = arccos(1198601198632

+ 1198601198612

minus 1198611198632

2119860119863 times 119860119861)

ang119861119862119863 = arccos(1198611198622

+ 1198621198632

minus 1198611198632

2119861119862 times 119862119863)

(8)



119860119863 gt 119877ER (ang119863119860119861 lt120579

2)

119861119862 gt 119877ER (ang119861119862119863 lt120579

2)

(9)


2

1

4

6

3

5





Tim

e slo

ts al

loca

ted

g1

g3

4

2

1

6

3

5

g3

2

1 3

3

5

6 4

GreenRed

Yellow

50

50

40

40

36

36

200

200

66

66

133133

2 4 6 1 4 5

1 4 5

3 6

2 6

50

40

36

200

66

133



119877ER = (1198961119866119905119866119903119875119905

1198730119882

)

1119899

(10)


1prop (1205824120587)


119905and 119866







CM(6times6)

=

[[[[[[[

[

0 1 0 0 0 1

0 0 1 0 0 0

1 1 0 0 0 0

0 0 1 0 0 0

0 0 0 0 0 0

1 0 0 0 1 0

]]]]]]]

]

(11)










119908 (119894) =sum119881

119894=1

119889 (119894)

119889 (119894) (13)




119905


119900






Weight=200 (4) 133 (6) 66 (5) 50 (1) 40 (2) 36 (3) (15)



= (REDGREEN) (16)








(7) 119863 = 119863119894119904119905119886119899119888119890(119877119900119908 119862119900119897119906119898119899)


(20) end for(21) for 119862119899119905 = 1 119862119899119905 lt 119881 119862119899119905 + + do(22) 119908(119862119899119905) = 119865119906119899119888119905119894119900119899 119882119890119894119892ℎ119905(119863(119862119899119905))


(27) 119908(119909) = 0

(28) end for


10

9

8

7

6

5

4

3

2

1

04 6 8 10 12 14

Number of flows

Flow

s per

slot





10

20 30 40 50 60 70 80

9

8

7

6

5

4

3

2

1

0

Flow

s per

slot



Beamwidth (deg)




10

15

5

04 6 8 10 12 14

Number of flows

Net

wor

k th

roug

hput

(Gbp

s)




20

20 30 40 50 60 70 80

18

16

14

12

10

8

6

4

2

0

Beamwidth (deg)

Net

wor

k th

roug

hput

(Gbp

s)









119877 = 119882119891120578 log2

(1 +120574th120574119891

) (17)





120574th = 120574119891 (2(2119877119882119891120578) minus 1) (18)


119875out = 119875119903 (min (120574119862119877 120574119877119863)) lt 120574th (19)


Thus we have

119875out (1198891 1198892 119889119868 120574th)

= 119875119903 (min (120574119862119877(1198891) 120574

119877119863(119889119868 1198892)) lt 120574th)


= 119865119862119877(1198891 120574th) + 119865119877119863 (1198891 119889119868 120574th)

minus 119865119862119877(1198891 120574th) 119865119877119863 (119889119868 1198892 120574th)

(20)





119875120574119862119877(119909) =

1

119875119903

exp(minus 119909119875119903

) (21)


119865119862119877= 119875119903 (119909 lt 120574th1198730)

= 1 minus 119875119903 (119909 gt 120574th1198730)

= 1 minus int

infin

120574th1198730

1

119875119903

exp(minus 119909119875119903) 119889119909


119875119903

)

(22)

where 119875119903(119909) = 119875

119862

119905

119870119862119877(1198890radic1198672 + 119889

2

1

)

119899

120576119862119877


119865119877119863= 119875119903 (119909 lt 120574th (119910 + 1198730))

= 1 minus 119875119903 (119909 gt 120574th (119910 + 1198730))

= 1 minus int

infin

0

119891 (119910)int

infin

120574th(119910+1198730)119891 (119909) 119889119909119889119910

= 1 minus int

infin

0

1

119875119903119868(119877119863)

exp(minus119910

119875119903119868(119877119863)

)

times int

infin

120574th(119910+1198730)

1

119875119903119877119863

exp(minus 119909

119875119903119877119863

)119889119909119889119910

= 1 minus119875119903119877119863

119875119903119877119863+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903119877119863

)

(23)

Out

age p

roba

bilit

y



10minus1

10minus2

10minus3

10minus4

100

2 4 6 8 10 12 14 16 18 20



119875out (1198891 1198892 120574th)


)

+ 1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

)


))

times (1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

))

(24)



utag

e pro

babi

lity


Direct transmission


10minus1

10minus2

10minus3

10minus4

100

5 10 15 20



Direct transmission

Ergo

dic c

apac

ity (b

itss

Hz)


15 2054

6

8

10

12

14

16

18

10




3

25

2

15

1

05

05 10 15 20 25 30 35 40 45 50


Aver

age fl

ow th

roug

hput

(Gbp

s)




0

4

2

6

8

10

12

14

16

18

20

5 10 15 20 25 30 35 40 45 50


Net

wor

k th

roug

hput

(Gbp

s)







6 Conclusion




Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










25

20

15

10

5

00 5 10 15 20

Distance (m)

Capa

city

(Gbp

s)

n = 3n = 2



Tx Rx

R2

R3

R1

2m 3m5m

45m35m

6m

6m


B

C

A

D

120579

120579






ang119863119860119861 gt120579

2 ang119861119862119863 gt

120579

2 (7)


ang119863119860119861 = arccos(1198601198632

+ 1198601198612

minus 1198611198632

2119860119863 times 119860119861)

ang119861119862119863 = arccos(1198611198622

+ 1198621198632

minus 1198611198632

2119861119862 times 119862119863)

(8)



119860119863 gt 119877ER (ang119863119860119861 lt120579

2)

119861119862 gt 119877ER (ang119861119862119863 lt120579

2)

(9)


2

1

4

6

3

5





Tim

e slo

ts al

loca

ted

g1

g3

4

2

1

6

3

5

g3

2

1 3

3

5

6 4

GreenRed

Yellow

50

50

40

40

36

36

200

200

66

66

133133

2 4 6 1 4 5

1 4 5

3 6

2 6

50

40

36

200

66

133



119877ER = (1198961119866119905119866119903119875119905

1198730119882

)

1119899

(10)


1prop (1205824120587)


119905and 119866







CM(6times6)

=

[[[[[[[

[

0 1 0 0 0 1

0 0 1 0 0 0

1 1 0 0 0 0

0 0 1 0 0 0

0 0 0 0 0 0

1 0 0 0 1 0

]]]]]]]

]

(11)










119908 (119894) =sum119881

119894=1

119889 (119894)

119889 (119894) (13)




119905


119900






Weight=200 (4) 133 (6) 66 (5) 50 (1) 40 (2) 36 (3) (15)



= (REDGREEN) (16)








(7) 119863 = 119863119894119904119905119886119899119888119890(119877119900119908 119862119900119897119906119898119899)


(20) end for(21) for 119862119899119905 = 1 119862119899119905 lt 119881 119862119899119905 + + do(22) 119908(119862119899119905) = 119865119906119899119888119905119894119900119899 119882119890119894119892ℎ119905(119863(119862119899119905))


(27) 119908(119909) = 0

(28) end for


10

9

8

7

6

5

4

3

2

1

04 6 8 10 12 14

Number of flows

Flow

s per

slot





10

20 30 40 50 60 70 80

9

8

7

6

5

4

3

2

1

0

Flow

s per

slot



Beamwidth (deg)




10

15

5

04 6 8 10 12 14

Number of flows

Net

wor

k th

roug

hput

(Gbp

s)




20

20 30 40 50 60 70 80

18

16

14

12

10

8

6

4

2

0

Beamwidth (deg)

Net

wor

k th

roug

hput

(Gbp

s)









119877 = 119882119891120578 log2

(1 +120574th120574119891

) (17)





120574th = 120574119891 (2(2119877119882119891120578) minus 1) (18)


119875out = 119875119903 (min (120574119862119877 120574119877119863)) lt 120574th (19)


Thus we have

119875out (1198891 1198892 119889119868 120574th)

= 119875119903 (min (120574119862119877(1198891) 120574

119877119863(119889119868 1198892)) lt 120574th)


= 119865119862119877(1198891 120574th) + 119865119877119863 (1198891 119889119868 120574th)

minus 119865119862119877(1198891 120574th) 119865119877119863 (119889119868 1198892 120574th)

(20)





119875120574119862119877(119909) =

1

119875119903

exp(minus 119909119875119903

) (21)


119865119862119877= 119875119903 (119909 lt 120574th1198730)

= 1 minus 119875119903 (119909 gt 120574th1198730)

= 1 minus int

infin

120574th1198730

1

119875119903

exp(minus 119909119875119903) 119889119909


119875119903

)

(22)

where 119875119903(119909) = 119875

119862

119905

119870119862119877(1198890radic1198672 + 119889

2

1

)

119899

120576119862119877


119865119877119863= 119875119903 (119909 lt 120574th (119910 + 1198730))

= 1 minus 119875119903 (119909 gt 120574th (119910 + 1198730))

= 1 minus int

infin

0

119891 (119910)int

infin

120574th(119910+1198730)119891 (119909) 119889119909119889119910

= 1 minus int

infin

0

1

119875119903119868(119877119863)

exp(minus119910

119875119903119868(119877119863)

)

times int

infin

120574th(119910+1198730)

1

119875119903119877119863

exp(minus 119909

119875119903119877119863

)119889119909119889119910

= 1 minus119875119903119877119863

119875119903119877119863+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903119877119863

)

(23)

Out

age p

roba

bilit

y



10minus1

10minus2

10minus3

10minus4

100

2 4 6 8 10 12 14 16 18 20



119875out (1198891 1198892 120574th)


)

+ 1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

)


))

times (1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

))

(24)



utag

e pro

babi

lity


Direct transmission


10minus1

10minus2

10minus3

10minus4

100

5 10 15 20



Direct transmission

Ergo

dic c

apac

ity (b

itss

Hz)


15 2054

6

8

10

12

14

16

18

10




3

25

2

15

1

05

05 10 15 20 25 30 35 40 45 50


Aver

age fl

ow th

roug

hput

(Gbp

s)




0

4

2

6

8

10

12

14

16

18

20

5 10 15 20 25 30 35 40 45 50


Net

wor

k th

roug

hput

(Gbp

s)







6 Conclusion




Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










2

1

4

6

3

5





Tim

e slo

ts al

loca

ted

g1

g3

4

2

1

6

3

5

g3

2

1 3

3

5

6 4

GreenRed

Yellow

50

50

40

40

36

36

200

200

66

66

133133

2 4 6 1 4 5

1 4 5

3 6

2 6

50

40

36

200

66

133



119877ER = (1198961119866119905119866119903119875119905

1198730119882

)

1119899

(10)


1prop (1205824120587)


119905and 119866







CM(6times6)

=

[[[[[[[

[

0 1 0 0 0 1

0 0 1 0 0 0

1 1 0 0 0 0

0 0 1 0 0 0

0 0 0 0 0 0

1 0 0 0 1 0

]]]]]]]

]

(11)










119908 (119894) =sum119881

119894=1

119889 (119894)

119889 (119894) (13)




119905


119900






Weight=200 (4) 133 (6) 66 (5) 50 (1) 40 (2) 36 (3) (15)



= (REDGREEN) (16)








(7) 119863 = 119863119894119904119905119886119899119888119890(119877119900119908 119862119900119897119906119898119899)


(20) end for(21) for 119862119899119905 = 1 119862119899119905 lt 119881 119862119899119905 + + do(22) 119908(119862119899119905) = 119865119906119899119888119905119894119900119899 119882119890119894119892ℎ119905(119863(119862119899119905))


(27) 119908(119909) = 0

(28) end for


10

9

8

7

6

5

4

3

2

1

04 6 8 10 12 14

Number of flows

Flow

s per

slot





10

20 30 40 50 60 70 80

9

8

7

6

5

4

3

2

1

0

Flow

s per

slot



Beamwidth (deg)




10

15

5

04 6 8 10 12 14

Number of flows

Net

wor

k th

roug

hput

(Gbp

s)




20

20 30 40 50 60 70 80

18

16

14

12

10

8

6

4

2

0

Beamwidth (deg)

Net

wor

k th

roug

hput

(Gbp

s)









119877 = 119882119891120578 log2

(1 +120574th120574119891

) (17)





120574th = 120574119891 (2(2119877119882119891120578) minus 1) (18)


119875out = 119875119903 (min (120574119862119877 120574119877119863)) lt 120574th (19)


Thus we have

119875out (1198891 1198892 119889119868 120574th)

= 119875119903 (min (120574119862119877(1198891) 120574

119877119863(119889119868 1198892)) lt 120574th)


= 119865119862119877(1198891 120574th) + 119865119877119863 (1198891 119889119868 120574th)

minus 119865119862119877(1198891 120574th) 119865119877119863 (119889119868 1198892 120574th)

(20)





119875120574119862119877(119909) =

1

119875119903

exp(minus 119909119875119903

) (21)


119865119862119877= 119875119903 (119909 lt 120574th1198730)

= 1 minus 119875119903 (119909 gt 120574th1198730)

= 1 minus int

infin

120574th1198730

1

119875119903

exp(minus 119909119875119903) 119889119909


119875119903

)

(22)

where 119875119903(119909) = 119875

119862

119905

119870119862119877(1198890radic1198672 + 119889

2

1

)

119899

120576119862119877


119865119877119863= 119875119903 (119909 lt 120574th (119910 + 1198730))

= 1 minus 119875119903 (119909 gt 120574th (119910 + 1198730))

= 1 minus int

infin

0

119891 (119910)int

infin

120574th(119910+1198730)119891 (119909) 119889119909119889119910

= 1 minus int

infin

0

1

119875119903119868(119877119863)

exp(minus119910

119875119903119868(119877119863)

)

times int

infin

120574th(119910+1198730)

1

119875119903119877119863

exp(minus 119909

119875119903119877119863

)119889119909119889119910

= 1 minus119875119903119877119863

119875119903119877119863+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903119877119863

)

(23)

Out

age p

roba

bilit

y



10minus1

10minus2

10minus3

10minus4

100

2 4 6 8 10 12 14 16 18 20



119875out (1198891 1198892 120574th)


)

+ 1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

)


))

times (1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

))

(24)



utag

e pro

babi

lity


Direct transmission


10minus1

10minus2

10minus3

10minus4

100

5 10 15 20



Direct transmission

Ergo

dic c

apac

ity (b

itss

Hz)


15 2054

6

8

10

12

14

16

18

10




3

25

2

15

1

05

05 10 15 20 25 30 35 40 45 50


Aver

age fl

ow th

roug

hput

(Gbp

s)




0

4

2

6

8

10

12

14

16

18

20

5 10 15 20 25 30 35 40 45 50


Net

wor

k th

roug

hput

(Gbp

s)







6 Conclusion




Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















119908 (119894) =sum119881

119894=1

119889 (119894)

119889 (119894) (13)




119905


119900






Weight=200 (4) 133 (6) 66 (5) 50 (1) 40 (2) 36 (3) (15)



= (REDGREEN) (16)








(7) 119863 = 119863119894119904119905119886119899119888119890(119877119900119908 119862119900119897119906119898119899)


(20) end for(21) for 119862119899119905 = 1 119862119899119905 lt 119881 119862119899119905 + + do(22) 119908(119862119899119905) = 119865119906119899119888119905119894119900119899 119882119890119894119892ℎ119905(119863(119862119899119905))


(27) 119908(119909) = 0

(28) end for


10

9

8

7

6

5

4

3

2

1

04 6 8 10 12 14

Number of flows

Flow

s per

slot





10

20 30 40 50 60 70 80

9

8

7

6

5

4

3

2

1

0

Flow

s per

slot



Beamwidth (deg)




10

15

5

04 6 8 10 12 14

Number of flows

Net

wor

k th

roug

hput

(Gbp

s)




20

20 30 40 50 60 70 80

18

16

14

12

10

8

6

4

2

0

Beamwidth (deg)

Net

wor

k th

roug

hput

(Gbp

s)









119877 = 119882119891120578 log2

(1 +120574th120574119891

) (17)





120574th = 120574119891 (2(2119877119882119891120578) minus 1) (18)


119875out = 119875119903 (min (120574119862119877 120574119877119863)) lt 120574th (19)


Thus we have

119875out (1198891 1198892 119889119868 120574th)

= 119875119903 (min (120574119862119877(1198891) 120574

119877119863(119889119868 1198892)) lt 120574th)


= 119865119862119877(1198891 120574th) + 119865119877119863 (1198891 119889119868 120574th)

minus 119865119862119877(1198891 120574th) 119865119877119863 (119889119868 1198892 120574th)

(20)





119875120574119862119877(119909) =

1

119875119903

exp(minus 119909119875119903

) (21)


119865119862119877= 119875119903 (119909 lt 120574th1198730)

= 1 minus 119875119903 (119909 gt 120574th1198730)

= 1 minus int

infin

120574th1198730

1

119875119903

exp(minus 119909119875119903) 119889119909


119875119903

)

(22)

where 119875119903(119909) = 119875

119862

119905

119870119862119877(1198890radic1198672 + 119889

2

1

)

119899

120576119862119877


119865119877119863= 119875119903 (119909 lt 120574th (119910 + 1198730))

= 1 minus 119875119903 (119909 gt 120574th (119910 + 1198730))

= 1 minus int

infin

0

119891 (119910)int

infin

120574th(119910+1198730)119891 (119909) 119889119909119889119910

= 1 minus int

infin

0

1

119875119903119868(119877119863)

exp(minus119910

119875119903119868(119877119863)

)

times int

infin

120574th(119910+1198730)

1

119875119903119877119863

exp(minus 119909

119875119903119877119863

)119889119909119889119910

= 1 minus119875119903119877119863

119875119903119877119863+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903119877119863

)

(23)

Out

age p

roba

bilit

y



10minus1

10minus2

10minus3

10minus4

100

2 4 6 8 10 12 14 16 18 20



119875out (1198891 1198892 120574th)


)

+ 1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

)


))

times (1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

))

(24)



utag

e pro

babi

lity


Direct transmission


10minus1

10minus2

10minus3

10minus4

100

5 10 15 20



Direct transmission

Ergo

dic c

apac

ity (b

itss

Hz)


15 2054

6

8

10

12

14

16

18

10




3

25

2

15

1

05

05 10 15 20 25 30 35 40 45 50


Aver

age fl

ow th

roug

hput

(Gbp

s)




0

4

2

6

8

10

12

14

16

18

20

5 10 15 20 25 30 35 40 45 50


Net

wor

k th

roug

hput

(Gbp

s)







6 Conclusion




Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












(7) 119863 = 119863119894119904119905119886119899119888119890(119877119900119908 119862119900119897119906119898119899)


(20) end for(21) for 119862119899119905 = 1 119862119899119905 lt 119881 119862119899119905 + + do(22) 119908(119862119899119905) = 119865119906119899119888119905119894119900119899 119882119890119894119892ℎ119905(119863(119862119899119905))


(27) 119908(119909) = 0

(28) end for


10

9

8

7

6

5

4

3

2

1

04 6 8 10 12 14

Number of flows

Flow

s per

slot





10

20 30 40 50 60 70 80

9

8

7

6

5

4

3

2

1

0

Flow

s per

slot



Beamwidth (deg)




10

15

5

04 6 8 10 12 14

Number of flows

Net

wor

k th

roug

hput

(Gbp

s)




20

20 30 40 50 60 70 80

18

16

14

12

10

8

6

4

2

0

Beamwidth (deg)

Net

wor

k th

roug

hput

(Gbp

s)









119877 = 119882119891120578 log2

(1 +120574th120574119891

) (17)





120574th = 120574119891 (2(2119877119882119891120578) minus 1) (18)


119875out = 119875119903 (min (120574119862119877 120574119877119863)) lt 120574th (19)


Thus we have

119875out (1198891 1198892 119889119868 120574th)

= 119875119903 (min (120574119862119877(1198891) 120574

119877119863(119889119868 1198892)) lt 120574th)


= 119865119862119877(1198891 120574th) + 119865119877119863 (1198891 119889119868 120574th)

minus 119865119862119877(1198891 120574th) 119865119877119863 (119889119868 1198892 120574th)

(20)





119875120574119862119877(119909) =

1

119875119903

exp(minus 119909119875119903

) (21)


119865119862119877= 119875119903 (119909 lt 120574th1198730)

= 1 minus 119875119903 (119909 gt 120574th1198730)

= 1 minus int

infin

120574th1198730

1

119875119903

exp(minus 119909119875119903) 119889119909


119875119903

)

(22)

where 119875119903(119909) = 119875

119862

119905

119870119862119877(1198890radic1198672 + 119889

2

1

)

119899

120576119862119877


119865119877119863= 119875119903 (119909 lt 120574th (119910 + 1198730))

= 1 minus 119875119903 (119909 gt 120574th (119910 + 1198730))

= 1 minus int

infin

0

119891 (119910)int

infin

120574th(119910+1198730)119891 (119909) 119889119909119889119910

= 1 minus int

infin

0

1

119875119903119868(119877119863)

exp(minus119910

119875119903119868(119877119863)

)

times int

infin

120574th(119910+1198730)

1

119875119903119877119863

exp(minus 119909

119875119903119877119863

)119889119909119889119910

= 1 minus119875119903119877119863

119875119903119877119863+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903119877119863

)

(23)

Out

age p

roba

bilit

y



10minus1

10minus2

10minus3

10minus4

100

2 4 6 8 10 12 14 16 18 20



119875out (1198891 1198892 120574th)


)

+ 1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

)


))

times (1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

))

(24)



utag

e pro

babi

lity


Direct transmission


10minus1

10minus2

10minus3

10minus4

100

5 10 15 20



Direct transmission

Ergo

dic c

apac

ity (b

itss

Hz)


15 2054

6

8

10

12

14

16

18

10




3

25

2

15

1

05

05 10 15 20 25 30 35 40 45 50


Aver

age fl

ow th

roug

hput

(Gbp

s)




0

4

2

6

8

10

12

14

16

18

20

5 10 15 20 25 30 35 40 45 50


Net

wor

k th

roug

hput

(Gbp

s)







6 Conclusion




Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










10

15

5

04 6 8 10 12 14

Number of flows

Net

wor

k th

roug

hput

(Gbp

s)




20

20 30 40 50 60 70 80

18

16

14

12

10

8

6

4

2

0

Beamwidth (deg)

Net

wor

k th

roug

hput

(Gbp

s)









119877 = 119882119891120578 log2

(1 +120574th120574119891

) (17)





120574th = 120574119891 (2(2119877119882119891120578) minus 1) (18)


119875out = 119875119903 (min (120574119862119877 120574119877119863)) lt 120574th (19)


Thus we have

119875out (1198891 1198892 119889119868 120574th)

= 119875119903 (min (120574119862119877(1198891) 120574

119877119863(119889119868 1198892)) lt 120574th)


= 119865119862119877(1198891 120574th) + 119865119877119863 (1198891 119889119868 120574th)

minus 119865119862119877(1198891 120574th) 119865119877119863 (119889119868 1198892 120574th)

(20)





119875120574119862119877(119909) =

1

119875119903

exp(minus 119909119875119903

) (21)


119865119862119877= 119875119903 (119909 lt 120574th1198730)

= 1 minus 119875119903 (119909 gt 120574th1198730)

= 1 minus int

infin

120574th1198730

1

119875119903

exp(minus 119909119875119903) 119889119909


119875119903

)

(22)

where 119875119903(119909) = 119875

119862

119905

119870119862119877(1198890radic1198672 + 119889

2

1

)

119899

120576119862119877


119865119877119863= 119875119903 (119909 lt 120574th (119910 + 1198730))

= 1 minus 119875119903 (119909 gt 120574th (119910 + 1198730))

= 1 minus int

infin

0

119891 (119910)int

infin

120574th(119910+1198730)119891 (119909) 119889119909119889119910

= 1 minus int

infin

0

1

119875119903119868(119877119863)

exp(minus119910

119875119903119868(119877119863)

)

times int

infin

120574th(119910+1198730)

1

119875119903119877119863

exp(minus 119909

119875119903119877119863

)119889119909119889119910

= 1 minus119875119903119877119863

119875119903119877119863+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903119877119863

)

(23)

Out

age p

roba

bilit

y



10minus1

10minus2

10minus3

10minus4

100

2 4 6 8 10 12 14 16 18 20



119875out (1198891 1198892 120574th)


)

+ 1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

)


))

times (1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

))

(24)



utag

e pro

babi

lity


Direct transmission


10minus1

10minus2

10minus3

10minus4

100

5 10 15 20



Direct transmission

Ergo

dic c

apac

ity (b

itss

Hz)


15 2054

6

8

10

12

14

16

18

10




3

25

2

15

1

05

05 10 15 20 25 30 35 40 45 50


Aver

age fl

ow th

roug

hput

(Gbp

s)




0

4

2

6

8

10

12

14

16

18

20

5 10 15 20 25 30 35 40 45 50


Net

wor

k th

roug

hput

(Gbp

s)







6 Conclusion




Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Thus we have

119875out (1198891 1198892 119889119868 120574th)

= 119875119903 (min (120574119862119877(1198891) 120574

119877119863(119889119868 1198892)) lt 120574th)


= 119865119862119877(1198891 120574th) + 119865119877119863 (1198891 119889119868 120574th)

minus 119865119862119877(1198891 120574th) 119865119877119863 (119889119868 1198892 120574th)

(20)





119875120574119862119877(119909) =

1

119875119903

exp(minus 119909119875119903

) (21)


119865119862119877= 119875119903 (119909 lt 120574th1198730)

= 1 minus 119875119903 (119909 gt 120574th1198730)

= 1 minus int

infin

120574th1198730

1

119875119903

exp(minus 119909119875119903) 119889119909


119875119903

)

(22)

where 119875119903(119909) = 119875

119862

119905

119870119862119877(1198890radic1198672 + 119889

2

1

)

119899

120576119862119877


119865119877119863= 119875119903 (119909 lt 120574th (119910 + 1198730))

= 1 minus 119875119903 (119909 gt 120574th (119910 + 1198730))

= 1 minus int

infin

0

119891 (119910)int

infin

120574th(119910+1198730)119891 (119909) 119889119909119889119910

= 1 minus int

infin

0

1

119875119903119868(119877119863)

exp(minus119910

119875119903119868(119877119863)

)

times int

infin

120574th(119910+1198730)

1

119875119903119877119863

exp(minus 119909

119875119903119877119863

)119889119909119889119910

= 1 minus119875119903119877119863

119875119903119877119863+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903119877119863

)

(23)

Out

age p

roba

bilit

y



10minus1

10minus2

10minus3

10minus4

100

2 4 6 8 10 12 14 16 18 20



119875out (1198891 1198892 120574th)


)

+ 1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

)


))

times (1 minus119875119903(119877119863)

119875119903(119877119863)

+ 119875119903119868(119877119863)

120574thexp(minus

120574th1198730119875119903(119877119863)

))

(24)



utag

e pro

babi

lity


Direct transmission


10minus1

10minus2

10minus3

10minus4

100

5 10 15 20



Direct transmission

Ergo

dic c

apac

ity (b

itss

Hz)


15 2054

6

8

10

12

14

16

18

10




3

25

2

15

1

05

05 10 15 20 25 30 35 40 45 50


Aver

age fl

ow th

roug

hput

(Gbp

s)




0

4

2

6

8

10

12

14

16

18

20

5 10 15 20 25 30 35 40 45 50


Net

wor

k th

roug

hput

(Gbp

s)







6 Conclusion




Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










utag

e pro

babi

lity


Direct transmission


10minus1

10minus2

10minus3

10minus4

100

5 10 15 20



Direct transmission

Ergo

dic c

apac

ity (b

itss

Hz)


15 2054

6

8

10

12

14

16

18

10




3

25

2

15

1

05

05 10 15 20 25 30 35 40 45 50


Aver

age fl

ow th

roug

hput

(Gbp

s)




0

4

2

6

8

10

12

14

16

18

20

5 10 15 20 25 30 35 40 45 50


Net

wor

k th

roug

hput

(Gbp

s)







6 Conclusion




Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











6 Conclusion




Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article capacity enhancement in 60ghz based d2d...

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