Relay Selection based on Bayesian Decision Theoryin Cooperative Wireless Networks

Lilatul Ferdouse1, Alagan Anpalagan1, Jeeva Nadaraj21Department of Electrical and Computer Engineering, Ryerson University, Toronto, Canada

2PESIPlex Inc., Brampton, Canada

Abstract—In cooperative wireless networks, proper relay se-lection is needed for assuring maximum diversity gain. Inother words, user relaying helps to improve the transmissionperformance in wireless multiuser scenario by allowing each userto cooperate with each other and acts as a MIMO system bysharing their antennas in a timely and distributed way. Amongseveral challenges in such networks, this paper focuses on theselection problem of relay node, and then we propose a schemeto select relay nodes by using Bayes theory. In this schema,at first each source node calculates prior and class conditionalprobability based on the channel state information and then relaynodes are selected based on the posterior probability of eachsource and relay node pair, which is estimated by applying Bayestheorem. The proposed relay assignment schema maximizes theoverall data rate of the networks and it works well independentof the number of relay nodes or source-destination pairs in thenetwork.Index Terms: Cooperative Communication, Relay Assign-ment, Bayesian Theory

I. INTRODUCTION

Cooperative wireless networks increase the transmissionrate and channel capacity by assigning relay node in thenetworks. In cooperative communication, the main idea ofspatial diversity is that between sender and receiver nodes,there can be another node which can be used to providediversity by forming a virtual multi-antenna system. One ofthe important issues of multiuser cooperative networks is howpartners are assigned and managed. Systems such as cellular,ad hoc and sensor networks need different mechanisms andprotocols to select appropriate partner node, as an improperlychosen relay node could make the capacity under cooperativecommunications be smaller than direct transmissions. There-fore, many researchers work on developing appropriate relaynode assignment algorithms with the objective to improvenetwork performance.

In [1], Dejun Yang et al. considered multiple source-destination pairs and proposed a system model and an optimalrelay assignment algorithm (OPRA). They studied the problemof relay assignment in cooperative networks such that thetotal capacity is maximized among all possible assignments.The similar work was done by Shi et al. [2]. They workedwith relay assignment problem in cooperative ad hoc net-works, such that the minimum capacity among all source-destination pairs is maximized, constrained to assign a relaynode to at most one source-destination pair. They proposeda polynomial time complexity algorithm called optimal relayassignment (ORA). Afterwards, Zhang et al. [3] considered

the relay assignment problem with interference mitigation.They found solution to the relay problem via exhaustivesearch among all possible relay node assignments; however,the complexity of this approach is exponential. In terms ofpower consumption and relay node selection, Cai et al. [4]considered relay selection and power allocation for amplifyand forward wireless relay networks. The authors proposed asemi-distributed algorithm on relay node selection for multiplesource and destination pairs.

Relay assignment strategies in cooperative networks dependon various aspects of the network condition, such as distri-bution of channel state information (CSI), distance betweensource to destination node, propagation modes, available band-width, signal-to-noise ratio between source and relay nodes. In[5] authors proposed an opportunistic relay selection schemathat selects the best relay among the available relays consider-ing the measurements of signal strength rather than distance.Relay node can be selected based on some threshold value. Arelay node can send data only when its channel gain is largerthan some threshold value. Either channel gain information orSNR information is considered as a threshold depending upondifferent system models. Authors in [6] [7] designed a outputthreshold based multiple relay selection scheme in cooperativewireless networks. In this paper, we consider current channelstate information, SNR value between source and destinationpairs and source-relay pairs, and formulate the relay selectionproblem using Bayes theory.

The key contributions of this paper are i) we formulate relayassignment problem based on Bayes theory with the objectiveto improve throughput, ii) relay node selection is done bycalculating posterior probability while a single relay node canbe assigned to multiple sources, and iii) the final capacity foreach source-destination pair is guaranteed to be no less thandirect transmissions.

The remainder of this paper is organized as follows. Insection II, we describe the system model that is used in ouranalysis. In section III, we discuss about Bayesian decisiontheory, formulate the selection problem and propose a schemathat maximizes the overall capacity of the networks. Numer-ical results and comparisons among ORA schema and directtransmission (DT) are given in section IV. Finally, section V,concludes the paper.

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II. SYSTEM MODEL

Figure 1 shows the system model of the wireless relay net-work which consists of 𝑁𝑠 sources nodes, 𝑁𝑟 available relaynodes and a single destination node. This system representsIEEE 802.16 point-to-multi point network, where source nodesrepresent the end users with packets waiting for transmissionand the destination node represents the access point (AP). Weconsider a ad hoc network environment where destination nodeis not limited to one but the number of relay nodes selectedfor each source node is limited to one. Each relay node canassist more than one source node in the networks. Each relaynode works under the amplify and forward (AF) mode, i.e.,the relay node simply amplifies the received signal and thenforwards to its destination. In AF mode, each pair of nodes 𝑖

Source

RelayDestination

Source

Fig. 1. System model of wireless relay network.

and 𝑗 experiences a flat fading channel with channel gain ℎ𝑖𝑗

[8]. The channel gain may integrate the effects of propagationpath loss and shadowing between nodes 𝑠 and 𝑑, 𝑠 and 𝑟, and𝑟 and 𝑑 respectively. 𝑧𝑑 denotes zero mean background noisewith variance 𝜎2

𝑑. The signal 𝑥𝑠 is transmitted by source node𝑠 in the first time slot and the received signal at destinationnode 𝑑 is 𝑦𝑠𝑑 and it can be expressed as

𝑦𝑠𝑑 = ℎ𝑠𝑑.𝑥𝑠 + 𝑧𝑑, (1)

𝑧𝑟 denotes zero mean background noise with variance 𝜎2𝑟 and

the received signal at relay node 𝑟 is

𝑦𝑠𝑟 = ℎ𝑠𝑟.𝑥𝑠 + 𝑧𝑟. (2)

In the second time slot, relay node 𝑟 transmits to destinationnode 𝑑. The received signal at 𝑑 can be expressed as

𝑦𝑟𝑑 = ℎ𝑟𝑑.𝛼𝑟.𝑦𝑠𝑟 + 𝑧𝑑, (3)

where 𝛼𝑟 is the amplifying factor at relay node 𝑟 that shouldsatisfy power constraint 𝛼2

𝑟 = 𝑃𝑟

∣ℎ𝑠𝑟∣2𝑃𝑠+𝜎2𝑟

where 𝑃𝑠 and 𝑃𝑟

are the transmitting powers at node 𝑠 and 𝑟 respectively. It hasbeen shown in [8] that the above channel, which combinesboth direct path (𝑠 to 𝑑) and relay path (𝑠 to 𝑟 to 𝑑) canbe modeled as a one input and two output complex Gaussiannoise channel. The achievable data rate 𝐶𝐴𝐹 (𝑠, 𝑟, 𝑑) from 𝑠to 𝑑 is given in (4) where 𝑆𝑁𝑅𝑠𝑑 = 𝑃𝑠

𝜎2𝑑∣ℎ𝑠𝑑∣2, 𝑆𝑁𝑅𝑠𝑟 =

𝑃𝑠

𝜎2𝑑∣ℎ𝑠𝑟∣2, 𝑆𝑁𝑅𝑟𝑑 = 𝑃𝑟

𝜎2𝑑∣ℎ𝑟𝑑∣2 and available bandwidth 𝑊 .

𝐶𝐴𝐹 (𝑠, 𝑟, 𝑑) = 𝑊.𝐼𝐴𝐹 (𝑆𝑁𝑅𝑠𝑑, 𝑆𝑁𝑅𝑠𝑟, 𝑆𝑁𝑅𝑟𝑑) (4)

where,

𝐼𝐴𝐹 (𝑆𝑁𝑅𝑠𝑑, 𝑆𝑁𝑅𝑠𝑟, 𝑆𝑁𝑅𝑟𝑑)

= 12 log

(1 + 𝑆𝑁𝑅𝑠𝑑 +

𝑆𝑁𝑅𝑠𝑟.𝑆𝑁𝑅𝑟𝑑

𝑆𝑁𝑅𝑠𝑟+𝑆𝑁𝑅𝑟𝑑+1

)(5)

We have

𝐶𝐴𝐹 (𝑠, 𝑟, 𝑑) =𝑊

2log

(1 +

𝑃𝑠

𝜎2𝑑

∣ℎ𝑠𝑑∣2

+𝑃𝑠∣ℎ𝑠𝑟∣2𝑃𝑟∣ℎ𝑟𝑑∣2

𝑃𝑠𝜎2𝑑∣ℎ𝑠𝑟∣2 + 𝑃𝑟𝜎2

𝑟 ∣ℎ𝑟𝑑∣2 + 𝜎2𝑟𝜎

2𝑑

) (6)

and the achievable data rate from 𝑠 to 𝑑 is

𝐶𝐷(𝑠, 𝑑) = 𝑊 log

(1 +

𝑃𝑠

𝜎2𝑑

∣ℎ𝑠𝑑∣2)

(7)

III. RELAY SELECTION BASED ON BAYESIAN DECISION

THEORY

Bayesian decision theory is a fundamental statistical ap-proach to the problem of classification. This approach is basedon quantifying the tradeoffs between various classificationdecisions using probability and costs that accompany suchdecision [9]. Naive Bayes classifier based on Bayesian ma-chine learning algorithm is used in various areas, for example,medical diagnosis, machine perception, image processing etc.It is used to solve the problem of spam filtering, medicaldiagnosis, pattern classification and credit card fraud detectionproblem. The decision problem that depends on Bayes formulaassumes that all the relevant probabilities are known. In thissection, the formulation of Bayes rule is discussed first and thesubsequent section shows how to formulate the relay selectionproblem using Bayes theory.

Let the states of nature be 𝑤𝑖 and 𝑤𝑗 .Prior probability: These probabilities reflect our prior knowl-edge. The prior probability of 𝑤𝑖 and 𝑤𝑗 is 𝑃 (𝑤𝑖) and 𝑃 (𝑤𝑗).Class conditional probability: This is the probability densityfunction for some variable 𝑋 given that the state of nature is𝑤𝑖 and is expressed as 𝑝(𝑥∣𝑤𝑖).Bayes formula: Suppose that the probability of state of nature𝑝(𝑤𝑗) and class conditional probability 𝑝(𝑥∣𝑤𝑗) is known, thejoint probability density of finding a pattern that is category𝑤𝑗 and has feature value 𝑥 can be written as 𝑝(𝑤𝑗 , 𝑥) =𝑃 (𝑥∣𝑤𝑗)𝑝(𝑥) = 𝑝(𝑥∣𝑤𝑗)𝑃 (𝑤𝑗). Rearranging these, we getBayes’ formula to derive the posterior probability 𝑝(𝑤𝑗 ∣𝑥)

𝑃 (𝑤𝑗 ∣𝑥) = 𝑝(𝑥∣𝑤𝑗)𝑃 (𝑤𝑗)

𝑝(𝑥), (8)

in this case of two categories 𝑝(𝑥) =∑2

𝑗=1 𝑝(𝑥∣𝑤𝑗)𝑃 (𝑤𝑗).

A. Problem formulation

Assume that the channel state information, the achievabledata rate under amplify-and-forward 𝐶𝐴𝐹 , and direct trans-mission 𝐶𝐷 are known. The prior probability of source node𝑛 will be

𝑃 (𝑆𝑛) =𝐶𝐷𝑛∑

𝑗=𝑁𝑆𝐶𝐷𝑗

, (9)

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and the class conditional density of relay node 𝑅𝐾 will becalculated as

𝑃 (𝑅𝑘∣𝑆𝑛) =𝐶𝐴𝐹𝑘∑

𝑛=𝑁𝑟𝐶𝐴𝐹𝑛

, (10)

where 𝑁𝑠 and 𝑁𝑟 represent the total number of source nodesand relay nodes. According to Bayes’ rule, we can formulateposterior probability of 𝑃 (𝑆𝑛∣𝑅𝑘) as

𝑃 (𝑆𝑛∣𝑅𝑘) =𝑃 (𝑅𝑘∣𝑆𝑛)𝑃 (𝑆𝑛)

𝑝(𝑥), (11)

where 𝑝(𝑥) will be 𝑝(𝑥) =∑𝑁𝑠

𝑛=1 𝑃 (𝑅𝑘∣𝑆𝑛)𝑃 (𝑆𝑛). We canassign relay node based on this posterior probability. Source𝑆𝑛 selects 𝑅𝑘 if

𝐶𝐴𝐹𝑘> 𝐶𝐷𝑛

AND 𝑃 (𝑆𝑛∣𝑅𝑘) > 𝑃 (𝑆𝑛∣𝑅𝑗), for all 𝑘 ∕= 𝑗(12)

Example 1: We consider a relay network which consists oftwo source nodes 𝑆1 and 𝑆2 and two relay nodes 𝑅1 and𝑅2. Table I shows the channel gains among sources and relaynodes.

TABLE ICHANNEL GAIN IN AF AND DIRECT TRANSMISSION

Source 𝐶𝐷 𝑅1 𝑅2

𝑆1 12 20 15𝑆2 18 23 21

The prior probability of 𝑆1 and 𝑆2 can be calculated as𝑃 (𝑆1) = 12

12+18 and 𝑃 (𝑆2) = 1812+18 , that is 𝑃 (𝑆1) = 0.4,

𝑃 (𝑆2) = 0.6 and 𝑃 (𝑆1) + 𝑃 (𝑆2) = 1. Next, we estimateclass conditional probability of 𝑅1 when source node is 𝑆1,𝑃 (𝑅1∣𝑆1) =

𝐶𝑅1

𝐶𝑅1+𝐶𝑅2

= 2020+23 = 0.47 and 𝑃 (𝑅1∣𝑆2) =

2320+23 = 0.53, which implies 𝑃 (𝑅1∣𝑆1)+𝑃 (𝑅1∣𝑆2) = 1. Sim-ilarly, we can get the conditional probability of 𝑅2. Applying

TABLE IIPRIOR AND CONDITIONAL PROBABILITY

Source Prior 𝑃 (𝑅1∣𝑆𝑛) P(𝑅2∣𝑆𝑛)𝑆1 0.4 0.47 0.42𝑆2 0.6 0.53 0.58

Bayes’ formula, we can calculate the posterior probability ofeach source and relay node.

TABLE IIIPOSTERIOR PROBABILITY

source 𝑃 (𝑆𝑛∣𝑅1) 𝑃 (𝑆𝑛∣𝑅2)𝑆1 0.37 0.32𝑆2 0.63 0.68

According to (12) source node 𝑆1 selects relay node 𝑅1 as𝑃 (𝑆1∣𝑅1) > 𝑃 (𝑆1∣𝑅2) and source node 𝑆2 selects 𝑅2. TableIII shows the result of posterior probability.

B. Bayes-Relay Schema

Probability calculation of Bayes theory depends on someprior knowledge. In the proposed Bayes-relay algorithm(BRA), at first the prior and class conditional probability is de-rived with the knowledge of proper channel state informationand channel capacity and then, the estimation of probabilityof each source with the available relay nodes is calculated.Each source node selects a relay whose posterior probabilityratio is higher than others. The flow chart of relay selection isgiven in Figure 2. Bayes-relay algorithm is formulated in twoparts:∙ Probability calculation: i) Perform probability calcula-

tion of each source node using (9). ii) Derive class condi-tional probability of each relay node using (10). iii) ApplyBayes’ rule e.g., (11), calculate posterior probability ofeach source and relay node.

∙ Relay assignment: Using decision rule of (12), each userselects a relay node based on the posterior probability.

First calculate SNRD,SNRAF or SNRDF based on channel state information.

Calculate channel capacity of source to destination, source to relay node, CD, CAF, or CDF based on

corresponding SNR value.

Calculate prior probability of each source P(S1)………….P(Sn) and class conditional probability of relay nodes

P(R1|S1)……….P(Rn|Sn).

Apply Bayesian theorem to calculate posterior probability of each source and relay nodes in the networks.P(S1|R1)………...P(Sn|Rn).

Relay assignment based on maximum posterior probability.If P(Sn|Rk) > P(Sn|Rj) for all k j. Sn selects relay node Rk.

Fig. 2. Flow chart of relay assignment based on Bayesian theory.

IV. NUMERICAL RESULTS

Here, we consider a 100-node cooperative ad hoc network.All simulation parameters and the locations of each node andthe role of each node (either source, destination, relay) areset as in [2]. For simulation, the bandwidth of each channelis W=10MHz and the maximum transmission power of eachnode set as to 1Watt. The path loss component between sourceto destination is given by ∣ℎ𝑠𝑑∣2 = ∣∣𝑠− 𝑑∣∣−4, where ∣∣𝑠− 𝑑∣∣is the distance (in meters) between 𝑠 and 𝑑 and the path lossindex is 4. For AWGN channel, the variance of noise assumesas 𝜎2 = 10−10. Here, each relay node uses AF mode forcooperative communication.

In this simulation, two cases are considered. Case I: thenumber of relay node is no less than the number of sourcenode (𝑁𝑟 ≥ 𝑁𝑠) and Case II: the number of relay node is lessthan that of source node (𝑁𝑟 < 𝑁𝑠).

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1) Case I: In this case, we have 30 source-destination pairsand 40 relay nodes. After computing probability estimation ofeach source and relay nodes, the final assignment of relaynode for each source is given in Table IV. In this table, thesecond column shows the data rate for each source-destinationpair under direct transmission. The fourth column indicatesthe final data rates that are achieved by applying Bayes-relayschema. The last column shows the final data rate of ORA [2]algorithm for comparison.

TABLE IVRELAY ASSIGNMENT FOR CASE I: 𝑁𝑟 ≥ 𝑁𝑆

Session

Direct transmission

capacity (C_D Mbps)

Relay Assignment

based on BRA

Final rate in BRA (Mbps)

Final rate in ORA (Mbps)

S1 2.75 R2 6.94 6.54S2 4.83 R7 9.92 9.46S3 4.00 R2 9.15 8.73S4 2.89 R34 5.45 4.66S5 3.30 R14 6.78 6.47S6 4.37 R6 9.70 9.25S7 1.92 R8 4.99 4.76S8 3.13 R12 7.57 7.22S9 5.16 R10 10.28 9.81S10 5.03 R19 10.29 4.8S11 4.33 R20 9.57 9.13S12 3.39 R16 6.89 5.89S13 3.86 R19 8.43 4.84S14 4.44 R16 8.25 7.87S15 2.75 R16 5.87 4.86S16 3.46 R22 7.65 7.29S17 3.45 R22 7.46 5.62S18 6.33 R21 7.72 7.37S19 9.18 R22 15.31 8.76S20 7.29 R25 11.81 6.95S21 1.99 R27 5.14 4.9S22 8.02 R29 14.17 8.71S23 7.91 R29 11.81 11.26S24 2.23 R40 4.65 4.43S25 4.10 R31 9.40 5.87S26 6.38 R36 7.14 6.81S27 3.79 R33 5.53 5.44S28 2.14 R35 5.54 5.29S29 2.44 R31 4.91 4.68S30 6.93 R33 10.12 9.65

Case I: N_r N_s

It is observed that the minimum rate among all pairs is1.92 Mbps under direct transmission whereas in BRA findsthat the minimum data rate is 4.65 Mbps which is higherthan ORA’s minimum rate. Similarly, the highest data rate ofthe overall network also increases when we use Bayes-relayalgorithm compared to that of ORA and direct transmission.The highest data rate of BRA is 14.17 Mbps whereas inORA, direct transmission has 11.26 Mbps and 9.18 Mbpsrespectively. Figure 3 shows the overall data rate performanceof the networks. Both user relaying algorithms, ORA andBRA, outperform the direct transmission.

2) Case II: In this case, we have 40 source-destination pairsand 20 relay nodes. Table V shows the results of case II. Fromthe second column, we get minimum the data rate of directtransmission to be 1.92 Mbps. BRA increases this rate to 4.65Mbps which is also higher than ORA’s minimum rate (3.8Mbps). The minimum capacity of the network is maximized byBRA. Figure 4 shows the overall performance of the network

8

10

12

14

16

18

nal R

ate(

Mbp

s)

DT BRA ORA

0

2

4

6

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930

Fin

Number of Source Node

Fig. 3. Case 1((𝑁𝑟 ≥ 𝑁𝑠): Performance improvement from user relaying inthe multiple-source, relay networks.

in terms of source-destination pairs. For each source, the datarate of BRA always shows higher value than other two.

20

25

30

35

40

45

50

al R

ate(

Mbp

s)

DT BRA ORA

0

5

10

15

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

Fin

Number of Source Node

Fig. 4. Case 2((𝑁𝑟 < 𝑁𝑠):Performance improvement from user relaying inthe multiple-source,relay networks

3) Throughput Estimation: Table VI and Figure 5 showthe average throughput and maximum throughput calculationfor case I and II. In both cases, BRA shows the highestthroughput value than the others. In case I, it will improve 40%average throughput than direct schema and around 15% thanORA schema. In case II, BRA shows 25% and 19% averagethroughput improvement than other two. When compared withestimating maximum throughput of the network, our proposedschema shows better performance than others. This proposedBayes-relay schema uses posterior probability based relayselection mechanism that ensures to improve channel capacityas well as channel efficiency. Moreover, each node selectsproper relay node, and it helps to improve the diversity ofthe network.

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TABLE VRELAY ASSIGNMENT FOR CASE II: 𝑁𝑟 < 𝑁𝑠

Session

Direct transmission

capacity (C_D Mbps)

Relay Assignment

based on BRA

Final rate in BRA (Mbps)

Final rate in ORA (Mbps)

S1 2.75 R1 6.94 6.62S2 4.83 R5 9.38 4.6S3 4.00 R1 9.15 3.81S4 2.89 R5 5.61 4.66S5 3.30 R6 6.78 3.8S6 4.37 R4 9.70 4.17S7 1.92 R5 4.99 4.76S8 3.13 R6 4.64 4.43S9 5.16 R4 6.28 4.92S10 5.03 R11 10.29 4.8S11 4.33 R11 7.83 4.13S12 3.39 R8 6.89 5.55S13 3.86 R11 8.43 8.04S14 4.44 R8 8.25 4.23S15 2.75 R11 6.12 5.6S16 3.46 R12 7.65 7.3S17 3.45 R12 7.46 4.17S18 6.33 R12 9.85 6.03S19 9.18 R12 15.31 8.76S20 7.29 R14 9.67 6.95S21 1.99 R14 5.14 4.9S22 8.02 DT 8.02 7.65S23 7.91 DT 7.91 7.55S24 2.23 R20 4.65 5.15S25 4.10 R16 9.40 3.91S26 6.38 R17 7.92 6.08S27 3.79 R17 5.53 5.27S28 2.14 R19 5.54 5.29S29 2.44 R16 4.91 4.68S30 6.93 R17 10.12 6.6S31 11.60 R5 13.32 11.06S32 18.32 DT 18.32 17.47S33 5.10 DT 5.10 4.86S34 32.86 DT 32.86 31.34S35 39.71 DT 39.71 37.87S36 31.24 DT 31.24 29.79S37 11.17 DT 11.17 10.65S38 40.13 DT 40.13 38.27S39 12.68 DT 12.68 12.1S40 43.72 DT 43.72 41.7

Case II: N_r<N_s

TABLE VITHROUGHPUT ANALYSIS FOR CASE I AND II

Average throughputCase 1 Case 2

BRA 8.28 11.97DT 4.39 9.46

ORA 6.91 9.99Maximum throughput

Case 1 Case 2BRA 14.17 43.72DT 9.18 43.72

ORA 11.26 41.70

V. CONCLUSION

There are many issues and challenges in multiuser wirelesscooperative networks. This paper investigated one of the keychallenging issues that is relay selection. During the beaconperiod, each source node knows about the current channel stateinformation between destination and relay nodes and estimatessignal-to-noise ratio. Most of the relay assignment schemeswork on this information. Threshold based relay assignmentschema set the optimal threshold based on SNR value butthis schema does not show any significant improvement inthroughput. Some probability based relay selection schemasuch as fixed probability based relay selection and probability

8.28

11.97

4.39

9.46

6.91

9.99

Case 1 Case 2

Average Throughput(Mbps)BRA DT ORA

43.72 43.72 41.7

Maximum Throughput(Mbps)BRA DT ORA

14.179.18 11.26

Case 1 Case 2

Fig. 5. Throughput estimation in relay selection schemes

of received SNR ensures diversity, but does not give guaran-tee to improve data rate. The proposed Bayes-relay schemashowed significant improvement in data rate. We numericallyevaluated our proposed schema and compared our results withthe direct transmission and ORA schema. Numerical resultsshowed that the proposed relay selection schema based onBayesian decision theory improves minimum capacity as wellas maximum capacity of the overall network.

ACKNOWLEDGMENT

This work was supported in part by the research grant fromOCE TPS program in collaboration with PESIPlex Inc.

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The 2013 International Conference on Advanced Technologies for Communications (ATC'13)

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