Cooperative Communications with Multiple Sourcesand Relays in Ad-Hoc Networks

Peng Huo, Lei Cao and Esam ObiedatDepartment of Electrical Engineering

University of MississippiOxford, Mississippi, 38677, USA

Email: {phuo,lcao,eaobieda}@olemiss.edu

Abstract—In this paper, we investigate the cooperative commu-nication performance involving space-time block codes (STBC),channel coding, network coding and turbo decoding in a wirelessAd-hoc network scenario where two relays are employed forcommunications from a number of senders to a common sink.To reduce bandwidth and achieve diversity gain, STBC is appliedat the two relays. Based on whether network coding is adopted atthe relays, two systems are specifically proposed and compared.One is a simple decode-and-forward (DF) system without networkcoding at the relays and conducts only one round of channeldecoding after diversity operations at the receiver. The othersystem uses network coding at the relays and carries out turbodecoding at the receiver. We show through simulations that thesecond system has a fast turbo decoding convergence within twoor three iterations and generally provides a better performance.However, in the cases where the direct links between the sourcesand the sink are weak, the first system with a simple decodingprocess actually can outperform. This result indicates thatdifferent channel conditions may require different system designsand a more complex one does not necessarily result in a betterperformance at all times.

I. INTRODUCTION

A wireless Ad-Hoc Network is a decentralized network.In such a network there is no preexisting infrastructure andeach node participates in routing by forwarding data for othernodes.In conventional relay-based cooperative communicationsystems, cooperation is often conducted for data of a singleuser and based on one relay [1] [2] [3]. In ad-hoc networks,a few intermediate nodes may simultaneously receive anddecode information from multiple surrounding nodes andhence a communication mode with the cooperation of multiplesenders based on multiple relays is more desired. One scenariois shown in Fig. 1 where a number of soldiers (four as shownin the figure) want to transmit their collected information tothe commander. When the direct communications links are notstrong enough, other soldiers in between may jump in to relaythis information in a cooperative way to the commander. Thistype of communications can also be envisioned in the sensornetworks where information is gathered from outside sensorsand sent to some central nodes.

Focusing on this scenario, we propose and investigate twocommunication systems. The source information will be firstcoded with channel codes and sent out from each sender. Weassume that the relays can correctly decoded the source bitswith this code. Since two relays are involved, to minimize the

use of bandwidth and achieve diversity, we propose the useof STBC cooperatively at the two relays, which is the samefor both systems. The difference, however, lies on whetherwe adopt network coding at the relays. The first systemdoes not have network coding and the relays send out thedecoded symbols directly with STBC. The second system,however, network encodes the decoded symbols at the relaysbefore sending out via STBC. The first system clearly hasits advantage in simplicity but lacks full cooperation amongdifferent senders. The second system, on the other hand, withhigher complexity, provides a full potential of cooperativecommunication among different senders through turbo decod-ing at the receiver. In this paper, we study through simulationsthe performance of these two systems in different channelconditions. Interestingly, we have found that the second systemis not always superior in all channel conditions. This resultconnects to the trade-off between the the secondary level ofdiversity (in addition to STBC) possessed in the first systemand the network coding gain among senders in the secondsystem in various channel conditions.

The rest of this paper is organized as follows. Section IIintroduces the coding structures of the system models. SectionIII details the decoding processes of both systems, includingthe diversity, calculation of the channel reliability values(Lc),the log-likelihood ratio (LLR) and iterative turbo decodingprinciple. Section IV presents the simulation results and someconclusion remarks.

II. SYSTEM MODELS

Systems I and II are shown in Figs. 1 and 2 where there arefour senders and two relays joining the cooperative commu-nications without the loss of generality. In both systems, thesenders encode their source information using channel codeand send them ( denoted as a, b, c, d) to both relays and thereceiver in the first time slot. After receiving and decodinginformation from the four senders, data can be regeneratedat the relays and send out to the receiver using STBC in thesecond time slot, to reduce the bandwidth usage and achievetransmit diversity. Rayleigh fading channels are used. Themultiplicative fading coefficients can be modeled as complexrandom variables of 1√

2N (0, 1) + j 1√

2N (0, 1). The factor of

1√2

for both real and imaginary parts is to ensure that the

978-1-4244-3709-2/10/$25.00 ©2010 IEEE

Soldier a

Soldier f

Soldier b

commander

Soldier c

Soldier e

Soldier d

a -b*

a* d

-d*

c*

b

c

Fig. 1. Structure of system I

Soldier a

Soldier f

Soldier b

commander

Soldier c

Soldier e

Soldier d

p1-p2*

p1* p4

-p4*

p3*

p2

p3

Fig. 2. Structure of system II

channel gain is normalized to unity. Consequently, the complexwhite noise is modeled as 1√

2N (0, σ2) + j 1√

2N (0, σ2).

A. System I

System I is simply a decode-forward (DF) system where thetwo relays use STBC to send out original symbols coopera-tively, i.e., {a,−b∗, c,−d∗} and {b, a∗, d, c∗} from each relayto the receiver. The Rayleigh fading channel during one spacecode duration does not change as commonly assumed.

STBC offers the diversity of the two relays and also a levelof cooperation due to the restoration of information of twosenders simultaneously. After STBC, a secondary diversityexists between the relayed symbol in the second time slot andthe one received in the direct link in the first time slot. Thisis the receiver diversity and the Maximum ratio combining(MRC) will be used before the final channel decoding can beapplied.

B. System II

The physical structure of system II (as shown in Fig 2) isidentical as system I. However, instead of transmitting originalinformation a, b, c, d, the relays transmit their network codeddata p1, p2, p3, p4. For example, p1 = a ⊕ b ⊕ c.

There are many ways, such as random network codingand linear block codes, can be employed for the codingat RS. In system II, we consider this coding based on therequirements in rank and information spreading. Let UT ={ut

1, ut2, . . . , u

tK} be symbols from K senders that are received

and decoded at the relays at time t. The relay output will beP = AU, where A = {ai,j} is a K × K coding matrix andai,j ∈ {0, 1}. In order to give the maximum spreading, wecan set each row of A with all “1”s except one “0”. Frommathematical induction, it can be easily seen that A designedas above is in full rank only when K is an even number. Tomake A invertible for odd values of K, we can simply set onerow, such as the 1st row, to be all “1”’s. Verification, again,can be readily obtained from the mathematical induction.Therefore, the matrices used are as follows [4].

AKeven =

⎡⎢⎢⎣

1 · · · 1 00 1 · · · 11 0 · · · 11 · · · 0 1

⎤⎥⎥⎦ , AKodd =

⎡⎢⎢⎣

1 · · · 1 10 1 · · · 11 0 · · · 11 · · · 0 1

⎤⎥⎥⎦ .

(1)It is interesting to recognize that the above design for K = 4

is exactly the extended-Hamming (8,4,4) code.

III. DECODING DESCRIPTION

A. Decoding of System I

1) STBC Diversity and Maximum Ratio Combining: Thereare two levels of diversity in system I. One is obtained fromSTBC and the other is from the relayed symbols and thosereceived from the direct links. Use of STBC can make thetwo relays share the same physical channel as well as combatfading. With the Alamouti codes, as shown in [5] we can getthe space-time decoded symbols yST

2i and yST2i+1 as:

yST2i = (| hST

2i |2 + | hST2i+1 |2) · 1√

2xST

2i +

(hST2i )∗nST

2i + hST2i+1(n

ST2i+1)

∗ (2)

yST2i+1 = (| hST

2i |2 + | hST2i+1 |2) · 1√

2xST

2i+1 −hST

2i (nST2i+1)

∗ + (hST2i+1)

∗nST2i (3)

After normalizing the signal power, we get

ySTj = xj + nST

j , j = 2i, 2i + 1

where nj ∼ CN (0, σ2ST ) and the noise variance is

σST2 =

| hST2i |2 ·σ2

R+ | hST2i+1 |2 ·σ2

R

(| hST2i |2 + | hST

2i+1 |2)2/2

=2σ2

R

| hST2i |2 + | hST

2i+1 |2 (4)

where the σR is the standard deviation of the noise at relaychannel. The additional multiplier 1√

2in front of xST

2i andxST

2i+1 is due to the need of reducing transmit power into tworelays.

Let yDj represent the symbol received from the direct link

at time instant j. Let hDj be the fading coefficient in Rayleigh

channel and nDj ∼ N (0, σ2

D) be the AWGN noise in the directlink. Then,

yDj = hD

j · xj + nDj

After normalization,

yDj = xj + nD

j

where nj ∼ CN (0, σ2Direct) and

σ2Direct =

σ2D

| hDi |2 (5)

After STBC decoding, the Maximal Ratio Combining (MRC)can be used to combine the symbols received from the directlinks and the relays. i.e.,

yMRCj =

√γST

j ySTj +

√γD

j yDj

=( | hD

j |2σ2

D

+| hST

2i |2 + | hST2i+1 |2

2σ2R

)xj

+

{| hD

j |2σ2

D

nDj

hDj

+√

22σ2

R

[(hST

2i )∗nST2i + hST

2i+1(nST2i+1)

∗]} (6)

for all j = 2i and nDj ∼ CN (0, σ2

D) and nST2i ,nST

2i+1

∼ CN (0, σ2R). γD

j and γSTj are the instance signal to noise

ratio for both symbols.2) The channel reliability value Lc: After obtaining the

optimal symbol detection uses MRC for each sender, thechannel decoding is used to finally get the original sourcesymbols of each sender. In the conventional BCJR maximuma-posteriori probability (MAP) algorithm, the a-posterioriLog-Likelihood Ratio L(uk | y) consists of three soft-metricterms: the a-priori L(uk), channel information Lcyks, andextrinsic information Le(uk). yks is the soft output of thechannel, based on the systematic bit uk. The channel reliabilityvalue Lc is important to the operation of MAP decoding. Wehave

L(i)c =

2ai

σ2MRC

, i = 1, 2, . . . , framelength (7)

where ai is the channel fading of the ith bit in the frame afterMRC and σMRC is the standard deviation of the noise signalafter MRC. From MRC, it can be found that

σ2MRC =

| hDi |2

σ2D

+1

2σ2R

(| hST2i |2 + | hST

2i+1 |2)

L(i)c =

2ai

σ2MRC

= 2 (8)

It is interesting to see that this channel reliability value Lc insystem I is a constant number and it is not changing with signaland channel parameter. In other words, the MAP decodingnow becomes the direct Viterbi decoding of the output data ofMRC.

B. Decoding of System II

1) LLR value in Network Decoding: In the second system,after decoding of STBC, network decoding is needed tocalculate the a-posteriori probability of the information fromeach sender. Before decoding, we should make clear about

the channel influence, Lc, channel reliability value of blockdecoding and turbo decoding on each bit.

L(j)c,Direct =

2σ2

Direct

=2 | hD

j |2σ2

D

, j = 2i.

L(2i)c,STBC =

2σ2

ST

=(| hST

2i |2 + | hST2i+1 |2)

σ2R

. (9)

The purpose of network decoding is to get the soft informa-tion of the source symbols uk (i.e., a, b, c, d from the senders)given a block symbols y received (i.e., corrupted version of{a, b, c, d, p1, p2, p3, p4} and the channel reliability values. LetC be the codeword space of the network coding at the relaysand u be a specific codeword with uk at position k. (N,K)(N = 8,K = 4 here) is the network code used in the relay.Following the derivation in [6], we can get [4]

L(uk|y) = ln

∑u∈C,uk=+1

P (u|y)∑u∈C,uk=−1

P (u|y)

= L(uk) + L(k)c yk

+ ln

∑u∈C,uk=+1

ΠNj=1,j �=k exp(L(uj ; yj)uj/2)∑

u∈C,uk=−1ΠN

j=1,j �=k exp(L(uj ; yj)uj/2)(10)

where

L(uj ; yj) = L(j)c yj + L(uj), 1 ≤ j ≤ N (11)

and

L(j)c = Lj

c,Direct, 1 ≤ j ≤ K

L(j)c = Lj

c,STBC , K + 1 ≤ j ≤ N (12)

2) Turbo Decoding Principle in System II: The receiverreceives two sets of data: one from the direct link and theother from the relays. Each source symbol joins both processesof channel coding and network coding. It is known that thea-posteriori probability after MAP decoding of any linearcode can always be decomposed into three parts as shownin eqn. (10) that include the a-priori information, the channelinformation and the extrinsic information. Therefore, we caninitially set the a-priori as zero and generate some extrinsicinformation after decoding of one coding process. Then, thisextrinsic information will be used as the a-priori for the decod-ing of the other coding process. As a result, a turbo decodingprocess can be built up by using the extrinsic information ofone decoding process as the a-priori of the other decodingprocess iteratively. This process is illustrated in Fig 3. Thisinformation exchange can continue with several iterations untilno more improvement is observed. The simulation (Fig 4)shows that our decoding result converges after 3 or 4 iterations.

IV. SIMULATION AND COMPARISON

In this part, some simulation results are presented to com-pare the above two systems in various channel conditions.First, we fix the average SNR of the direct link and varythe SNR of the relay links. Figs. 4 and 5 show the decodingperformance of the two cooperative communication systemswhen the SNR of the direct link is 3 dB and -3 dB respectively.

Multi-userdecoder + +

Received data

a-prioriLLR

Chase decoding Block coding/

network coding

Modified BCJR, Convollutional

codes based

a-prioriOutput____

__

__LLRSingle-user

decoders

Fig. 3. Turbo decoding structure for single sender and across multiple senders

-1 0 1 2 3 4 5 6 7 8 910-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100Direct SNR = 3

Relay SNR(dB)

BE

R

Sys I MRCSys I channel-decdSys II 1st ite.Sys II 2nd ite.Sys II 3rd ite.Sys II 4th ite.

Fig. 4. The performance of two systems at direct link SNR = 3

Fig. 4 shows that the performance of system II is better thanthat of system I, which means the turbo coding gain is betterthan diversity gain plus the convolutional coding gain whenthe direct links are mild (SNRD = 3dB). Convergence of thesecond system within 3 or 4 iterations can also be observed inthe simulations. On the other hand, in Fig. 5, when the directlinks have very low signal to noise ratio (SNRD = −3dB),system I performs better than system II. The reason is thatin this case the direct link is too weak to be utilized in the

-1 0 1 2 3 4 5 6 7 8 910-6

10-5

10-4

10-3

10-2

10-1

100Direct SNR = -3

Relay SNR(dB)

BE

R

Sys I MRCSys I channel-decdSys II 1st ite.Sys II 2nd ite.Sys II 3rd ite.Sys II 4th ite.

Fig. 5. The performance of two systems at direct link SNR = -3

-5 -4 -3 -2 -1 0 1 2 3 4 510-7

10-6

10-5

10-4

10-3

10-2

10-1Relay SNR = 3

Direct SNR(dB)

BE

R

Sys I MRCSys I channel-decdSys II 1st ite.Sys II 2nd ite.Sys II 3rd ite.Sys II 4th ite.

Fig. 6. The performance of two systems by fixing the relay link conditionto SNR = 3

turbo decoding. This part, acting as the systematic part in bothnetwork coding and channel coding, has a strong impact onthe joint decoding performance.

Second, we fix the SNR of relay channels and change theSNR of direct links. The result is shown in Fig. 6 whereSNRR = 3dB. It can be found again that it is better toselect system I when MS-BS direct link condition is bad(SNRD < −1dB) and select system II if direct link conditionis better than that.

V. DISCUSSIONS AND CONCLUSIONS

In this paper, we have proposed and compared two co-operative communications systems in the Ad-hoc networksthat involves multiple senders and multiple relays. While asimple system uses direct DF-mode and exploits two levelsof diversity together with channel decoding, the other systemutilizes joint network coding and channel coding and turbodecoding. It is shown via simulations that neither system issuperior to the other at all times. Rigorous theoretic analysisof this trade-off will be the focus of the future work.

REFERENCES

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[2] E. Kurniawan, A. Madhukumar, and F. Chin, “Performance analysisof distributed space time coding: A geometric approach,” IEEE 18thInternational Symposium on Personal, Indoor and Mobile Radio Com-munications, vol. 3, no. 7, pp. 1 – 5, September 2007.

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[6] J. Hagenauer, E. Offer, and L. Papke, “Iterative decoding of binary blockand convolutional codes,” IEEE Transactions on Information Theory,vol. 42, no. 2, pp. 429–445, March 1996.