A Dual Relay Transmission System for Wireless Communications: PowerAllocations and Channel Capacity

Syed Ali HassanSchool of ECE

Georgia Institute of TechnologyAtlanta, Georgia 30332-0250

alihassan@gatech.edu

Abstract

Cooperative relaying methods have attracted a lot ofin­terest in the past several years. A conventional coopera­tive relaying scheme has a source, destination and a sin­gle relay. To overcome the effects of asymmetrical natureofone relay network, we have proposed a dual relay systemthat achieves significant system performance in terms ofbit­error rate, signal-to-noise ratio and channel capacity overthe conventional one relay and direct transmission systems.This paper presents the protocol of the dual relay systemand addresses the issues ofoptimal power allocations at theterminals and the increase ofsystem performance in termsofchannel capacity.

1. Introduction

Cooperative diversity is an attractive technique inachieving higher system performance in terms of capac­ity and diversity gains in wireless systems. Exploiting thebroadcast nature of wireless networks, relay nodes help thetransmission of data through different channels, resulting inconsiderable improvement in system performance. Conven­tional cooperative strategies employ a single node as relay[1-6], which provides performance gain as compared to adirect transmission scenario. The relay station is usuallyhalf-duplex, that is, it can not transmit and receive data inthe same time slot. Due to half-duplex characteristic of therelay, the diversity gain is asymmetrical which results in aloss of spectral efficiency. By asymmetry, we imply that thediversity gain is not applied to every transmitted symbol andthus the performance is only partially improved. Anotherapproach to cater for this problem is the use ofdual relays inthe communication model which provides balanced diver­sity gain to each transmitted symbol [7]. In this work, wedemonstrate that the use dual relays achieve higher chan-

Peter S. S. WangNokia Siemens Network

Irving Texas 75039peter.wang@nsn.com

nel capacity and the performance is improved using optimalpower allocations at the terminals.

Power allocations also play an important role in cooper­ative relaying [8-9]. We have shown that adjusting power toterminals according to signal-to-noise ratio (SNR), resultsin considerable improvement in system performance. Ana­lyzing the system as a whole, we also measure the channelcapacity as compared to conventional and direct transmis­sion system and show the increase in capacity for dual re­lay transmission system (DRTS). Two approaches are com­monly used in cooperative relaying scenarios. The first isknown as amplify-and-forward transmission (AF), wherethe relay amplifies the received signal and forwards it to thereceiver [1]. The second approach is decode-and-forwardtransmission (DF) where relay decodes the incoming signalfirst and then re-encodes and sends to the destination. In thispaper, we use the AF mode and try to improve performanceover the conventional cooperative relaying with single relayand direct transmission between a source and destination.

The paper is organized as follows. Section 2 presents thebasic architecture, functionality and mathematical model ofthe dual relay transmission system. Sections 3 and 4 providedetailed analysis for the power allocations at the terminalsand the increase in channel capacity for DRTS. The paperthen concludes with certain comments in Section 5.

2. System Model

Figure 1 shows the symmetrical cooperative relayingscheme consisting of a source, S, destination, D, and apair of relay stations R 1 and R2 . hp q captures the effectof pathloss, shadowing and frequency non-selective fadingfrom transmitter p to receiver q. The fading is assumed tobe independently and identically distributed (i.i.d.) drawnfrom a set of complex Gaussian elements. This schemeworks as follows. The source is always sending data to des­tination at every time slot. At odd time slot, one relay, for

978-1-4244-4565-3/09/$25.00 ©2009 IEEE

where P, Q, R and Ok and are given in the following equa­tions.

and the noise vector is given as

Figure 1. Dual Relay Transmission systemwhere

nD and OR are the noise vectors at destination and relays,respectively, with i.i.d complex Gaussian elements.

v'ER(3R2h2DER(3Rl (3R2h1Dh12

[nD(2k - 1) ]

nD(2k) ,

example R1, is also transmitting what it received at the pre­vious time slot, while the other relay, in this example R2 ,

is listening to what the source and the relay R1 are sending.The destination receives the signal transmitted by the sourceand by one of the relays, in this example R1, at every oddtime slot. At even time slot, the role ofthe two relays will beinverted and the destination now receives data from sourceand relay R 2 • Throughout the paper, we assume Rayleighfading channel, perfect channel state information at the re­ceivers, and perfect synchronization. The received signalsat the destination can be expressed as

y(2k - 1) ==~h2D(3R2XR2 (2k - 2)+

yfE;hSDX(2k - 1) + nD(2k - 1) (1)

y(2k) ==~hlD(3Rl XRl(2k - 1)+

yfE;hsDx(2k) + nD(2k), (2)

where E s is the transmit power of the source, E R is thetransmit power ofrelays, 1 and XRl (2k -1) and XR2(2k - 2)are the signals received by the relay R1 at time 2k - 1 andby the relay R 2 at time 2k - 2, respectively [7]. The factor (3normalizes the received symbol energy at the correspondingrelay. Defining the transmitted and received symbol vectoras

_ [ x(2k - 1) ]Xk - x(2k) , [

y(2k - 1) ]and Yk == y(2k) ,

3. Power Allocations

An important issue in AF relaying is that during thetransmission of data from relay, the amplifying factor andthe power gain of relay enhances not only the signal butalso the noise. Thus power control of relays especially atlow SNR becomes critical. Another factor is the channelbetween the two relays. An interesting case arises becauseofthe inter-relay channel conditions, i.e., at hight inter-relaychannel gain, the noise gets enhanced in addition to the sig­nal. Thus it is necessary to control the power according tothe channel to get an optimal performance. Figure 2 showsthe effect of power allocations for the dual relay system forboth high and low inter-relay channel gains. Power is dis­tributed to the source and relays so that the following equal­ity holds

(6)

the input-output relation of DRTS can be expressed in thematrix form as

1assuming the transmit power of relays to be equal

where Eo is the total transmit power of the system. Forwithout PA case, equal power is allocated to both the sourceand relays. It can be seen that the system performs betterwith PA at the terminals in each case. It can further be no­ticed that high inter-relay channel gain necessarily requirespower control to limit the noise propagating back and forth

() det~0-2) [9(f1 2 ,fSl)9(f1 2 ,fS2)(1 -~~:) 1> +fSD(fSD + 'lj;)] (5)

1> =Es2~ {hSDh~l h2D } o-bh12

'lj; =1+ 9 (f12, f sd 9 (f12, f s 2) ~:: (1 - ~ll: ) + 9 (fs1,fd (1 + 9 (f12, f s 2) ~21: )

det(0-2) =o-b [1 - 9 (f12, f S1)9 (f12, f S2) (f12 - f lD) (f12 + f 2D) - 9 (f12, f s 2) f 2D (f~D - f~J

+ ~~:9(f12,fSl)]

between the relays. During optimal PA, it has been observedthat at low SNR, more power should be allocated to sourceand vice versa. Thus it can be seen that the network per­forms better and allocating more power to relays at highSNR results in a considerable improvement.

. . Highinter- relay

... . channel "· · · ·

Figure 3. A single relay cooperative system

the source and destination. In this case, the average mutualinformation ofthe input and output, in other words capacity,for LLd complex Gaussian inputs, is given by [10]

(8)C1 = 10g(1 + f SD)

where f SD = Esl~f [)1 2 is the signal to noise ratio and 0-2

is the variance of noise. For the single relay case shown inFigure 3, the input output relationship is given as [7]

Low. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. inter-relay"

. .... ............ ............... channel ..gain

-*- With PA....... With PA~Without PA

- ... - Without PA

(10)

Yk=Hxk+nk (9)

where the equivalent channel matrix, H can be expressed as

H- [ ..fEShSD 0]- ..fESJER{3hSRhs D ..fEShSD .

504525 30 35 40Total Transmit Power (dB)

2015

Figure 2. Effect of Power Allocation

10-' '-----_--'---_---L-_----'.__"----_--'--_---'--_-----'_-----'10

from transmitter p to receiver q, the channel capacity isgiven as [1]

C2 = 10g [1 + f SD{1 + f (f SR, f RD)+

g(fSR,fRD) +fsDf(f s R,fs D)}] (12)

4. Channel Capacity

Cooperative communications not only improves systemperformance in terms of BER reduction but also providescapacity increase over the traditional communication sys­tems. This section focuses on the capacity issues for DRTSbesides one relay and direct transmission scenarios. For adirect transmission case, the rec eived symbol at the destina­tion is given by

Defining the SNR for one relay case as,

f _ Ep lhpq l2

pq - 0-2q

(II)

(7) where

where hSD captures the effect of pathloss, shadowing andfrequency non-selective fading ofwireless channel between

l + x xf( x , y) = l + x +y and g(x , y) = l + ~ +y

16,----,------,--- ---,-----.------,------,--.-----.------,

14

12

25

Figure 4. Capacity behavior for the threeschemes

For dual relay transmission system, defining the SNR foreach link as in (II), the channel capacity is given as

References

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5. Conclusion

where 8 is defined in (5) with its other parameters.

Figure 4 shows the comparison of C1, C2 , and C3 withrespect to SNR. Dual relay system shows maximum channelcapacity as compared to the other systems over a specificSNR. Thus dual relay system can provide high rate datatransmission with lower probability of error under sameconditions.

C3 = log (1 + r S D + 8) (13) [7] P. Wang, S.A. Hassan, Ye G. Li, "A full rate symmetri­cal cooperative relay approach for Wireless systems," inproc. 4th IEEE ICCSC, pp. 104-108, Shanghai, China,May 2008.

[8] Q. Zhang and 1. Zhang et. el., "Power allocation for re­generative relay channel with Rayleigh fading," in proc.59th IEEE Vehicular Technology Conf., vol. 2, pp. 1167 ­1171, May 2004.

[9] I. Hammerstrom, A. Wittneben, "Power allocationschemes for Amplify-and-Forward MIMO-OFDM relaylinks," IEEE Trans. Commun., vol. 6, pp. 2798-2802,Aug. 2008.

We have proposed a novel cooperative relaying schemewith dual relays and full rate transmission capabilities.Based on the analysis and simulation results, this newscheme provides balanced diversity gain to each transmittedsymbol and thus enhance system performance and channelcapacity over the conventional one relay scheme and point­to-point communication. Since the AF mode is used, powerallocations at the relays is necessary for robust transmissionand to control the propagating noise from one terminal toother. In short, AF mode performs better at high SNR be­cause oflow noise propagation. Hence it can be argued thatDF mode at low SNR would work better as compared to theAF mode and vice versa. An adaptive AF-DF mode can beutilized for the dual relay transmission for further systemperformance.

[10] T. M. Cover and 1. A. Thomas, Elements ofInformationTheory. New York: John Wiley and Sons, 1991.

[11] S.A. Hassan, P. Wang, M. Green , and Ye G. Li, "Equal­ization for symmetrical cooperative relay scheme forwireless communications," in proc. IEEE Radio andWirelessSymposium, San Diego, CA, January 2009.