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INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS

SHORT COMMUNICATION

Decode-and-forward with full-duplex relaying

Xianyi Rui,, Jia Hou and Liulei Zhou

School of Electronic and Information Engineering, Soochow University, Suzhou 215006,

Peoples Republic of China

SUMMARY

This paper addresses the full-duplex relaying. Some expressions for outage and average capacity of atwo-hop cooperative system with a full-duplex relay are derived under an independent but not identicallydistributed Rayleigh fading environment. Using these expressions, we provide the performance analysiswithout Monte Carlo simulations. The impact of interference between the relay output and input isinvestigated. Copyright 2011 John Wiley & Sons, Ltd.

Received 25 August 2010; Revised 15 November 2010; Accepted 12 February 2011

KEY WORDS: average capacity; outage probability; decode-and-forward; Rayleigh fading; full-duplexrelaying

1. INTRODUCTION

Cooperative relaying communications [13] have recently attracted the attention of wireless

researchers across the world thanks to the increase in the coverage and capacity without using

high power levels at the transmitter. In [4], the authors presented an upper bound on the diversity-multiplexing trade-off for the single-user relay channel. Distributed spacetime block coding for

decode-and-forward (DF) protocols was proposed in [5]. However, their work is studied assuming

that the relay is operating in half-duplex mode, where reception and transmission are performed

in time-orthogonal channels, and therefore, the system capacity is degraded. In view of the spec-

tral efficiency loss of half-duplex protocols, full-duplex protocol has been investigated recently in

[69]. Compared with half-duplex relaying, full-duplex relaying allows the user to receive and

transmit data at the same time in the same frequency band [6]. The subsequent interference occurs

due to signal leakage between the relay output and input. The feasibility of full-duplex relaying was

discussed in [7]. In [8], an antenna sharing method was proposed to suppress the interference and

to improve the spectral efficiency of full-duplex relaying. In [9], outage probabilities of DF relay

systems were investigated and based on these results, the optimal duplex mode is determined to

satisfy the target outage probability. However, these studies do not involve the impact of interferencewithin the relay to capacity gain of full-duplex relaying relative to half-duplex relaying.

In this work, we investigate capacity performance of the full-duplex relaying. Some expressions

for outage and average capacity are derived for a DF-based full-duplex relay system, and using

them, we can provide the analysis of system performance and interference in an independent but

not identically distributed (INID) Rayleigh fading environment.

Correspondence to: Xianyi Rui, School of Electronic and Information Engineering, Soochow University, Suzhou215006, Peoples Republic of China.

E-mail: [email protected]

Copyright 2011 John Wiley & Sons, Ltd.

Int. J. Commun. Syst.2012; 25:270275Published online 4 April 2011 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/dac.1257


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2. SIGNAL AND SYSTEM MODEL

We consider a two-hop cooperative network in which a source ( S) transmits data to a destination

(D) via a DF relay (R). It is assumed that there is no direct link between Sand D. The nodes S

and D operate in half-duplex mode and are equipped with a single antenna, but the node R with

one receive antenna and one transmit antenna operates in full-duplex mode. Let h S R, hR D and

hIdenote the channel impulse responses between S and R, between R and D and between relayoutput and input, respectively. The received signal at nodes R and D can be expressed as

yR= h S RxS+hIxR+nR (1)

y= hR DxR+nD (2)

where xS and xR represent the transmitted symbols at nodes S and R, respectively. And nR and

nD are the additive white Gaussian noise terms with zero mean. On the right of the equal sign in

(1), the second term denotes the interference within node R.

In this paper, all the links are assumed to be INID Rayleigh distributed. The independent exponen-

tially distributed random variables1=|h S R|2,2=|hR D|

2 and3=|hI|2 have their corresponding

variances S, D and I, respectively. In our paper, we define three parameters S=1/S,

D =1/D andI=1/I. Therefore, the signal-to-interference and noise ratio (SINR) of the firsthop and signal-to-noise ratio (SNR) of the second hop can be obtained respectively by

1= 01/(03+1) (3)

2= 02 (4)

where 0 and 0 denote the average transmit SNR at nodes S and R, respectively. As regards a

DF protocol, the end-to-end output SNR at node D can be tightly approximated in the high SNR

regime as follows [3]:

eq=min{1,2} (5)

3. PERFORMANCE ANALYSIS

Different from half-duplex relaying mode, full-duplex relaying introduces interference channel

between the relay output and input. For the first hop, the cumulative distribution function (CDF)

of1 in (3) can be given by

F1()=Pr

01

03+1


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and the corresponding PDF

f()=R (S+D )(S+R)+SR0

20

0(S0+R0)2

e(S/0+D/0) (9)

If the half-duplex relay is used, the interference term of (1) equals zero, and (7) is simplified to

F1()=eS/0 (10)

And then, PDF of the end-to-end SNR can be given by

fhalf()= (S/0+D/0)e(S/0+D/0) (11)

Next, some expressions for outage and average capacity of a full-duplex relay system are derived

to obtain the performance analysis accurately and conveniently.

3.1. Outage probability

The end-to-end mutual information of a full-duplex relay system can be expressed as

I= log2(1+) (12)

Outage probability is an important performance for a wireless system and can be defined as the

probability Pout that the instantaneous mutual information I in (12) is less than a target rate Cth.

Therefore, a simple closed-form expression for outage probability can be given by

Pout=Pr{I


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4. NUMERICAL AND SIMULATED RESULTS

In this section, some numerical examples are presented to illustrate and verify the analytical

expressions derived in the previous sections. Figure 1 shows outage probability in (13) when Cth=

0.1 bits/s/Hz,0=0/2 and I=1/5. From Figure 1, it can be seen that the analytical results are in

good agreement with the results obtained from Monte Carlo simulations. In Figure 2, performance

curves for average capacity are plotted when I=1/5 and S=D =1. For comparison, we alsoprovide the results of half-duplex relying. From Figure 2, we can conclude that the use of the full-

duplex relay can improve the spectral efficiency of relaying. To observe the impact of interference

within relay, Figure 3 shows the average capacity as a function of I when S=D =1 and

0=0=10dB. In Figure 3, when the normalized interference channel gain E{|hI|2}=Iis larger,

the average capacity of full-duplex relaying decreases, and moreover, it is below than that of

half-duplex relaying when I>0.85. It can be concluded that compared with half-duplex relaying,

the average capacity gain of full-duplex relaying will decrease with increase in interference level

Figure 1. Outage probability of full-duplex relaying.

Figure 2. Average capacity of full-duplex relaying.


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DECODE-AND-FORWARD WITH FULL-DUPLEX RELAYING


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Figure 3. Average capacity versus I.

between the relay output and input. Therefore, an effective method to suppress the interference

can show and strengthen the advantage of full-duplex relaying.

5. CONCLUSIONS

In this paper, a DF-based cooperative network with a full-duplex relay operating under INID

Rayleigh fading channels was considered, and some analytical expressions for outage and average

capacity were provided to obtain the performance analysis conveniently.

ACKNOWLEDGEMENTS

This work is supported by the Natural Science Foundation of the Jiangsu Higher Education Institutionsof China (Grant No. 10KJB510023).

REFERENCES

1. Laneman J, Tse D, Wornell G. Cooperative diversity in wireless networks: efficient protocols and outage behavior.

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3. Bletsas A, Khisti A, Reed DP, Lippman A. A simple cooperative diversity method based on network path

selection. IEEE Journal on Selected Areas Communications 2006; 24(3):659672.

4. Azarian K, Gamal HE, Schniter P. On the achievable diversity-multiplexing tradeoff in half-duplex cooperative

channels. IEEE Transactions on Information Theory 2005; 51(12):41524172.

5. Yiu S, Schober R, Lampe L. Distributed spacetime block coding. IEEE Transactions on Communications 2006;

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relay and full-duplex relay. IEEE Communications Magazine 2009; 47(9):5865.7. Riihonen T et al. On the feasibility of full-duplex relaying in the presence of loop interference. IEEE Workshop

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8. Ju H, Oh E, Hong D. Improving efficiency of resource usage in two-hop full duplex relay systems based on resource

sharing and interference cancellation. IEEE Transactions on Wireless Communications 2009; 8(8):39333938.9. Kwon T. et al. Optimal duplex mode for DF relay in terms of the outage probability. IEEE Transactions on

Vehicular Technology 2010; 59(7):36283634.

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AUTHORS BIOGRAPHIES

Xianyi Rui received the MS and PhD degrees from Soochow University and ShanghaiJiao Tong University, respectively in China. He is now working as a teacher at SoochowUniversity. His research interests include cooperative diversity and MIMO technique forwireless communication.

Jia Hou received his BS degree in Communication Engineering from Wuhan Universityof Technology in 2000, China, and his MS and PhD degrees in Information & Commu-nication from Chonbuk National University, Korea, in 2002 and 2005, respectively. Heis now the associate professor in Soochow University, Suzhou, China. His main researchinterests are sequences, CDMA mobile communication systems, error coding and spacetime signal processing.

Liulei Zhou received the BS degree in Electronics and Information Engineering fromSoochow University, Suzhou, China, in 2003, and the MS and PhD degrees in WirelessCommunication and Electromagnetic Compatibility from Nanjing University of Postsand Telecommunications, Nanjing, China, in 2008. She is currently a Lecturer in theSchool of Electronics and Information Engineering, Soochow University. Her researchinterests include computer networks, space communications, wireless communications,and cognitive radio technology.


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DECODE-AND-FORWARD WITH FULL-DUPLEX RELAYING

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