IEEE COMMUNICATIONS LETTERS, VOL. 15, NO. 12, DECEMBER 2011 1353

Combining Cooperative Diversity and Multiuser Diversity:A Fair Scheduling Scheme for Multi-Source Multi-Relay Networks

Zhang Zhang, Tiejun Lv, Member, IEEE, and Xin Su, Member, IEEE

Abstract—In this letter, we propose a round-robin (RR) basedfair scheduling scheme (RRFS) to achieve both cooperative diver-sity (CD) and multiuser diversity (MUD) in multi-source, multi-relay amplify-and-forward (AF) cooperative networks. Differentfrom traditional schemes in multiuser scenarios which only allowthe “best” source to transmit and cause transmission unfairness,all the sources transmit in a RR fashion first in RRFS. In order toachieve both kinds of diversity in the relay phase, we then exploita joint source-relay selection strategy which selects the “best”relay to help the “worst” source’s transmission in each relaytime slot. Therefore, RRFS brings MUD benefit to cooperationcommunication systems while maintaining transmission fairness.

Index Terms—Cooperative diversity, multiuser diversity, diver-sity order, fair scheduling.

I. INTRODUCTION

COOPERATIVE diversity (CD) is a kind of spatial di-versity achieved by cooperation communication systems

in a distributed way. In a 𝑀 -relay amplify-and-forward (AF)cooperative system, opportunistic relaying (OR) [1] whichachieves full CD order of 𝑀+1 by selecting the “best” relayto help transmission shows low implementation complexityand attracts much attention. On the other hand, it is wellknown that multiuser diversity (MUD) is an inherent diversityof a multiuser network [2]. Since users experience independentfading, MUD can be obtained by selecting the “best” user totransmit. Therefore, there is potential for the achievement ofboth CD and MUD in a multi-source cooperative communica-tion system. So far some studies have focused on the combineduse of both CD and MUD to improve outage probability [3]–[5], [7] and/or capacity performance [6]. Among these studies,[4], [5] consider a practical multi-source multi-relay networkwhere all the sources share all the relays, and [4] exploitscapacity-aware only scheduler and achieves minimum outageprobability. However, in [4], [5], only the “best” source ischosen to transmit and this fact causes transmission unfairness,especially in short-term transmission scenario.

On the other hand, round-robin (RR) scheduling guaranteeseach user has the same transmission opportunity in both long-term transmission and short-term transmission scenario. Innon-cooperative systems, RR scheduling leads to the total lossof MUD. However, in this letter, we show that RR scheduling

Manuscript received August 9, 2011. The associate editor coordinating thereview of this letter and approving it for publication was T. Ho.

Z. Zhang and T. Lv are with the School of Information and CommunicationEngineering, Beijing University of Posts and Telecommunications, Beijing,China (e-mail: {zhangzhang, lvtiejun}@bupt.edu.cn).

X. Su is with the Tsinghua National Laboratory for Information Scienceand Technology (TNList), Beijing, China (e-mail: suxin@tsinghua.edu.cn).

This work is supported in part by the National Natural Science Foundationof China (No.60972075), and by Beijing Natural Science Foundation (No.4110001).

Digital Object Identifier 10.1109/LCOMM.2011.102611.111715

1S

2S

NS

3S ....

.

.

1R

2R

MR

D

Fig. 1. System model.

Fig. 2. Time resource allocation of RRFS.

does not conflict with MUD in cooperative systems. Wepropose a round-robin based fair scheduling (RRFS) scheme tocombine CD and MUD for a multi-source multi-relay networkas in [4]. In RRFS, we divide the whole transmission into twophases: the broadcast phase and the relay phase. Distinct from[4] where only the selected user has the opportunity to trans-mit, each source in RRFS transmits individual informationin a RR way to assure transmission fairness. During the relayphase, we exploit a source-relay pair selection strategy in eachrelay time slot to indicate which source’s information shouldbe relayed by which relay. The key idea of the strategy is to usethe “best” relay to help the “worst” source’s transmission. Boththeoretical analysis and simulation results show that RRFSprovides CD and MUD simultaneously while maintainingtransmission fairness. This result implies that CD and MUDcan both be obtained with RR scheduling.

II. SYSTEM MODEL AND THE PROPOSED SCHEME

A. System Model

As shown in Fig.1, 𝑁 sources (𝑆𝑖,1 ≤ 𝑖 ≤ 𝑁 ) transmit theirindividual information to one destination (𝐷) with the help of𝑀 relays (𝑅𝑗,1 ≤ 𝑗 ≤ 𝑀 ). All the nodes are assumed to havesingle antenna and transmit with unit power, and work in half-duplex mode. All the channels in the network are assumed tobe independent non-frequency selective block-fading rayleighchannels with additive white Gaussian noise (AWGN).

B. The Proposed Scheme

The whole transmission is divided into two phases: thebroadcast phase and the relay phase. Each phase occupies 𝑁time slots. Fig.2 illustrates the time resource allocation.

1089-7798/11$26.00 c⃝ 2011 IEEE

1354 IEEE COMMUNICATIONS LETTERS, VOL. 15, NO. 12, DECEMBER 2011

In the broadcast phase, each source broadcasts its data inturn. The received signals of the relay 𝑗 and the destinationfrom the source 𝑖 are

𝑦𝑆𝑖𝑅𝑗 = ℎ(0)𝑆𝑖𝑅𝑗

𝑥𝑖 + 𝑛𝑆𝑖𝑅𝑗 , (1)

𝑦𝑆𝑖𝐷 = ℎ(0)𝑆𝑖𝐷

𝑥𝑖 + 𝑛𝑆𝑖𝐷, (2)

respectively, where ℎ(0)𝑆𝑖𝑅𝑗

and ℎ(0)𝑆𝑖𝐷

are the fading coefficientsof the links 𝑆𝑖 → 𝑅𝑗 and 𝑆𝑖 → 𝐷 in the broadcast phase,respectively. 𝑥𝑖 is the transmitted symbol of 𝑆𝑖. 𝑛𝑆𝑖𝑅𝑗 and𝑛𝑆𝑖𝐷 denote the AWGN with zero mean and variance 𝜎2.

In the relay phase, the proposed scheme employs source-relay pair selection and AF transmission. Briefly speaking,we choose the “best” relay to help the transmission of the“worst” source in each time slot. After relay’s transmission,the destination performs data combining and then updates thequality record of each source in order to prepare for the nextrelay time slot. Since selective combining (SC) is able toprovide diversity order with rather low complexity, we focuson SC in this letter. It should be noted that the other combiningschemes can be easily introduced into RRFS in the same way.The details and signal formats are represented as follows.

We denote 𝜌(𝑘)𝑖 as the signal-to-noise ratio (SNR) of the

received signals at the destination from 𝑆𝑖 (i.e., from all thelinks 𝑆𝑖 → 𝐷 and 𝑆𝑖 → 𝑅𝑗 → 𝐷 through which 𝑥𝑖 hasbeen transmitted to the destination) after combining beforethe 𝑘th relay time slot, 𝜙𝑘 as the set of 𝜌

(𝑘)𝑖 , where 1 ≤

𝑘 ≤ 𝑁 . Suppose ℎ(𝑘)𝑆𝑖𝑅𝑗

, ℎ(𝑘)𝑆𝑖𝐷

, ℎ(𝑘)𝑅𝑗𝐷

are the channel fadingcoefficients of the links 𝑆𝑖 → 𝑅𝑗 , 𝑆𝑖 → 𝐷, 𝑅𝑗 → 𝐷 in the𝑘th relay time slot, respectively. Note that 𝜌

(1)𝑖 denotes the

SNR of the received signals at the destination from 𝑆𝑖 afterthe broadcast phase, it is computed as

𝜌(1)𝑖 =

∣∣∣ℎ(0)𝑆𝑖𝐷

∣∣∣2/𝜎2. (3)

Denote ℎ𝑆𝑖𝑅𝑗 as the channel coefficient of the link 𝑆𝑖 → 𝑅𝑗

from which 𝑅𝑗 gets its current observation of the informationof 𝑆𝑖. After broadcast phase, ℎ𝑆𝑖𝑅𝑗 is initialized as

ℎ𝑆𝑖𝑅𝑗 = ℎ(0)𝑆𝑖𝑅𝑗

. (4)

In the 𝑘th relay time slot, the destination first selects the“worst” source and broadcasts its index number 𝑙𝑘, where

𝑙𝑘 = 𝑎𝑟𝑔 𝑚𝑖𝑛𝑖=1,...,𝑁

𝜌(𝑘)𝑖 . (5)

Then the “best” relay with index number 𝑚𝑘 is chosen tohelp the transmission of 𝑆𝑙𝑘 . However, there is a possibilitythat all the 𝑀 relays do not hear from 𝑆𝑙𝑘 correctly during thebroadcast phase. In this case, if we only allow 𝑅1, 𝑅2, ..., 𝑅𝑀

to transmit as traditional relay selection schemes, relays willnot help 𝑆𝑙𝑘 ’s transmission at all, thus we can just obtain adiversity order of 𝑀 + 1 (i.e, only CD). To overcome thisproblem, we must give the relays the opportunities to updatetheir observations of 𝑥𝑙𝑘 during the relay phase. Therefore,𝑆𝑙𝑘 itself is seen as a relay and is denoted as 𝑅0 in the 𝑘threlay time slot. It means that there are 𝑀 + 1 relays in thenetwork actually, thus 0 ≤ 𝑚𝑘 ≤ 𝑀 . 𝑚𝑘 is written as

𝑚𝑘 = 𝑎𝑟𝑔 𝑚𝑎𝑥𝑞=0,...,𝑀

𝛿(𝑘)𝑞 , (6)

where 𝛿(𝑘)𝑞 represents the SNR of the link 𝑅𝑞 → 𝐷 to the

destination, and is expressed as

𝛿(𝑘)𝑞 =

⎧⎨⎩∣∣∣ℎ𝑆𝑙𝑘

𝑅𝑞ℎ(𝑘)𝑅𝑞𝐷

∣∣∣2

𝜎2

(∣∣∣ℎ𝑆𝑙𝑘𝑅𝑞

∣∣∣2+∣∣∣ℎ(𝑘)

𝑅𝑞𝐷

∣∣∣2+𝜎2

) , 𝑞 ∕= 0

∣∣∣∣ℎ(𝑘)𝑆𝑙𝑘

𝐷

∣∣∣∣2

𝜎2 , 𝑞 = 0

. (7)

The received signals at the destination is expressed as

𝑦(𝑘)𝑅𝐷 =

{ℎ(𝑘)𝑅𝑚𝑘

𝐷𝑥𝑙𝑘,𝑚𝑘+ 𝑛𝑅𝑚𝑘

𝐷, 𝑚𝑘 ∕= 0

ℎ(𝑘)𝑆𝑙𝑘

𝐷𝑥𝑙𝑘 + 𝑛𝑅𝑚𝑘𝐷, 𝑚𝑘 = 0

, (8)

where 𝑥𝑙𝑘,𝑚𝑘is the observation (i.e., the amplified signals) of

𝑥𝑙𝑘 at 𝑅𝑚𝑘when 𝑚𝑘 ≥ 1, 𝑛𝑅𝑚𝑘

𝐷 is AWGN with power 𝜎2.If 𝑅0 is selected, the source 𝑆𝑙𝑘 broadcasts its data to the

relays and the destination, and all the relays update 𝑥𝑙𝑘,𝑗 andℎ𝑆𝑙𝑘

𝑅𝑗 . Thus 𝑥𝑙𝑘,𝑗 and ℎ𝑆𝑙𝑘𝑅𝑗 is written as

𝑥𝑙𝑘,𝑗 =(ℎ(𝑘)𝑆𝑙𝑘

𝑅𝑗𝑥𝑙𝑘 + 𝑛

(𝑘)𝑆𝑙𝑘

𝑅𝑗

)/

√∣∣∣ℎ(𝑘)𝑆𝑙𝑘

𝑅𝑗

∣∣∣2 + 𝜎2, (9)

ℎ𝑆𝑙𝑘𝑅𝑗 = ℎ

(𝑘)𝑆𝑙𝑘

𝑅𝑗, (10)

respectively, where 𝑛(𝑘)𝑆𝑙𝑘

𝑅𝑗is AWGN with noise power 𝜎2.

After receiving 𝑦(𝑘)𝑅𝐷, the destination performs data combin-

ing and then updates 𝜌(𝑘)𝑙𝑘

to 𝜌(𝑘+1)𝑙𝑘

and reconstructs a new

SNR set 𝜙𝑘 + 1. 𝜌(𝑘+1)𝑙𝑘

is calculated by

𝜌(𝑘+1)𝑙𝑘

= 𝑚𝑎𝑥(𝛿(𝑘)𝑚𝑘

, 𝜌(𝑘)𝑙𝑘

). (11)

Then the 𝑘 + 1th relay time slot begins. The relay phaselasts for 𝑁 time slots. The whole transmission finishes afterthe relay phase.

III. BRIEF ANALYSIS ON DIVERSITY ORDER

Diversity order is a crucial measurement of a cooperativecommunication system, thus we focus on the analysis of thediversity order of the proposed scheme.

It can be seen that 𝜌(𝑁+1)𝑖 is the SNR of the com-

bined signals of 𝑆𝑖 at the destination after the whole trans-mission. Define A as the set of

{𝜌(1)𝑖 ∣𝑖 = 1, 2, ...𝑁

}∪{

𝛿(𝑘)𝑗 ∣𝑗 = 0, 1, ...𝑀, 𝑘 = 1, 2, . . . , 𝑁

}. It should be noted

that the elements in A are not jointly independent. How-ever, according to (5) and (6), we can always find asubset B = {𝛽𝑡∣𝑡 = 1, 2, ..., 𝑁 +𝑀 + 1} ⊂ A where𝛽1, 𝛽2, . . . , 𝛽𝑁+𝑀+1 are jointly independent and 𝛽𝑡 ≤𝜌(𝑁+1)𝑖 .Suppose the given target end-to-end spectral efficiency is

𝑟 𝑏𝑖𝑡/𝑠/𝐻𝑧. After the whole transmission, the spectral effi-ciency of 𝑆𝑖 can be computed by its corresponding SNR aftercombining at the destination (i.e., 𝜌

(𝑁+1)𝑖 ).Thus the outage

probability of RRFS can be expressed as

𝑃𝑜𝑢𝑡 (𝑟) = Pr(𝑙𝑜𝑔2

(1 + 𝜌

(𝑁+1)𝑖

)< 𝑟

)≤

𝑁+𝑀+1∏𝑡=1

Pr (𝑙𝑜𝑔2 (1 + 𝛽𝑡) < 𝑟) . (12)

ZHANG et al.: COMBINING COOPERATIVE DIVERSITY AND MULTIUSER DIVERSITY: A FAIR SCHEDULING SCHEME FOR MULTI-SOURCE . . . 1355

Fig. 3. Outage probabilities of RRFS and [4] with different numbers of 𝑀and 𝑁 . SC is employed.

Fig. 4. Short-term data-rate fairness of RRFS and [4] with different numbersof users. SC is employed. 𝑀 = 3 and 𝐸𝑏/𝑁0 = 10𝑑𝐵.

Since diversity order is defined under the condition thataverage SNR goes to infinity [8] , we can assume that all the𝛿(𝑘)𝑞 and 𝜌

(1)𝑖 are identically distributed random variables and

Pr (𝑙𝑜𝑔2 (1 + 𝛽𝑡) < 𝑟) = 𝑃 for catching the essence. From(12), we have 𝑃𝑜𝑢𝑡 (𝑟) ≈ 𝑃𝑁+𝑀+1. Therefore the diversityorder of RRFS is 𝑁 +𝑀 + 1.

IV. SIMULATION RESULTS

In this section, we provide simulation results to verifythe validity of the proposed scheme. Simulations have beenperformed over rayleigh block fading channels with AWGN.We generate the network in a 2-dimensional plane as in [4]where 𝐷 is located at (1,1), and the other nodes are uniformlydistributed in the first quadrant of the 1× 1 square. The lossexponent is set to be 2. We define 𝐸𝑏 as the average transmitpower in each node, 𝑁0 as noise power.

Fig. 3 illustrates the outage probabilities of RRFS andtraditional scheme in [4]. It should be mentioned that in [4],all the channel coefficients in the network need to remain fixedduring both the selected source’s and relay’s transmission to

exploit the joint source-relay selection. Therefore the diversityorder and outage performance of [4] can not be enhanced byallowing the selected source to participate during the relayphase, and the diversity order of [4] is 𝑁 + 𝑀 . It can beseen that RRFS combines CD and MUD and achieves a totaldiversity order of 𝑁 +𝑀 + 1, thus provides superior outageperformance to [4] in high SNR regime. This result coincideswith our analysis on diversity order.

To show the short-term fairness of RRFS, weuse the data-rate fairness criterion [9]: 𝐹𝑟(𝐿) =[∑𝑁

𝑖=1 𝑟𝑖 (𝐿)]2

/[𝑁 ⋅∑𝑁

𝑖=1 𝑟𝑖 (𝐿)2], where 𝐿 is the

number of overall transmission time slots, 𝑟𝑖 (𝐿) is the datarate of source 𝑖 during 𝐿 time slots. 𝐹𝑟(𝐿) varies from 0 to1, and larger 𝐹𝑟(𝐿) indicates fairer transmission. The resultin Fig. 4 implies that RRFS is able to balance user’s datarate. Since in RRFS each source occupies the same amountof broadcast time slots, this conclusion is straightforward.

V. CONCLUSIONS

This letter proposes a round-robin based fair schedulingscheme to combine CD and MUD in multi-source multi-relaynetworks. First all the sources transmit in turn to assure fair-ness, then a joint “source-relay” selection strategy is proposedto achieve both kinds of diversity. Both diversity analysis andsimulation results show RRFS achieves a total diversity gainof 𝑁 +𝑀 + 1 while maintaining transmission fairness.

REFERENCES

[1] A. Bletsas, H. Shin, and M. Win, “Outage optimality of opportunisticamplify-and-forward relaying,” IEEE Commun. Lett., vol. 11, no. 3, pp.261–263, 2007.

[2] D. Tse, “Multiuser diversity in wireless networks,” in Wireless Commu-nications Seminar. Standford University, 2001.

[3] S. Chen, W. Wang, and X. Zhang, “Performance analysis of multiuserdiversity in cooperative multi-relay networks under rayleigh-fadingchannels,” IEEE Trans. Wireless Commun., vol. 8, no. 7, pp. 3415–3419,2009.

[4] L. Sun, T. Zhang, L. Lu, and H. Niu, “On the combination of cooperativediversity and multiuser diversity in multi-source multi-relay wirelessnetworks,” IEEE Signal Process. Lett., vol. 17, no. 6, pp. 535–538,2010.

[5] H. Ding, J. Ge, D. Benevides da Costa, and Z. Jiang, “A new effi-cient low-complexity scheme for multi-source multi-relay cooperativenetworks,” IEEE Trans. Veh. Technol., vol. 60, no. 2, pp. 716–722, 2011.

[6] H. Joung and C. Mun, “Capacity of multiuser diversity with cooperativerelaying in wireless networks,” IEEE Commun. Lett., vol. 12, no. 10,pp. 752–754, 2008.

[7] X. Liu, X. Zhang, and D. Yang, “Outage probability analysis of mul-tiuser amplify-and-forward relay network with the source-to-destinationlinks,” IEEE Commun. Lett., vol. 15, no. 2, pp. 202–204, 2011.

[8] L. Zheng and D. Tse, “Diversity and multiplexing: a fundamentaltradeoff in multiple-antenna channels,” IEEE Trans. Inf. Theory, vol. 49,no. 5, pp. 1073–1096, 2003.

[9] R. Jain, D. Chiu, and W. Hawe, “A quantitative measure of fairnessand discrimination for resource allocation in shared computer system,”Eastern Research Laboratory, Digital Equipment Corp., 1984.