journal 2013 - incentive mechanism for multiuser cooperative relaying in wireless ad hoc networks -...

8/10/2019 Journal 2013 - Incentive Mechanism for Multiuser Cooperative Relaying in Wireless Ad Hoc Networks - A Resource-Exchange Based Approach

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Wireless Pers Commun (2013) 73:697715DOI 10.1007/s11277-013-1211-z

Incentive Mechanism for Multiuser Cooperative Relayingin Wireless Ad Hoc Networks: A Resource-ExchangeBased Approach

Guopeng Zhang Kun Yang Peng Liu Xiaolong Feng

Published online: 26 May 2013 Springer Science+Business Media New York 2013

Abstract This paper studies the resource allocation (RA) and the relay selection (RS) prob-lems in cooperative relaying (CR) based multiuser ad hoc networks, and a multiuser cooper-ative game is proposed to stimulate selsh user nodes to participate in the CR. The noveltyof the game scheme lies in that it takes explicit count of that a wireless user can act as adata-source as well as a potential relay for other users. Consider a user has the selsh incen-tive to consume his/her spectrum resource solely to maximize his/her own data-rate and the

selection cooperation (SC) rule which restricts relaying for a user to only one relay is explic-itly imposed. To stimulate user nodes to share their energy and spectrum resource efcientlyin the Pareto optimal sense, rst, we formulate the RA problem for multiuser CR as a bar-gaining game. By solving the Nash bargaining solution of the game, Pareto optimal RA forcooperative partners can be achieved. Next, to implement the SC-rule imposed RS, a simpleheuristic is proposed with the main method being to maintain the long-term priority fairnessfor cooperative partner selection for each selsh user. The proposed RS with RA (RS-RA)algorithm has a low computational complexity of O ( K 2) , where K is the number of usersin a network. Simulation results demonstrate the system efciency and fairness properties of the proposed bargaining game theoretic RS-RA scheme.

G. Zhang ( B ) P. LiuInternet of Things Research Center, China University of Mining and Technology,Xuzhou 221008, Jiangsu, Chinae-mail: [email protected]

P. Liue-mail: [email protected]

K. Yang

School of Computer Science and Electronic Engineering (CSEE), University of Essex, Wivenhoe Park,Colchester CO4 3SQ, Essex, UKe-mail: [email protected]

X. FengSchool of Information and Electrical Engineering, China University of Mining and Technology,Xuzhou 221116, Jiangsu, Chinae-mail: [email protected]

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Keywords Cooperative relaying Resource allocation Relay selection Cooperativebargaining game Nash bargaining solution Pareto optimal

1 Introduction

Cooperative relaying (CR) [1] allows exploiting the spatial diversity gains inherent in multi-user wireless networks without the need of multiple antennas at each user node. Recently,CR techniques have evolved from the early information theoretic results [2] to a practicalapplication stage. For example, xed infrastructure based relay nodes (RNs) have emergedin cellular networks [ 3,4], and multi-hop communication via the RNs can effectively extendbase stations (BSs) coverage. In cellular networks, xed RNs are dedicatedly deployed tohelp wireless users uplink/downlink transmissions without having their own data to trans-mit. However, an ad hoc network is composed of multiple distributed user nodes and doesnot rely on any infrastructure [ 5]. Each user node plays an equal role and has its own datato transmit. It thus can act as a data-source as well as a potential relay for other nodes.In such decentralized network environments, a node has the right to determine whether tocooperate with others according to its own willingness, and it tends to be selsh to consumeits resource solely to optimize its own performance [6]. Therefore, cooperation cannot betaken for granted in such a selsh scenario. The relay selection (RS) and resource allocation(RA) problem become more complicated. It is necessary to develop cooperation stimulatingmechanisms that allow cooperation to emerge in the presence of selsh nodes.

In literatures, cooperation incentive mechanisms for selsh nodes are broadly divided into

the following three categories.

Reputation based mechanisms [ 79], in which cooperation behaviors of nodes are mea-sured by other nodes in the same network. Selsh behaviors are then discouraged by thethreat of partial or total refusal of forwarding of any trafc originated from these selshnodes. However, reputation mechanisms always rely on the usage of tamper-proof hard-ware to store and check reputation credit. This strategy may hinder their ability to ndwide-spread acceptance.

Pricing based mechanisms [1013], in which relay nodes are usually assumed to havetemporarily idled spectrum and energy resource that are not fully utilized. Therefore theyhave opportunities to sell the idle resource to the nodes that are seeking extra spectrum(via cooperation), and thereby to generate revenue. The revenue can be used by the relaynodes later to reward and encourage other nodes to cooperate. In this research area,Huang [10] and Zhang and Cong [ 11 ,12] investigate the problems of how a relay shouldsell its power and bandwidth to multiple competing source nodes using auction theoryand non-cooperative pricing game theory, respectively. Based on the Stackberg pricinggame theory, Wang [13] studies the scenario in which multiple relays compete with eachother in terms of price to gain the highest prot from selling power to a single source.Although pricing mechanisms could stimulate selsh nodes to cooperate, it does not

function in full-loaded network situations where all nodes in a wireless system alwayshave their own data to transmit, and, thus leads to a situation where some nodes as relayswill have no more resource left for selling to other nodes.

Resource-exchange based mechanisms [ 1416], in which one node can trade its resourcefor the partner nodes CR directly, and, as a result, two cooperative partner nodes can actas a source as well as a potential relay for each other symmetrically. By this way, rstly,the tamper-proof hardware used in reputation mechanisms can be avoided. Secondly, the

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A Resource-Exchange Based Approach 699

full-loaded situation mentioned above can also be dealt with effectively, since resource-exchange mechanisms provide cooperative incentives for selsh user nodes by promisingto lead to a win-win situation, e.g., transmission rate gains for both cooperative partnernodes. However, the authors in [14] and [15] only consider the special case of two-node

cooperation in cellular and ad hoc networks, respectively. As the selection coopera-tion (SC) rule which restricts relaying for a source node to only one relay is explicitlyimposed in both the works, the authors do not actually touch the RS problem, whichis an important issue in multiuser networks. Moreover, in [ 15], the authors also studythe bandwidth allocation in the one-to-many CR network model. However, again, theRS problem is not discussed. It requires the extension of the one-to-many CR model toaccommodate the many-to-many case. In [ 16], the authors provide a resource-exchangebased non-cooperative game to perform the RA in the paradigm of CR based cognitiveradio networks.

Different from [ 1416], in this paper, we study the resource-exchange based cooperationstimulating mechanismforCR based multiuserad hocnetworks, and theRS and RA problemsare considered jointly. Specically, our main contributions include the following:

A resource-exchange based cooperative bargaining game is proposed, whose aim is tostimulate a subset of potential relays of a source node to forward the sources data. In thegame, to stimulate a relay to cooperate, the source should reward the relay by forwardingthe data originated from the relay. Assuming each selsh node is willing to cooperateonly if the transmission rate achieved through cooperation is not lower than that achieved

without the cooperation by consuming the same amount of energy, we can prove thereexists a unique Nash bargaining solution (NBS) for the proposed game. By solving theNBS, all the cooperative partner nodes can achieve rate-gains in comparison with thatachieved through direct transmission.

As the algorithm to solve the original game is with a high computational complexity of O ( L2 K ) , where K is the total number of the potential relays available to a source and L is the number of data symbols that can be transmitted in a frame of a source, the SCrule is applied to the game which could also bring the cooperative partner nodes win-win benets and the solution method to the SC-rule based game is featured with a lowcomputational complexity of O ( K ) .

To implement the RS and the RA jointly, a simple heuristic RS with RA (RS-RA) schemeis proposed to maintain the long-term priority fairness for the cooperative partner selec-tion. Based on the SC rule, the method of the RS-RA heuristic is to assign each sourcea different priority at the network initialization stage, and a source with a higher priorityhas privilege to select its cooperative partner. With the priority of each source beingupdated after each RS-RA cycle, the long-term priority fairness for the whole network can be guaranteed.

The rest of this paper is organized as follows. In Section II, we propose the investigated

multiuser CR-based ad hoc network model. In Sect. 3, we describe the resource-exchangebased cooperation incentive mechanism. In Sect. 4, we formulate the RA problem for coop-erative nodes as a cooperative bargaining game, and we also prove the existence of a uniqueNBS to the game. In Sect. 5, a simplied SC-rule imposed multiuser CR game is proposed andis solved in a closed form. In Sect. 6, a simple heuristic RS scheme is proposed to maintainthe long-term priority fairness for cooperative partner selection in the network. Simulationresults are presented in Sect. 7. Finally, conclusions are drawn in Sect. 8.

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Fig. 1 Multiuser CR basedad hoc network

2 System Model

In wireless ad hoc networks, an end-to-end data-ow may cross several hops in the link layer.The rate requested by the ow is checked against the link layer capacity hop-by-hop to nd afeasible path. The data-rate that can be achieved by such ow is determined by the capacityof the bottleneck link. As a rst step to study the resource-exchange based CR stimulatingmechanism, this paper only focuses on the one-hop CR case. The studied multiuser ad hocnetwork is sketched in Fig. 1. It consists of K + 1 one-hop source-to-destination links, fromsource f i to destination F i , i = 1, . . . , K , and from source m to destination M , where hm, M represents the channel from source m to destination M , hm , f i represents the channel fromsource m to source f i , h f i , M represents the channel from source f i to destination M , h f i , F i

represents the channel from source f i to destination F i , h f i , m represents the channel fromsource m to source f i , and hm , F i represents the channel from source m to destination F i .Note that we only focus on thesourcescooperation, i.e., only sources {m , f 1 , . . . , f K }can

serve as relays for other sources. The cooperation results for destinations { M , F 1 , . . . , F K }can beobtained in a similar way which is omitted here. Considering the direct link from sourcem to destination M is weak due to the long distance transmission or the line of sight (LoS)being obstructed by a building block, other sources { f 1 , . . . , f K } may serve as the relays forsource ms transmission, in view of CR may provide intermediate facility for improve rateperformance. Since all sources are peer in ad hoc network setups, so each potential relay f i (1 i K ) also has the right to serve as a source.

Throughout the following analysis, we assume the system bandwidth is W Hz and theorthogonal channels for multiple access are synthesized by existing CR oriented carrier sensemultiple access with collision avoidance (CSMA/CA) protocols, e.g., [ 17]. We also assumethe sources are scheduled to transmit in a rapid succession, one after the other, each using onescheduling time interval called a data-frame. A data-frame carrying several data symbols thenrepresents one basic time-frequency unit for the sequel CR based RA. We consider the worstfull-loaded network situation, where all sources {m , f 1 , . . . , f K } are active simultaneouslyand have innite backlogged data to send. Thus, the pricing based CR stimulating mechanism[1013] do not function in such situations since there is no extra idle spectrum resource left

for the sources to lease. The novelty of the proposed resource-exchange based CR stimulatingmechanism is in taking explicitly account of that each cooperative source has its own data totransmit and all the cooperative sources could get performance gains through the CR.

Recently, new emerged full-duplex (FD) CR offers great potential for increasing spectral-efciency than traditional half-duplex (HD) CR [ 18]. The FD mode can receive and forwardsimultaneously on the same frequency-band, however, it orders that each node should beequipped with at least two isolated receive and transmit antennas which is infeasible for

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small size wireless nodes. Therefore, for easy practical implementation, compact single-antenna user nodes and thus HD mode [ 18] is used in this paper. Without loss of generality,we employ the amplify-and-forward (AF) CR protocol [ 15] in the system. The HD-AF basedCR for source m helped by any source f i ( f i F , F = { f i | i = 1, . . . , K }) can be described

as follows.At time instant t , source m transmits a symbol x m [t ] to its destination M with power

pm = E | x m [t ]|2 where E {}is the expectation operator. The transmission is also overheardby each potential relay f i , and the received signals at destination M and source f i can begiven by

r M [t ] = hm , M x m [t ] + n M [t ] (1)

and

r f i [t ] = hm, f i x m [t ] + n f i [t ] (2)

respectively, where n M [t ] and n f i [t ] represent the thermal noises at the receivers of nodes M and f i , respectively. We assumethat thewhiteGaussiannoise are with powers E |n M [t ]|2 =

2 M and E n f i [t ]2 = 2 f i , respectively. Thus, the signal-to-noise ratio (SNR) resulting

from the direct transmission (DT) from source m to its destination M can be expressed by [ 18]

m , M = pm gm , M

2 M (3)

where gm , M = E hm , M 2 denotes the channel power gain. Note that the desired signal

component in ( 2) is hm, f i x m [t ], and, the received SNR at relay f i can be expressed by

m , f i = pm gm , f i

2 f i(4)

where gm , f i = E h m , f i2 is the channel power gain.

Using the AF protocol, source f i as the relay will amplify the received signal r f i [t ] byfactor f i and forward it to destination M . Since a long enough integer delay 1 symbol-times should be introduced to the forwarding [ 18], the forwarded signal by relay f i at timeinstant t + can be expressed by

x f i [t + ] = f i r f i [t ] (5)

After the forwarding, the received signal at destination M can be expressed by

r M [t + ] = h f i , M x f i [t + ] + n M [t ] = h f i , M f i r f i [t ] + n M [t ] (6)

In (6) the desired signal component is h f i , M f i r f i [t ]. Assume the amplication factorfor the AF protocol is selected as

f i =

p f i

pm gm , f i + 2 f i(7)

Then we have p f i = E x f i [t + ]2 = E h f i , M f i r f i [t ]

2 . And the relayedSNR received at destination M can be given by

f i , M = p f i g f i , M

2 M (8)

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where g f i , M = E h f i , M 2 denotes the channel power gain.

The above expressions ( 4) and (8) allow to state the instantaneous end-to-end SNR of theAF relaying channel of node-pair m and M as

m , f i , M = m, f i f i , M

1 + m , f i + f i , M (9)

Referring to Fig. 1, there always exists total K sources { f 1 , . . . , f K } that may serve asthe relays for source m. If any k (k K ) relay nodes enumerated with { f 1 , . . . , f k } areultimately chosen, according to [10,11], the instantaneous SNR received at destination M can be denoted by

m, { f 1 ,..., f k }, M =k

i= 1

m, f i , M =k

i = 1

m , f i f i , M 1 + m , f i + f i , M

(10)

So we can express the instantaneous CR rate for source m and destination M helped by anyk relays as

RCm ,{ f 1 ,..., f k }, M = log 2 1 + m , { f 1 ,..., f k }, M = log2 1 +k

i = 1

m, f i f i , M 1 + m , f i + f i , M

(11)

Also, if source m denies using any relay, the instantaneous data rate deriving from the DTcan be expressed as

RDm, M = log 2 1 + m, M (12)

In some situations, node-pair m and M will have a rate requirement which is much higherthan RDm , M . It the rate requirement cannot be met by the DT scheme, any source f i whichhas better channel condition can serve as a relay for source m . However, the willingness of cooperation of source f i cannot be taken for granted, since it always has its own data totransmit. It is necessary to develop incentive-mechanisms that allow cooperation to emergein such situations.

3 Resource-Exchange Based Cooperation Incentive Mechanism

In this paper, a data-frame just consists of one basic time-frequency unit for the CR basedRA. We suppose a potential relay f i ( f i F ) is willing to take out a i (0 a i L) symbol-times in one frame to forward a i symbols originated from source m , and, each relay f i alsohas its own data to transmit, i.e., relay f i also has the right to serve as a source. In such asituation, to stimulate source f i to cooperate, source m could reward source f i by takingout bi (0 bi L) symbol-times in one frame to forward bi symbols of source f i to itsdestination F i . To analyze the benets of sources m and { f 1 , . . . , f k }, in what follows, werst analyze the instantaneous rate expression for node-pair f i and F i . Since the derivationis similar to the case of node-pair m and M , we omit the detail of the deriving process here.

Similar to (3) and (4), the SNRs achieved through the DT from source f i to its destinationF i and from source f i to source m can be expressed by

f i , F i = p f i g f i , F i

2F i(13)

and

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f i , m = p f i g f i , m

2m(14)

respectively, where g f i , F i and gm , f i denote the channel power gains, and 2F i and

2m denote

the powers of the white Gaussian noise at the receivers of nodes F i and m , respectively.Using the AF protocol, we assume source m as a relay will amplify the received signal

from source f i by factor

m = pm p f i g f i ,m + 2m (15)and then forwards it to destination F i . Similar to ( 8), the relayed SNR can be denoted by

m , F i = pm gm , F i

2F i(16)

The above expressions ( 14) and (16) thus allow to state the instantaneous end-to-end SNRof the AF relaying channel of node-pair f i and F i as

f i ,m , F i = f i , m m , F i

1 + f i , m + m , F i(17)

At last, the instantaneous data rate achieved through the DT from source f i to destinationF i can be expressed by

RD f i , F i = log 2 1 + f i , F i (18)

and, the instantaneous CR rate of node-pair f i and F i helped by relay m can be expressed by

RC f i , m, F i = log 2 1 + f i ,m , F i (19)

Note that the channels are assumed as constants during the time of two frame-times forone CR based transmission. The time duration of one frame is set to T and a symbol periodT 0 . Hence, during each frame total L = T / T 0 symbols can be transmitted by a source.To facilitate explaining the proposed resource-exchange mechanism, we show the designedframe structures for sources m and f i ( f i F ) in Figs. 2 and 3, respectively. In addition,the following assumptions are made as in [ 15]:

Although source f i could choose to relay any ai symbols of one frame of source m, itwill only relay the rst a i symbols of the frame;

T T 0

a 1a K b1 bK

11

K

ii

L a b=

1K

ii

L b=

Fig. 2 Designed frame structure for source m

T T 0

a ib i L a ib i

Fig. 3 Designed frame structure for source f i

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Each relay will only forward the symbols originating from the cooperative partners andwill not forward the symbols originating from itself and then relayed by the cooperativepartners. It avoids the same symbols being relayed again by the same node.

One data symbol of source m can be forwarded by multiple relays, i.e., if source f i

as a relay forwards ai symbols originated from source m, and some of these symbolscan be also forwarded by other relays f j , f j F and f j = f i . The potential relay set{ f 1 , . . . , f K } for source m are arranged by source m in a descending order according totheir cooperation strategy {a 1 , . . . , a K }. So, a1 , . . . , a K .

Dene a K + 1 = 0. According to the former analysis, we can express the average rate fornode-pair m and M in one frame as

Ravgm = 1 L

K + 1

k = 2

(a k 1 ak ) RCm ,{ f 1 ,..., f k }, M + L a1 K

i = 1

bi RDm, M (20)

and the average rate for node-pair f i and F i in one frame as

Ravg f i = 1 L

bi RC f i ,m , F i + ( L a i bi ) RD f i , F i (21)

Consider each selsh node is willing to cooperate only if the average data-rate achievedthrough CR will not be lower than that achieved through DT by consuming the same amountof resource. That means if source m cannot reward source f i through the resource-exchange,i.e., Ravg f i < R

D f i , source f i will quit the CR selshly to save energy. In what follows, we

formulate the RA problem between sources m and { f 1 , . . . , f K } as a cooperative bargaininggame, whichcould provide a fair andefcient rate distribution amongthecooperativepartnersin the Pareto optimal sense.

4 Bargaining Game Model For CR Based RA

According to the cooperative bargaining game theory [ 19], we dene U = {m , f 1 , . . . , f K }be the set of bargainers in the discussed CR based RA problem. We also dene the symbol-times that a source is willing to use for the relaying purpose in one frame as its bargaining

strategy.In the proposed multiple user CR game (MU-CRG), we dene the disagreement pointfor node-pair m and M as RDm , M , and dene the disagreement point for node-pair f i andF i as RD f i , F i . According to the bargaining policy [19], if an agreement between sources mand f i cannot be reached, the payoffs/rates that the two sources will receive are given by

the disagreement points RDm , M , RD f i , F i . We denote the set of disagreement points in the

MU-CRG as R min = RDm, M , RD f 1 , F 1 , . . . , R

D f K , F K , and denote the set of feasible points of

the sources as R = Ravgm , Ravg f 1 , . . . , R

avg f K . The goal of the proposed MU-CRG is to get the

Pareto optimal rate allocation R = Ravgm , Ravg f 1 , . . . , Ravg f K for the cooperative sources. Inliteratures, the notion of Pareto optimal as a selection criterion for payoff/rate allocation canbe formally dened as follows [19].

Denition 1 The payoff/rate allocation R = R1 , R2 , . . . , RK for K bargainers issaid to be Pareto optimal, if and only if there is no other payoff/rate allocation

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R = R1 , R2 , . . . , RK that leads to superior performance for some bargainers withoutcausing performance deterioration for some other bargainers.

Pareto optimal RA can be found by solving the Nash bargaining solutions (NBSs) of the cooperative bargaining games [ 19]. The following Theorem 1 proves that there exists aunique NBS for the proposed MU-CRG.

Theorem 1 There exists a unique NBS for the proposed MU-CRG.

Proof According to [20], the MU-CRG will have a unique NBS if and only if the feasible setR = Ravgm , R

avg f 1 , . . . , R

avg f K is a closedconvex subset of

K + 1 . From (20)and (21),weknow

that Ravgm and Ravg f i , f i F are all liner functions of variables a i and bi , i {1, . . . , K },

and, the constraints for the variables are also liner. So, according to [ 21], we can concludethat R is a convex set.

We have proved that there is a unique NBS for the proposed MU-CRG. According to [ 19],the NBS to the MU-CRG can be acquired by solving the following optimization problem.

a 1 , . . . , a K , b1 , . . . , bK = arg max(a1 ,..., a K , b1 ,..., bK ) Ravgm RDm , M

K

i = 1

Ravg f i RD f i , F i

subject to : 0 a i L and 0 bi L, i {1, . . . , K }

L a1 K

i = 1

bi 0 (22)

Assuming global channel state information (CSI) is known by all the cooperative nodesas in [22,23], the NBS strategies (a 1 , . . . , a K , b1 , . . . , bK ) can then be acquired by thenodes by solving problem (22). However, a mathematical algorithm to search for the globaloptimal point of problem (22) has a very high computational complexity of O ( L2 K ) . Thus,it is prohibitive to nd the NBS for the proposed MU-CRG especially when the number of potential relays in the system is large. Considering the wireless nodes are laptops or smartphones which always have limited computing power, in what follows we propose a simpliedCR game, which could also deliver good performance for both cooperative partner nodes,and, more importantly, the NBS to the simplied CR game can be derived in closed-form.

So, the new game is featured with low computational complexity.

5 Simplied Multiuser CR Game

The simplication approach to the CR game is to restrict the cooperative partner for a nodee.g., source m to only one relay. It has recently been shown that most of the benets of cooperative diversity can be achieved with minimum overhead if a single best relay isselected to cooperate with a source [24]. So the SC rule is adopted in this paper as in [ 25].According to the SC rule, only one source f i from the potential relay set F will be selected as

the cooperative partner for source m, which should bring source m the maximum rate-gain.

5.1 Solving the SC-rule Based Cooperative Game

First, we assume source f i ( f i F ) is allowed to participate in the cooperation with sourcem , then the SC-rule based CR game, called the SC-CRG, is formulated. By ( 20), we canexpress the average rate of node-pair m and M in the SC-CRG as

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LT 0

b ia i L a ib i

Fig. 4 Frame structure for source m in the SC-CRG

Ravgm = 1 L

a i RCm , f i , M + ( L a i bi ) RDm , M (23)

where

RCm, f i , M = log2 1 + m, f i , M = log2 1 + m , f i f i , M

1 + m, f i + f i , M (24)

And, the frame structure for source m in the SC-CRG is depicted in Fig. 4.

Note that the rate expression Ravg f i and R

D f i , F i for source f i is the same as in ( 18) and (21),and its frame structure is also the same as in Fig. 3. These are omitted here. According to

Theorem 1, we know that for sources f i and m , the following SC-CRG problem will have aunique NBS.

a i , bi = arg max(a i ,bi ) Ravgm RDm , M R

avg f i R

D f i , F i

subject to : 0 a i L and 0 bi L, i {1, . . . , K }

L a i bi 0 (25)

Noting that the achievable SNRs are all wide-sense stationary, RCm , f i , M

, RDm , M

, RC f i ,m , F iand RD f i , F i are thus all constants during an RA cycle. Hence, the parameters to be optimized

in (25) are only a i and bi . For easy expression, we relax a i and bi as continuous values anddene

l = ai + bi , 0 l L

A = RDTm , M , B = RCRm , f i , M , C = R

DT f i , F i , and D = R

CR f i ,m , F i (26)

After substituting ( 26) into the objective function of problem ( 25), we take the rst-orderderivative of the objective function to a i and bi , respectively. By equating the derivations tozero, we have

(a i , bi ) =l2

C D

A B

+ 1 ,l2

A B

C D

+ 1 (27)

Now, we study the cases where the CR channels are better than the DT channels for boththe cooperative partners m and f i , which means B A > 0 and D C > 0. By jointlyconsidering the average data-rates achieved by sources m and f i shown in (21) and (23), wenote that, for sources m and f i , the data-rates achieved by utilizing one frame amount of resource for the DT will be denitely lower than that achieved by trading the frame resourcewith its cooperative partner for the CR. Since the transaction could always bring rate gainsfor both the cooperative partners m and f

i, so they have incentives to continue the trading

until the constraints for RA in ( 25) is reached. That means when

l = a i + bi = L (28)

the shared resource of the cooperative partners m and f i can be most efciently utilized. So,in such a case when B A > 0 and D C > 0, by substituting ( 28) into (27), the NBSbased RA for the cooperative partners m and f i can be obtained as

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a i , bi = L2

C D

A B

+ 1 , L2

A B

C D

+ 1 (29)

where is the oor function to remain a i and bi as integers.Next, we analyze another case, where one of the source-to-destinations relay channels is

worse than the DT channel, i.e., B A 0 or D C 0. Without loss of generality, weconsider B A 0. By observing ( 23), we note that, for source m , the data-rate achievedby trading one frame amount of resource for CR with source f i will be lower (or not better)than that achieved through the DT scheme. Hence, selsh source m has no incentive to tradeany resource for the CR with source f i . So it will set a i = 0 in the SC-CRG. In view of this,selsh source f i will also set bi = 0 correspondingly. Both the selsh actions of sources mand f i will result in

l = x i + x j = 0 (30)

So, in such cases B A 0 or D C 0, by substituting ( 30) into (27), the NBS basedRA for sources m and f i can be obtained as

a i , bi = (0, 0) (31)

It just corresponds to the prediction that all the selsh nodes retain the right to turn to the DTscheme if the cooperation can not compensate their rate loss.

5.2 Solving the Multiuser SC-CRG

In our game, the SC rule is imposed explicitly, and, the method of the SC-CRG is to restrictthe cooperative partner for source m to only one relay f i from the potential relay set F .Considering source m has the incentive to select the relay which could bring the maximumrate-gain, we denote the cooperative rate of source m achieved by solving problem (31) as

RNBSm, f i = 1 L

a i RCm, f i , M + L a i bi R

Dm (32)

Then, the optimal relay f i in the SC-CRG can be found by solving the following problem

i = arg maxi {1,..., K }

RNBSm, f i = 1 L

a i RCm, f i , M + L a i bi R

Dm (33)

Finally, the optimal solution for the multiuser SC-CRG can be achieved by solving ( 25)and (33) jointly which is with liner computational complexity of O ( K ) .

6 Relay Selection For Multiuser SC-CRG

In an ad hoc network consisting of K source-to-destination node-pairs, the primary objectiveof the RS is to pair the K sources as K / 2 cooperative partners for CR under the SC rule.However the pairing cannot be always success, since the possibility that two independent

sources choose each other as their cooperative partners for CR is only1

K 11

K 11

= 1

( K 1)2 (34)

For example, we assume that f 1 chooses f 2 as its cooperative partner in an RS-RA cycle,since f 2 could bring it the maximal rate gain by solving problems (25) and (33). However, it

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cannot be the symmetric case for f 2 to choose f 1 as its cooperative partner. As there are alsoK 1 potential relays for f 2 , the probability that f 1 brings f 2 the maximal rate gain is only1/( K 1). Specically, if f 2 chooses f 3 as the cooperative partner in that cycle the pairingof f 1 with f 2 is failure. As this kind of pairing failure spread across the whole network, it

will nally results in no pairing solution for the SC-rule based RS.In this paper, to implement the SC-rule based RS, i.e., to solve the above one-to-one

cooperative partner pairing problem, a simple heuristic which is explicitly imposed to paircooperative partners is proposed. The method of the heuristic is to assign each source adifferent priority at the network initialization stage. A source with a higher priority hasprivilege to select its cooperative partner. With the priority of each source being updated aftereach RS-RA cycle, the long-term priority fairness for the whole network can be guaranteed.In what follows, we summarize the proposed heuristic for the SC-rule based RS with theNBS based RA in Algorithm 1.

In Algorithm 1, we assume that there is a PS in the decentralized multiuser network. Themain objective of the PS is two folds:

Manage and distribute priority for cooperative partner selection for the sources in thenetwork;

Ensure that there are no malicious behavior of the selsh sources, e.g., denying loweringthe priority or tampering with a higher priority for the next RS-RA cycle.

The mechanisms for detecting and defending the malicious behaviors of selsh nodes havebeen studied in many works, e.g., [26], and, hence, are not discussed here. Note that the PSmay not necessarily be a central controller. For example, sources can follow a pre-denedprotocol to schedule their transmissions, or they can compete/cooperate with each other forthe RS priority.

Assuming the delay for the sources to wait the time scheduling of the PS and the CR basedCSMA/CA protocol is negligible, Algorithm 1 would be with a computational complexity

of O ( K 2 ) as there are totally K K 11 candidate cooperative partners in an K source-to-destination network.

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X

m

Y

M

f 1

f 3

(0,0)1500

1000500

f 2

F 1

F 2F 3

250 750 1250-250

250

250

500

-500

Fig. 5 Simulated CR system model

7 Simulation Results

To test the system performance of the proposed resource-exchange based RS-RA scheme,i.e., Algorithm 1, we set up a simulated multiuser ad hoc network as shown in Fig. 5, whichconsists of four source-to-destination node-pairs, including source m and its destination M ,source f 1 at (750, 250) and its destination F 1 at ( 250 , 250),source f 2 at (1,000, 0) and itsdestination F 2 at (0, 0), and source f 3 at (750, 250) and its destination F 3 at ( 250 , 250). Theunit is meter. As shadowing and small-scale channel fading are not considered, the channelsare determined merely by distance dependent large scale fading as in [10,11] and [14]. Thus,the Y coordinate of source m represents the nodes channel conditions. And, if the time-

varying fading is considered, the y-axis represents the channel conditions instead of the Y coordinate of source m. We set the path gain 0.097/ d 4 [12], where d is the distance froma transmitter to the receiver, and, the noise level for each wireless channel in the system 2 = 1 10 14 W. Since long-term priority fairness can be guaranteed by the proposed PS,we only analyze the result for one source-to-destination link (e.g., node-pair m and M ) aftereach RS-RA cycle, and the results can be extended to other links with different RS priorities.For that, we assign the highest RS priority always to source m in each RS-RA cycle, and wex the coordinates of destination M at (1,500, 0) and the X coordinate of source m at 500,respectively, while the Y coordinate of source m is varied from 1,000 to 1,000 at a step of 10. This simulation setup made us can focus on the rate performance variation of the link from source m to its destination M when the direct and the cooperative channels (relativeto other sources) varied. Finally, we select the frame length of the system as T = 5 ms, thetransmission energy of each node as E = 2.5 10 5 J, the number of symbols that can betransmitted within a frame-time L = 500. So the transmission power for each source can becomputed as 5 mW.

In Fig. 6, we show the individual data-rates achieved by node-pairs, f 1 and F 1 , f 2 andF 2and f 3 and F 3 in the SC-CRG [without performing the best RS ( 33)] and the DT schemes,respectively. And the data-rate achieved by node-pair m and M when source m cooperatingwith different relays is shown in Fig. 7. The unit of data-rate is bits/s/Hz.

From Figs. 6 and 7, we can see that when source m

moves along the line from (500, 1,000) to (500, 1,000) all the cooperative node-pairs could obtain rate-gains through theSC-CRG in comparison with the DT scheme. It demonstrates that the NBS results of theSC-CRG are Pareto optimal. It also justies that the proposed resource-exchange based RAcould stimulate selsh user nodes to share their energy and spectrum resource efciently.

Next, we take sources m and f 1 as an example to analyze the cooperative strategies of thesources in the network. The analysis for sources f 2 and f 3 can be conducted in a similar way

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Fig. 6 Data-rates of the sources as the relays for source m

Fig. 7 Data-rates of source m

and thus is omitted here. For cooperative partner sources m and f 1 , when 1,000 < Y < 520, the channel condition from source m to destination F 1 is poor. It means that source mcannot reward source f 1s CR through the resource-exchange, which results in that both thesources prefer to transmit independently, and, hence, can not get any rate-gains. As sourcem moves further from (500, 520) to (500, 40), both the sources could get rate-gains

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Fig. 8 CR strategies for different cooperative source-pairs in their two-user CR game

Fig. 9 Data-rate of source m in the multi-node game

through the CR, which owes to that the channel condition from source m to destinationF 1 become better and better within this region. Afterwards, when 40 < Y < 1,000, thechannel condition from source m to destination F 1 becomes worse and worse. Thus, both thecooperative sources m and f 1 denies the CR.

According to the above analysis, one can think that the channel condition of a particularsource in the CR based RA is its bargaining power towards other sources. Also taking sources

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Fig. 10 Data-rates of the relays/sources in the SC-CRG

m and f 1 as an example, we can observe from Fig. 8 that when source f 1 as a relay is with

better channel condition than its cooperative partner source m (e.g., source f 1 within therange 520 < Y < 380), it can contribute less energy and spectrum to source m , whichresults in a 1 < b1 within this region. Thereafter, as source m moves further from (500, 380)to (500, 40), source m is with better channel condition than that of source f 1 . The situationof sources m and f 1 reverse. Therefore, we observe from Fig. 8 that source m rewards lessenergy and spectrum to source f 1 , which results in b1 > a1 within this region. The results just agree to the fairness property of the bargaining game theory.

In Fig. 9, we show the achieved rate of source m in the multiuser SC-CRG by solvingproblems (25) and (33) jointly. Comparing Figs. 9 with 7, we can see that source m canalways choose the best source/relay to cooperate with from the potential relay set { f 1 , f 2 , f 3}.Therefore node-pair m and M could always achieve the optimal rate-gains from the CRaccording to the bargaining power of source m towards the available sources.

Next, the best RS algorithm (33) is jointly performed. In Fig. 10, we show the achievedrates of different cooperative relays/sources in the SC-CRG, respectively. In Fig. 11 , we showthe CR strategies adopted by the cooperative partner sources m and f i in the SC-CRG. Again,it demonstrates that the SC-CRG could bring a high spectrum and energy efciency for thedistributed selsh CR networks.

8 Conclusion

In this paper, we analyze the cooperation behavior of selsh nodes in distributed CR based adhoc networks. Without resorting to the conventional pricing or reputation based cooperationstimulating mechanisms, we propose a resource-exchange based mechanism by formulatingthe energy-efcient RS problem among selsh nodes as a cooperative game. Particularly, theexistence of a unique NBS to the CR game is proved. To further decrease the computational

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Fig. 11 Cooperative strategies of the source-pairs

complexity to solve the CR game, a simplied game approach is proposed. By restricting thecooperative partner for a source to only one relay from the potential relay set, the simpliedgame could bring the maximum rate-gain for the source. And, to implement the RS ruleimposed RS, a heuristic has also been developed, by which the long-term fairness for RS foreach node can be guaranteed. Finally, the simulation results show that the resource-exchangebased CR game is energy efcient in that both cooperative sides of the game could experiencebetter performance than they work independently.

Acknowledgments This work was fundedby theUK EPSRCProject DANCER(EP/K002643/1), theEUFP7Project MONICA(GA-2011-295222), the Priority Academic Program Development of Jiangsu Higher Edu-cation Institutions (PAPD), the Natural Science Foundation of Jiangsu Province of China (BK2012141), theNatural Science Foundation of China (51204176), and the Post Doctoral Fellowship Program of the China

Scholarship Council.

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Author Biographies

Guopeng Zhang received his Ph.D. from the School of Communi-cation Engineering at Xidian University, China, his M.Sc. from theSchool of Computer Science at South China Normal University, China,and his B.Sc. from the Department of Computer Science at Jiangsu(original Xuzhou) Normal University, China. He is currently a full-time researcher in the Internet of Things (IoT) Research Center, ChinaUniversity of Mining and Technology (CUMT), and conducts his post-doctoral research in the same institute. Before joining the CUMT in2009, he worked for about one year at the Nanjing branch of ZTE Cor-poration, with the research area of management software developmentfor operational networks. In 2012, he won the Post Doctoral FellowshipProgram from the China Scholarship Council. His main research inter-ests include micro and macro economics, game theory, wireless sen-sor networks, and cognitive radio networks etc. He has published morethan 30 journal papers. He is a member of IEEE.

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Kun Yang received his Ph.D. from the Department of Electronic andElectrical Engineering at University College London (UCL), UnitedKingdom, and his M.Sc. and B.Sc. from the Computer Science Depart-ment of Jilin University, China. He is currently a full professor in theSchool of Computer Science and Electronic Engineering, University

of Essex, United Kingdom. Before joining the University of Essex in2003, he worked at UCL on several European Union (EU) researchprojects for several years. His main research interests include hetero-geneous wireless networks, xed mobile convergence, pervasive ser-vice engineering, future Internet technology and network virtualization,and cloud computing. He manages research projects funded by vari-ous sources such as U.K. EPSRC, EU FP7, and industries. He has pub-lished more than 60 journal papers. He serves on the editorial boards of both IEEE and non-IEEE journals. He is a Fellow of IET, and a seniormember of IEEE.

Peng Liu received his Ph.D. from the School of Information and Elec-trical Engineering at CUMT, and his M.Sc. and B.Sc. from the Com-puter Science Department of Nanjing University, China. He is currentlyan associate professor in the IoT Research Center, CUMT. Before join-ing CUMT in 2003, he worked for ZTE Corporation between 1998and 2002 as a telecommunication products developer, with the researcharea of intelligent networks and soft-switch. His current research inter-ests include wireless cooperative communication, parallel cloud com-puting and their application in coal mine. He has published more than20 journal and conference papers.

Xiaolong Feng received his Ph.D., M.Sc. and B.Sc. from the Schoolof Information and Electrical Engineering at CUMT. He is currentlyan associate professor in the same institute. His main research interestsinclude wireless mesh networks and the application of wireless com-munication in coal mine. He has published more than 20 journal andconference papers.

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