Cooperative Relay in Cognitive Radio Networks:Decode-and-Forward or Amplify-and-Forward?

Donglin Hu and Shiwen MaoDept. ECE, Auburn University, Auburn, AL 36849-5201

Abstract—Cognitive radios (CR) and cooperative communica-tions represent new paradigms that both can effectively improvethe spectrum efficiency of future wireless networks. In this paper,we investigate the problem of cooperative relay in CR networksfor further improved network performance. The objective is toprovide an analysis for the comparison of two representativecooperative relay strategies, decode and forward (DF) and amplifyand forward (AF), in the context of CR networks. We consideroptimal spectrum sensing and p-Persistent CSMA for spectrumaccess, and derive closed-form expressions for network-widethroughput achieved by DF and AF. Our analysis is validatedby simulations. We find each of the strategies performs better ina certain parameter range; there is no case of dominance for thetwo strategies. The considerable gaps between the cooperativerelay results and the direct link results exemplify the diversitygain achieved by cooperative relays in CR networks.

I. INTRODUCTION

According to Cisco’s recent study, wireless data traffic isexpected to increase by a factor of 66 times by 2013. Muchof this future wireless data traffic will be video based servicesdriven by the need for ubiquitous access to wireless multi-media content. Such drastic increase in traffic demand willsignificantly stress the capacity of future wireless networks.

Cognitive radios (CR) provide an effective solution to meet-ing this critical demand, by exploiting co-deployed networksand aggregating underutilized spectrum for future wirelessnetworks [1], [2]. CR was motivated by the spectrum measure-ments by the FCC, where a significant amount of the assignedspectrum is found to remain underutilized. CR represents aparadigm change in spectrum regulation and access, from ex-clusive use by primary users to shared spectrum for secondaryusers, which can enhance spectrum utilization and achievehigh throughput capacity. Cooperative communications repre-sents another new paradigm for wireless communications [3],[4]. It allows wireless nodes assisting each other in informationdelivery, with the objective of gaining greater reliability andefficiency than they could obtain individually (i.e., to achievethe so-called cooperative diversity). It enables opportunisticuse of network energy and bandwidth, and delivers salientadvantages over legacy point-to-point communications.

Recently, there has been some interesting work on coop-erative relay in CR networks [5], [6]. In [5], the authorsconsidered the case of two single-user links, one primary andone secondary. The secondary transmitter is allowed to actas a “transparent” relay for the primary link, motivated bythe rationale that helping primary users will lead to moretransmission opportunities for CR nodes. In [6], the authorspresented an excellent overview of several cooperative relayscenarios and various related issues. A new MAC protocol was

proposed and implemented in a testbed to select a spectrum-rich CR node as relay for a CR transmitter/receiver pair.

In this paper, we investigate the problem of cooperativerelay in CR networks. We assume a primary network withmultiple licensed bands and a CR network consisting ofmultiple cooperative relay links. Each cooperative relay linkconsists of a CR transmitter, a CR relay, and a CR receiver.The objective is to provide an analysis for the comparison oftwo representative cooperative relay strategies, i.e., decode andforward (DF) and amplify and forward (AF), in the context ofCR networks. We first consider cooperative spectrum sensingby the CR nodes. We model both types of sensing errors, i.e.,miss detection and false alarm, and derive the optimal value forthe sensing threshold. Next, we incorporate DF and AF into thep-Persistent Carrier Sense Multiple Access (CSMA) protocolfor channel access for the CR nodes. We develop closed-formexpressions for the network-wide capacities achieved by DFand AF, respectively, as well as that for the case of direct linktransmission for comparison purpose.

Through analytical and simulation evaluations of DF andAF-based cooperative relay strategies, we find the analysisprovides upper bounds for the simulated results, which arereasonably tight. We also find cross-point with the AF andDF curves when some system parameter is varied, indicatingthat each of them performs better in a certain parameter range.There is no case that one completely dominates the other forthe two strategies. The considerable gaps between the coop-erative relay results and the direct link results exemplify thediversity gain achieved by cooperative relays in CR networks.

The remainder of this paper is organized as follows. Thesystem model is described in section II. We analyze the twoCR cooperative relay strategies in Section III. Our simulationevaluations are presented in Section IV. Related work isdiscussed in Section V and Section VI concludes the paper.

II. SYSTEM MODEL

We assume a primary network and a spectrum band that isdivided into M licensed channels, each modeled as a time slot-ted, block-fading channel. The state of each channel evolvesindependently following a discrete time Markov process [1].The status of channel m in time slot t is denoted as Sm(t),for m = 1, 2, · · · ,M . When Sm(t) = 0, the channel is in theidle state; when Sm(t) = 1, the channel is in the busy state(i.e., being used by primary users). Let λm and μm be thetransition probability to remain in state 0 and the transitionprobability from state 1 to 0 for channel m, respectively.The utilization of channel m with respect to primary usertransmissions, denoted by ηm = Pr{Sm(t) = 1}, can bewritten as: ηm = limT→∞ 1

T

∑Tt=1Sm(t) = 1−λm

1−λm+μm.

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There is a CR network colocated with the primary network.The CR network consists of N sets of cooperative relaylinks, each including a CR transmitter, a CR relay and a CRreceiver. Each CR node (or, secondary user) is equipped withtwo transceivers, each incorporating a software defined radio(SDR) that is able to tune to any of the M licensed channelsand a control channel and operate from there.

We assume CR nodes access the licensed channels followingthe same time slot structure [1]. Each time slot is divided intotwo phases, the sensing phase and the transmission phase.In the sensing phase, a CR node chooses one of the Mchannels to sense using one of its transceivers, and thenexchanges sensed channel information with other CR nodesusing the other transceiver over the control channel. During thetransmission phase, the CR transmitter and/or relay transmitdata frames on licensed channels that are believed to be idlebased on sensing results, using one or both of the transceivers.We consider cooperative relay strategies AF and DF, andcompare their performance in the following sections.

III. COOPERATIVE RELAY IN CR NETWORKS

In this section, we present an analysis of the cooperativerelay strategies in CR networks. We first examine cooperativespectrum sensing and derive the optimal sensing threshold.We then consider cooperative relay and spectrum access, andderive the network-wide throughput performance.

A. Spectrum Sensing

Although precise and timely channel state information isdesirable for spectrum access and primary user protection,continuous, full-spectrum sensing is both energy inefficientand hardware demanding [1]. Since each CR node is equippedwith two transceivers and one has to be used for distributingsensing results over the control channel, it can sense only oneof the channels at a time, using the remaining transceiver. Weassume that each CR node senses a fixed channel throughoutthe time slots and receives from the control channel sensingresults on other channels, i.e., distributed by other CR nodes.

During the sensing process, two kinds of detection errorsmay occur. With a false alarm, an idle channel is consideredbusy and a spectrum opportunity will be wasted. With a missdetection, a busy channel is considered idle, which may leadto collision with primary users. We adopt hypothesis test todetect the availability of channel m. The null hypothesis Hm

0is “channel m is idle.” The alternative hypothesis Hm

1 is“channel m is busy.” Let εm

i and δmi be the probabilities of

false alarm and miss detection, respectively, when CR nodei senses channel m. We have εm

i = Pr{Θmi = 1|Hm

0 } andδmi = Pr{Θm

i = 0|Hm1 }, where Θm

i ∈ {0, 1} is the channelm sensing result at node i.

Assume there are Nm CR nodes sensing channel m. Afterthe sensing phase, each CR node obtains a sensing resultvector �Θm = [Θm

1 ,Θm2 , · · · ,Θm

Nm] for channel m. The condi-

tional probability am(�Θm) on channel m availability is

am(Θm1 ,Θm

2 , · · · ,ΘmNm

) ∼= Pr{Hm0 |Θm

1 ,Θm2 , · · · ,Θm

Nm}

=Pr{Θm

1 ,Θm2 , · · · ,Θm

Nm|Hm

0 )}Pr{Hm0 }∑

j∈{0,1} Pr{Θm1 ,Θm

2 , · · · ,ΘmNm

|Hmj }Pr{Hm

j }

=∏Nm

i=1 Pr{Θmi |Hm

0 }Pr{Hm0 }∑

j∈{0,1}∏Nm

i=1 Pr{Θmi |Hm

j }Pr{Hmj }

=

[1 +

Pr{Hm1 }

Pr{Hm0 }

Nm∏i=1

Pr{Θmi |Hm

1 }Pr{Θm

i |Hm0 }

]−1

=

[1 +

ηm

1 − ηm

Nm∏i=1

(δmi )1−Θm

i (1 − δmi )Θ

mi

(εmi )Θm

i (1 − εmi )1−Θm

i

]−1

. (1)

If am(�Θm) is greater than a sensing threshold τm, channel mis believed to be idle; otherwise, channel m is believed to bebusy. The decision variable Dm is defined as follows.

Dm ={

0, if am(�Θm) > τm

1, if am(�Θm) ≤ τm.(2)

CR nodes only attempt to access channel m where Dm

is 0. Since function am(�Θm) in (1) has Nm binary variables,there can be 2Nm different combinations corresponding to 2Nm

values for am(�Θm). We sort the 2Nm combinations according

to their am(�Θm) values in the non-increasing order. Let a(j)m

be the jth largest function value and �θ(j)m the argument that

achieves the jth largest function value a(j)m , where �θ

(j)m =

[θm1 (j), θm

2 (j), · · · , θmNm

(j)].In the design of CR networks, we consider two objectives:

(i) how to avoid harmful interference to primary users, and(ii) how to fully exploit spectrum opportunities for the CRnodes. For primary user protection, we limit the collisionprobability with primary user with a threshold. Let γm be thetolerance threshold, i.e., the maximum allowable interferenceprobability with primary users on channel m. The probabilityof collision with primary users on channel m is given asPr{Dm = 0 | Hm

1 }; the probability of detecting an availabletransmission opportunity is Pr{Dm = 0 |Hm

0 }. Our objectiveis to maximize the probability of detecting available channels,while keeping the collision probability below γm, i.e.,

maxτm

Pr{Dm = 0|Hm0 } (3)

subect to: Pr{Dm = 0|Hm1 } ≤ γm. (4)

From their definitions, both Pr{Dm = 0 | Hm1 } and

Pr{Dm = 0 | Hm0 } are decreasing functions of τm. As

Pr{Dm = 0 | Hm1 )} approaches its maximum allowed value

γm, Pr{Dm = 0 | Hm0 } also approaches its maximum.

Therefore, solving the optimization problem (3) ∼ (4) isequivalent to solving Pr{Dm = 0 |Hm

1 } = γm. If τm = a(j)m ,

we have

Pr{Dm = 0|Hm1 }(a(j)

m ) = Pr{am(�Θm) > a(j)m |Hm

1 } (5)

=j−1∑l=1

Pr{am(�Θm)=a(l)m |Hm

1 }=j−1∑l=1

(δmi )1−θm

i (l)(1 − δmi )θm

i (l).

Obviously, Pr{Dm = 0 | Hm1 }(a(j)

m ) is an increasing function

of j. The optimal sensing threshold τ∗m can be set to a

(j)m ,

such that Pr{Dm = 0 | Hm1 }(a(j)

m ) ≤ γm and Pr{Dm =0 | Hm

1 }(a(j+1)m ) > γm. The algorithm for computing the

optimal sensing threshold τ∗m is presented in Table I.

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TABLE IALGORITHM FOR COMPUTING THE OPTIMAL SENSING THRESHOLD

1: Compute a(j)m and the corresponding �θ

(j)m , for all j;

2: Initialize τm = a(1)m and pc = Pr{am(�Θm) = a

(1)m |Hm

1 };3: Set j = 1;4: WHILE (pc ≤ γm)5: j = j + 1;

6: τm = a(j)m ;

7: pc = pc + Pr{am(�Θm) = a(j)m |Hm

1 };8: END WHILE

Once the optimal sensing threshold τ∗m is determined,

Pr{Dm = 0 | Hm1 } can be computed as given in (5) and

Pr{Dm = 0 | Hm0 } can be computed as:

Pr{Dm = 0|Hm0 } = Pr{am(�Θm) > τ∗

m|Hm0 } (6)

=j−1∑l=1

Pr{am(�Θm)=a(l)m |Hm

0 }=j−1∑l=1

(εmi )θm

i (l)(1 − εmi )1−θm

i (l).

B. Cooperative Relay

During the transmission phase, CR transmitters and relaysattempt to send data through the channels that are believed tobe idle. We assume fixed length data frames. Let Gk

1 and Gk2

denote the path gains from the transmitter to relay and fromthe relay to receiver, respectively, and let σ2

r,k and σ2d,k denote

the noise powers at the relay and receiver, respectively, for thekth cooperative relay link. We examine the two cooperationrelay strategies DF and AF, and direct link transmission below.

1) Decode-and-Forward: With DF, the CR transmittersends data frames to its relay in an odd time slot. Therelay decodes the data and forwards it to the receiver in thefollowing even time slot. The receiver can successfully decodethe frame if it is not lost or corrupted on both links. We assumea data frame can be successfully decoded if the received signal-to-noise ratio (SNR) is no less than a decoding threshold κ.We assume gains on different links are independent to eachother. The decoding rate of DF at the kth receiver, denotedby P k

DF , can be computed as,

P kDF = Pr

{(PsG

k1/σ2

r,k ≥ κ)

and(PrG

k2/σ2

d,k ≥ κ)}

= F̄Gk1

(σ2

r,kκ/Ps

)F̄Gk

2

(σ2

d,kκ/Pr

), (7)

where Ps and Pr are the transmit powers at the transmitter andrelay, respectively, F̄Gk

1(x) and F̄Gk

2(x) are the complementary

cumulative distribution functions (CCDF) of path gains Gk1

and Gk2 , respectively.

2) Amplify-and-Forward: With AF, the relay amplifies thereceived signal and forwards it to the receiver in the sametime slot. The relay receives data from the transmitter usingone transceiver operating on one or more idle channels; itforwards the data simultaneously to the receiver using the othertransceiver operating on one or more different idle channels.A data frame can be successfully decoded if the SNR at thereceiver is no less than κ. The decoding rate of AF at the kth

receiver, denoted as P kAF , can be computed as,

P kAF = Pr

{Pr

Gk1Ps + σ2

r,k

PsGk1Gk

2

σ2d,k

≥ κ

}

=∫ +∞

0

F̄Gk2

((Psx + σ2

r,k)σ2d,kκ

PsPrx

)dFGk

1(x). (8)

3) Direct Link Transmission: For comparison purpose, wealso consider the case of direct link transmission (DL), wherethe CR transmitter transmits to the receiver via the direct linkwithout using the relay. Let the path gain be Gk

0 with CCDFF̄Gk

0(x) for the kth direct link. Following similar analysis, the

decoding rate of DL at the kth receiver, denoted as P kDL, can

be computed as,

P kDL = Pr

{PsG

k0/σ2

d,k ≥ κ}

= F̄Gk0

(σ2

d,kκ/Ps

). (9)

C. Channel Access

We assume greedy transmitters that always have data tosend. The CR nodes use p-Persistent CSMA for channelaccess. At the beginning of the transmission phase of an oddtime slot, CR transmitters send Request-to-Send (RTS) withprobability p over the control channel. Since there are N CRtransmitters, the transmission probability p is set to 1/N tomaximize the throughput (i.e., to maximize P1 in (10) givenbelow). Three cases may occur:

• no CR transmitter sends RTS for channel access.• only one CR transmitter sends RTS, and it successfully

receives Clear-to-Send (CTS) from the receiver over thecontrol channel. It then accesses some of or all thechannels that are believed to be idle for data transmission.

• more than one CR transmitters send RTS and collisionoccurs on the control channel. No CR node can accessthe licensed channels.

Let P0, P1 and P2 denote the probability corresponding tothe three cases enumerated above, respectively. We have⎧⎨

⎩P0 = (1 − p)N = (1 − 1/N)N

P1 = Np(1 − p)N−1 = (1 − 1/N)N−1

P2 = 1 − P0 − P1.(10)

The CR cooperative relay link that wins the channels in theodd time slot will continue to use the channels in the followingeven time slot. A new round of channel competition will startin the next odd time slot following these two time slots.

Since a licensed channel is accessed with probability P1

in the odd time slot, we modify the tolerance threshold γm

as γ′m = γm/P1, such that the maximum allowable collision

requirement can still be satisfied. In the even time slot, thechannels will continue to be used by the winning cooperativerelay link, i.e., to be accessed with probability 1. Thereforethe tolerance threshold is still γm for even time slots.

D. Capacity Analysis

Once the CR transmitter wins the competition, as indicatedby received CTS, it begins to send data over the licensedchannels that are inferred to be idle (i.e., Dm = 0). We assumethe channel bonding and aggregation technique is used, suchthat multiple channels can be used collectively by a CR nodefor data transmission [7].

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With DF, the winning CR transmitter uses all the availablechannels to transmit to the relay in the odd time slot. In the fol-lowing even time slot, the CR transmitter stops transmission,while the relay uses the available channels in the even timeslot to forward data to the receiver. If the number of availablechannels in the even time slot is equal to or greater than that inthe odd time slot, the relay uses the same number of channelsto forward all the received data. Otherwise, the relay uses allthe available channels to forward part of the received data; theexcess data will be dropped due to limited channel resourcein the even time slot. The dropped data will be retransmittedin some future odd time slot by the transmitter.

With AF, no matter it is an odd or even time slot, the CRtransmitter always uses half of the available licensed channelsto transmit to the relay. The relay uses one of its transceiversto receive from the chosen half of the available channels.Simultaneously, it uses the other transceiver to forward thereceived data to the receiver using the remaining half of theavailable channels. Let Dod

m and Devm be the decision variables

of channel m in the odd and even time slot, respectively (see(2)). Let Sod

m and Sevm be the status of channel m in the odd

and even time slot, respectively. We have,

Pr{Dodm = i, Sod

m = j,Devm = k, Sev

m = l} (11)

= Pr{Devm = k|Sev

m = l}Pr{Dodm = i|Sod

m = j} ×Pr{Sev

m = l|Sodm = j}Pr{Sod

m = j}, for i, j, k, l ∈ {0, 1}.where Pr{Sod

m = j} are the probabilities that channel mis busy or idle, Pr{Sev

m = l | Sodm = j} are the channel

m transition probabilities. Pr{Devm = k | Sev

m = l} andPr{Dod

m = i | Sodm = j} can be computed as in (5) and (6).

Let NDF , NAF and NDL be the number of frames success-fully delivered to the receiver in the two consecutive time slotsusing DF, AF and DL, respectively. Define S̄od

m = 1 − Sodm ,

S̄evm = 1−Sev

m , D̄odm = 1−Dod

m and D̄evm = 1−Dev

m . We have⎧⎪⎪⎪⎨⎪⎪⎪⎩

NDF =(∑M

m=1S̄odm D̄od

m

)∧(∑M

m=1S̄evm D̄ev

m

)NAF =

⌊12

∑Mm=1S̄

odm D̄od

m

⌋+⌊

12

∑Mm=1S̄

evm D̄ev

m

⌋NDL =

(∑Mm=1S̄

odm D̄od

m

)+(∑M

m=1S̄evm D̄ev

m

),

(12)

where x ∧ y represents the minimum of x and y, and �x�means the maximum integer that is not larger than x.

As discussed, the probability that a frame can be success-fully delivered is P k

DF , P kAF , or P k

DL for the three schemes,respectively. Recall that time slot/channels are allocated dis-tributedly every two time slots. We derive the capacity for thethree schemes as⎧⎪⎨⎪⎩

CDF = E [NDF ] ·∑Nk=1(P

kDF P1L)/(2NTs)

CAF = E [NAF ] ·∑Nk=1(P

kAF P1L)/(2NTs)

CDL = E [NDL] ·∑Nk=1(P

kDLP1L)/(2NTs),

(13)

where L is the packet length and Ts is the duration of a timeslot. The expectations are computed using (11) ∼ (12).

IV. PERFORMANCE EVALUATION

We evaluate the performance of the cooperative relay strate-gies with analysis and simulations. The analytical capacities of

TABLE IISIMULATION PARAMETERS

Symbol Value DefinitionM 5 number of licensed channelsλ 0.7 channel transition probability from idle to idleμ 0.2 channel transition probability from busy to idleη 0.6 channel utilizationγ 0.08 maximum allowable collision probabilityN 7 number of CR cooperative relay linksPs 10 dBm transmit power of the CR transmittersPr 10 dBm transmit power of CR relaysL 1 kb packet lengthTs 1 ms duration of a time slot

the schemes are obtained as in Section III. The actual through-put is obtained using MATLAB simulations. The simulationparameters are listed in Table II, unless specified otherwise.We consider five licensed channels and a CR network withseven cooperative relay links. The channels have identicalparameters for the Markov chain models. Each point in thesimulation curves is the average of 10 simulation runs withdifferent random seeds. We plot 95% confidence intervals forthe simulation results, which are negligible in all the cases.

We first examine the impact of the number of licensedchannels. To illustrate the effect of spectrum sensing, we letthe decoding rate P k

AF be equal to P kDF . In Fig. 1(a), we plot

the throughput of AF, DF, and DL under increased number oflicensed channels. The analytical curves are upper bounds forthe simulation curves in all the cases, and the gap betweenthe two is reasonably small. Furthermore, as the number oflicense channels is increased, the throughput of both AF andDF are increased. The slope of the AF curves is larger thanthat of the DF curves. There is a cross point between fiveand six, as predicted by both simulation and analysis curves.This indicates that AF outperforms DF when the number ofchannels is large. This is because AF is more flexible thanDF in exploiting the idle channels in the two consecutive timeslots. The DL analysis and simulation curves also increaseswith the number of channels, but with the lowest slope andthe lowest throughput values.

In Fig. 1(b), we demonstrate the impact of channel utiliza-tion on the throughput of the schemes. The channel utilizationη is increased from 0.3 to 0.9, when primary users get moreactive. As η is increased, the transmission opportunities forCR nodes are reduced and all the throughputs are degraded.We find the throughputs of AF and DF are close to each otherwhen the channel utilization is high. AF outperforms DF inthe low channel utilization region, but is inferior to DF in thehigh channel utilization region. There is a cross point betweenthe AF and DF curves between η = 0.5 and η = 0.6. Whenthe channel utilization is low, there is a big gap between thecooperative relay curves and and the DL curves.

In Fig. 1(c), we examine the channel fading factor. Weconsider Rayleigh block fading channels, where the receivedpower is exponentially distributed with a distance-dependentmean. We fix the transmitter power at 10 dBm, and increasethe relay power from one dBm to 18 dBm. As the relay poweris increased, the throughput is also increased since the SNR atthe receiver is improved. We can see the increasing speed ofAF is larger than that of DF, indicating that AF has superiorperformance than DF when the relay transmit power is large.The capacity analysis also demonstrate the same trend. The

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3 4 5 6 7 8 90

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Number of channels

Thr

ough

put (

Mbp

s)AF throughput (simulation)DF throughput (simulation)DL throughput (simulation)AF capacity (analysis)DF capacity (analysis)DL capacity (analysis)

(a) Number of licensed channels

0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Channel Utilization (η)

Thr

ough

put (

Mbp

s)

AF throughput (simulation)DF throughput (simulation)DL throughput (simulation)AF capacity (analysis)DF capacity (analysis)DL capacity (analysis)

(b) Primary user channel utilization

0 5 10 15 200

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Relay’s Transmit Power (dBm)

Thr

ough

put (

Mbp

s)

AF throughput (simulation)DF throughput (simulation)DL throughput (simulation)AF capacity (analysis)DF capacity (analysis)DL capacity (analysis)

(c) Transmit power of relay nodes

Fig. 1. Throughput performance versus system parameters.

throughput of DL does not depend on the relay node. Itsthroughput is better than that of AF and DF when the relaytransmit power is low, since both AF and DF are limited bythe relay-to-receiver link in this low power region. However,the throughputs of AF and DF quickly exceed that of DLand grow fast as the relay-to-receiver link is improved withthe increased relay transmit power. The considerable gapsbetween the cooperative relay link curves and the DL curves inFigs. 1(a), 1(b) and 1(c) exemplify the diversity gain achievedby cooperative relays in CR networks.

V. RELATED WORK

The theoretical foundation of relay channels was laid bythe seminal work [8]. The capacities of the Gaussian relaychannel and certain discrete relay channels are evaluated, andthe achievable lower bound to the capacity of the generalrelay channel is established in this work. In [3], the au-thors described cooperative diversity, where diversity gainsare achieved via the cooperation of mobile users. In [4], theauthors developed and analyzed low-complexity cooperativediversity protocols. Several cooperative strategies, includingAF and DF, were described and their performance characteri-zations were derived in terms of outage probabilities.

In practice, there is a restriction that each node cannottransmit and receive simultaneously in the same frequencyband. The “cheap” relay channel concept was introducedin [9], where the authors derived the capacity of the Gaussiandegraded “cheap” relay channel. Multiple relay nodes for atransmitter-receiver pair are investigated in [10] and [11]. Theauthors showed that, when compared with complex protocolsthat involve all relays, the simplified protocol with no morethan one relay chosen can achieve the same performance. Thisis the reason why we consider single relay in this paper.

In [12], Ng and Yu proposed a utility maximization frame-work for joint optimization of node, relay strategy selection,and power, bandwidth and rate allocation in a cellular network.Cai et al. [13] presented a semi-distributed algorithm for AFrelay networks. A heuristic was adopted to select relay andallocate power. Both AF and DF were considered in [14],where a polynomial time algorithm for optimal relay selectionwas developed and proved to be optimal. In [15], a protocolis proposed for joint routing, relay selection, and dynamicspectrum allocation for multi-hop CR networks, and its per-formance is evaluated through simulations.

VI. CONCLUSION

In this paper, we studied the problem of cooperative relay inCR networks. We modeled the two cooperative relay strategies,i.e., DF and AF, which are integrated with p-Persistent CSMA.We analyzed their throughput performance and compared themunder various parameter ranges. Cross-point with the AF andDF curves are found when some parameter is varied, indicatingthat each of them performs better in a certain parameter range;there is no case of dominance for the two strategies.

ACKNOWLEDGMENT

This work is supported in part by the NSF under GrantsECCS-0802113, IIP-0738088 and IIP-1032002.

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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.