Coop sens transm

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A Cooperative Sensing Based Cognitive Relay TransmissionScheme without a Dedicated Sensing Relay Channel in

Cognitive Radio NetworksYulong Zou, Student Member, IEEE, Yu-Dong Yao, Senior Member, IEEE, Baoyu Zheng, Member, IEEE

Abstract—In this paper, we investigate a selective relay spectrum sensingand best relay data transmission (SRSS-BRDT) scheme for multiple-relaycognitive radio networks. Specifically, in the spectrum sensing phase,only selected cognitive relays are utilized to transmit/forward their initialdetection results (without a dedicated sensing relay channel) to a cognitivesource for fusion, where the dedicated sensing channel refers to thechannel transmitting initial spectrum sensing results from cognitive relaysto the cognitive source. In the data transmission phase, only the best relayis selected to assist the cognitive source for its data transmissions. Byjointly considering the two phases, we derive a closed-form expressionof the outage probability for the SRSS-BRDT scheme over Rayleighfading channels. We show that the SRSS-BRDT scheme outperformsthe traditional cognitive transmission scheme (with a limited dedicatedsensing channel) in terms of the outage probability performance. Inaddition, numerical results illustrate that the outage probability of theSRSS-BRDT scheme can be minimized through an optimal allocation ofthe time durations between the spectrum sensing and data transmissionphases.

Index Terms—Cooperative sensing, cognitive transmission, cognitiveradio, cognitive relay, outage probability.

I. INTRODUCTION

COgnitive radio is proposed as a means to improve the utiliza-tion of wireless spectrum resources, which enables unlicensed

users to communicate with each other over licensed bands (throughspectrum holes) [1], [2]. As discussed in [3], [4], [5], each cognitivetransmission process requires two essential phases: 1) a spectrumsensing phase, in which a cognitive source attempts to detect anavailable spectrum hole; and 2) a data transmission phase, in whichsecondary data traffic (of the cognitive source) is transmitted to thedestination through the detected spectrum hole. The two individualphases have been studied extensively in terms of different sensing [6]- [12] or different transmission [13] - [19] techniques.

However, as mentioned in [3], [4], [5], the spectrum sensingand data transmission phases can not be designed and optimizedin isolation since the two phases affect each other. In [3], theauthors focus on the maximization of secondary throughput under theconstraint of primary user protection over additive white Gaussian

Copyright (c) 2010 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected].

Y. Zou is with the Institute of Signal Processing and Transmission, Nan-jing University of Posts and Telecommunications, Nanjing, Jiangsu 210003,China, and with the Electrical and Computer Engineering Department,Stevens Institute of Technology, Hoboken, NJ 07030, USA. Tel: (+1)201-216-8907. Fax: (+1)201-216-8246. E-mail: {[email protected],[email protected].}

Y.-D. Yao is with the Electrical and Computer Engineering Department,Stevens Institute of Technology, Hoboken, NJ 07030, USA. Tel: (+1)201-216-5264. Fax: (+1)201-216-8246. E-mail: {[email protected].}

B. Zheng are with the Institute of Signal Processing and Transmission, Nan-jing University of Posts and Telecommunications, Nanjing, Jiangsu 210003,China.

This work was partially supported by the Postgraduate Innovation Pro-gram of Scientific Research of Jiangsu Province (Grant Nos. CX08B 080Z,CX09B 150Z) and the National Natural Science Foundation of China (GrantNo. 60972039).

noise (AWGN) channels. In [4], we have explored the sensing-and-transmission tradeoff issue over Rayleigh fading channels andshown that the outage probability of cognitive transmissions can beminimized through the optimization of spectrum sensing overhead.Furthermore, we have investigated the cognitive transmissions withmultiple relays in [5], where multiple cognitive relays are availableto assist a cognitive source for both the spectrum sensing and datatransmissions. In [5], we first propose a fixed fusion spectrum sensingand best relay data transmission (FFSS-BRDT) scheme and showthat, as the number of cognitive relays increases, the performanceof the FFSS-BRDT scheme improves initially and then begins todegrade when the number of cognitive relays is larger than a certainvalue. We then propose a selective fusion spectrum sensing and bestrelay data transmission (SFSS-BRDT) scheme, which performs betterthan FFSS-BRDT scheme. Moreover, the performance of SFSS-BRDT always improves as the number of cognitive relays increases.

Notice that both the FFSS-BRDT and SFSS-BRDT schemesemploy the traditional cooperative sensing framework [8] - [11],where a dedicated channel is used when the cognitive relays forwardtheir initial detection results to the cognitive source for fusion.This is somehow against the cognitive radio design principle, sincecognitive radio is supposed to reuse the unoccupied licensed spectrumwithout dedicated channel (or, with very limited dedicated channelresources). Recently, in [12], we have proposed a selective-relaybased cooperative sensing scheme, which can save the dedicatedchannel without receiver operating characteristics (ROC) performancedegradation. In this paper, we consider the use of such a selectiverelay spectrum sensing scheme for cognitive transmissions to removethe dedicated sensing relay channel. The main contributions of thispaper are described as follows. First, we propose a selective relayspectrum sensing and best relay data transmission (SRSS-BRDT)scheme, where only selected cognitive relays are utilized to transmittheir initial detection results to a cognitive source for fusion andonly the best relay is used to assist the cognitive source for itsdata transmissions. Secondly, jointly considering both the spectrumsensing and data transmission phases, we derive a closed-formexpression of the outage probability for the SRSS-BRDT scheme.Finally, we show that the proposed SRSS-BRDT scheme can achievea better outage probability performance, compared to the traditionalSFSS-BRDT scheme with a limited dedicated channel resource.

The remainder of this paper is organized as follows. In SectionII, we propose the SRSS-BRDT scheme for multiple-relay cognitiveradio networks. Section III derives a closed-form expression of theoutage probability for the proposed SRSS-BRDT scheme. Next, inSection IV, we conduct numerical outage probability evaluations forthe SFSS-BRDT and SRSS-BRDT schemes. Finally, we provideconcluding remarks in Section V.


Fig. 1. Coexistence of a primary network and a cognitive radio network.

Fig. 2. Cognitive transmission protocol of the proposed selective fusionspectrum sensing and best relay data transmission (SFSS-BRDT) scheme.

II. PROPOSED SFSS-BRDT SCHEME IN COGNITIVE RADIO

NETWORKS

A. System Description

As shown in Fig. 1, we consider a cognitive radio network, wheremultiple cognitive relays (CRs) are available to assist a cognitivesource (CS) for both the spectrum sensing and data transmissionphases. Following [13] and [14], a half-duplex relaying mode isadopted for CRs. Notice that there are M CRs denoted by R ={CRi|i = 1, 2, · · · , M}. Fig. 2 shows the transmission protocolof the proposed selective relay spectrum sensing and best relaydata transmission scheme. As seen from Fig. 2, each cognitivetransmission process of the proposed SRSS-BRDT scheme includestwo phases (i.e., the spectrum sensing and data transmission phases),where the parameter α is referred to as spectrum sensing overhead,which can be adjusted to optimize the performance of cognitivetransmissions.

Fig. 2 depicts that the spectrum sensing phase consists of two sub-phases. In the first sub-phase, CS and CRs independently detect thepresence of a primary user (PU). Then, in the subsequent sub-phase,all CRs encode their initial detection results with an error detectioncode (such as, cyclic redundancy code), and transmit their encodedbits to CS over M orthogonal primary licensed sub-channels (insteadof a dedicated channel), which will potentially interfere PU. In orderto mitigate this interference, we consider the use of a selectiverelay spectrum sensing (SRSS) scheme [12], where each cognitiverelay (CR) forwards its initial detection result in a selective fashion.Specifically, if a CR detected the absence of PU in its detection phase,it will transmit a CRC-encoded indicator signal to CS; otherwise,nothing is transmitted from the CR to avoid interfering PU. Then,CS will perform CRC checking for the received signals from allthe M orthogonal sub-channels. If the CRC checking is successfulover i-th orthogonal sub-channel, CS will consider the absence ofPU as the initial result detected by CRi; otherwise, it will considerthe presence of PU as the CRi’s initial detection result. Accordingly,in the SRSS scheme, a CR will interfere the primary transmissionsonly if it fails to detect the presence of the primary user when PU isactive. It has been proven in [12] that this interference is controllableand can be reduced to satisfy any given primary quality-of-service(QoS) requirement.

In the data transmission phase, there are also two sub-phases. Ifa spectrum hole was detected earlier (in the sensing phase), CS will

start transmitting its data to CD and CRs in the first data transmissionsub-phase. Then, all CRs attempt to decode the CS’ signal and thoseCRs which decode successfully constitute a set D, called a decodingset. Accordingly, the sample space of all the possible decodingsets is described as {∅ ∪ Dm, m = 1, 2, · · · 2M − 1}, where ∪represents an union operation, ∅ is an empty set, and Dm is a non-empty subcollection of the M cognitive relays. In the second datatransmission sub-phase, if the decoding set (D) is not empty, the bestrelay (i.e., with the highest instantaneous signal-to-interference-and-noise ratio) chosen within the decoding set will forward its decodedresult to CD. If D is empty, i.e., no relay is able to decode the CS’signal successfully, CS will repeat the transmission of the originalsignal to CD through its direct link. Finally, CD combines the twocopies of received signals by using maximum ratio combining (MRC)method.

B. Signal Modeling

In the following, we formulate the signal model for the proposedSRSS-BRDT scheme. The transmit powers of the primary user andsecondary users are denoted by Pp and Ps, respectively. Let Hp(k)represent, for time slot k, whether or not there is a spectrum hole.Specifically, Hp(k) = H0 represents that a spectrum hole is availablefor secondary users; otherwise, Hp(k) = H1. We model Hp(k)as a Bernoulli random variable with parameter Pa (the probabilityof the channel being available), i.e., Pr(Hp(k) = H0) = Pa andPr(Hp(k) = H1) = 1−Pa. In addition, the time-bandwidth productof the licensed channel is denoted by BT . In the first sub-phase oftime slot k, the signal received at CS is expressed as

ys(k, 1) =√

Pphps(k)θ(k, 1) + ns(k, 1) (1)

where hps(k) is the fading coefficient of the channel from PU to CS,ns(k, 1) is AWGN with zero mean and variance N0, and θ(k, 1) isdefined as

θ(k, 1) =

{0, Hp(k) = H0

xp(k, 1), Hp(k) = H1

where xp(k, 1) is the transmit signal of PU in the first sub-phaseof time slot k. Notice that Hp(k) = H0 denotes that the channel isunoccupied by PU and nothing is transmitted from PU, and Hp(k) =H1 represents that a PU signal is transmitted. Meanwhile, the signalreceived at CRi is written as

yi(k, 1) =√

Pphpi(k)θ(k, 1) + ni(k, 1), i = 1, 2, · · · , M (2)

where hpi(k) is the fading coefficient of the channel from PU to CRi

and ni(k, 1) is AWGN with zero mean and variance N0. Based on thereceived signals as given by Eq. (1) and Eq. (2), CS and CRi obtaintheir initial detection results, denoted by Hs(k, 1) and Hi(k, 1),respectively. Then, in the subsequent sub-phase, CRi transmits asignal βi(k) over the corresponding orthogonal sub-channel and thereceived signal at CS can be written as

yis(k, 2) =

√Pshis(k)βi(k) +

√Pphps(k)θ(k, 2) + ni

s(k, 2)

i = 1, 2, · · · , M(3)

where his(k) and hps(k) are, respectively, the fading coefficients ofthe channel from CRi to CS and that from PU to CS, and βi(k) andθ(k, 2) are defined as

βi(k) =

{xi(k), Hi(k, 1) = H0

0, Hi(k, 1) = H1

where xi(k) is an indicator signal that is encoded by a CRC code,and

θ(k, 2) =

{0, Hp(k) = H0

xp(k, 2), Hp(k) = H1


where xp(k, 2) is the transmit signal of PU in the second sub-phaseof time slot k. From Eq. (3), CS attempts to decode the signal βi(k)and perform CRC checking. As known in [13] - [15], if the channelcapacity is below a required data rate, an outage event is said tooccur and the decoder fails to recovery the original signal no matterwhat decoding algorithm is adopted. In this case, the CRC checkingis assumed to fail and CS will consider that no indicator signal istransmitted from CRi, i.e., the corresponding initial detection resultreceived at CS from CRi is given by Hi(k, 2) = H1; otherwise,Hi(k, 2) = H0. Accordingly, we obtain

Hi(k, 2) =

{H1, Θis(k, 2) = 1

H0, Θis(k, 2) = 0(4)

where Θis(k, 2) = 1 denotes that an outage event occurs over thechannel from CRi to CS and Θis(k, 2) = 0 represents the othercase. In an information-theoretic sense [12] - [15], the outage eventΘis(k, 2) = 1 can be described from Eq. (3) as

Θis(k, 2) = 1 :α

2Mlog2(1 +

|his(k)|2γs|βi(k)|2

|hps(k)|2γp|θ(k, 2)|2 + 1) <

1

BT(5)

where γs = Ps/N0, γp = Pp/N0, and BT is the time-bandwidthproduct of the licensed channel. Finally, CS combines all Hi(k, 2)and its own initial detection result Hi(k, 1) through a given fusionrule, leading to its final decision, Hs(k). Considering an “AND” rule,the final decision Hs(k) can be expressed as

Hs(k) = Hi(k, 1)M⊗

i=1Hi(k, 2) (6)

where ⊗ represents the logic AND operation. Next, we focus on thesignal modeling for the data transmission phase. In the first part ofthe data transmission, i.e., the third sub-phase of time slot k, thesignal received at CD is expressed as

yd(k, 3) =√

Pshsd(k)β(k, 3)+√

Pphpd(k)θ(k, 3)+nd(k, 3) (7)

where hsd(k) and hpd(k) are the fading coefficients of the channelfrom CS to CD and that from PU to CD, respectively, and theparameters β(k, 3) and θ(k, 3) are defined as

β(k, 3) =

{xs(k), Hs(k) = H0

0, Hs(k) = H1

and

θ(k, 3) =

{0, Hp(k) = H0

xp(k, 3), Hp(k) = H1

where xs(k) and xp(k, 3) are the transmit signals of CS and PU,respectively. Meanwhile, the signal received at CRi can be writtenas

yi(k, 3) =√

Pshsi(k)β(k, 3) +√

Pphpi(k)θ(k, 3) + ni(k, 3) (8)

where hsi(k) and hpi(k) are the fading coefficients of the channelfrom CS to CRi and that from PU to CRi, respectively. In the fourthsub-phase, there are two possible cases for the data transmissiondepending on whether or not the decoding set (D) is empty. Forsimplicity, let D = ∅ represent the first case of an empty decodingset and D = Dm correspond to the other case, where Dm is a non-empty subcollection set of all CRs.

• Case D = ∅: This case corresponds to the scenario where all

CRs fail to decode the signal from CS, implying

(1 − α)

2log2(1 +

|hsi(k)|2 γs |β(k, 3)|2

|hpi(k)|2 γp |θ(k, 3)|2 + 1) < Rs (9)

where Rs is the data transmission rate of CS. In the given caseD = ∅, CS will determine whether or not to repeat the transmissionof signal xs(k) to CD depending on its final spectrum sensing resultHs(k), and thus the received signal at CD is given by

yd(k, 4|D = ∅) =√

Pshsd(k)β(k, 4)+√

Pphpd(k)θ(k, 4)+nd(k, 4)(10)

where

β(k, 4) =

{xs(k), Hs(k) = H0

0, Hs(k) = H1

and

θ(k, 4) =

{0, Hp(k) = H0

xp(k, 4), Hp(k) = H1

By combining Eq. (7) and Eq. (10) with the MRC method, CD canachieve an enhanced signal version with a signal-to-interference-and-noise ratio (SINR) as

SINRd(D = ∅) =|hsd(k)|2 γs |β(k, 3)|2 + |hsd(k)|2 γs |β(k, 4)|2

|hpd(k)|2 γp |θ(k, 3)|2 + |hpd(k)|2 γp |θ(k, 4)|2 + 2(11)

• Case D = Dm: This case corresponds to the scenario where

CRs in decoding set Dm are able to decode CS’ signal successfully,i.e.,

(1 − α)

2log2(1 +

|hsi(k)|2 γs |β(k, 3)|2

|hpi(k)|2 γp |θ(k, 3)|2 + 1) > Rs, i ∈ Dm

(1 − α)

2log2(1 +

|hsj(k)|2 γs |β(k, 3)|2

|hpj(k)|2 γp |θ(k, 3)|2 + 1) < Rs, j ∈ Dm

(12)

where Dm = R−Dm is the complementary set of Dm. In this case,the cognitive relay, which can successfully decode the CS’ signal andcan achieve the highest received SINR at CD, is viewed as the “best”one and selected to forward the CS’ signal to CD. Therefore, in thegiven case D = Dm, the combined SINR at CD is given by

SINRd(D = Dm)

= maxi∈Dm

|hsd(k)|2 γs + |hid(k)|2 γs

|hpd(k)|2 γp |θ(k, 3)|2 + |hpd(k)|2 γp |θ(k, 4)|2 + 2(13)

where Dm is the decoding set. One can observe from Eq. (13) thatthe best cognitive relay selection criterion takes into account thechannel state information |hsd(k)|2, |hid(k)|2 and |hpd(k)|2. UsingEq. (13), we can further develop a specific relay selection algorithmin a centralized or distributed manner [17] - [20]. To realize the bestcognitive relay selection, we can utilize a fraction of the detectedspectrum holes of a licensed primary channel, instead of a dedicatedcontrol channel, for coordinating the different cognitive relays. Notethat, if no spectrum hole is found, we do not need a dedicated channelfor the best relay selection algorithm, since the cognitive source willnot start transmitting data traffic in this case.

III. OUTAGE PROBABILITY ANALYSIS OF SFSS-BRDT SCHEME

In this section, we derive a closed-form outage probability expres-sion for the SRSS-BRDT scheme over Rayleigh fading channels.Following [13] - [15], an outage event is considered to occur whenchannel capacity falls below a predefined data transmission rate R.Accordingly, the outage probability of the proposed SRSS-BRDT


scheme is calculated as

Pout =Pr

{1 − α

2log2(1 + SINRd) < Rs

}=Pr{SINRd(D = ∅) < γs∆, D = ∅}

+

2M−1∑m=1

Pr{SINRd(D = Dm) < γs∆, D = Dm}

(14)

where ∆ = [22Rs/(1−α) − 1]/γs, SINRd(D = ∅) and SINRd(D =Dm) are given by Eq. (11) and Eq. (13), respectively. According toEq. (9) and Eq. (11), the term Pr{SINRd(D = ∅) < γs∆, D = ∅}in the second equation of Eq. (14) can be expanded as

Pr{SINRd(D = ∅) < γs∆, D = ∅}

= Pa(1 − Pfs) Pr{|hsd(k)|2 < ∆}M∏

i=1

Pr{|hsi(k)|2 < ∆}

+ (1 − Pa)(1 − Pds) Pr{|hsd(k)|2 − |hpd(k)|2γp∆ < ∆}

×M∏

i=1

Pr{|hsi(k)|2 − |hpi(k)|2γp∆ < ∆}

+ PaPfs + (1 − Pa)Pds

(15)

where Pa = Pr{Hp(k) = H0} is the probability that there is aspectrum hole, Pds = Pr{Hs(k) = H1|Hp(k) = H1} and Pfs =Pr{Hs(k) = H1|Hp(k) = H0} are, respectively, the probabilitiesof overall detection and false alarm of the PU’s presence at CS afterfinal fusion, as shown in Eq. (6). Besides, the probabilities in Eq.(15) (e.g., Pr{|hsi(k)|2 < ∆}, Pr{|hsd(k)|2−|hpd(k)|2γp∆ < ∆},and so on) can be easily calculated with closed-form solutions,since random variables |hsd(k)|2, |hpd(k)|2, |hsi(k)|2 and |hpi(k)|2follow exponential distributions and are independent from each other.From Eq. (12) and Eq. (13), the term Pr{SINRd(D = Dm) <γs∆, D = Dm} in the second equation of Eq. (14) is found as

Pr{SINRd(D = Dm) < γs∆, D = Dm}= Pa(1 − Pfs) Pr{max

i∈Dm

|hid(k)|2 < 2∆ − |hsd(k)|2}

×∏

i∈Dm

Pr{|hsi(k)|2 > ∆}∏

j∈Dm

Pr{|hsj(k)|2 < ∆}

+ (1 − Pa)(1 − Pds)

× Pr{maxi∈Dm

|hid(k)|2 < 2∆ − |hsd(k)|2 + 2|hpd(k)|2γp∆}

×∏

i∈Dm

Pr{|hsi(k)|2 − |hpi(k)|2γp∆ > ∆}

×∏

j∈Dm

Pr{|hsj(k)|2 − |hpj(k)|2γp∆ < ∆}

(16)

where the closed-form solution to Pr{maxi∈Dm

|hid(k)|2 < 2∆ −|hsd(k)|2 + 2|hpd(k)|2γp∆} has been derived as given by Eq. (24)in [20]. Now, we start the analysis of the probabilities of overalldetection and false alarm of the PU’s presence at CS, i.e., the termsPds and Pfs as given in Eq. (15) and Eq. (16). Using Eqs. (4) -(6) and following [12], the overall detection probability Pds for theselective relay spectrum sensing is calculated as

Pds = Pds,1

M∏i=1

[1 − σ2is(1 − Pdi,1)

σ2psγpΛ + σ2

is

exp(− Λ

σ2is

)] (17)

where σ2is = E[|his(k)|2], σ2

pd = E[|hpd(k)|2], Λ = [22M/(αBT ) −1]/γs, Pds,1 = Pr{Hs(k, 1) = H1|Hp(k) = H1} and Pdi,1 =Pr{Hi(k, 1) = H1|Hp(k) = H1} are the probabilities of individual

detection of the PU’s presence at CS and CRi, respectively. Similarly,the false detection probability Pfs is given by

Pfs = Pfs,1

M∏i=1

[1 − (1 − Pfi,1) exp(− Λ

σ2is

)] (18)

where Pfs,1 = Pr{Hs(k, 1) = H1|Hp(k) = H0} and Pfi,1 =Pr{Hi(k, 1) = H1|Hp(k) = H0} are the probabilities of individualfalse alarm of the PU’s presence at CS and CRi, respectively.Considering an energy detector, Pds,1 and Pfs,1 can be calcu-lated as Pds,1 = Pr{T [ys(k, 1)] > δ|Hp(k) = H1} and Pfs,1 =Pr{T [ys(k, 1)] > δ|Hp(k) = H0}, where δ is an energy detectionthreshold and T [ys(k, 1)] is an output statistic of the energy detectoras given by

T [ys(k, 1)] =1

N

N∑n=1

|yns (k, 1)|2 (19)

where N is the number of samples. Using the results of AppendixA in [12], we can obtain

Pfs,1 =

{Pds,1, Pds,1 = Q(−

√N)

Pds,1 − Q(Q−1(Pds,1) + 1σ2

psκs) exp(ξs), otherwise

(20)where κs = γpQ−1(Pds,1)+

√Nγp, ξs =

Q−1(Pds,1)

σ2psκs

+ 12σ4

psκ2s

, and

the number of samples should satisfy N ≥ [Q−1(Pds,1)]2. Similar

to the derivation of Eq. (20) and following Eq. (2), we obtain

Pfi,1 =

{Pdi,1, Pdi,1 = Q(−

√N)

Pdi,1 − Q(Q−1(Pdi,1) + 1σ2

piκi) exp(ξi), otherwise

(21)where κi = γpQ−1(Pdi,1) +

√Nγp, ξi =

Q−1(Pdi,1)

σ2piκi

+ 12σ4

piκ2i

,

and N ≥ [Q−1(Pdi,1)]2. Note that, in the proposed SRSS-BRDT

scheme, a primary user may be interfered by the cognitive usersduring both the spectrum sensing and data transmission phases.Specifically, in the spectrum sensing phase, a cognitive relay willinterfere the primary user if it fails to detect the presence ofthe primary user and, in the data transmission phase, the primaryuser will be interfered by the secondary transmissions when thecognitive source node made a miss detection of the PU’s presence.Nevertheless, any given primary QoS requirement can be satisfied byadjusting the individual detection probability Pdi,1 as given by Eq.(40) in [12].

IV. NUMERICAL RESULTS AND ANALYSIS

In this section, we conduct numerical outage probability evalua-tions for the traditional SFSS-BRDT scheme (with a dedicated chan-nel) [5] and the proposed SRSS-BRDT scheme (without a dedicatedchannel). Notice that, in the following numerical evaluations, thefading variances of the channel between each sender-receiver withina same network (primary or secondary networks) and that acrossdifferent networks are specified to 1 and 0.5, respectively. Fig. 3shows the outage probability versus spectrum sensing overhead ofthe traditional SFSS-BRDT and proposed SRSS-BRDT schemes fordifferent number of CRs, M , where the time-bandwidth productsof the licensed primary channel and dedicated sensing channel areBT = 500 and BdTd = 50, respectively. This considers that thecognitive radio is typically designed to reuse the licensed spectrumwith very limited dedicated channel resources. As shown in Fig. 3,the outage probabilities of the proposed SRSS-BRDT scheme arelower than that of the traditional SFSS-BRDT scheme for M = 1and M = 4, respectively. In addition, one can see from Fig. 3that the outage probabilities of both the traditional and proposed


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Spectrum sensing overhead (α)

Out

age

prob

abili

ty

SFSS−BRDT with M = 1SRSS−BRDT with M = 1SFSS−BRDT with M = 4SRSS−BRDT with M = 4

Fig. 3. Outage probability versus the spectrum sensing overhead α ofthe traditional SFSS-BRDT and proposed SRSS-BRDT schemes for differentnumber of CRs M with Pa = 0.8, Pds = 0.99, γp = 10 dB, γs = 10 dB,Rs = 1 bit/s/Hz, BT = 500, BdTd = 50, fs = 50 kHz, Rp = 2 bits/s/Hz,and Poutpri,thr = 10−3, where Rp and Poutpri,thr are the primary data rateand primary outage probability requirement, respectively.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Out

age

prob

abili

ty

SFSS−BRDT with Rs=1.2 bits/s/Hz

SRSS−BRDT with Rs=1.2 bits/s/Hz

SFSS−BRDT with Rs=1 bits/s/Hz

SRSS−BRDT with Rs=1 bits/s/Hz

Fig. 4. Outage probability versus the spectrum sensing overhead α of thetraditional SFSS-BRDT and proposed SRSS-BRDT schemes for different datatransmission rates Rs with Pa = 0.8, Pds = 0.99, γp = 10 dB, γs =10 dB, R = 1 bit/s/Hz, M = 4, BT = 500, BdTd = 50, fs = 50 kHz,Rp = 2 bits/s/Hz, and Poutpri,thr = 10−3.

schemes can be minimized through adjusting the spectrum sensingoverhead. Therefore, a joint analysis of the spectrum sensing and datatransmission phases is essential to optimize the cognitive transmissionperformance.

Fig. 4 illustrates the outage probability versus spectrum sensingoverhead of the SFSS-BRDT and SRSS-BRDT schemes for differentdata transmission rates Rs. All cases in Fig. 4 show that theproposed SRSS-BRDT scheme outperforms the traditional SFSS-BRDT scheme in terms of the outage probability. From Fig. 4, onecan also observe that an optimal spectrum sensing overhead exists tominimize the outage probability and, moreover, the optimal spectrumsensing overhead value decreases gradually with an increasing datarate Rs. This is due to the fact that, as the data rate Rs increases, thedata transmission phase should be assigned a longer time duration,resulting in a shorter time duration for the spectrum sensing phase.

In Fig. 5, we show the outage probability comparison between theSFSS-BRDT scheme (with different time-bandwidth products of thededicated channel BdTd) and SRSS-BRDT scheme (with differentprimary outage probability requirements Poutpri,thr). As shown in Fig.5, as the time-bandwidth product BdTd increases from BdTd = 50

0 0.1 0.2 0.3 0.4 0.5 0.60.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Out

age

prob

abili

ty

SFSS−BRDT with BdTd=50



SRSS−BRDT with PoutPri,thr=1e−5

SRSS−BRDT with PoutPri,thr=1e−3

Fig. 5. Outage probability comparison between the traditional SFSS-BRDTscheme and proposed SRSS-BRDT scheme for different time-bandwidthproducts of the dedicated channel BdTd with Pa = 0.8, Pds = 0.99,γp = 10 dB, γs = 10 dB, Rs = 1 bit/s/Hz, M = 4, BT = 500,fs = 50 kHz, and Rp = 2 bits/s/Hz.

to 2000, the outage probability curves of the traditional SRSS-BRDTscheme become closer to that of the proposed SRSS-BRDT schemewith Poutpri,thr = 10−3. One can also see from Fig. 5 that, whenthe primary outage probability requirement is very stringent, i.e.Poutpri,thr = 10−5, the SRSS-BRDT performs worse than the SFSS-BRDT in terms of the outage probability. However, notice that anoverly strict primary outage probability requirement is not practicaland thus the advantage of the SRSS-BRDT scheme is achievable inpractical wireless transmission systems.

V. CONCLUSION

In this paper, we have investigated a selective relay spectrumsensing and best relay data transmission scheme for multiple-relaycognitive radio networks. We have derived a closed-form outageprobability expression for the SRSS-BRDT scheme over Rayleighfading channels. Numerical results have demonstrated that the SRSS-BRDT scheme can save the dedicated channel without outage prob-ability degradation, compared to the SFSS-BRDT scheme with alimited dedicated channel resource. We have also shown that aminimum outage probability can be achieved through an optimalallocation of the time durations between the spectrum sensing anddata transmission phases.

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