sensing-throughput tradeoff for cognitive radio networks

1326 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 4, APRIL 2008

Sensing-Throughput Tradeoff forCognitive Radio Networks

Ying-Chang Liang, Senior Member, IEEE, Yonghong Zeng, Senior Member, IEEE,Edward C.Y. Peh, and Anh Tuan Hoang, Member, IEEE

Abstract In a cognitive radio network, the secondary usersare allowed to utilize the frequency bands of primary userswhen these bands are not currently being used. To support thisspectrum reuse functionality, the secondary users are requiredto sense the radio frequency environment, and once the primaryusers are found to be active, the secondary users are required tovacate the channel within a certain amount of time. Therefore,spectrum sensing is of significant importance in cognitive radionetworks. There are two parameters associated with spectrumsensing: probability of detection and probability of false alarm.The higher the probability of detection, the better the primaryusers are protected. However, from the secondary users perspec-tive, the lower the probability of false alarm, the more chancesthe channel can be reused when it is available, thus the higherthe achievable throughput for the secondary network. In thispaper, we study the problem of designing the sensing duration tomaximize the achievable throughput for the secondary networkunder the constraint that the primary users are sufficientlyprotected. We formulate the sensing-throughput tradeoff problemmathematically, and use energy detection sensing scheme to provethat the formulated problem indeed has one optimal sensing timewhich yields the highest throughput for the secondary network.Cooperative sensing using multiple mini-slots or multiple sec-ondary users are also studied using the methodology proposedin this paper. Computer simulations have shown that for a 6MHzchannel, when the frame duration is 100ms, and the signal-to-noise ratio of primary user at the secondary receiver is 20dB,the optimal sensing time achieving the highest throughput whilemaintaining 90% detection probability is 14.2ms. This optimalsensing time decreases when distributed spectrum sensing isapplied.

Index Terms Cognitive radio, sensing-throughput tradeoff,spectrum reuse, spectrum sensing, throughput maximization.

I. INTRODUCTION

THE last decade has witnessed the increasing popularityof wireless services. Based on fixed spectrum allocationmethodology, in many countries, most of the available radiospectrum has been assigned for various services. On theother hand, careful studies of the spectrum usage patternhave revealed that the allocated spectrum experiences lowutilization. In fact, recent measurements by Federal Commu-nications Commission (FCC) have shown that 70% of the

Manuscript received October 25, 2006; revised August 18, 2007; acceptedJanuary 2, 2008. The associate editor coordinating the review of this paperand approving it for publication was W. Yu. This paper was presented in partat the IEEE International Conference on Communications (ICC), Glasgow,UK, June 2007.

The authors are with the Institute for Infocomm Research, ASTAR,21 Heng Mui Keng Terrace, Singapore 119613 (e-mail: {ycliang, yhzeng,athoang}@i2r.a-star.edu.sg.

Digital Object Identifier 10.1109/TWC.2008.060869.

allocated spectrum in US is not utilized. Furthermore, timescale of the spectrum occupancy varies from milliseconds tohours [1]. This motivates the concept of spectrum reuse thatallows secondary users/network to utilize the radio spectrumlicensed/allocated to the primary users/network when thespectrum is temporally not being utilized.

The core technology behind spectrum reuse is cognitiveradio [3], [4], which consists of three essential components:(1) Spectrum sensing: The secondary users are required tosense and monitor the radio spectrum environment within theiroperating range to detect the frequency bands that are not oc-cupied by primary users; (2) Dynamic spectrum management:Cognitive radio networks are required to dynamically selectthe best available bands for communications; and (3) Adaptivecommunications: A cognitive radio device can configure itstransmission parameters (carrier frequency, bandwidth, trans-mission power, etc) to opportunistically make best use of theever-changing available spectrum.

In December 2003, FCC issued a Notice of Proposed RuleMaking that identifies cognitive radio as the candidate forimplementing opportunistic spectrum sharing [2]. The IEEEthen formed the 802.22 Working Group to develop a standardfor wireless regional area networks (WRAN) [6], which isan alternative broadband access scheme operating in unusedVHF/UHF TV bands. By doing so, it is required that noharmful interference is caused to the incumbent primary users,which, in the VHF/UHF bands, include TV users and the FCCpart 74 wireless microphones [6].

Fig. 1 illustrates the topology of a WRAN system wherethe primary users are TV users and wireless microphones,and the secondary users include both WRAN base station(BS) and WRAN customer premise equipments (CPEs). TheWRAN systems are designed to provide wireless broadbandaccess to rural and suburban areas, with the average cov-erage radius of 33 km. The operating principle of WRANis based on opportunistic access to temporarily unused TVspectrum. The fundamental objective for a WRAN systemis to maximize the spectrum utilization of the TV channelswhen they are not used by the primary users. To protect theprimary users, whenever the primary users become active, theWRAN system has to vacate that channel within a certainamount of time (say 2 seconds as specified by 802.22 workinggroup). Thus spectrum sensing is of significant importancefor cognitive radio systems. In 802.22 WRAN, each mediumaccess control (MAC) frame consists of one sensing slot andone data transmission slot, thus periodic spectrum sensing

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LIANG et al.: SENSING-THROUGHPUT TRADEOFF FOR COGNITIVE RADIO NETWORKS 1327

Fig. 1. A deployment scenario for IEEE 802.22 WRAN: the primary usersare TV receivers and wireless microphones.

is carried out. Associated with spectrum sensing are twoparameters: probability of detection and probability of falsealarm. The higher the detection probability, the better theprimary users can be protected. However, from the secondaryusers perspective, the lower the false alarm probability, themore chances the channel can be reused when it is available,thus the higher the achievable throughput for the secondaryusers. Thus there could exist a fundamental tradeoff betweensensing capability and achievable throughput for the secondarynetwork.

In this paper, we study the fundamental problem of sensing-throughput tradeoff for cognitive radio networks. Particularly,we are interested in the problem of designing the sensingslot duration to maximize the achievable throughput for thesecondary users under the constraint that the primary usersare sufficiently protected. Using energy detection scheme, weprove that there indeed exists an optimal sensing time whichachieves the best tradeoff. Cooperative sensing using multiplesecondary users and diversity reception using multiple mini-slots are also studied based on the proposed tradeoff method-ology.

While spectrum sensing is a conventional signal detectionproblem [16], [9], it has received growing attention recently inthe area of wireless sensor networks [17], [18] and cognitiveradio networks [12], [13], [14]. In sensor networks, the focusis on detecting the presence of an event using multipledistributed sensors. In cognitive radio networks, the criterionconsidered so far is in terms of protecting the primary user, i.e.,maximizing the probability of detection under the constraint ofprobability of false alarm. In this paper, in order to formulatethe sensing-throughput tradeoff problem, the objective turnsout to be minimizing the probability of false alarm, under theconstraint of probability of detection. We thus formulate thesensing-throughput tradeoff problem from this perspective.

In [20], the authors considered a different tradeoff problemfrom the one we are interested in this paper. In particular,in [20], when the present band used by the secondary usersis detected to be busy due to the re-appearance of primaryuser, the secondary user then searches an out-band so that its

transmission can be continued. The first problem studied in[20] is to minimize the average search time while targetinghigh chance that the secondary user can find at least oneavailable out-band channel. Once the average search time isfound, paper [20] continues to optimize the in-band sensingtime in order to achieve maximum average throughput.

This paper is organized as follows. Section II presentsthe general model for spectrum sensing and reviews theenergy detection scheme. The relation between probability ofdetection and probability of false alarm is also established inthis section. In Section III, we study the sensing-throughputtradeoff problem, and prove the existence of optimal sensingtime based on energy detection scheme. Section IV studies thesensing scheme based on multiple mini-slots which achievestime diversity. Distributed spectrum sensing using multiplesecondary users is studied in Section V. Performance eval-uation and comparisons are given in Section VI, and finally,conclusions are drawn in Section VII.

II. SPECTRUM SENSING PRELIMINARIESIn this section, we first present the general model for spec-

trum sensing, then review the energy detection scheme andanalyze the relationship between the probability of detectionand the probability of false alarm.

A. General Model for Spectrum SensingSuppose that we are interested in the frequency band with

carrier frequency fc and bandwidth W and the received signalis sampled at sampling frequency fs. When the primary useris active, the discrete received signal at the secondary user canbe represented as

y(n) = s(n) + u(n), (1)which is the output under hypothesis H1. When the primaryuser is inactive, the received signal is given by

y(n) = u(n), (2)and this case is referred to as hypothesis H0. We make thefollowing assumptions.

(AS1) The noise u(n) is a Gaussian, independent andidentically distributed (iiid) random process with meanzero and variance E[|u(n)|2] = 2u;

(AS2) The primary signal s(n) is an iid random processwith mean zero and variance E[|s(n)|2] = 2s ;

(AS3) The primary signal s(n) is independent of thenoise u(n).

Denote = 2s

2uas the received signal-to-noise ratio (SNR)

of the primary user measured at the secondary receiver ofinterest, under the hypothesis H1. We consider both real-valued Gaussian noise case and circularly symmetric complexGaussian (CSCG) noise case. For the primary signal s(n),we consider four scenarios: (1) BPSK modulated signal; (2)complex PSK modulated signal; (3) real-valued Gaussiansignal and (4) CSCG signal.

Two probabilities are of interest for spectrum sensing: prob-ability of detection, which defines, under hypothesis H1, theprobability of the algorithm correctly detecting the presence of



primary signal; and probability of false alarm, which defines,under hypothesis H0, the probability of the algorithm falselydeclaring the presence of primary signal. From the primaryusers perspective, the higher the probability of detection,the better protection it receives. From the secondary usersperspective, however, the lower the probability of false alarm,there are more chances for which the secondary users can usethe frequency bands when they are available. Obviously, for agood detection algorithm, the probability of detection shouldbe as high as possible while the probability of false alarmshould be as low as possible.

B. Energy DetectorEnergy detection is the most popular spectrum sensing

scheme. Let be the available sensing time and N the numberof samples (N is the maximum integer not greater than fs,and for notation simplicity, we assume N = fs). The teststatistic for energy detector is given by

T (y) =1N

Nn=1

|y(n)|2. (3)

Under hypothesis H0, the test static T (y) is a random variablewhose probability density function (PDF) p0(x) is a Chi-square distribution with 2N degrees of freedom for complex-valued case, and with N degrees of freedom for real-valuedcase. If we choose the detection threshold as , the probabilityof false alarm is then given by

Pf (, ) = Pr(T (y) > |H0) =

p0(x)dx. (4)Using central limit theorem (CLT), we have the following

proposition.Proposition 1: For a large N , the PDF of T (y) under

hypothesis H0 can be approximated by a Gaussian distributionwith mean 0 = 2u and variance 20 = 1N

[E|u(n)|4 4u

].

Further, If u(n) is real-valued Gaussian variable, then E|u(n)|4 =

34u, thus 20 = 2N 4u.

If u(n) is CSCG, then E|u(n)|4 = 24u, thus 20 = 1N 4u.Next, we focus on the CSCG noise case for which the

probability of false alarm is given by

Pf (, ) = Q((

2u 1

)fs

), (5)

where Q() is the complementary distribution function of thestandard Gaussian, i.e.,

Q(x) = 12

x

exp( t

2

2

)dt. (6)

Under hypothesis H1, denote p1(x) as the PDF of thetest static T (y). For a chosen threshold , the probability ofdetection is given by

Pd(, ) = Pr(T (y) > |H1) =

p1(x)dx. (7)

Proposition 2: For a large N , the PDF of T (y) underhypothesis H1 can be approximated by a Gaussian distributionwith mean 1 = ( + 1)2u and variance

21 =1N

[E|s(n)|4 + E|u(n)|4 (2s 2u)2

], (8)

if s(n) and u(n) are both circularly symmetric and complex-valued, and

21 =1N

[E|s(n)|4 + E|u(n)|4 (2s 2u)2 + 22s2u

], (9)

if s(n) and u(n) are both real-valued. Furthermore, If s(n) is complex PSK modulated and u(n) is CSCG,

then 21 = 1N (2 + 1)4u;

If s(n) is BPSK modulated and u(n) is real-valuedGaussian, then 21 = 2N (2 + 1)

4u;

If s(n) and u(n) are both CSCG, E|s(n)|4 = 24s andE|u(n)|4 = 24u, then 21 = 1N ( + 1)24u;

If s(n) and u(n) are both real-valued Gaussian,E|s(n)|4 = 34s and E|u(n)|4 = 34u, then 21 =2N ( + 1)

24u.

Proof: The proof is again based on CLT. Detailed proof isgiven in Appendix A.

Remark: For the four cases of primary users signal andadditive noise we considered, the complex counterpart yieldshalf the variance as that of the real-valued case. This can beunderstood by considering the fact that the complex case, infact, provides twice the samples as compared to the real-valuedcase.

We focus on the complex-valued PSK signal and CSCGnoise case. Based on the PDF of the test static, the probabilityof detection can be approximated by

Pd(, ) = Q((

2u 1

)fs

2 + 1

). (10)

For a target probability of detection, Pd, the detection thresh-old can be determined by

(

2u 1

)fs

2 + 1= Q1(Pd). (11)

From (5), on the other hand, this threshold is related to theprobability of false alarm as follows:

Q1(Pf ) =(

2u 1

)fs. (12)

Therefore, for a target probability of detection Pd, the proba-bility of false alarm is related to the target detection probabilityas follows:

Pf = Q(

2 + 1Q1(Pd) +

fs). (13)

On the other hand, for a target probability of false alarm, Pf ,the probability of detection is given by

Pd = Q(

12 + 1

(Q1(Pf )

fs))

. (14)

Finally, for a given pair of target probabilities (Pd, Pf ), thenumber of required samples to achieve these targets can bedetermined from (11) and (12) by cancelling out the thresholdvariable . The minimum number of samples is given by

Nmin =12

[Q1(Pf )Q1(Pd)

2 + 1

]2. (15)



Fig. 2. Frame structure for cognitive radio networks with periodic spectrumsensing ( : sensing slot duration; T : data transmission slot duration.)

III. SENSING-THROUGHPUT TRADEOFFIn the previous section, the relationship between proba-

bility of detection and probability of false alarm has beenestablished. In this section, we study the fundamental tradeoffbetween sensing capability and achievable throughput of thesecondary networks. Using energy detection scheme, we willprove that there indeed exists the optimal sensing time withwhich the highest throughput for the secondary network isachieved, yet the primary users are sufficiently protected.

A. Problem FormulationFig. 2 shows the frame structure designed for a cognitive

radio network with periodic spectrum sensing where eachframe consists of one sensing slot and one data transmissionslot. Suppose the sensing duration is and the frame du-ration is T . Denote C0 as the throughput of the secondarynetwork when it operates in the absence of primary users,and C1 as the throughput when it operates in the presence ofprimary users. For example, if there is only one point-to-pointtransmission in the secondary network and the SNR for thissecondary link is SNRs = Ps/N0, where Ps is the receivedpower of the secondary user and N0 is the noise power. LetPp be the interference power of primary user measured atthe secondary receiver, and assume that the primary userssignal and secondary users signal are Gaussian, white andindependent of each other. Then C0 = log2(1 + SNRs)and C1 = log2

(1 + PsPp+N0

)= log2

(1 + SNRs1+SNRp

), where

SNRp = Pp/N0. Obviously, we have C0 > C1. Note if theprimary users signal is non-Gaussian, the above formula forC1 can be treated as the lower bound of achievable rate forsecondary link when the primary user is active.

For a given frequency band of interest, let us define P (H1)as the probability for which the primary user is active, andP (H0) as the probability for which the primary user isinactive. Then P (H0) + P (H1) = 1.

There are two scenarios for which the secondary networkcan operate at the primary users frequency band.

Scenario I: When the primary user is not present andno false alarm is generated by the secondary user, theachievable throughput of the secondary link is TT C0.

Scenario II: When the primary user is active but it is notdetected by the secondary user, the achievable throughputof the secondary link is TT C1.

The probabilities for which Scenario I and Scenario IIhappen are (1 Pf (, ))P (H0) and (1 Pd(, ))P (H1),

respectively. If we define

R0(, ) =T

TC0(1 Pf (, ))P (H0), (16)

and

R1(, ) =T

TC1(1 Pd(, ))P (H1), (17)

then the average throughput for the secondary network is givenby

R() = R0(, ) + R1(, ). (18)

Obviously, for a given frame duration T , the longer thesensing time , the shorter the available data transmissiontime (T ). On the other hand, from (13), since Q(x) isa monotonically decreasing function of x, for a given targetprobability of detection, Pd, the longer the sensing time, thelower the probability of false alarm, which corresponds to thecase that the secondary network can use the channel with ahigher chance. The objective of sensing-throughput tradeoff isto identify the optimal sensing duration for each frame suchthat the achievable throughput of the secondary network ismaximized while the primary users are sufficiently protected.Mathematically, the optimization problem can be stated as

max

R() = R0(, ) + R1(, ) (19)s.t. Pd(, ) Pd, (20)

where Pd is the target probability of detection with which theprimary users are defined as being sufficiently protected. Inpractice, the target probability of detection Pd is chosen tobe close to but less than 1, especially for low SNR regime.For instance, in IEEE802.22 WRAN, we choose Pd = 0.9 forthe SNR of 20dB. It is pointed out that if the primary usersrequire 100% protection in its frequency band, it will then benot allowed for the secondary usage in that frequency band.Also, we suppose the activity probability P (H1) of primaryusers is small, say less than 0.3, thus it is economicallyadvisable to explore the secondary usage for that frequencyband. Since C0 > C1, the first term in the right hand sideof (18) dominates the achievable throughput. Therefore theoptimization problem can be approximated by

max

R() = R0(, ) (21)s.t. Pd(, ) Pd. (22)

For a given sensing time , according to (10), we maychoose a detection threshold 0 such that Pd(0, ) = Pd.We may also choose a detection threshold 1 < 0 suchthat Pd(1, ) > Pd. Obviously, Pf (1, ) > Pf (0, ). Thusfrom (16) and (17), we have R0(1, ) < R0(0, ) andR1(1, ) < R1(0, ). Therefore, the optimal solution to (21)and (22) is achieved with equality constraint in (22). Finally,R0(1, )+R1(1, ) < R0(0, )+R1(0, ), thus the optimalsolution to (19) and (20) is also achieved when the equalityconstraint in (20) is satisfied.



B. Energy Detection SchemeWhen energy detector is applied, using (13) and choosing

Pd = Pd, we have

R() = C0P (H0)(1

T

)(1Q

( +

fs

)). (23)

where =

2 + 1Q1(Pd). Thus, from (23), we can seethat the achievable throughput of the secondary network is afunction of the sensing time .

Theorem 1: Under the assumptions (AS1) - (AS3), if theprimary signal is complex-valued PSK and the noise processis CSCG, for any target probability of detection, there existsan optimal sensing time which yields the maximum achievablethroughput for the secondary networks.

Proof: It can be verified from (23) thatR()

C0P (H0) =

fs(1 T )2

2exp

( ( +

fs)2

2

)

1T

+1TQ( +

fs). (24)

Obviously,

limT

R() < C0P (H0)( 1

T+

1TQ()

)< 0, (25)

lim0

R() = +. (26)

In deriving (25), we have used the fact that Q(x) is adecreasing function and upper bounded by 1. Eqs (25) and(26) mean that R() increases when is small and decreaseswhen approaches T . Hence, there is a maximum point ofR() within interval (0, T ).

Furthermore, from (18), we have

R() = R() 1T

C1P (H1)(1 Pd). (27)Thus, again

limT

R() < limT

R() < 0, (28)

lim0

R() = lim0

R() 1T

C1P (H1)(1 Pd)= +. (29)

Hence, there is a maximum point of R() within interval(0, T ).

In Appendix B, we further show that R() is concave for therange of in which Pf () 0.5. This makes the maximumpoint of R() to be unique in this range. If the optimal sensingtime falls into this range, which should be the case for mostfrequency reuse scenarios, efficient search algorithms can thenbe developed. Otherwise, exhaustive search is needed in orderto find the optimal sensing time. Finally, while Theorem 1assumes that the signal is complex-valued PSK and the noiseis CSCG, the fact that there exists the optimal sensing timewithin the interval (0, T ) is also valid for other cases (real-valued or CSCG signal).

IV. MULTI-SLOT SPECTRUM SENSINGIn this section, we are interested in the case when the

sensing slot in each frame is split into multiple discontiguousmini-slots. Let M be the number of mini-slots, 1 the sensing

time for each mini-slot, and again T the duration for eachframe. We fix the the total sensing time in each frame to = M1, and the number of samples for each mini-slot isN1 = N/M (without loss of generality, we assume that N1is an integer.)

Let us consider the following hypotheses for the ith mini-slot:

H1 : yi(n) = hisi(n) + ui(n), (30)H0 : yi(n) = ui(n), (31)

and make the following assumptions: The channel coefficients his are zero-mean, unit-

variance complex Gaussian random variables; The noises are independent of each other for each of the

M mini-slots; The signal power and noise power are constant over the

M mini-slots, i.e., E[|si(n)|2] = 2s , and E[|ui(n)|2] =2u for all i;

The primary user is either active or inactive for all theM mini-slots.

The objective of multi-slot spectrum sensing is, using theavailable data measurements from the M mini-slots, to decidewhether the primary user is active or not.

The decision can be made through two methods: data fusionand decision fusion.

Data Fusion: Process the measurements from all mini-slots jointly and then make the final decision based onthe calculated statistics;

Decision Fusion: Process each mini-slots data separately,and make individual decisions. The final decision is thenmade by fusing the individual decisions.

For time varying channels, multi-slot spectrum sensing isexpected to achieve time diversity for sensing the presence ofprimary user even with the help of a single secondary user.

A. Data Fusion

Let Ti(y) be the test statistic for the ith mini-slot:

Ti(y) =1N1

N1n=1

|yi(n)|2, (32)

Using data fusion, the test statistic used for final decision isthen represented as

T (y) =Mi=1

giTi(y), (33)

where gi 0 is the weighting factor associated with theith mini-slot. Without loss of generality, we assume thatM

i=1 g2i = 1.

Proposition 3: For a large N , the PDF of T (y) underhypothesis H0 can be approximated by a Gaussian distri-bution with mean 0 = 2u

Mi=1 gi and variance 20 =

1N1

Mi=1 g

2i

[E|u(n)|4 4u

].

Proposition 4: For a large N , the PDF of T (y) underhypothesis H1 can be approximated by a Gaussian distribution



with mean 1 = 2uM

i=1 gi(|hi|2 + 1) and variance

21 =1N1

Mi=1

g2i [|hi|4E|s(n)|4 + E|u(n)|2

(|hi|22s 2u)2], (34)if the primary signal and noise are both circularly symmetricand complex-valued, and

21 =1N1

Mi=1

g2i [|hi|4E|s(n)|4 + E|u(n)|2

(|hi|22s 2u)2 + 2|hi|22s2u], (35)if the primary signal and noise are both real-valued.

Again, let us consider complex PSK modulated signal andCSCG noise, we then have

20 =4uN1

, (36)

21 =4uN1

(1 + 2

Mi=1

g2i |hi|2)

. (37)

Mimicking the process of deriving (13) and (14), we havethe following relation between Pd and Pf :

Pf = Q (f1(g1, , gM ;Pd)) , (38)Pd = Q (f2(g1, , gM ;Pf )) , (39)

where

f1(g1, , gM ;Pd) = 1Q1(Pd) +

N1

Mi=1

gi|hi|2, (40)

f2(g1, , gM ;Pf )

=11

(Q1(Pf )

N1

Mi=1

gi|hi|2)

, (41)

where 1 =

1 + 2M

i=1 g2i |hi|2. Since Q(x) is a decreas-

ing function of x, from the primary users interest, for a targetprobability of false alarm Pf , we want to design the optimalgi by maximizing the probability of detection, which gives:

ming1, ,gM :

Mi=1 g

2i=1

f2(g1, , gM ; Pf ). (42)

From the sensing-throughput tradeoff perspective, we wish atarget probability of detection Pd to be achieved for eachframe, thus the optimal gi is designed to achieve minimumprobability of false alarm:

maxg1, ,gM :

Mi=1 g

2i=1

f1(g1, , gM ; Pd). (43)

We are now interested in the low SNR regime where 0,thus 1 0. In this case, Eqs (40) and (41) are approximatedby

f1(g1, , gM ;Pd) Q1(Pd) +

N1

Mi=1

gi|hi|2, (44)

f2(g1, , gM ;Pf ) Q1(Pf )

N1

Mi=1

gi|hi|2. (45)

Theorem 2: Suppose the low SNR regime is of interest. Fora target probability of detection Pd, the optimal gi achievingminimum probability of false alarm is given by

gi =|hi|2Mi=1 |hi|4

. (46)

Proof: For low SNR regime, (43) is equivalent to thefollowing optimization function:

maxg1, ,gM :

Mi=1 g

2i=1

Mi=1

gi|hi|2. (47)

Using Cauchy-Schwarz inequality, we obtain the optimalcombining coefficients given by (46).

On the other hand, the following theorem describes the opti-mal weighting coefficients from the primary users perspective.

Theorem 3: Suppose the low SNR regime is of interest. Fora target probability of false alarm Pf , the optimal gi achievingmaximum probability of detection is also given by (46).

When the channel coefficients are unknown, a simple wayfor data fusion is to choose gi = 1M . In this case, we obtain:

Pf = Q(

2Q1(Pd) +

N1M

Mi=1

|hi|2)

, (48)

Pd = Q(

12

(Q1(Pf )

N1M

Mi=1

|hi|2))

, (49)

where 2 =

1 + 2MM

i=1 |hi|2.Finally, let us consider a special case where hi = 1 for all

i, and gi is chosen as gi = 1M . From (38), for a target Pd,the probability of false alarm is given by:

Pf = Q(

2 + 1Q1(Pd) +

MN1

). (50)

Since MN1 = N , the use of M mini-slots for the case ofstatic channel does not provide any performance gain whendata fusing is applied.

From (38), for a fading channel environment, in order toachieve same probability of detection for each frame, thedetection threshold will change from one frame to another,thus the probability of false alarm will vary. Let us denote, fora given sensing duration , Pf () as the average probabilityof false alarm over all frames. We then define the normalizedachievable throughput as

B() =T

T(1 Pf ()). (51)

B. Decision FusionDenote P (i)d and P

(i)f as the probability of detection and

probability of false alarm at the ith mini-slot, respectively.By choosing the detection threshold as 0, the probability ofdetection for the ith time slot is

P(i)d = Q

((02u

|hi|2 1)

N12|hi|2 + 1

), (52)



and the probability of false alarm for the ith slot is given by

P(i)f = Q

((02u

1)

N1

). (53)

Once the decision is made for each time slot, there are differentrules available for making final decision on the presence ofthe primary user.

1) Optimal Decision Fusion Rule: Let Ii be the binarydecision from the ith time slot, where Ii {0, 1} for i =1, ,M . The optimal decision fusion rule is the Chair-Varshney fusion rule [16], which is a threshold test of thefollowing statistic:

0 =Mi=1

[Ii log

P(i)d

P(i)f

+ (1 Ii) log 1 P(i)d

1 P (i)f

]

+ logP (H1)P (H0) . (54)

If 0 0, then the primary user is present; otherwise, thereis no primary user.

2) Logic-OR (LO) Rule: LO rule is a simple decisionrule described as follows: if one of the decisions says thatthere is a primary user, then the final decision declares thatthere is a primary user. Mathematically, define =

Mi=1 Ii,

if 1, then the primary user is present; otherwise, there isno primary user.

Assuming that all decisions are independent, the probabilityof detection and probability of false alarm of the final decisionare, respectively,

Pd = 1Mi=1

(1 P (i)d ), (55)

Pf = 1Mi=1

(1 P (i)f ). (56)

3) Logic-AND (LA) Rule: LA rule works as follows: ifall decisions says that there is a primary user, then the finaldecision declares that there is a primary user. Mathematically,define =

Mi=1 Ii, if = 1, then the primary user is present;

otherwise, there is no primary user. Again, assuming that alldecisions are independent, the probability of detection andprobability of false alarm of the final decision are, respectively,

Pd =Mi=1

P(i)d , (57)

Pf =Mi=1

P(i)f . (58)

4) Majority Rule: Another decision rule is based on ma-jority of the individual decisions. If half of the decisions ormore say that there is a primary user, then the final decisiondeclares that there is a primary user. Mathematically, define =

Mi=1 Ii, if M2 , where x denotes the smallest

integer not less then x, then the primary user is declared tobe present; otherwise, there is no primary user. Assumingthat all decisions are independent, and supposing that P (1)d = P (M)d = Pd,0 and P (1)f = P (M)f = Pf,0, the probability

of detection and probability of false alarm of the final decisionare given by,

Pd =MM2

j=0

(M

M2 + j)

(1 Pd,0)MM2 j P

M2 +j

d,0 , (59)

Pf =MM2

j=0

(M

M2 + j)

(1 Pf,0)MM2 j P

M2 +j

f,0 , (60)

respectively, where(ck

)= c!k!(ck)! .

V. DISTRIBUTED SPECTRUM SENSINGIn this section, we consider cooperative spectrum sens-

ing using multiple distributed secondary users. The tradeoffmethodology proposed in the previous section can be applieddirectly. Define the hypotheses for the ith receiver as:

H1 : yi(n) = his(n) + ui(n), (61)H0 : yi(n) = ui(n), (62)

for i = 1, ,M . We make the following assumptions: The channel coefficients his are zero-mean, unit-

variance complex Gaussian random variables; The noises are independent of each other for the M

receivers. Further, the noise power is constant over theM receivers, i.e., E[|ui(n)|2] = 2u, for all i.

A. Data FusionSuppose the channel coefficients from the primary user to

each receiver are known. Using maximal ratio combining,

y(n) =Mi=1

hiMi=1 |hi|2

yi(n). (63)

The hypotheses (61) and (62) are equivalent to:

H1 : y(n) =M

i=1 |hi|2s(n) + u(n), (64)H0 : y(n) = u(n), (65)

where E[|u(n)|2] = 2u. Obviously, it is equivalent to sensethe primary user with SNR

Mi=1 |hi|2 and sampling size

N . From (13) and (14), for a target probability of detection,Pd, the probability of false alarm becomes:

Pf = Q(

3Q1(Pd) +

N

Mi=1

|hi|2)

, (66)

where 3 =

2M

i=1 |hi|2 + 1. On the other hand, fora target probability of false alarm, Pf , the probability ofdetection is given by

Pd = Q(

13

(Q1(Pf )

NMi=1

|hi|2))

. (67)

When the channel coefficients are unknown, similar to (32)and (33), a simple way for data fusion is to choose gi = 1M .In this case, we obtain:

Pf = Q(

4Q1(Pd) +

N

M

Mi=1

|hi|2)

, (68)



0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6x 104

103

102

101

100

Number of samples

Prob

abilit

y of

det

ectio

n/fa

lse a

larm

Prob. of detection simulatedProb. of detection theoryProb. of false alarm simulatedProb. of false alarm theory

Fig. 3. Comparison of simulated and theoretical probability of detection andprobability of false alarm: Pd = 0.9, SNRp = 15dB.

Pd = Q(

14

(Q1(Pf )

N

M

Mi=1

|hi|2))

, (69)

where 4 =

1 + 2MM

i=1 |hi|2.

B. Decision FusionSuppose that Pd,i and Pf,i are the probability of detection

and probability of false alarm from the ith secondary user,respectively. Similar to the multiple mini-slot case, the prob-ability of detection and probability of false alarm of the finaldecision can be derived accordingly, from which the sensing-throughput tradeoff can be carried out.

VI. COMPUTER SIMULATIONSIn this section, computer simulation results are presented to

evaluate the sensing-throughput tradeoff for energy detectiontechnique with various data/decision fusion schemes. Theprimary user is assumed to be a QPSK modulated signal withbandwidth of 6MHz. The sampling frequency is the same asthe bandwidth of the primary user. The additive noise is azero-mean CSCG process. We are interested in low SNRpregime, and choose P (H1) = 0.2, and the target probabilityof detection as Pd = 0.9.

A. One Secondary User for Spectrum SensingFirst, we compare the probability of detection and proba-

bility of false alarm calculated from Monte Carlo simulationsand the theoretical results derived in this paper. 20000 MonteCarlo simulations are performed. In the simulations, for eachsample size and under hypothesis H1, we first find out thedetection threshold to achieve the target detection probabilitybased on the 20000 test statistics, then apply this thresholdto the hypothesis H0 and derive the probability of falsealarm. Fig. 3 shows the comparison between simulated andtheoretical probabilities for Pd = 0.9 and SNRp = 15dB.It is seen that the target probability of detection is achieved,and the probability of false alarm decreases with the increaseof the number of samples.

1 1.5 2 2.5 3 3.5 4 4.5 54.7

4.8

4.9

5

5.1

5.2

5.3

5.4

Sensing time (ms)

Achi

evab

le th

roug

hput

(bits

/Sec

/Hz)

Fig. 4. Achievable throughput for the secondary network (o for R(),+ for R()): T = 100ms, SNRp = 15dB.

1 1.5 2 2.5 3 3.5 4 4.5 50.88

0.89

0.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

Sensing time (ms)

Achi

evab

le th

roug

hput

(bits

/Sec

/Hz)

SimulatedTheory

Fig. 5. Normalized achievable throughput for the secondary network: T =100ms, SNRp = 15dB.

Next, suppose the SNR for secondary transmission isSNRs = 20dB, thus C0 = log2(1 + SNRs) = 6.6582and C1 = log2

(1 + SNRs1+SNRp

)= 6.6137. We also choose

the frame duration T = 100ms. Fig. 4 shows the achievablethroughput versus the sensing time allocated to each framefor the secondary network. In this figure, two results areshown: R() of (18), and R() of (23). It is seen that forboth quantities, the maximum is achieved at the sensing timeof about 2.55ms. Fig. 5 illustrates the normalized achievablethroughput for the secondary network, which is defined asB() =

(1 T

)(1 Pf ). Again, it reveals a maximum

point at the sensing time of about 2.55ms. Furthermore, thesimulated results match to the theoretical results very well.Because of this consistency, in the following evaluations, wewill only consider the theoretical results.



1 1.5 2 2.5 3 3.5 4 4.5 50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Sensing time (ms)

P f o

f the

net

work

M=1 ; channel knownM=2 ; channel knownM=3 ; channel knownM=4 ; channel knownM=1 ; channel unknownM=2 ; channel unknownM=3 ; channel unknownM=4 ; channel unknown

Fig. 6. The average probability of false alarm Pf () using multi-slotspectrum sensing.

B. Multi-Slot Spectrum Sensing

Instead of using one sensing slot in each frame, we nowconsider spectrum sensing using multiple mini-slots. The totalsensing time in each frame is divided equally among themultiple mini-slots. The SNRps for primary user at differentmini-slots are independent, and each follows an exponentialdistribution with mean SNRp of 15dB. The target probabil-ity of detection for each frame is 90%, the frame duration ischosen to be T = 100ms, and the number of frames simulatedis 100000. The fading coefficients are either completely knownor completely unknown. When these coefficients are known,the weighting factors for fusing the test statistics of the mini-slots are computed from (46). When the fading coefficientsare unknown, the weighting factors are chosen to be the samefor all the mini-slots, i.e., gi = 1M .

Fig. 6 shows the average probability of false alarm Pf ()using different numbers of mini-slots as a function of thetotal sensing time . From this figure, it is seen that, for agiven total sensing time, increasing the number of mini-slotsimproves the performance of the spectrum sensing especiallywhen one sensing slot is split into two mini-slots. This isdue to the effect of diversity reception. In fact, in order toachieve the same probability of detection for each frame, thedetection threshold will vary from one frame to another, andthe diversity reception helps to increase the received SNR ofthe primary user, thus to reduce the probability of false alarm.However the gain in improvement reduces when the numberof mini-slots is getting larger. This figure also shows thatthe performance of data fusion without knowing the fadingcoefficients can approach that with known fading coefficientswhen the total sensing time is long enough.

Fig. 7 and Fig. 8 illustrate the normalized throughput forthe secondary network with the fading coefficients knownand unknown, respectively. As the number of mini-slots in-creases, the maximum normalized throughput increases, butthe required sensing time to achieve the maximum normalizedthroughput decreases. With only one sensing slot and fadingcoefficients known, the normalized achievable throughput is0.763 with a total sensing time of 7ms, but when five mini-

1 2 3 4 5 6 7 8

0.65

0.7

0.75

0.8

0.85

0.9

0.95

Sensing time (ms)

Nor

mal

ized

thro

ughp

ut

M=1M=2M=3M=4M=5

Fig. 7. Normalized throughput for multi-slot spectrum sensing when thefading coefficients are known.

1 2 3 4 5 6 7 8

0.65

0.7

0.75

0.8

0.85

0.9

0.95

Sensing time (ms)

Nor

mal

ized

thro

ughp

ut

M=1M=2M=3M=4M=5

Fig. 8. Normalized throughput for multi-slot spectrum sensing when thefading coefficients are unknown.

slots are used, the normalized achievable throughput is 0.94at a total sensing time of 3.6ms. Using five mini-slots andwhen the fading coefficients are unknown, the normalizedachievable throughput is 0.925 at a total sensing time of4.75ms. Fig. 9 is plotted to compare the maximum normalizedthroughput between the cases when the fading coefficients areknown or unknown. It is seen that when the number of mini-slots is large, there is a constant gap between the maximumnormalized throughputs for the two cases.

C. Distributed Spectrum SensingNext, we consider the case when multiple secondary users

are used to sense the presence of primary user. For simplicity,we assume that the received SNRs for primary user at eachsecondary user are all equal. Fig. 10 shows the optimal sensingtime versus the number of sensing users when various decisionfusion schemes are applied and SNRp = 15dB. It isseen that for each fusion scheme, the optimal sensing timedecreases when the number of sensing terminals increases.Fig. 11 illustrates the maximum normalized throughput of thesecondary network with different number of sensing users. It



1 2 3 4 5 6 7 8 9 100.75

0.8

0.85

0.9

0.95

0.975

Number of minislots

Max

. nor

mal

ized

thro

ughp

ut

channel knownchannel unknown

Fig. 9. Maximum normalized throughput for multi-slot spectrum sensing.

is also seen that this normalized throughput increases with theincrease of number of sensing users. Fig. 12 shows the optimalsensing time for various frame duration and receive SNRpusing logic-AND decision fusion rule. If only one secondaryuser is used, the optimal sensing time increases from 2.55msto 14.2ms, when the SNRp drops from 15dB to 20dB.When four secondary users are used, the optimal sensing timeincreases from 1.5ms to 9.5ms, when SNRp drops from15dB to 20dB. Further, if the frame duration increases,the optimal sensing time also increases, for a given receivedSNR of primary user at the sensing users.

VII. CONCLUSIONSIn cognitive radio networks, the interests of primary users

and secondary users are contradictory. In this paper, weconsider MAC frame structure design supporting periodicspectrum sensing and formulate the sensing-throughput trade-off problem by considering both users interests. Particularly,we study the problem of designing the sensing slot duration tomaximize the achievable throughput for the secondary usersunder the constraint that the primary users are sufficientlyprotected. Using energy detection scheme, we have proved thatthere indeed exists an optimal sensing time which achieves thebest tradeoff. Cooperative sensing has also been studied basedon the proposed tradeoff methodology. Computer simulationshave shown that for a frame duration of 100ms, and the SNRof primary user of 20dB, the optimal sensing time achiev-ing the highest throughput while maintaining 90% detectionprobability is 14.2ms. This optimal sensing time decreases to9.5ms when 4 distributed secondary users cooperatively sensethe channel using Logic-AND decision fusion rule.

APPENDIX A: PROOF OF PROPOSITION 2From (1), under hypothesis H1, if both s(n) and u(n) are

complex-valued, we have

21 = E[|T (y) 1|2] (70)

= E

(

1N

Nn=1

|s(n) + u(n)|2 (2s + 2u))2(71)

2 4 6 8 10 12 14 16 18 20

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

Number of users

Opt

imal

sen

sing

time

(ms)

LogicANDLogicORLogicMajority

Fig. 10. Optimal sensing time for distributed spectrum sensing with variousdecision rules: SNRp = 15dB, T = 100ms.

=1N

E[(|s(n)|2 + |u(n)|2 + s(n)u(n)+ s(n)u(n) 2s 2u)2]. (72)

If s(n) is circularly symmetric, then it can be representedas s(n) = sr(n) + jsi(n) with E[s2r(n)] = E[s2i (n)] =

2s2 ,

and E[sr(n)si(n)] = 0. Thus we have E[s2(n)] = 0, andsimilarly E[u2(n)] = 0. Using the fact that s(n) and u(n) areindependent and with zero mean, we arrive at (8) by expanding(72).

On the other hand, if both s(n) and u(n) are real-valued,we have

21 = E[(T (y) 1)2

] (73)= E

( 1

N

Nn=1

(s(n) + u(n))2 (2s + 2u))2(74)

=1N

E[(s2(n) + u2(n) + 2s(n)u(n)

2s 2u)2]. (75)Eq. (9) can then be derived by using the zero-mean and mutualindependence property of s(n) and u(n).

APPENDIX B: CONCAVITY OF R()Proposition 5: Under the assumptions (AS1) - (AS3), if the

primary signal is complex-valued PSK and the noise processis CSCG, then Pf () is decreasing and convex for the rangeof in which Pf () 0.5.

Proof: From (13), and notice = 2 + 1Q1(Pd), wehave:

Pf () = Q( +

fs). (76)Differentiating Pf () with respect to gives:

P f () =dPf ()

d

=

fs

2

21/2 exp(( +

fs)2/2).(77)

For > 0, it is clear that P f () < 0 so Pf () is decreasingin . Furthermore, when Pf () 0.5, from (76) we have



2 4 6 8 10 12 14 16 18 200.97

0.975

0.98

0.985

0.99

0.995

Number of users

Max

imum

nor

mal

ized

cap

acity

LogicANDLogicORLogicMajority

Fig. 11. Normalized achievable throughput for distributed spectrum sensingusing various decision rules: SNRp = 15dB, T = 100ms.

1 1.5 2 2.5 3 3.5 40

2

4

6

8

10

12

14

16

18

Number of users

Opt

imal

sns

ing

time

(ms)

SNRp = 15dB, T=100 msSNRp = 20dB, T=100 msSNRp = 15dB, T=200 msSNRp = 20dB, T=200 ms

Fig. 12. Optimal sensing time for distributed spectrum sensing using logic-AND decision fusion rule.

+

fs 0. This, together with (77), implies that P f () ismonotonically increasing in when Pf () 0.5, i.e., Pf ()is convex in when Pf () 0.5.

Proposition 6: For the range of such that Pf () isdecreasing and convex in , R() is concave in , 0 T .

Proof: Let

R() = C0P (H0)T T

(1 Pf ()), (78)

then

R() = C0P (H0)(Pf ()

T(1

T

)P f ()

1T

). (79)

When Pf () is decreasing and convex in , P f () is nega-tive and increasing in . Further, Pf () is decreasing in .Therefore, from (79), it follows that R() is decreasing in, 0 T , which further implies R() is concave in .

From Propositions 5 and 6, it follows that R() is concavefor the range of in which Pf () 0.5. This further impliesthat there is a unique maximum point of R() within thisrange.

REFERENCES[1] Federal Communications Commission, Spectrum policy task force

report, FCC 02-155, Nov. 2002.[2] Federal Communications Commission, Facilitating opportunities for

flexible, efficient, and reliable spectrum use employing cognitive radiotechnologies, notice of proposed rule making and order, FCC 03-322,Dec. 2003.

[3] J. Mitola and G. Q. Maguire, Cognitive radios: Making software radiosmore personal, IEEE Pers. Commun., vol. 6, no. 4, pp. 13-18, Aug.1999.

[4] J. Mitola, Cognitive radio: An integrated agent architecture for softwaredefined radio, PhD. diss., Royal Inst. Technol. (KTH), Stockholm,Sweden, 2000.

[5] S. Haykin, Cognitive radio: Brain-empowered wireless communica-tions, IEEE J. Selected Areas Communications, vol. 23, no. 2, pp. 201-220, Feb. 2005.

[6] IEEE 802.22 Wireless RAN, Functional requirements for the 802.22WRAN standard, IEEE 802.22- 05/0007r46, Oct. 2005.

[7] A. Sahai and D. Cabric, Spectrum sensing: fundamental limits andpractical challenges, in Proc. IEEE DySPAN 2005, [Online]. Available:http://www.eecs.berkeley.edu

[8] S. M. Mishra, A. Sahai, and R. W. Brodensen, Cooperative sensingamong cognitive radios, in Proc. IEEE Int. Conf. Commun. (ICC), June2006, pp. 1658-1663.

[9] W. A. Gardner, Exploitation of spectral redundancy in cyclostationarysignals, IEEE Signal Processing Mag., vol. 8, pp. 14-36, Apr. 1991.

[10] Y.-C. Liang, et al., System description and operation principles forIEEE 802.22 WRANs, [Online]. Available: http://www.ieee802.org/22/

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[14] A. Ghasemi and E. S. Sousa, Collaborative spectrum sensing foropportunistic access in fading environments, in Proc. IEEE Dyspan,Nov. 2005, pp. 131-136.

[15] D. Cabric, S. M. Mishra, and R. W. Brodersen, Implementation issuesin spectrum sensing for cognitive radios, in Proc. 38th Asilomar Conf.Signals, Syst., Computers, Nov. 2004, vol. 1, pp. 772-776.

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[19] Y.-C. Liang, Y. Zeng, E. Peh, and A. T. Hoang, Sensing-throughputtradeoff for cognitive radio networks, in Proc. IEEE Int. Conf. Com-mun.(ICC), June 2006, pp. 5330-5335.

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Ying-Chang Liang (SM00) received the PhD de-gree in Electrical Engineering in 1993. He is nowa Senior Scientist in the Institute for Infocomm Re-search (I2R), Singapore, where he has been leadingresearch activities in the area of cognitive radioand cooperative communications and standardiza-tion activities in IEEE 802.22 wireless regionalnetworks (WRAN), for which his team has madefundamental contributions in physical layer, MAClayer, and spectrum sensing solutions. He also holdsadjunct associate professorship positions in Nanyang

Technological University (NTU) and the National University of Singapore(NUS), both in Singapore, and an adjunct professorship position at theUniversity of Electronic Science and Technology, China (UESTC). He hasbeen teaching graduate courses in NUS since 2004. From Dec. 2002 to Dec.2003, Dr Liang was a visiting scholar with the Department of ElectricalEngineering, Stanford University. His research interests include cognitive ra-dio, dynamic spectrum access, reconfigurable signal processing for broadbandcommunications, space-time wireless communications, wireless networking,information theory and statistical signal processing.

Dr Liang served as an Associate Editor for the IEEE TRANSACTIONSON WIRELESS COMMUNICATIONS from 2002 to 2005, Lead Guest-Editor ofthe IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, SPECIALISSUE ON COGNITIVE RADIO: THEORY AND APPLICATIONS, and Guest-Editor of the Computer Networks Journal (Elsevier) Special Issue on Cog-nitive Wireless Networks. He received the Best Paper Awards from IEEEVTC-Fall1999 and IEEE PIMRC2005, and the 2007 Institute of EngineersSingapore (IES) Prestigious Engineering Achievement Award. Dr Liang hasserved for various IEEE conferences as a technical program committee (TPC)member. He was Publication Chair of the 2001 IEEE Workshop on StatisticalSignal Processing, TPC Co-Chair of the 2006 IEEE International Conferenceon Communication Systems (ICCS2006), Panel Co-Chair of the 2008 IEEEVehicular Technology Conference Spring (VTC2008-Spring), TPC Co-Chairof the 3rd International Conference on Cognitive Radio Oriented WirelessNetworks and Communications (CrownCom2008), Deputy Chair of the 2008IEEE Symposium on New Frontiers in Dynamic Spectrum Access Networks(DySPAN2008), and Co-Chair, Thematic Program on Random matrix theoryand its applications in statistics and wireless communications, Institute forMathematical Sciences, National University of Singapore, 2006. Dr Liang isa Senior Member of IEEE. He holds six granted patents and more than 15filed patents.

Yonghong Zeng (M00-SM05) received the B.S.degree from Peking University, Beijing, China, andthe M.S. degree and the Ph.D. degree from theNational University of Defense Technology, Chang-sha, China. He worked as an associate professorin the National University of Defense Technologybefore July 1999. From Aug. 1999 to Oct. 2004, hewas a research fellow in the Nanyang TechnologicalUniversity, Singapore, and the University of HongKong, respectively. Since Nov. 2004, he has beenworking in the Institute for Infocomm Research,

A*STAR, Singapore, as a scientist. His current research interests includesignal processing and wireless communication, especially on cognitive radioand software defined radio, channel estimation, equalization, detection, andsynchronization.

He has co-authored six books, including Transforms and Fast Algorithmsfor Signal Analysis and Representation, Springer-Birkhuser, Boston, USA,2003, published more than 60 refereed journal papers, and invented fourUS patents. He is an IEEE senior member. He received the ministry-levelScientific and Technological Development Awards in China four times. In2007, he received the IES prestigious engineering achievement award inSingapore.

Edward C.Y. Peh received the B.E. degree inElectrical and Electronic Engineering from NanyangTechnological University, Singapore, in 2005. From2005 to 2007, he was employed as a Research Of-ficer in the Institute for Infocomm Research, Singa-pore, researching on cognitive radio. He is currentlypursuing his PhD in Communication Engineeringat Nanyang Technological University, Singapore.His research interests are in the areas of wirelesscommunications and signal processing.

Anh Tuan Hoang (M07) received the Bachelordegree (with First Class Honours) in telecommuni-cations engineering from the University of Sydneyin 2000. He completed his Ph.D. degree in electricalengineering at the National University of Singaporein 2005.

Dr. Hoang is currently a Research Fellow atthe Department of Networking Protocols, Institutefor Infocomm Research, Singapore. His researchfocuses on design/optimization of wireless commu-nications networks. Specific areas of interest include

cross-layer design, dynamic spectrum access, and cooperative communica-tions.


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