Cooperative Spectrum Sensing in Cognitive Radios With ... - ECE@NUS

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IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 58, NO. 6, JUNE 2010

Cooperative Spectrum Sensing in Cognitive Radios With Incomplete Likelihood Functions Sepideh Zarrin and Teng Joon Lim

Abstract—This paper investigates the problem of cooperative spectrum sensing in cognitive radios with unknown parameters in the likelihood function. We first derive the optimal likelihood ratio test (LRT) statistic based on the Neyman-Pearson (NP) criterion at the fusion center for hard (one-bit), soft (infinite precision) and quantized (multi-bit) local decisions. This NP-based LRT detector is feasible only if primary signal statistics and channel parameters are known. This assumption may not be realistic in cognitive radio systems. Thus, we propose a linear composite hypothesis testing approach which estimates the unknown parameters, and further simplify it so that it does not even require these estimates. Under the scenarios of: i) unknown primary signal and channel statistics; and ii) unknown primary signal statistics but known channel statistics, we apply the proposed test and also, for case ii), derive the locally most powerful (LMP) detector for weak signals. For performance analysis and threshold setting, we derive the distributions of the linear test and LMP statistics under the signal-absent hypothesis. Our simulation results show that the linear test performs very closely to the optimal LRT while not requiring the primary statistics. As a result, this method enhances robustness in cooperative spectrum sensing to uncertainties in channel gains and signal statistics. Index Terms—Cognitive radio, hypothesis testing, likelihood ratio test, parameter estimation, sensor networks, spectrum sensing.

I. INTRODUCTION

C

OGNITIVE radio technology has recently emerged as a promising approach for improving spectrum utilization efficiency and meeting the increasing demand for wireless communications [1], [2]. Cognitive radio relies on the efficient detection of “white spaces” in the spectrum allocated to the licensed (primary) users and opportunistic utilization of these bands by the unlicensed (secondary) users. Furthermore, in order to avoid interfering with the primary network, the secondary users (SUs) need to vacate the frequency band as soon as the primary user (PU) starts its transmission. Thus, spectrum sensing plays a key role in cognitive radio technology. However, due to destructive channel conditions, it is hard to achieve reliable spectrum sensing by a single user. Cooperative spectrum sensing alleviates this problem by utilizing spatial diversity and hence improving detection reliability [3]–[6], [13].

Manuscript received June 27, 2009; accepted January 29, 2010. Date of publication March 11, 2010; date of current version May 14, 2010. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Ye (Geoffrey) Li. The authors are with the Department of Electrical and Computer Engineering, University of Toronto, Toronto, Ontario, Canada M5S 3G4 (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSP.2010.2045425

In this paper, we consider the problem of spectrum sensing at a central node (see Fig. 1) in a cooperative-sensing cognitive radio network, acting analogously to the fusion center (FC) in a distributed sensor network. The channels between the sensing nodes or secondary users and the FC are treated as noisy. The primary network, when active, is assumed to transmit a zero-mean signal unknown to the cognitive network, which is received over a Rayleigh flat-fading channel by each SU. Spectrum sensing at each SU can generally be based on any of these techniques: energy detection [7], [8], matched filtering [9], [10], and cyclostationary feature detection [11], [12]. Cyclostationary detection requires the knowledge of cyclic frequencies of the PU’s and matched filtering needs the knowledge of the waveforms and channels of the PU. If no knowledge of the primary signal is available at the SUs, energy detection can be applied. As we are looking for robust spectrum sensing methods in this paper, we assume energy-based detection in all the SUs. When the second- and fourth-order moments of the primary signal and the variance of channel gains are known, we will show that it is possible to derive the NP test at the FC based on various ways1 of making local decisions from the observations at the sensing nodes. These results are derived using general concepts introduced in the context of sensor networks [14]–[19], specialized to the scenario we just described. However, in practice, it is unlikely that the SUs or the FC would have knowledge of the moments of the transmitted primary signal or the channel between the primary transmitter and each SU. In fact, this is an important constraint in cognitive radio networks. Thus, we go on to address the above problem, using first the notion of the generalized likelihood ratio test (GLRT) and its asymptotically (as the number of observations increase without bound) equivalent form, and then further simplifying it heuristically to the sum of log-likelihood derivatives. The resulting test statistic, which we call the linear test statistic, does not require maximum likelihood estimates (MLEs) of the unknown parameters, which are hard to derive analytically in many realistic scenarios, while showing a comparable performance to the known-parameter optimal NP test. Compared to other well-known asymptotically-equivalent tests to GLRT, such as the Wald and Rao tests [8], this scheme is much simpler and does not require the calculation of the Fisher information matrix which is not easily attainable or invertible in many practical scenarios. The proposed simplified linear test is applied to the cases of: i) unknown primary signal and PU-SU channel statistics, and ii) unknown primary signal statistics but known PU-SU 1Binary,

M -level and no quantization of the received signal energy.

1053-587X/$26.00 © 2010 IEEE

ZARRIN AND LIM: COOPERATIVE SPECTRUM SENSING IN COGNITIVE RADIOS

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Fig. 1. Block diagram of cooperative spectrum sensing system with

K secondary users.

channel statistics. In case ii), for the practical case of weak constant-modulus primary signals, we additionally derive the LMP test [8]. Furthermore, for threshold setting and performance analysis, we derive the distributions of the linear test and LMP statistics under the null hypothesis. In this paper, we consider soft (infinite-precision) and quantized local decision scenarios and derive the LRT and linear test statistics for each case. The remainder of this paper is organized as follows. The system model and the NP-based LRT at the fusion center are presented in Section II. The proposed linear test for cooperative spectrum sensing is presented in Section III. Section IV comprises the derivation of the linear test statistics for different types of local decisions assuming unknown channel and primary signal statistics as well as the linear test and LMP statistics for known channel statistics and unknown primary signal moments along with the analytical threshold setting for linear test and LMP. Section V provides the simulation results and, finally, Section VI concludes the paper.

fusion center from sensor . We can consider different models for the channels between the secondary users and the fusion center, for example: binary symmetric channels (BSCs) with crossover probabilities ’s, and AWGN channels with addi. In the AWGN case, tive noise . The evidence available to the fusion center to make the global decision . Throughout is the set of channel outputs denotes the set , underscored varithis paper, ables are vectors, and no distinction is made between random variables and their values.

II. MODEL AND FORMULATION

The optimal decision rule at the fusion center in the sense of maximizing the probability of detection for a given probability if of false alarm is the NP-based LRT. This method decides and only if

A. System Model We consider a centrally coordinated cognitive radio network with secondary users. The -th secondary user observes a over a sensing interval complex baseband-equivalent signal of samples, where the underscore denotes a vector of samples in time. We denote the baseband-equivalent signal transmitted by the primary user by , also an -vector. This signal is propagated to the -th secondary user over a channel that is frequency nonselective and time invariant over sampling intervals, i.e.

B. NP-Based LRT at the Fusion Center Spectrum sensing is a binary hypothesis testing problem, with the null and alternative hypotheses Primary user not active Primary user active

(2)

(3) where the threshold lytically)

is found by solving (numerically or ana(4)

(1) denotes zero-mean additive white Gaussian noise where and (AWGN) at the secondary user, i.e., represents the circularly symmetric complex Gaussian (CSCG) channel gain i.e. . We assume that , and are independent, which is reasonable from a practical perspective. At the -th user, the signal is mapped onto another signal which is then transmitted to the fusion center where the final decision is made. The channel between each user and the fusion center is assumed to be noisy and charac, where denotes the signal received at the terized by

for a given desired probability of false alarm . We can apply the graphical model approach for cooperative sensing presented and in [21] to obtain the likelihood functions , for different system model assumptions. Given that the received energy is the sufficient test statistic for independent Gaussian PU-SU channels [16], we consider the received signal energies at the secondary users as the local test statistics. By the central limit theorem (CLT), the local received signal enis asymptotically Gaussian under either or ergy . Therefore, we have (5)

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where and mean

denotes one of the elements of , as they are i.i.d., is the variance of random variable . For zeroand , we have if (6) if if

(12)

By consistency of the MLE as , , and thus the last term which is of second order may be neglected [8]. Thus we have

(7) (13)

if As shown in [21], the likelihood ratio in (3) depends on the distribution of local energies, . Therefore, LRT-based methods are only applicable when and are known. III. THE PROPOSED COMPOSITE HYPOTHESIS TESTING APPROACH

(8) . attains the Cramer-Rao lower

results in (14)

The constant is bound to be totic likelihood function is

As discussed in Section II-B, the optimal NP-based method relies on knowledge of the primary signal and channel statistics. In practice, however, such knowledge may not be available to the cognitive radios and thus, the LRT-based schemes are not directly applicable. Therefore, in cognitive radios, detection schemes that are robust to unknown parameters should be employed. In a general scenario, we assume that no knowledge of the primary signal statistics and channel gains are availand able at the fusion center. We denote , for , as the unknown parameters in the likelihood ratio in (3). The vector of unknown pa. rameters is then A well-known composite hypothesis test which can replace the NP-based LRT in unknown parameter scenarios is the GLRT. This test first finds the MLE of the unknown parameters , and then forms the GLRT statistic under

where The unrestricted MLE of bound. Thus it satisfies [20]

Integrating both sides of (13) with respect to

By substituting reduces to

. Therefore the asymp-

(15) from (15) into (8), the GLRT statistic (16)

Therefore, the asymptotic equivalent for GLRT can be represented as (17) By substituting (13) into the asymptotic form of the GLRT in (17), the proposed asymptotically equivalent test statistic is derived as (18)

We call the proposed test the linear test as its test statistic con’s. sists of a linear combination of the For the set of unknown parameters in our model the linear test statistic can be written as

(9) The th element of

is given by [8] (19) (10) In scenarios where it is infeasible or computationally demanding to solve

By the first-order Taylor expansion (11)

we have

(20) , we alternatively propose to substitute uniquely for under the vector with a vector of ones, (21)


Our numerical results support this suggested scheme and show a close performance for the proposed linear scheme to that of the optimal NP-based LRT with known parameters. This simplified linear test statistic for the assumed model can be rewritten as

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and and where respectively, the mean and variance of the local energy as

are, given (25) (26)

(22) This method can be used for any detection problem with unknown or uncertain parameters. Unlike the Rao and Wald tests, the linear test does not have a quadratic form and does not require the calculation of the Fisher information matrix which is matrix for our system. Therefore, it is easier and a faster to implement compared to these schemes. In its simplified form (22), the linear test does not even require the MLEs of the unknown parameters which results in a much simpler and faster test compared to the Wald and GLRT tests. In fact, it is not feasible to analytically find the unrestricted MLEs of unknown parameters in most realistic scenarios [8], such as the soft and quantized local decision scenarios in this paper. This linear test is also much simpler than the Rao test which has a quadratic form and requires the inverse of the Fisher information matrix. The Rao test, in fact, is not practical as the Fisher information matrix is not easily attainable or invertible in many system models. Dealing with multiple unknown parameters (in parameters), exacerbates the complexity and inthis case feasibility of calculating this inverse matrix. IV. THE PROPOSED TEST FOR COOPERATIVE SPECTRUM SENSING A. Unknown Primary Signal and Channel Statistics In this section, we derive the NP-based LRT at the fusion center and apply the proposed linear test to cooperative fusion of quantized and soft local decisions with unknown primary signal moments and channel statistics. 1) Quantized Soft Local Decisions: In this section, we assume that the secondary users transmit locally quantized test statistics (received signal energies) and then derive the LRT and linear test statistics at the fusion center. In this paper, we do not deal with the optimization of the local thresholds and refer the readers to [15]–[18] for threshold optimization algorithms in distributed sensor networks. We assume that the th levels and user quantizes its received signal energy with and sends preset local thresholds of to the fusion center. In this case, the local decision sent to the fusion center based on the quantized local energy is determined as follows: (23) , , and . The likelihood where function in this case is derived in the Appendix as

(24)

Consequently, the LRT statistic at the fusion center is derived as

(27) We observe that the NP-based LRT depends on and . For -ary PSK (phase shift keying) modulated primary signals, and , where is the maximum transmit voltage. For -ary ASK (amplitude shift keying), we have (28) (29) Therefore, in order to apply the LRT, knowledge of the modulation type and maximum transmit voltage of the primary signal as well as the channel gain variance is required at the fusion center. For the realistic scenario that the primary signal moments and channel statistics are not available at the cognitive radios, we propose to apply the linear test rather than the LRT in (27). For this reason, we derive the partial derivatives of the logarithm of ’s and ’s and evaluate the LRT in (27) with respect to as follows: them at

(30)

(31) where

(32)

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Given the Gaussian distribution of or Gaussian distributed under

is also (39)

(33) Derivation of the MLEs of and is not feasible analytically in this scenario. Therefore, we apply the simplified linear test and derive its test statistic as in (34), as shown at the bottom of the page. For the spacial case of binary (hard) local decisions, the LRT statistic in (27) reduces to

as in (5),

where and under and , are given in (6) and (7), respectively. Therefore, by independence of the channels, the LRT statistic is derived as follows:

(40) (35) where is the local threshold at the th user. Based on the distribution of the local energy in (5), the local threshold that is determined as result in local probability of false alarm of (36)

The LRT decides if , where the threshold can be set using an empirical distribution of the log-likelihood ratio under the null hypothesis. We next derive the unknown-parameter linear test for soft local decisions by evaluating the derivatives of the log-likelihood function at

The linear test statistic at the fusion center, in this case, is obtained from (34) as (41) (42) (37) 2) Soft Local Decisions: In many previous studies in cooperative sensing [4]–[6], [13] the local test statistics (signal energies) were assumed to be transmitted with infinite precision to the fusion center over error-free control channels. In this section, we derive the LRT and then the linear test at the fusion center for such soft local decisions with noisy AWGN channels from the users to the fusion center. The signal received at the fusion center from the -th sensor , where is assumed to be zero-mean Gaussian is , so that noise with variance (38)

and

substituting

(41)

and (42) into (22). Solving and for and results in a third-order equation with respect to which must be solved numerically. Thus, we alternatively use the simplified linear test for this scenario and derive its statistic as

(43) depends on and , the AWGN variNote that ances in the SU-FC and PU-SU channels, respectively, but not

(34)


on the primary transmitted signal statistics or the PU-SU fading channel parameter.

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is a one-sided scalar-parameter test for small departures of the parameter from zero [8]. The LMP test statistic is derived as

B. Unknown Primary Signal Statistics and Known Channel Statistics 1) Linear Test: It may be practical to assume that the second-order statistics of the channel gain from the primary user to secondary users are available at the fusion center. Therefore, the set of unknown parameters in our model will and . In this case, unlike reduce to ’s and in the previous section where the ’s only consisted of terms that depend on , the and consist of summation of nonlinear terms in and over . Therefore the analytical derivation of the MLEs is infeasible for our general cooperative noisy channel model. Hence, we propose to apply the simplified linear test with statistic

(47) if is the only unknown parameter. We use this scalar-parameter test for the case of constant-modulus primary signal with and the unknown small power of . In this case, only unknown parameter is . This test can be applied to hard, soft and quantized local decision scenarios for constant-modulus primary signals. Here we derive the LMP test statistic for the binary local decision case as an example. For constant-modulus (e.g. -PSK modulated) primary signals, the LRT statistic in (35) reduces to

(44)

We can apply the linear test to all local decision scenarios discussed in Section III when the channel gain statistics are available but the primary signal statistics are not. For the binary local decision scenario, for instance, the derivatives of the log-likeliand are derived and evaluated hood ratio with respect to as follows: at

(48) Therefore, the LMP test statistic is derived as

(49)

(45)

We observe that the LMP test statistic for weak constant-modulus primary signals has a similar expression to the first part of the linear test statistic in (45) for general primary signals. For the case of quantized local decisions, we derive the LMP test statistic as

(50) (46) The simplified linear test statistic in this case is derived by inserting (45) and (46) into (44). We can similarly derive the linear test statistics of the soft and quantized local decisions for known channel parameters and unknown primary signal statistics, but do not show them here for conciseness. 2) LMP Test: When the channel gains are known and the only unknown parameters are the primary signal statistics, we can use the LMP test under certain assumptions. The LMP test

is given in (32). where By and large, the proposed linear test can be applied for all ranges of signal power, whereas the LMP is restricted to small signal powers. Moreover, the linear test accommodates multiple unknown parameters, while the LMP is confined to scalar parameter tests. C. Threshold Setting at the Fusion Center 1) Linear Test: In order to set the threshold at the fusion center when using the simplified linear test, we need the dis-

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tribution of the test statistic under . Under for , by regularity conditions [[20], p. 67] we have which

(51) (61) Moreover, the simplified linear test statistic can be written as

(52) Therefore, by CLT we have

(62) (53) where and are given in (32) and (33). Thus, using the derived distribution of the simplified linear test statistic under , the probability of false alarm for global threshold of is given by

where

(63) (54) and

(64)

(55) For binary local decisions and binary symmetric channels between the users and fusion center, with crossover probability of , we derive , , and as follows: (56)

In this way, we can analytically set the global threshold at the fusion center to maintain the target probability of false alarm, , as

(65) 2) LMP Test: The LMP test statistic in (66) can be rewritten as (66)

(57) Therefore, by CLT and regularity condition (58) where

(67) we have

(59) For the quantized local decision scenario, these information numbers can be derived as

(68) where (69) Thus, the global threshold at the fusion center to maintain a probability of false alarm of is analytically determined as (70)

(60)


Fig. 2. Complementary ROC (P

versus P ) curves for hard local decisions.

In the quantized local decision scenario, for example, the variance of the LMP test statistic under null hypothesis is derived as

(71) V. SIMULATION RESULTS In this section, we present our simulation results to evaluate the performance of the linear test in cooperative spectrum sensing. We consider the cases of hard, soft and quantized local decisions and use the performance of NP-based LRT cooperative sensing as an upperbound for comparison. We secondary users in the network which indeconsider pendently sense the primary user’s spectrum. The Rayleigh fading channel coefficients are assumed to be independently , where the variances ’s for the six drawn from PU-SU channels are assumed to be 1.28, 0.32, 4.5, 0.5, 2, and 0.08, respectively. The primary signal is assumed to be 4-ASK sampling modulated (multi-level) and sensed over intervals. The local decisions are BPSK modulated and sent to the fusion center through independent binary symmetric channels for hard and quantized local decisions. We use the complementary receiver operating characteristics (ROC) curves , versus (plots of probability of missed detection, probability of false alarm, ) to illustrate the performance of cooperative sensing schemes. Fig. 2 depicts the complementary ROC curves of the NP-based LRT, linear test and LMP detector with unknown primary statistics for hard local decisions. The local energy detection thresholds are chosen to achieve a target local probability of false alarm of , where the local noise . The crossover probabilities variances are set to be

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Fig. 3. Complementary ROC (P

versus P ) curves for soft local decisions.

for the six SU-FC BSC channels are 0.1, 0.15, 0.1, 0.2, 0.15, and 0.1, respectively. We observe that the linear test performs very closely to the optimal NP-based LRT fusion. Fig. 3 depicts the complementary ROC curves of the linear test with unknown primary statistics and NP-based LRT for soft . The local decisions. The local noise variances are set to AWGN channels are generated from a Gaussian distribution of where the variances for the six SU-FC channels are assumed to be 0.64, 1, 2.25, 0.81, 1, and 1.21, respectively. We observe that the linear test performs very closely to the optimal NP-based LRT fusion. This holds for different primary signal and ) and different levels of constellations (here, and ). transmit power (here, Fig. 4 depicts the complementary ROC curves of NP-based LRT and the linear test with unknown primary statistics for 2-bit quantized local decisions. The quantization thresholds are set to , and , where is deterbe mined as (36), and is assumed to be 0.8. We observe that the linear test performs very closely to the optimal NP-based LRT. As the BSC cross-over probabilities increase, the performance of the linear test converges to that of the optimal NP-based LRT. Fig. 5 depicts the complementary ROC curves of NP-based LRT and linear test with unknown channel gains and primary statistics for 2-bit quantized local decisions. The BSC cross-over probabilities of 0.1 and 0.05 and maximum transmit voltage of 1 have been assumed. We observe that the linear test performs closely to the optimal NP-based LRT with known primary and channel parameters. Our simulation results show that with knowledge of the channel gain variance at the FC, the performance of the linear test becomes closer to that of the LRT. We can also observe that as the SU-FC channel conditions deteriorate (e.g., increases in BSCs), the linear test performs closer to the known-parameter LRT. This also holds for lower SNRs and weaker primary signals (i.e., lower ). Therefore, the linear test performs close to optimal in lower SNRs and more unfavorable channel conditions, which once again highlights its practical significance.

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Fig. 4. Complementary ROC (P decisions.

versus P ) curves for 2-bit quantized local

Fig. 6. Probability distribution of the linear test statistic under null hypothesis.

more practical and simpler compared to the GLRT which requires the ML estimates of the unknown parameters. We derived the linear test statistic for decision making at the fusion center under hard, soft and quantized local decision scenarios. Furthermore, we applied the LMP detector at the fusion center for weak constant-modulus primary signals and derived its corresponding test statistic. Deriving the pdf of the linear test and LMP statistics under the signal-absent hypothesis, we analytically set the linear test and LMP thresholds at the fusion center. We showed that applying the linear test for cooperative sensing results in very close performance to that of the known-parameter NP-based LRT, without requiring prior knowledge of the primary statistics at the fusion center. APPENDIX DERIVATION OF THE LIKELIHOOD FUNCTION Fig. 5. Complementary ROC (P decisions.

versus P ) curves for 2-bit quantized local

Using the message-passing approach in [21], the message to node is derived as from node

Fig. 6 shows the analytical and numerical probability distribution of the linear test statistic under null hypothesis. We observe that the analytical pdf derived in (53) is very close to the numerical pdf which represents the exact pdf. VI. CONCLUSION In this paper, we presented a composite hypothesis testing approach for cooperative spectrum sensing in cognitive radios. For nonideal transmission channels, we derived the LRT statistic based on the Neyman-Pearson criterion at the fusion center. However, due to lack of knowledge about the primary signal and channel statistics at the secondary networks, the optimal LRT-based scheme which depends on these parameters, can not be applied in most cognitive radio networks. For this reason, we proposed linear composite hypothesis testing methods, which do not require any prior knowledge about the primary signal and channel statistics. In its simplified form, this test is much

(72) if event A is true, and where wise. Consequently, the outgoing message to the is computed as (see [21])

othernode from

(73)

By multiplying all the messages arrived at node and using the has Gaussian distribution as in (5), the likelihood fact that function is obtained by (74)


(75) where under under under under with

and

,

(76) (77)

, respectively, given in (25) and (26). REFERENCES

[1] J. Mitola and G. Q. Maguire, “Cognitive radios: Making software radios more personal,” IEEE Pers. Commun., vol. 6, no. 4, pp. 13–18, Aug. 1999. [2] S. Haykin, “Cognitive radio: Brain-empowered wireless communications,” IEEE J. Sel. Areas Commun., vol. 23, no. 2, pp. 201–220, Feb. 2005. [3] A. Ghasemi and E. S. Sousa, “Collaborative spectrum sensing for opportunistic access in fading environments,” in Proc. IEEE Int. Symp. New Frontiers in Dyn. Spectrum Access Netw. (DySPAN), Baltimore, MD, Nov. 2005. [4] E. Visotsky, S. Kuffner, and R. Peterson, “On collaborative detection of TV transmissions in support of dynamic spectrum sharing,” in Proc. IEEE Int. Symp. New Frontiers in Dyn. Spectrum Access Netw. (DySPAN), Baltimore, MD, Nov. 2005. [5] H. Uchiyama, K. Umebayashi, Y. Kamiya, Y. Suzuki, T. Fujii, F. Ono, and K. Sakaguchi, “Study on cooperative sensing in cognitive radio based ad-hoc network,” in Proc. IEEE Int. Symp. Pers., Indoor Mobile Radio Commun. (PIMRC), Sep. 2007, pp. 1–5. [6] Z. Quan, S. Cui, and A. H. Sayed, “Optimal linear cooperation for spectrum sensing in cognitive radio networks,” IEEE J. Sel. Topics Signal Process., vol. 2, no. 1, pp. 28–40, Feb. 2008. [7] H. Urkowitz, “Energy detection of unknown deterministic signals,” Proc. IEEE, vol. 55, no. 4, pp. 523–531, 1967. [8] S. M. Kay, Fundamentals of Statistical Signal Processing: Detection Theory. Englewood Cliffs, NJ: Prentice-Hall, 1998, vol. 2. [9] A. Sahai and D. Cabric, “Spectrum sensing: Fundamental limits and practical challenges,” in Proc. IEEE Int. Symp. New Frontiers in Dyn. Spectrum Access Netw. (DySPAN), Baltimore, MD, Nov. 2005. [10] D. Cabric, A. Tkachenko, and R. W. Brodersen, “Experimental study of spectrum sensing based on energy detection and network cooperation,” in Proc. ACM 1st Int. Workshop on Technol. Policy for Accessing Spectrum (TAPAS), Aug. 2006. [11] W. A. Gardner, “Exploitation of spectral redundancy in cyclostationary signals,” IEEE Signal Process. Mag., vol. 8, pp. 14–36, 1991. [12] S. Enserink and D. Cochran, “A cyclostationary feature detector,” in Proc. 28th Asilomar Conf. Signals, Syst., Comput., Oct. 1994, pp. 806–810. [13] L. Chen, J. Wang, and S. Li, “An adaptive cooperative spectrum sensing scheme based on the optimal data fusion rule,” in Proc. IEEE Int. Symp. Wireless Commun. Syst. (ISWCS) 2007, Oct. 2007, pp. 582–586. [14] B. Chen, R. Jiang, T. Kasetkasem, and P. K. Varshney, “Channel aware decision fusion in wireless sensor networks,” IEEE Trans. Signal Process., vol. 52, no. 12, pp. 3454–3458, Dec. 2004.

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[15] J.-F. Chamberland and V. V. Veeravalli, “Decentralized detection in sensor networks,” IEEE Trans. Signal Process., vol. 51, no. 2, pp. 407–416, Feb. 2003. [16] B. Liu and B. Chen, “Channel-optimized quantizers for decentralized detection in sensor networks,” IEEE Trans. Inf. Theory, vol. 52, no. 7, pp. 3349–3358, Jul. 2006. [17] I. Hoballah and P. K. Varshney, “Distributed Bayesian signal detection,” IEEE Trans. Inf. Theory, vol. 35, no. 5, pp. 995–1000, Sep. 1989. [18] S. A. Aldosari and J. M. F. Moura, “Fusion in sensor networks with communication constraints,” in Proc. Third Int. Symp. Inf. Process. (IPSN 2004), Apr. 2004, pp. 108–115. [19] I. Bahceci, G. Al-Regib, and Y. Altunbasak, “Parallel distributed detection for wireless sensor networks: Performance analysis and design,” in Proc. IEEE IEEE Global Commun. Conf. (GLOBECOM), Dec. 2005, vol. 4. [20] S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Englewood Cliffs, NJ: Prentice-Hall, 1998, vol. 1. [21] S. Zarrin and T. J. Lim, “Belief propagation on factor graphs for cooperative spectrum sensing in cognitive radio,” in Proc. IEEE Int. Symp. New Frontiers in Dyn. Spectrum Access Netw. (DySPAN), Chicago, IL, Oct. 2008. [22] S. Zarrin and T. J. Lim, “Composite hypothesis testing for cooperative spectrum sensing in cognitive radio,” in Proc. IEEE Int. Conf. Commun. (ICC), Dresden, Germany, Jun. 2009. [23] F. R. Kschischang, B. J. Frey, and H.-A. Loeliger, “Factor graphs and the sum-product algorithm,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 498–519, Feb. 2001. Sepideh Zarrin received the B.S. degree in the electrical engineering from the University of Tehran, Iran, in 2004, and the M.Sc. degree from Queen’s University in 2006. She is currently pursuing the Ph.D. degree in the Electrical Engineering Department, University of Toronto, Canada. Her research interests are in the areas of wireless communications and signal processing. Specific areas of interest include dynamic spectrum access, spectrum sensing in cognitive radios, and cooperative communications.

Teng Joon Lim grew up in Singapore. He received the B.Eng. degree with first-class honors in electrical engineering from the National University of Singapore in 1992, and the Ph.D. degree from the University of Cambridge, Canbridge, U.K., in 1996. From 1995 to 2000, he was on the research staff of the Centre for Wireless Communications (now part of the Institute for Infocomm Research), and since the end of 2000, he has been with the ECE Department, University of Toronto, Toronto, Canada, where he is now a Professor. His research spans a range of topics in communication theory. Recent contributions are in limited-feedback MIMO downlink precoding, iterative receivers based on variational inference and belief propagation, cooperative diversity, and cognitive radio spectrum sensing. Dr. Lim is an IEEE volunteer, and his activities include Co-Chairing the TPC of the Signal Processing Symposium at ICC 2010 (Cape Town), Co-Chairing the local arrangements team at ISIT 2008 (Toronto), Associate Editorship of the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY and of the IEEE SIGNAL PROCESSING LETTERS, as well as participating in numerous IEEE conference TPC’s.