Bayesian Spectrum Sensing for Digitally Modulated Primary Signals in Cognitive Radio Shoukang Zheng ∗ , Pooi-Yuen Kam † , Ying-Chang Liang ∗ and Yonghong Zeng ∗ ∗ Institute for Infocomm Research, Agency for Science, Technology & Research (A*STAR), Singapore Email: {skzheng, ycliang, yhzeng}@i2r.a-star.edu.sg † Dept. of Electrical and Computer Engineering, National University of Singapore Email: py.kam@nus.edu.sg Abstract—Based on the high probability that primary user is idle in cognitive radio networks, we propose an optimal Bayesian detector structure for spectrum sensing. Although the optimal detector by Neyman-Pearson theorem maximizes the detection probability for a given false alarm probability, Bayesian detector can achieve a higher overall spectrum utilization and SU throughput and at the same time the primary user is well protected from secondary user’s interference. For BPSK modulated primary signals we show that the optimal Bayesian detector can be reduced to an energy detector in lower SNR regime, and it can be approximated to a detector employing the sum of received signal magnitudes in high SNR regime to detect primary signals. We give the analysis for optimal Bayesian detector and the corresponding suboptimal detector structure in both low and high SNR regimes, and verify the performance of the detector with simulation results. I. I NTRODUCTION To improve the spectrum utilization, research on cognitive radio (CR) and dynamic spectrum access (DSA) has been actively carried out during the past few years [1],[2],[3]. One of the important techniques is spectrum sensing that determines the signal presence or absence of primary user (PU) at the receiver of secondary user (SU). In an earlier study [7], the author addressed the problem of how to detect an unknown deterministic signal over a flat bandlimited Gaussian noise channel with a receiver comprising only an energy detector. The research in [4] is extended to signals over fading channels and an alternative approach is obtained in [5]. A recent survey [12] comprehensively summarizes the sensing methods and compares the advantages and disadvantages among them, e.g. [7]-[10]. Most of the earlier work focused on the signals such as analog signals but little has been done for digitally modulated signals. In this paper we propose an optimal detector for such digital signals over AWGN channels without decoding the primary signals. We take into consideration the fact that spectrum utilization of allocated spectrum in US could be as low as 15% [1] and determine the detection threshold based on the unequal probabilities of the two hypotheses. The prior statistics of PU activity is helpful to improve the SU throughput and the overall spectrum utilization of both PUs and SUs, when we consider an optimal Bayesian detector to minimize the Bayesian risk (or maximize the overall spectrum utilization equivalently). This detector is a likelihood ratio test (LRT) detector which can be approximated by its correspond- ing suboptimal structure in low and high signal-to-noise-ratio (SNR) regimes. We show that the suboptimal detector is an energy detector in the low SNR regime, while it employs the sum of received signal magnitudes to detect the presence of primary signals in the high SNR regime, which indicates that the energy detector is not optimal in this regime. We develop the approximate analysis to compute detection and false alarm probabilities, though it is not in closed-form; also we give the closed-form expressions for the suboptimal detectors in both low and high SNR regimes. The extension of the above to MPSK modulated signals over fading channels can be seen later. A similar detector structure in low SNR regime based on Neyman-Pearson theorem is also discussed briefly in [13]. The rest of the paper is organized as follows. In Section II, the system model is described along with the assumptions and Bayesian detector for BPSK modulated primary signals is proposed. Suboptimal detector structure for low and high SNR regimes is derived in Section III. We analyze the probabilities of detection and false alarm in Section IV and further present the detection threshold and number of samples in Section V. Simulation results on the performance of Bayesian detector, Neyman-Pearson detector and energy detector are provided in Section VI. Finally we conclude the paper in Section VII. II. SYSTEM MODEL AND OPTIMAL DETECTOR STRUCTURE Following the signal model in [5], we consider time-slotted primary signals over AWGN channels in Fig. 1, where N primary signals are used to detect the existence of PU signals. The PU symbol duration is T that is known to the SU and the received signal r(t)=  2Es T cos(ω 0 t + φ) is sampled at a rate of 1/T at secondary receiver with a perfect knowledge on channel state information for deterministic channel gain. We assume PU signal is BPSK modulated with signal energy E s and n(k) is a real AWGN signal, the received signal of k-th symbol at CR detector, r(k), is: r(k)=  n(k), H 0 : PU absent √ E s e jφ(k) + n(k), H 1 : PU present (1) where φ(k)=0,π and n(k) ∼N (0,N 0 /2). Denote r =[r(0) r(1) ··· r(N - 1)] and φ =[φ(0) φ(1) ··· φ(N - 1)]. We as- sume the SU receiver has no information with regarding to the 978-1-4244-8331-0/11/$26.00 ©2011 IEEE