Optimal Cooperative Sensing and Its Robustness to Decoding Errors Yonghong Zeng, Ying-Chang Liang, Shoukang Zheng, Edward C. Y. Peh Institute for Infocomm Research, A*STAR, Singapore Abstract—Based on the Neyman-Pearson theorem, the optimal cooperative sensing for distributed sensors with time independent signals is derived. It is shown that the optimal scheme is simply a linearly combined energy detection and the combining coefficient is a simple function of the signal to noise ratio (SNR). To reduce the required information at the fusion center and simplify the decision-making process and threshold setting, an approximated optimal cooperative sensing is proposed and compared with some other sub-optimal methods. Finally the impact of decoding error in the reported results is analyzed. Based on the closed-form expression for the performance, it is proved that the impact of decoding error is equivalent to the reduction of sensing time. Simulations are provided to support the results. I. I NTRODUCTION In recent years, cognitive radio is gradually moving from imagination to reality. Spectrum sensing in cognitive radio has a few special challenges, among others, as follows. (1) A cognitive radio may need to sense the primary signal at very low signal to noise ratio (SNR). (2) Propagation channel uncertainty makes the spectrum sensing difficult. The unknown time dispersive channel turns most coherent detections unreli- able. (3) It is hard to synchronize the received signal with the primary signal in time and frequency. This will cause some methods like preamble/pilot based detections less effective. (4) The noise level may change with time and location, which yields the noise power uncertainty issue for detection [1], [2]. (5) The noise may not be white, which will affect many methods with white noise assumption. Although there have been many methods (refer to [3], [4], [5], [6] and the references therein), most of them may not work well in such a hostile radio environment. It is extremely difficult for a single sensor to meet the sensing requirement in some cognitive radio applications. Cooperative sensing, i.e., multiple sensors sensing the common signal in a coordinated approach, is proved to be more reliable or have a better performance than single sensor sensing [7], [8], [9], [10], [11], [12], [13], [14], [15]. As a result, cooperative sensing for cognitive radio has received substantial concern in recent years. In this paper, we first derive the optimal cooperative sensing for distributed sensors with time independent signals. It is proved that, if the sensors are distributed far apart and their signals are independent in time, the optimal scheme is simply a linearly combined energy detection and the combining coefficient is a simple function of the signal to noise ratio (SNR). The major difficulty of the optimal scheme is that its decision and threshold are related to the SNRs of the sensors. To avoid this difficulty we then consider sub-optimal cooper- ative methods. Especially a new method called approximated optimal cooperative sensing is proposed. Finally we analyze the impact of decoding error in the reported results to the detection performance. Based on the closed-form expression of the performances we find the ultimate constraint of decoding errors. It is proved that the impact of decoding error is equivalent to the reduction of sensing time. Simulations are provided to support the results. II. SYSTEM MODEL We consider a cognitive radio network with M ≥ 1 sec- ondary users, which share the same spectrum (one or multiple bands) with primary users. The network coordinates some or all secondary users to cooperatively sense the primary signals. It is assumed that a centralized unit is available for processing the signals from all the sensors. There are two other similar scenarios: (1) multi-antenna sensing, if we treat one antenna as a sensor; (2) multiple time slot sensing: the sensing is done in M equal length time slots, where each time slot is treated as a sensor. In the following, we consider a system model which can be applied to all the three scenarios. There are two hypotheses: H 0 , signal absent; and H 1 , signal present. The received signal at sensor i is given by H 0 : x i (n)= η i (n) and H 1 : x i (n)= s i (n)+ η i (n),i = 1,...,M, where η i (n) is the noise. At hypothesis H 1 , s i (n) is the received source signal at antenna/receiver i. Note that s i (n) is the transmitted primary signal after going through the fading and multipath propagation channel, and also time delay. That is, s i (n) can be written as s i (n)= Np  k=1 q ik  l=0 h ik (l)˜ s k (n - l - τ ik ), (1) where N p is the number of primary signals, ˜ s k (n) stands for the transmitted primary signal from primary user or antenna k, h ik (l) denotes the propagation channel coefficient from the kth primary user or antenna to the ith receiver/antenna, q ik is the channel order for h ik , τ ik is the relative time delay from the primary user k to sensor i. We form M × 1 vectors from the signals of M sensors as follows: x(n) =  x 1 (n) ··· x M (n)  T , s(n) =  s 1 (n) ··· s M (n)  T , η(n) =  η 1 (n) ··· η M (n)  T . The hypothesis testing problem based on N signal samples is then equivalent to H 0 : x(n)= η(n) H 1 : x(n)= s(n)+ η(n), n =0,...,N - 1. (2) The probability of detection, P d , and probability of false alarm, P fa , are defined as follows: P d = P (H 1 |H 1 ) and P fa = P (H 1 |H 0 ). In general a sensing algorithm is said to 978-1-61284-231-8/11/$26.00 ©2011 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings