# On Optimal Cooperative Sensing with Energy Detection in Cognitive Radio
###### Abstract  
In this paper, we propose an optimal cooperative sensing technique for cognitive radio to maximize sensing performance based on energy detection. In most spectrum sensing research, many cooperation methods have been proposed to overcome the sensitivity of energy detection so that both primary and secondary users are better off in terms of spectral efficiency. However, without assigning a proper sensing threshold to each sensing node, cooperation may not be effective unless the received average primary user signal-to-noise ratio (SNR) is _identical_. We show that equal threshold energy detection severely degrades sensing performance when cooperative sensing nodes experience diverse average SNRs, and it is not unusual for even single-node sensing to be better than cooperative sensing. To this end, based on the Neyman-Pearson criterion we formulate an optimization problem to maximize sensing performance by using optimized thresholds. Since this is a non-convex optimization problem, we provide a condition that convexifies the problem and thus serves as a sufficient optimality condition. We find that, perhaps surprisingly, in all _practical_ cases one may consider this condition satisfied, and thus optimal sensing performance can be obtained. Through extensive simulations, we demonstrate that the proposed technique achieves a globally optimal solution, i.e., it maximizes the probability of detection under practical operating parameters such as the target probability of false alarm, different SNRs, and the number of cooperative sensing nodes. c 2017 17 2111 2017 17 2017 17 2017 17 2017 17 2017 properties of TVWS [4]. LTE-CR was proposed as a cellular application to extend the LTE time-division duplex (TDD) to support TVWS [5]. In addition to TVWS, 3 GPP has developed LTE in an unlicensed spectrum so that LTE can harmoniously coexist with other wireless systems in a 5-GHz spectrum [6]. To support CR, one of the key roles of SUs is to sense the PU with high detection probability and evacuate the PU's band immediately. There are several detection techniques, such as energy detection, matched filter detection, cyclostationary detection, and compressive sensing, [7]. Among these techniques, energy detection of [8] has been widely adopted in practice because it has low complexity and does not require prior knowledge of the PU [9]. However, since sensing performance of energy detection can deteriorate when the signal-to-noise ratio (SNR) is low [10], many cooperative sensing techniques have been proposed to overcome performance degradation [11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24]. Specifically, to maximize sensing performance, a series of cooperation algorithms have been investigated in terms of sensing duration, the number of cooperative sensing nodes, and thresholds of energy detection [11; 12; 13; 14; 15; 16; 17; 18]. In [11], sensing-throughput tradeoff depending on sensing duration was investigated. The author of [12] jointly optimized sensing time and reporting time to maximize throughput based on maximal ratio combination (MRC)-based soft decision. The fundamental performance limits of the cooperative sensing using energy detection were analyzed by considering the unlimited number of sensing nodes, and it has been shown that the OR rule achieves _zero_ false alarm probability for any given target detection probability irrespective of the received PU SNR [13]. In [14], the authors proposed optimal counting rules of hard decision under the Neyman-Pearson criterion and Bayesian criterion, respectively. In [15], both sensing duration and fusion rule were jointly optimized to maximize the throughput of SUs under the constraint of the probability of detection. In [16; 17], an optimal \(k\) was investigated for the so called \(k\)-out-of-\(N\) rule, and then the _same_ threshold for all sensing nodes is optimized by a given \(k\).