IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 12, DECEMBER 2009 5761 Optimization of Cooperative Spectrum Sensing with Energy Detection in Cognitive Radio Networks Wei Zhang, Member, IEEE, Ranjan K. Mallik, Senior Member, IEEE, and Khaled Ben Letaief, Fellow, IEEE Abstract—We consider cooperative spectrum sensing in which multiple cognitive radios collaboratively detect the spectrum holes through energy detection and investigate the optimality of cooperative spectrum sensing with an aim to optimize the detection performance in an efficient and implementable way. We derive the optimal voting rule for any detector applied to cooperative spectrum sensing. We also optimize the detection threshold when energy detection is employed. Finally, we propose a fast spectrum sensing algorithm for a large network which requires fewer than the total number of cognitive radios in cooperative spectrum sensing while satisfying a given error bound. Index Terms—Cognitive radio, energy detection, optimization, spectrum sensing. I. I NTRODUCTION O VER the last decade, wireless technologies have grown rapidly and more and more spectrum resources are needed to support numerous emerging wireless services. Within the current spectrum regulatory framework, however, all of the frequency bands are exclusively allocated to specific services and no violation from unlicensed users is allowed. The issue of spectrum scarcity becomes more obvious and worries the wireless system designers and telecommunications policy makers. Interestingly, a recent survey of the spectrum utilization made by the Federal Communications Commission (FCC) has indicated that the actual licensed spectrum is largely under-utilized in vast temporal and geographic dimensions [1]. In order to solve the conflicts between spectrum scarcity and spectrum under-utilization, cognitive radio (CR) technology has been recently proposed. It can improve the spectrum utilization by allowing secondary networks (users) to borrow unused radio spectrum from primary licensed networks (users) or to share the spectrum with the primary networks (users) [2]. As an intelligent wireless communication system, a cognitive radio is aware of the radio frequency environment. It selects the communication parameters (such as carrier frequency, bandwidth, and transmission power) to optimize the spectrum usage and adapts its transmission and reception accordingly. Manuscript received December 29, 2008; revised May 20, 2009 and August 5, 2009; accepted August 11, 2009. The associate editor coordinating the review of this letter and approving it for publication was S. Affes. W. Zhang is with the School of Electrical Engineering and Telecommunica- tions, University of New South Wales, Sydney, NSW 2052, Australia (e-mail: wzhang@ee.unsw.edu.au). R. K. Mallik is with the Department of Electrical Engineering, India Institute of Technology - Delhi, Hauz Khas, New Delhi 110016, India (e- mail: rkmallik@ee.iitd.ernet.in). K. B. Letaief is with the Department of Electronic and Computer Engi- neering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong (e-mail: eekhaled@ee.ust.hk). This work was partially supported by a research grant awarded by the Hong Kong Research Grant Council under Grant No. N_ HKUST622/06. Digital Object Identifier 10.1109/TWC.2009.12.081710 One of the most critical components of cognitive radio tech- nology is spectrum sensing. By sensing and adapting to the environment, a cognitive radio is able to fill in spectrum holes and serve its users without causing harmful interference to the licensed user. One of the great challenges of implementing spectrum sensing is the hidden terminal problem, which occurs when the cognitive radio is shadowed, in severe multipath fading or inside buildings with high penetration loss, while a primary user (PU) is operating in the vicinity [3]. Due to the hidden terminal problem, a cognitive radio may fail to notice the presence of the PU and then will access the licensed channel and cause interference to the licensed system. In order to deal with the hidden terminal problem in cognitive radio networks, multiple cognitive users can cooperate to conduct spectrum sensing. It has been shown that spectrum sensing performance can be greatly improved with an increase of the number of cooperative partners [4]–[8]. In this letter, we consider the optimization of cooperative spectrum sensing with energy detection to minimize the total error rate. It should be mentioned that optimal spectrum sensing under data fusion was investigated in [9], where the optimal linear function of weighted data fusion has been obtained. In other recent works [10], [11], optimal sensing- throughput tradeoff was studied. Optimal distributed signal de- tection with likelihood ratio test using reporting channels from the CRs to the fusion center has been dealt with in [12]. Here we investigate the optimality of cooperative spectrum sensing using the sensing channels between the primary transmitter and the CRs when energy detection and distributed decision fusion are applied to a cognitive radio network. Specifically, we derive the optimal voting rule, i.e., the optimal value of  for the “-out-of-” rule. We also determine the optimal detection threshold to minimize the error rate. We further propose a fast spectrum sensing algorithm for large cognitive networks which requires only a few, not all, cognitive radios in cooperative spectrum sensing to get a target error bound. The rest of this letter is organized as follows. In Section II, spectrum sensing and cooperative spectrum sensing are briefly introduced. In Section III, the optimization of cooperative spectrum sensing is presented. In particular, the optimal voting rule, the optimal threshold, and a fast spectrum sensing method are proposed. Finally, we draw our conclusions in Section IV. II. SPECTRUM SENSING We consider a CR network composed of  CRs (secondary users) and a common receiver, as shown in Fig. 1. We assume that each CR performs spectrum sensing independently and then the local decisions are sent to the common receiver which 1536-1276/09$25.00 c ⃝ 2009 IEEE