## 1 Introduction

[2] Wireless networks today are characterized by a fixed spectrum allocation strategy. With the rapid increasing demand for wireless communications and the limited availability of frequency resources, the Federal Communications Commission (FCC) has decided to make a paradigm shift by allowing more unlicensed users to transmit their signals in the bands licensed to primary users (PUs) so as to efficiently improve spectrum utilization [*Politis*, 2009; *Weiss and Jondral*, 2004]. The motivating factor behind this decision is a measurement by FCC which has shown that 70% of the allocated spectrum in the United States has not been well utilized [*Krenik and Batra*, 2005]. Cognitive radio (CR) is proposed as an efficient spectrum sharing technique for unlicensed users [*Akyildiz et al*., 2006].

[3] CR can smartly sense and adapt for the changing environment by altering its transmitting parameters, such as modulation, frequency, and frame format [*Mitola*, 1999]. The main challenge is that CR should sense the PU signal exactly in order to avoid disturbing the PU [*Cabric et al*., 2006]. Energy detection is widely used by CR due to its simple implementation and unnecessary signal knowledge; however, its performance may decrease when the signal is in the shadowing and fading [*Zhang et al*., 2009]. Cooperative spectrum sensing is proposed to solve this problem, where each CR senses the spectrum by energy detection independently, and the fusion center combines the detection results from all the CRs in order to obtain the final decision on the presence of the PU [*Liu and Tan*, 2012]. If the local detection results of the CRs are binary decisions (0/1), they are combined by hard-decision rules such as AND Logic, OR Logic, and K-OUT-N Logic; if the local detection results are the energy statistics, they are combined by soft decision [*Letaief and Zhang*, 2009].

[4] An iterative threshold selection scheme for cooperative spectrum sensing with OR Logic was proposed in *Teo et al*. [2010], which significantly outperformed the conventional spectrum sensing with the uniform threshold in terms of the error detection probability (mean of false alarm probability and misdetection probability); however, the cooperative spectrum sensing with AND Logic and K-OUT-N Logic was not considered. A fast and accurate threshold searching method was proposed in *Liu et al*. [2010], which minimizes the error detection probability if the SNR was identical; however, its performance might decrease if the SNR was different. The optimization algorithms in *Teo et al*. [2010] and *Liu et al*. [2010] were both about single-channel cooperative spectrum sensing. The optimal multichannel cooperative spectrum sensing was investigated in *Quan et al*. [2009] and *Michele and Maurizio* [2011], maximizing the total throughput of all the subchannels; however, how to decrease the multichannel error detection probability was still a problem.

[5] In this paper, the detection threshold is optimized in order to minimize both the error detection probabilities of single-channel and multichannel cooperative spectrum sensing. In single-channel cooperative spectrum sensing, the iterative optimal thresholds with AND Logic, OR Logic, and K-OUT-N Logic are respectively proposed, which can greatly decrease the error detection probability if the SNR is different. In multichannel cooperative spectrum sensing, the nonrestrained multichannel threshold optimization (NRMTO) and the restrained multichannel threshold optimization (RMTO) are proposed. The NRMTO can achieve the minimal total error detection probability, while the RMTO can guarantee the false alarm and misdetection probabilities of each subchannel but with a higher total error detection probability.

[6] The rest of this paper is structured as follows. In section 2, the energy detection and its optimal threshold are analyzed. In section 3, single-channel cooperative spectrum sensing is described, and the iterative optimal thresholds with different hard fusion rules are described. In section 4, multichannel-channel cooperative spectrum sensing with soft decision is analyzed, and the two threshold optimization methods, namely NRMTO and RMTO, are proposed. The simulation results and relevant discussions are given in section 5. Finally, we conclude the work in section 6.