Cognitive radio (CR) has been proposed to improve the spectrum utilization by exploiting the temporarily unused radio spectrum allocated to the primary user (PU) [Mitola and Maguire, 1999; Haykin, 2005; Hossain et al., 2009]. Before data transmission, CR must continuously sense the spectrum and identify the presence of PU in order to avoid causing any harmful interference to PU. Hence, the spectrum sensing has become an important research area [Cabric et al., 2004; Liang et al., 2008].
 Energy detection has been widely used as a single-user sensing method because of its simple implementation without using any prior information of PU's signal [Urkowitz, 1967; Shen et al., 2008; Zhang et al., 2009]. However, the performance of energy detection may be degraded if PU is in a fading and shadowing environment as a hidden terminal [Digham et al., 2003]. Multiple CRs are designed to perform cooperative sensing in order to improve the accuracy of sensing the hidden PU. In cooperative sensing, a fusion center is needed to obtain a final decision on the presence of PU by combining the sensing results of individual CRs [Tan et al., 2012; Uchiyama et al., 2007; Ganesan and Li, 2005]. False alarm probability (the probability of detecting the presence of PU falsely) and detection probability (the probability of claiming the presence of PU accurately) are commonly used to measure the performance of spectrum sensing [Wei et al., 2008].
 Wideband CR can operate over multiple idle subchannels to make improvement on throughput. An optimal multiband joint detection for spectrum sensing is proposed in Fan and Jiang  and Quan et al. . The spectrum sensing problem is formulated as a class of optimization problems about sensing threshold, which maximizes the aggregated throughput of CR under some constraints on the interference to PU. An iterative sensing threshold optimization is proposed in Liu et al.  and Teo et al. , and the optimal thresholds are selected in order to minimize the sum of the probabilities of false alarm and miss detection. However, the works reported in the above references all assume that each CR has a fixed transmission power and rate, and the gain of dynamic power allocation is not exploited.
 A joint optimization of detection and power allocation for multichannel CR is proposed in [Fan et al., 2011; Huang and Baltasar, 2010; Liu et al., 2013], where an efficient algorithm was reported to maximize the total throughput of CR by optimizing jointly both the detection operation and the power allocation. However, this algorithm includes the interference as a part of the throughput, which is produced by the transmission of CR when the miss detection happens. Therefore, the interference to PU may be increased if the throughput is improved. In addition, the algorithm reported in Quan et al.  and Fan et al.  solves the proposed optimization problem based on the interior point method that requires high iteration complexity, because multiple iterations have to be implemented for each constraint condition.
 In this paper, a joint optimization of sensing threshold and transmission power is proposed, which maximizes the total throughput of wideband CR subject to the constraints on the total interference, the total power, and the probabilities of false alarm and detection of each subchannel. An alternative optimization algorithm is also proposed, which minimizes the total interference under the constraints of the total throughput, the total power, and the sensing probabilities. The weighed cooperative sensing is then proposed to maximize the detection probability by selecting the optimal weighed factors, and the joint optimization of sensing threshold and transmission power based on weighed cooperative sensing is also analyzed and solved. The bilevel optimization method with reduced iteration complexity is used to solve the proposed optimization problems. The simulations have shown that the proposed joint optimization algorithm can obtain desirable improvement on the throughput of CR and decrease the interference to PU greatly.
 The rest of the paper is organized as follows. The system models including energy detection model and wideband CR model are described in section 2. In section 3, we develop the joint optimization algorithms of sensing threshold and transmission power including maximizing throughput and minimizing interference. The joint optimization of weighed cooperative sensing is formulated in section 4. The advantages of the proposed joint optimization algorithm are illustrated by simulations in section 5, and conclusions are finally drawn in section 6.