## 1 Introduction
The proposed detector in [14] reduces the negative effects on the CR system performance, which are forming under the in-phase and quadrature-phase (I/Q) imbalance, based on the orthogonal frequency division multiplexing (OFDM) multiple access scheme, and presents a promising solution for any noise power uncertainties or _SNR_ wall problem that could be caused by this I/Q imbalance. Cooperative spectrum sensing, in the course of which the multiple sensors are involved in cooperative spectrum sensing, demonstrates an effective approach to improve the spectrum sensing performance under several problems such as the noise power uncertainty, multipath fading, shadowing, and receiver uncertainties issues. The cooperative spectrum sensing can also solve the critical energy efficiency issue as shown in [15] where the energy efficient cooperative spectrum sensing is proposed and the optimal scheduling of active time for each spectrum sensor helps to extend the network lifetime. Selective grouping based on the cooperative sensing is discussed in [16] where during the sensing time each sensors group senses different radio channels while sensors in the same group perform the joint detection by the targeted channel. This process assures obtaining the more robust and efficient sensing performance comparing with the individual spectrum sensor case under the noise power uncertainty. To mitigate the negative effects of noise power uncertainty at the low _SNR_, an implementation of the generalized detector (GD), which is constructed based on the generalized approach to signal processing (GASP) in noise, for the spectrum sensing in CR networks based on antenna array is proposed. The GD represents a combination of the correlation detector, which is optimal in the Neyman-Pearson (NP) criterion sense when there is _a priori_ information about the PU signal parameters, and ED, which is optimal in the NP criterion sense if there is no any _a priori_ information about the PU signal parameters that are random [17, 18, 19]. The GD likelihood ratio test, based on which we can make a decision about the PU signal presence or absence in the process incoming at the SU input, demonstrates a definition of the jointly sufficient statistics of the mean and variance of the likelihood ratio and does not require any information about the PU signal and its parameters [17], ([18], Chapter 3). As was discussed in detail in ([18]  
obtain more information about the PU signal parameters under GD employment in CR networks in comparison with the conventional MF, ED, correlation receiver and so on. A great difference between the GD ED and conventional ED is a presence of the additional linear system (the additional bandpass filter at the GD input) considered as the secondary data or reference noise source. The PU signal bandwidth is mismatched with the additional linear system bandwidth. The PU signal bandwidth is matched only with another linear system bandwidth at the GD front-end. Thus, the GD has two input linear systems, namely, the preliminary filter (PF) and the additional filter (AF). The last is considered as the reference noise source ([18], Chapter 3), [19]. The GD PF central frequency is detuned relatively to the GD AF central frequency to ensure, firstly, the PU signal passing only through GD PF and, secondly, the independence and uncorrelatedness between the stochastic processes at the GD PF and AF outputs. Thus, it is possible to obtain the PU signal plus noise at the GD PF output in the case of \"a yes\" PU signal at the GD input and only the noise in the opposite case. Consequently, only the noise is obtained at the GD AF output for both cases of \"a yes\" and \"a no\" PU signal at the GD input, in other words, under the hypotheses \(\
ot\!\!\gamma_{1}\) and \(\
ot\!\!\gamma_{0}\). The case when there is the PU signal generated by another source with the frequency content within the limits of the GD AF bandwidth, and considered as the additional interference, is discussed in [20].