## 1 Introduction  
The main aim of the cognitive radio (CR) network is to improve the spectrum utilization efficiency, by introducing an opportunistic use of unemployed frequency band by the primary user (PU) (see Figure 1). The spectrum sensing is needed to define the frequency holes that could be allocated for the secondary user (SU). The spectrum sensors search continuously an availability of frequency holes and assign them to SU without causing harmful interference to the PU. Fundamental limitations in practice are involved in spectrum sensing process [1, 2, 3]. The sensitivity to noise power uncertainty, for example, variations in the noise variance as a function of real time, is one of the most common and serious problems among the well-known spectrum sensors such as the energy detector (ED), matched filter (MF), and even the cyclostationary detector under some conditions at the low signal-to-noise ratio (_SNR_) [4]. The impact of noise power uncertainty is quantified by _SNR_ wall location, _i.e._, if the _SNR_ value is less than the _SNR_ wall, the PU signal detector will fail to achieve the desired performance and maintain a robustness against power noise uncertainty independently of how long the sensing time is [3, 4, 5]. Both theoretical and experimental analysis confirmed the _SNR_ wall phenomenon existence under the noise power uncertainty conditions. This phenomenon negatively effects the receiver operation characteristic (ROC). Other uncertainties also can be considered as _SNR_ wall generators, for example, the noise power estimation error, assumptions made under the white and stationary noise, fading process, shadowing, non-ideal filters, non-precise analog-to-digital (A/D) converters, quantization noise, aliasing effect caused by imperfect front-end filters, and interference between the PU and SU. An alternative presentation for the _SNR_ wall is given by the number of samples \(N\) as a function of _SNR_, the probability of false alarm \(P_{FA}\) and probability of miss \(P_{miss}\), _i.e._, \(N=f(SNR,P_{FA},P_{miss})\). The PU signal detector should minimize the number of samples \(N\) required to achieve the desired detection performance. The lowest _SNR_ satisfying the probability of false alarm \(P_{FA}\) and the probability of miss \(P_{miss}\) constraints is called the detector sensitivity [3]. In general, the ideal ED does not have the _SNR_ wall, but owing to the noise power uncertainty the ED suffers from the _SNR_ wall phenomenon making the ED non-robust under the low _SNR_[6, 7]. In many published papers, the ED spectrum sensing performance is investigated under the noise uncertainty conditions. Different solutions are presented in the form of the dynamic detection threshold [8], log-normal approximation of the noise uncertainty [9], falling the _SNR_ wall using the cross-correlation [10], improving the noise power estimation using the maximum likelihood (ML) estimator [6], _SNR_  
Figure 1: CR systems and SU with \(M\) antenna array elements. estimation based on the pseudo bit error rate (BER) for the modified ED [11], and algebraic spike detection method introduced in [12, 13]. In fact, the best non-coherent detector is non-robust as the ED under the noise power uncertainty. In the coherent detector case, the _SNR_ wall is pushed back only to a limited value and for a large channel coherence time \(K_{e}\rightarrow\infty\). In the MF case, the _SNR_ wall location is proportional to \(1/\,K_{e}\)[3], and in the case of feature detector, the _SNR_ wall value is less in comparison with the ED one and scales only as \(1/\sqrt{K_{e}}\) with the relevant channel coherence time [3]. An interesting new four-level hypothesis blind detector for spectrum sensing in CR systems is presented in [14].