## 1 Introduction
Hence, the energy detection can not perform in the presence of noise power uncertainty [10,11]. Furthermore, energy detection is considered to be optimal for detecting an independent and identically distributed (i.i.d.) signal, it is not optimal for detecting a correlated signal, which is the case for most practical applications [4,9]. As mentioned above, in more realistic CR environments, the required assumptions may limit the applicability of the traditional algorithms [3,4,9]. Hence, there is need for spectrum sensing schemes that are blind and do not require such prior information. Recently, multi-antenna receivers have become an integral part of many cognitive radios [12,13], thus giving us the chance to consider multi-antenna techniques to improve the performance of cooperative spectrum sensing. Multiple antennas can offer spatial diversity and improve the spectrum sensing performance [3,4]. Intuitively, the presence of any primary signal should result in some spatial correlation in the observations received at the multi-antenna receivers [4,14]. One solution to overcome the above shortcomings of the traditional detection schemes is to exploit the statistical correlation of the received signals [4,9,14]. In this paper we consider the presence of the spatial correlation as a detection metric since the noise processes can be safely assumed statistically independent [3]. Based on the above discussion, we consider a detection problem that takes into account the presence of some unknown inter-antenna and inter-receiver spatial correlation. Because of that uncertainty in the spatial correlation, the problem is typically formulated through the GLRT, which is a simple test that just decides whether the estimated covariance matrix departs from the signal-absent covariance matrix or not ([15,16], Chapers 9 and 10). Since the GLRT involves estimation of the unknown covariance matrix, it depends on the sample size and the dimensionality [17]. In the case of a large wireless network, the dimensionality of the problem can be on the order of the available sample size and thus the GLRT degenerates due to the ill-conditioned sample covariance matrix [17]. Moreover, the GLRT assumes no structure for the covariance matrix, except for the fact that it is a symmetric matrix. To cope with the problem of small sample support we propose two techniques that exploit the embedded spatial structures. In these techniques we propose the decomposition of a large covariance matrix into small matrices by exploiting the inter-receiver and inter-antenna spatial structures in the received observations. To be more specific, the two detectors use single-pair Kronecker product (SPKP) [18] and multi-pairs Kronecker product (MKPK) [19] of the inter-receiver and inter-antenna covariance matrices. By doing so, the demand for large sample size reduces, and hence, this results in an enhanced robustness against the small sample support. The remainder of the paper is organized as follows. Section 2 introduces the proposed methodology and the signal model. In Section 3, we solve the problem by using the traditional GLRT formulations. The proposed detection schemes are derived in Section 4. Numerical results are provided in Section 5. The conclusion is finally drawn in Section 6.