Novel collaborative spectrum sensing based on spatial covariance structure

In collaborative spectrum sensing, spatial correlation in the measurements obtained by sensors can be exploited by adopting Generalized Likelihood Ratio Test (GLRT). In this process the GLRT provides a test statistics that is normally based on the sample covariance matrix of the received signal samples. Unfortunately, problems arise when the dimensions of this matrix become excessively large, as it happens in the so-called large-scale wireless sensor networks. In these circumstances, a huge amount of samples are needed in order to avoid the ill-conditioning of the GLRT, which degenerates when the dimensionality of data is equal to the sample size or larger. To circumvent this problem, we modify the traditional GLRT detector by decomposing the large spatial covariance matrix into small covariance matrices by using properties of the Kronecker Product. The proposed detection scheme is robust in the case of high dimensionality and small sample size. Numerical results are drawn, which show that the proposed detection schemes indeed outperform the traditional approaches when the dimension of data is larger than the sample size.