Finite random matrices for blind spectrum sensing

We address the Primary User (PU) detection (spectrum sensing) problem, relevant to cognitive radio, from a finite random matrix theoretical (RMT) perspective. Utilizing recently-derived closed-form and exact expressions for the distribution of the standard condition number (SCN) of dual random Wishart matrices, we design a new blind algorithm to detect the presence of PU signals. An inherent property of the technique, which is due to the reliance on SCN´s, is that no SNR estimation or any other information on the PU signal is required. Like some similar asymptotic RMT-based techniques recently proposed, the algorithm also admits for a tolerated probability of false alarm α to be accounted for by design. The proposed finite RMT-based algorithm, however, outperforms all known similar alternatives, in consequence of the fact that the distribution of SCN´s utilized are in closed-form and exact, for any given matrix size.