Spectrum Sensing Algorithms via Finite Random Matrix Theory

We address the Primary User (PU) detection (spectrum sensing) problem, relevant to cognitive radio, from a finite random matrix theoretical (RMT) perspective. Specifically, we employ recently-derived closed-form and exact expressions for the distribution of the standard condition number (SCN) of uncorrelated and semi-correlated random dual Wishart matrices of finite sizes, to design Hypothesis-Testing algorithms to detect the presence of PU signals. An inherent characteristic of the SCN/RMT-based approach, is that no signal-to-noise ratio (SNR) estimation or any other information on the PU signal is required. On top of this property, other attractive advantages of the new techniques are: a) due to the accuracy of the finite SCN distributions, superior performance is achieved under a finite number of samples, compared to asymptotic RMT-based alternatives; b) since expressions to model the SCN statistics both in the absence (H₀) and presence (H₁) of PU signal are used, the statistics of the spectrum sensing problem in question is completely characterized; c) as a consequence of a) and b), accurate and simple analytical expressions for the receiver operating characteristic (ROC) - both in terms of P_D as a function of P_F and in terms of P_A as a function of P_M - are yielded. It is also shown that the proposed finite RMT-based algorithms outperforms all similar alternatives currently known in the literature, at a substantially lower complexity.