Exact non-asymptotic threshold for eigenvalue-based spectrum sensing

Eigenvalue-based detection is one of the most promising techniques proposed for spectrum sensing in cognitive radio as it is insensitive to the noise uncertainty problem. However, the eigenvalue-based detection schemes presented so far rely on asymptotic assumptions that are not suitable for many realistic scenarios, thus determining a substantial degradation of detection performance. In this paper, starting from the analytical distribution of the ordered eigenvalues of finite-dimension Wishart matrices, we derive an exact expression for the decision threshold as a function of the probability of false alarm. Since it is not based on asymptotical assumptions, the novel decision rule is valid for any, even small, number of samples and cooperating receivers. In addition to the exact expression, an alternative (approximated) formula is then derived to reduce the computational complexity. Simulation results show that the proposed detector, both with the exact and the approximated formula, outperforms the other existing eigenvalue-based techniques, especially when the receiver operates under non-asymptotical conditions.