Theoretical Performance Analysis of Eigenvalue-based Detection

Abstract: In this paper we develop a complete analytical framework based on Random Matrix Theory for the performance evaluation of Eigenvalue-based Detection. While, up to now, analysis was limited to false-alarm probability, we have obtained an analytical expression also for the probability of missed detection, by using the theory of spiked population models. A general scenario with multiple signals present at the same time is considered. The theoretical results of this paper allow to predict the error probabilities, and to set the decision threshold accordingly, by means of a few mathematical formulae. In this way the design of an eigenvalue-based detector is made conceptually identical to that of a traditional energy detector. As additional results, the paper discusses the conditions of signal identifiability for single and multiple sources. All the analytical results are validated through numerical simulations, covering also convergence, identifiabilty and non-Gaussian practical modulations.