  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.
