On Accurate Source Enumeration: A New Bayesian Information Criterion

This work addresses the issue of source number detection in the general asymptotic regime where the numbers of antennas and samples both tend to infinity but their ratio converges to a constant. Among the information criteria for source enumeration, Bayesian information criterion (BIC) is able to provide an elegant link between detection probability and a posterior probability. That is, maximizing detection probability amounts to maximizing a posterior probability which consists of the likelihood function (LF), a prior probability function (PPF) and penalty function (PF). Unfortunately, the PPF does not converge to a constant in the general regime, which is ignored in the existing information criteria, leading to considerable performance degradation in source enumeration. On the other hand, the PF relies on free parameters, which, however, cannot be accurately determined in the state-of-the-art approaches. To fill the performance gaps, this work calculates the PPF by utilizing random matrix theory, and derives the PF by re-organizing the parameter vector, leading to an accurate BIC. Moreover, it is proven that the proposed BIC is able to correctly detect the source number with probability one in the general asymptotic regime. Simulation results confirm our theoretical computations and validate the superiority of the proposed detection approach over the state-of-the-art schemes.

Automated summary

This work addresses the problem of source number detection in the general asymptotic regime and introduces an accurate Bayesian information criterion (BIC) by calculating the prior probability function and reorganizing the parameter vector. Theoretical computations and simulation results confirm the superiority of the proposed detection approach over existing schemes.