Bayesian Information Criterion for Source Enumeration in Large-Scale Adaptive Antenna Array

Abstract

Subspace-based high-resolution algorithms for direction-of-arrival (DOA) estimation have been developed for large-scale adaptive antenna arrays. However, its prerequisite step, namely, source enumeration, has not yet been addressed. In this paper, a new approach is devised in the framework of the Bayesian information criterion (BIC) to provide reliable detection of the signal source number for the general asymptotic regime , where $m,n\rightarrow\infty$ and $m/n\rightarrow c\in(\mbox{0},\infty)$ , with $m$ and $n$ being the numbers of antennas and snapshots, respectively. In particular, the a posteriori probability is determined by correctly calculating the LLFs and PFs for the general asymptotic case. By means of the maximum a posteriori probability, we are capable of effectively finding the signal number. An accurate closed-form expression for the probability of missed detection is also derived for the proposed BIC variant. In addition, the probability of false alarm for the BIC detector is proved to converge to zero as $m,n\!\rightarrow\!\infty$ and $m/n\!\rightarrow\! c$ . Simulation results are included to demonstrate the superiority of the proposed detection approach over state-of-the-art schemes and corroborate our theoretical calculations.