Monte Carlo Source Enumeration for Sparse Arrays

Linear sparse arrays with N physical sensors can resolve O(N-2) directions of arrival (DOAs) for uncorrelated sources. This attribute is associated with the difference coarray of size O(N-2). However, the number of sources is assumed to be known in many coarray-based DOA estimators. This paper proposes a Monte Carlo source enumerator (MCSE) for sparse arrays by maximizing the log-likelihood function (LLF). This LLF depends on an unbounded parameter space and a multiple integral, which are challenging for computation. This unbounded parameter space is replaced with a bounded space derived from coarse estimates and Cramer-Rao bounds. Next, the multiple integral is approximated with Monte Carlo methods. The MCSE applies to three scenarios: no sources, fewer sources than sensors, and more sources than sensors. Furthermore, some details in the MCSE can be computed in parallel. Numerical examples demonstrate the applicability of the MCSE to sparse arrays.