Stochastic ML estimation under misspecified number of signals

The maximum likelihood (ML) approach for estimating direction of arrival (DOA) plays an important role in array processing. Its consistency and efficiency have been well established in the literature. A common assumption is that the number of signals is known. In many applications, this information is not available and needs to be estimated. However, the estimated number of signals does not always coincide with the true number of signals. Thus it is crucial to know whether the ML estimator provides any relevant information about DOA parameters under a misspecified number of signals. In the previous study [3], we focused on the deterministic signal model and showed that the ML estimator under a misspecified number of signals converges to a well defined limit. Under mild conditions, the ML estimator converges to the true parameters. In the current work, we extend those results to the stochastic signal model and validate our analysis by simulations.