More on ML Estimation Under Misspecified Numbers 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 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 necessarily equal the true number of signals. Therefore, it is important to know whether the ML estimator provides any relevant information about the true parameters. Previous study on the ML estimattion under misspecified numbers of signals have focused on the asymptotic properties. In this work, we investigate the impact of misspecification on estimation performance and show that the covariance matrix grows monotonically with increasing degree of mismatch. Finally, we carry out numerical experiments under various cases of misspecification and further validate our analysis.