Asymptotic results for sensor array processing

The emphasis of this study is on direction-of-arrival (DOA) estimation of narrowband emitter signals. There are two main signal models that have been used in the sensor array problem, namely, stochastic and deterministic. A discussion is presented of the models, their effect on the Cramer-Rao lower bounds (CRB), cases where the maximum likelihood (ML) estimator asymptotically achieves this bound, and how the bounds are related. It is shown that the asymptotic variance of the ML method based on the stochastic model is lower than that of the ML method based on the deterministic model. The stochastic ML variance and CRB are based on the assumption of Gaussian emitter signals, which can be an unrealistic assumption when narrowband signals are assumed. The authors show that the ML estimator based on the Gaussian signal model achieves the stochastic CRB asymptotically, regardless of the signal distribution. Numerical evaluations of the theoretical variances for different scenarios are presented to clarify the relationship between the methods and bounds discussed