Threshold Region Performance of Maximum Likelihood Doa Estimation for a Single Source

This paper presents a performance analysis of Maximum Likelihood (ML) Direction-Of-Arrival (DOA) estimation using sensor arrays for the case of a single source in white Gaussian noise. Particular attention is paid to the threshold effect that is common in nonlinear estimation. The paper presents approximations to the probability of outlier and Mean Square estimation Error (MSE) of the ML estimator. Both the stochastic and deterministic signal models are treated. It is verified by simulations that the approximations predict the ML DOA estimation performance with high accuracy also at low Signal-to-Noise Ratio (SNR) where the Cramér-Rao bound is far too optimistic. It is also shown that, in the case of a single snapshot, the stochastic ML DOA estimator cannot reach the CRB as the SNR tends to infinity. This is due to that the errors caused by outliers cannot be neglected at high SNR in this case.