Maximum-likelihood DOA estimation at low SNR in Laplace-like noise

We consider the estimation of the direction of arrivals (DOAs) of plane waves hidden in additive, mutually independent, complex circularly symmetric noise at very low signal to noise ratio (SNR). The maximum-likelihood estimator (ML) for the DOAs of deterministic signals carried by plane waves hidden in noise with a Laplace-like distribution is derived. This leads to a DOA estimator based on the Least Absolute Deviation (LAD) criterion. We prove analytically that a weighted phase-only beamformer (which evaluates the scalar product between the steering vector and the complex signum function of the observed array data) is an approximation to a beamformer based on the Least Absolute Deviation (LAD) criterion. The root mean squared error of DOA estimators versus SNR is compared in a simulation study: the conventional beamformer (CBF), the weighted phase-only beamformer, and sparse Bayesian learning (SBL3). This shows show that the ML estimator and weighted phase-only beamformer are well performing DOA estimators at low SNR for additive homoscedastic and heteroscedastic Gaussian noise, as well as Laplace-like noise.