Doa Estimation in heteroscedastic noise

The paper considers direction of arrival (DOA) estimation from long-term observations in a very noisy environment. The concern is to derive methods obtaining reasonable DOAs at very low SNR. The noise is assumed zero-mean Gaussian and its variance varies in time and space, causing stationary data models to fit poorly over long observation times. Therefore a heteroscedastic Gaussian noise model is introduced where the variance varies across observations and sensors. The source amplitudes are assumed independent zero-mean complex Gaussian distributed with unknown variances (i.e. the source powers), inspiring stochastic maximum likelihood (ML) DOA estimation. The DOAs of plane waves are estimated from multi-snapshot sensor array data using sparse Bayesian learning (SBL) where the noise is estimated across both sensors and snapshots. This SBL approach is more flexible and performs better than other high-resolution methods since they cannot estimate the heteroscedastic noise process. An alternative to SBL is simple data normalization, whereby only the phase across the array is utilized. Simulations in noisy environments demonstrate that taking the heteroscedastic noise into account causes the DOA estimation to fail at lower SNR, often at 20 dB lower SNR.