A maximum a posteriori approach to beamforming in the presence of calibration errors

The performance of DF-based beamformers is seriously degraded in situations where the array is imprecisely calibrated, or when the spatial coherence of the signal wavefronts is perturbed. When the calibration errors or perturbation may be characterized by a set of parameters drawn from a known Gaussian distribution, a maximum a posteriori (MAP) estimator may be used to separately estimate the directions of arrival and the perturbation parameters, resulting in essentially an on-line auto-calibration. This paper examines the improvement that results from using the MAP auto-calibrated steering vectors in standard DF-based beamformers to estimate the received signal waveforms and suppress unwanted interference. For the special case of additive unstructured calibration errors and uncorrelated signals, it is shown that the MAP beamformer is similar in form to so-called “subspace corrected” approaches