A novel alternative to diagonal loading for robust adaptive beamforming

Abstract

Diagonal loading has proved an effective way to improve the robustness of the optimum beamformer. However, the diagonal loading value must be properly chosen to achieve this. In this paper we propose a Bayesian beamformer for dealing with uncertainty in array configuration and source direction of arrival. We then introduce a method for forming robust beamfomers without the need for diag- onal loading. Furthermore, when diagonal loading is used we give a simple and effective technique for determining a good value for the loading. Simulations and experimental results show that both techniques exhibit similar perfor- mance on simulated and real data. In this paper we develop a number of ideas. We briefly present a Bayesian method for dealing with uncertainity in array configurations and source DOA. We show that when this method is applied to DOA uncertainty we ob- tain a power minimisation problem which is identical to the distributed source problem of (4). We then present a method for extracting robust beamformers from this prob- lem without the need for diagonal loading. This is the main result of this paper. Finally, for comparison, we briefly present a new method we have developed for de- termining diagonal loading values for the minimum power distortionless response (MPDR) beamformer, based on an iterative power estimate. The paper is organised as follows. In Section 2 we briefly review minimum power beamforming and the ba- sic approaches to making such beamformers robust to model mismatch. Section 3 introduces Bayesian beamforming with expected response constraints (ERC). In Section 4 we propose an approximate solution to this problem which avoids the need for diagonal loading. We compare this technique with a new method we have developed for de- termining diagonal loading values based on an iterative power estimate; this techique is summarised in Section 5. A comparison using both simulation and experimental re- sults is shown in Section 6.