Estimating the optimum loading factor against the finite sample size effect in minimum variance beamformers

Diagonal loading is a commonly used technique that improves the robustness of minimum variance beamformers against multiple impairments. In this paper, we concentrate on the application of diagonal loading to mitigate the finite sample size effect. Up to now, the actual loading factor for this problem was chosen via rather ad-hoc approximations. Here, we propose an estimator of this factor that is optimum in the sense that maximizes the asymptotic signal to noise plus interference ratio (SINR) at the output of the beamformer. Our estimator is consistent even when the number of array elements is driven to infinity with the sample size, and consequently has an excellent performance even when the quotient between the number of observations and the number of elements of the array is low.