Automatic robust adaptive beamforming via ridge regression

In this paper we derive a class of new parameter free robust adaptive beamformers using the generalized sidelobe canceler reparameterization of the unit gain constrained minimum variance problem. In this parameterization the minimum variance beamformer is obtained as the solution of a linear least squares (LS) problem. In the case of an inaccurate steering vector and/or few data snapshots this marginally overdetermined system gives an ill fit causing signal cancellation in the standard minimum variance (LS) solution. By regularizing the LS problem using ridge regression techniques we get a whole class of robust adaptive beamformers, none of which requires the choice of a user parameter, as opposed to many existing methods. In this context we also propose a parameter free empirical Bayes-based ridge regression technique which, to the best of our knowledge, is novel. The performance of our approach is illustrated by numerical simulations and compared to other robust adaptive beamformers.