Adaptive reweighting homotopy algorithms applied to beamforming

We develop adaptive beamforming algorithms that are robust against sensor failure and ill-conditioning in the autocorrelation matrix (common in low-rank interference scenarios). Both goals are achieved simultaneously through the use of l1 regularization. The algorithms are based on the complex adaptive reweighting homotopy technique. We also develop iterative versions of the algorithms that take advantage of properties of homotopy l1 solvers and dichotomous coordinate iterations to reduce considerably the computational complexity, compared with other regularization methods.