Minimum variance beamforming with soft response constraints

Soft constraints on the beamformer response to the signal are examined in the context of minimum variance beamforming. A quadratic constraint on the beamformer weights is used to control the mean-squared error between a desired response and the actual response in the signal direction. The constraint is purposely chosen to permit distortion of the signal with the goal of achieving improved interference cancellation. Under the assumptions of known signal direction and spectral shape the signal-to-noise ratio is shown to be a nondecreasing function of the mean-square distortion. The distortion presented to the signal is easily computed from the beamformer weights and can be equalized after beamforming if desired. Properties of this beamforming method and its relationship to linear constrained beamforming are discussed. Simulations verify analytic results and illustrate the utility of the soft constrained approach