Soft constrained minimum variance beamforming

The mean-squared error between the desired and actual response is constrained, resulting in a quadratic constraint on the weights. The constraint is purposely chosen to permit signal distortion with the goal of achieving improved interference cancellation, motivating the term `soft constrained´ beamforming. The soft constrained minimum variance (SCMV) philosophy represents a trade of bias (signal distortion) for reduced variance (interference power). A key result is a proof guaranteeing that under ideal conditions the signal-to-noise ratio (SNR) is a nondecreasing function of the bound on the mean squared response error. This implies that by allowing the signal distortion to increase the beamformer can provide much better interference cancellation, such that the SNR improves or remains constant. The potential SNR improvement resulting from the use of soft constraints is greatest for systems operating at broad bandwidths