On the mean-square error performance of adaptive minimum variance beamformers based on the sample covariance matrix

The authors examine the mean-square error (MSE) performance of two common implementations of adaptive linearly constrained minimum variance (LCMV) beamformers that employ the sample covariance matrix. The Type I beamformer is representative of block processing methods where the same input data is used both to compute the adaptive weights and to form the beamformer output. The Type II beamformer, as in many recursive schemes, applies adaptive weights computed from previous data to the current input. Due to correlation between the adaptive weights and the input data, the Type I LCMV beamformer exhibits signal cancellation, which is shown here to cause signal estimate bias. To explicitly account for signal cancellation, the mean-square error (MSE) and output signal-to-noise ratio (SNR) measures of the bias-corrected Type I beamformer are analyzed, thus extending previous results. Further, new analytical results for these performance measures are given for the Type II LCMV beamformer. Comparison of bias-corrected Type I and Type II implementations indicate that both methods yield exactly the same MSE and output SNR performance