ON THE MEAN-SQUARE ERROR PERFORMANCE OF ADAPTIVE MINIMUM-VARIANCE BEAMFORMERS BASED ON THE SAMPLE COVARIANCE-MATRIX

This correspondence examines the mean-square error (MSE) performance o f 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 wh ere the same input data is used both to compute the adaptive weights a nd to form the beamformer output. The Type II beamformer, as in many r ecursive 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 beam-former exhibits signal cance llation, which is shown here to cause signal estimate bias. To explici tly account for signal cancellation, the mean-square error (MSE) and o utput signal-to-noise ratio (SNR) measures of the bias-corrected Type I beamformer are analyzed here, thus extending previous results. Furth er, new analytical results for these performance measures are given fo r 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.