Convergence of the SMI algorithm in partially adaptive linearly constrained beamformers

A statistical analysis of the adaptive convergence behavior of linearly constrained beamformers is given assuming the sample covariance estimator is used to estimate the covariance matrix. The sensor data is assumed to be Gaussian distributed and independent from snapshot to snapshot. The mean squared error in the absence of the desired signal is shown to be a multiple of a chi-squared random variable. The presence of the desired signal results in an excess mean squared error which is Beta distributed and depends only on the signal power, number of snapshots, and number of adaptive degrees of freedom. The average excess mean squared error is directly proportional to the signal power and number of adaptive degrees of freedom and inversely proportional to the number of snapshots. These results provide clear motivation for partially adaptive beamforming