Adaptive convergence of linearly constrained beamformers based on the sample covariance matrix

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 are assumed to be Gaussian distributed and independent from data vector to data vector. The output power and mean-squared error in the absence of the desired signal are shown to be multiples of chi-squared random variables. The presence of the desired signal results in an excess mean-squared error that is beta distributed and depends only on the signal power, number of data vectors, and number of adaptive degrees of freedom. The expected value of the excess mean-squared error resulting from the signal presence is directly proportional to the signal power and number of adaptive degrees of freedom, but is inversely proportional to the number of data vectors