Finite data performance analysis of LCMV antenna array beamformers with and without signal blocking

Abstract—A linearly constrained minimum variance (LCMV) antenna array beamformer using finite data samples suffers from slow convergence when the received array data contain the desired signal. It has been reported that signal blocking techniques speed up the convergence rate and increase the robustness of LCMV antenna array beamformers. However, the reason of this improvement has not been explored in the literature. Moreover, the existing formulas for the output signal-to-interference-plus-noise ratio (SINR) are too rough to realize the influence of signal blocking techniques on the performance. In this paper, we show that the correlation due to finite samples causes the redundant component (termed as the cross weight) embedded in the weight vector of a LCMV beamformer even if the signal sources and noise are independent. The cross power results from the cross weight degrades the performance when the sample size is small. In contrast, the cross weight and cross power can be fully eliminated when a signal blocking technique is used. The theoretical results presented in this paper provide a comprehensive description on the effectiveness and the price of using signal blocking for antenna array beamforming. Simulation results are also given for confirming the validity of the theoretical results