Diagonal loading has been regarded as an efficient manner to tackle the finite sample effect or the steering vector imprecision problem on adaptive array beamforming. However, the reason of the robustness improvement by the loading factor is still unknown and rarely discussed. In this paper, we consider the finite sample effect and derive the approximated output signal-to-interference-plus-noise ratio (SINR) of minimum variance distortionless response (MVDR) beamformers with diagonal loading. The obtained SINR expression is more explicit and compact than the existing formulas in the literature. Based on the theoretical results, we investigate the effects of a loading factor on the output SINR of MVDR beamformers. The theoretical analysis shows the effectiveness of diagonal loading on alleviating finite sample effect. Moreover, the price of using diagonal loading is also discussed. Simulation results are presented for confirming the validity of the research work.
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