Average SINR Calculation of a Persymmetric Sample Matrix Inversion Beamformer

Based on the Bartlett's decomposition of a Wishart random matrix, we study the normalized output signal-to-interference-plus-noise ratio (SINR) of a sample matrix inversion (SMI) beamformer with exploiting a priori information on persymmetric structures in the received signal. The persymmetric structure exists when a system is equipped with a symmetrically spaced linear array or symmetrically spaced pulse trains. In the matched case, we obtain an exact expression for the expectation of the normalized output SINR (i.e., average SINR loss) of the persymmetric SMI beamformer. Considering the mismatch in the signal steering vector, we derive an approximate expression for the average SINR loss of the persymmetric SMI beamformer in a non-homogeneous environment where the test and training data have different covariance matrices. These theoretical results are all verified by using Monte Carlo techniques. Simulation results reveal that the exploitation of the persymmetric structure is equivalent to doubling the amount of training data, and thus the SINR loss of the persymmetric SMI beamformer can be significantly reduced. In particular, the persymmetric SMI beamformer can work in the case of limited training data where the traditional beamformers cannot work.