SINR Distribution for the Persymmetric SMI Beamformer With Steering Vector Mismatches

In this paper, we examine the normalized output signal-to-interference-plus-noise ratio (SINR) of a sample matrix inversion beamformer exploiting the persymmetry of the received data. The persymmetry commonly exists in the received data, when a symmetrically spaced linear array and/or symmetrically spaced pulse trains are utilized. An exact expression for the probability density function (PDF) of the normalized output SINR is derived in the mismatched case. This PDF is verified using Monte Carlo simulations. Numerical examples indicate that the exploitation of persymmetry is equivalent to doubling the training data size, and hence can greatly alleviate the requirement of training data in adaptive processing.