False alarm rate of the GLRT-LQ detector in non-Gaussian and heterogeneous clutter

The generalized likelihood ratio test-linear quadratic (GLRT-LQ) detector has been proposed for target detection with multiple-input-multiple-output radar in non-Gaussian and heterogeneous clutter. However, the probability of false alarm (PFA) of this GLRT-LQ detector has been obtained only for a special case in which the numbers of antenna elements in all receive-transmit pairs are all identical. In this study, a closed-form expression for the PFA of the GLRT-LQ detector is derived for the general case where the numbers of antenna elements in all receive-transmit pairs may be distinct. This expression is verified with Monte Carlo simulations.