Diversity gain for MIMO radar employing nonorthogonal waveforms

Initially we formulate a very general hypothesis testing problem where we attempt to distinguish between zero-mean Gaussian clutter-plus-noise only and returns which are a linear transformed version of a zero-mean Gaussian random vector plus this clutter-plus-noise. We show that the diversity gain of the optimum processing for this hypothesis testing problem must be less than or equal to the rank of the linear transform. Next we apply this result to study diversity gain for optimum MIMO radar processors for cases with M transmit antennas, N receive antennas, and a target composed of Q scatterers. If the transmitted waveforms span a lower dimension M' than M, then the largest possible diversity gain is no greater than min(NM', Q). We also show a diversity gain of min(NM', Q) can be achieved under certain conditions. For a general correlated Gaussian clutter-plus-noise model and a general correlated Gaussian reflection coefficient vector, the diversity gain for noncoherent and coherent processing is discussed. Extensions of all results to cases with nonGaussian reflections and clutter-plus-noise are discussed.