MIMO radar diversity with Neyman-Pearson signal detection in non-Gaussian circumstance with non-orthogonal waveforms

The diversity gain of a multiple-input multiple-output (MIMO) system adopting the Neyman-Pearson (NP) criterion is derived for a signal-present versus signal-absent scalar hypothesis test statistic and for a vector signal-present versus signal-absent hypothesis testing problem. The results are applied to a MIMO radar system with M transmit and N receive antennas, used to detect a target composed of Q random scatterers with possibly non-Gaussian reflection coefficients in the presence of possibly non-Gaussian clutter-plus-noise. It is found that the diversity gain for the MIMO radar system is dependent on the cumulative distribution function (cdf) of the reflection coefficients while invariant to the cdf of the clutter-plus-noise under some reasonable conditions. If the noise-free received waveforms at each receiver span a space of dimension M´ ≤ M, the largest possible diversity gain is controlled by min (N M´, Q) and the cdf of the magnitude square of a linear transformed version of the reflection coefficient vector. It is shown that properly chosen nonorthogonal waveforms can achieve the same diversity gain as orthogonal waveforms.