Exact theoretical performance analysis of optimum detector in statistical multi-input multi-output radars

This study is concerned with the performance analysis of detection problem in statistical multiple-input multiple-output radars for Gaussian interference. This subject has been addressed in some publications for such special cases as white Gaussian noise and orthogonal transmission. However, theoretical performance analysis of optimum detector for general case including coloured Gaussian interference and arbitrary transmission signal has not been reported yet. In the present study, after developing the optimum detector for a general case, exact closed-form expressions are derived for the probability of detection and false alarm. As the derived expressions have complicated form, their interpretation is not tractable in the general case. Therefore lower and upper Chernoff bounds are obtained to provide better insight into the detector performance. Furthermore, the effect of various parameters on the detector performance is investigated by Monte-Carlo simulations. Numerical analysis shows a high degree of consistency between the theoretical and Monte-Carlo simulation results.