Invariant target detection of MIMO radar with unknown parameters

In this paper, three target detectors Uniformly Most Powerful Invariant (UMPI), Generalized Likelihood Ratio Test (GLRT) and a Separating Function Estimation Test (SFET) based on the scale group of transformations are proposed and applied to Widely Separated Antennas Multiple-Input Multiple-Output (WSA MIMO) radars. It is shown that for this problem the UMPI test depends on the scatter to noise ratio, hence the UMPI test provides the upper performance bound for all invariant tests. To derive the asymptotically optimal SFET the Maximum Likelihood Estimation (MLE) of unknown parameters are replaced into the induced maximal invariant, which is equal to the scatter to noise ratio. The MLE of the scatter to noise ratio does not have a closed form, hence we propose an iterative estimator to calculate the SFET statistic. Similarly an iterative GLRT is also proposed for this problem. The simulation results show that the performance of SFET tends to the optimal invariant bound by increasing the scatter to noise ratio.