The separating function estimation test and the UMPI test for target detection problem using optimal signal design in MIMO radar

In this paper, we study the MIMO signal detection problem using widely separated antennas in Gaussian interference. The interference is assumed to be colored with unknown N × N covariance matrix. We derive the Uniformly Most Powerful Invariant (UMPI) test for this detection problem as the upper performance bound for invariant tests. Also the Separating Function Estimation Test (SFET) is derived for this problem using the Signal and Scatter to Interference Ratio (SIR). Then, based on the eigenvalues expansion of SIR, we propose a set of orthogonal signals in transmitters which maximizes the detection probability of UMPI and SFET. Simulation results show that 1) the performance of our proposed detector is close to the UMPI bound and 2) the performance of the optimal invariant bound improves when the transmitters use the proposed set of signals instead of the orthogonal complex exponential signals.