MIMO radar under general waveform correlations/antenna spacing: Optimum detectors, detection performance and waveform design

The performance of a multiple-input multiple-output (MIMO) radar is highly dependent on the relative positioning of the transmitter and receiver elements as well as the choice of transmitter waveforms. MIMO radars with either closely spaced antennas or widely separated antennas have been well studied in literature. In this paper, we study the general case where the transmit and receiver antennas have arbitrary separations, while also assuming that the transmit waveforms are arbitrarily correlated with one another. Under this setting, we derive closed form expressions for the optimal Neyman-Pearson detector and the detector signal-to-noise ratio (SNR). It is also shown that for radars with widely separated antennas, orthogonal waveforms maximize detector SNR at high received SNRs. Simulation results are presented demonstrating the nature of the optimal transmit waveforms for various antenna separations. A new scalar measure to characterize the nature of the waveform correlation matrix and the channel covariance matrix is also introduced.