Although routinely utilized in literature, orthogonal waveforms may lose orthogonality in distributed multi-input multi-output (MIMO) radar with spatially separated transmit (TX) and receive (RX) antennas, as the waveforms may experience distinct delays and Doppler frequency offsets unique to different TX-RX propagation paths. In such cases, the output of each waveform-specific matched filter (MF), employed to unravel the waveforms at the RXs, contains both an auto term and multiple cross terms, i.e., the filtered response of the desired and, respectively, undesired waveforms. We consider the impact of non-orthogonal waveforms and their cross terms on target detection with or without timing, frequency, and phase errors. To this end, we present a general signal model for distributed MIMO radar, examine target detection using existing coherent/non-coherent detectors and two new detectors, including a hybrid detector that requires phase coherence locally but not across distributed antennas, and provide a statistical analysis leading to closed-form expressions of false alarm and detection probabilities for all detectors. Our results show that cross terms can behave like foes or allies, respectively, if they and the auto term add destructively or constructively, depending on the propagation delay, frequency, and phase offsets. Regarding sync errors, we show that phase errors affect only coherent detectors, frequency errors degrade all but the non-coherent detector, while all are impacted by timing errors, which result in a loss in the signal-to-noise ratio (SNR).
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