  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).
