This dissertation develops signal processing techniques to analyze and advance the use of non-orthogonal waveforms in multiple-input, multiple-output (MIMO) ground moving target indication (GMTI) radar applications. We introduce a coherent MIMO radar signal model that explicitly incorporates waveform correlation as a function of time delay and frequency offset in the matched filter operation, enabling analysis of their impact on transmit gain. We then demonstrate that nonzero waveform cross-correlations modify the transmit point spread function, degrading the MIMO virtual array spatial response compared to ideal orthogonal waveforms. For GMTI radar applications, we show that the accumulation of cross-correlation energy from clutter returns increases the clutter subspace rank within the interference-plus-noise space-time covariance matrix. To quantify these performance degradations, we extend existing space-time adaptive processing (STAP) benchmarking tools to MIMO radar, developing signal-to-interference-plus-noise ratio (SINR) loss approximations that account for waveform cross-correlation. We then propose an iterative minimum mean square error (MMSE) filter as a novel approach to suppress waveform interference in dense clutter environments, demonstrating significant target detection improvement compared to the matched filter. These contributions provide practitioners with the tools for both evaluating MIMO system performance with realistic waveform characteristics and suppressing waveform cross-correlation interference, thereby enabling more flexible waveform design for GMTI radar systems.