Performance Analysis of Mismatched Filtering for Stochastic Waveforms

Mismatched filtering (MMF) is a widely used pulse compression technique that reduces cross-correlation sidelobe levels at the cost of some loss in signal-to-noise ratio (SNR). Applying MMF to stochastically generated radar waveforms makes the filter's performance inherently random, which can be problematic if the variability is excessive. As well as the computational cost being relatively high, as per pulse, a new MMF optimization is required. In this thesis, the feasibility of a fixed MMF strategy for stochastic radar waveforms to reduce computational cost is investigated. Two MMF formulations were evaluated, the optimal MMF (Diagonal Loaded Filter) and a projection-based MMF. Both filters were designed to minimize sidelobe energy within specified regions of the Cross-Ambiguity Function (CAF) for Stochastic Waveform Generation (StoWGe) waveforms, and their performance was assessed across multiple time-bandwidth products and sidelobe-regions for two center frequencies, Fc = 30 Ghz and Fc  = 3.5 Ghz. The MMF performance was characterized using SNR loss and sidelobe depth over hundreds of trails. It is observed that the variability in SNR and sidelobe depth decreases as the waveform time-bandwdith product and the sidelobe region targeted for minimization increase, although the Fc = 3.5 GHz cases exhibited a plateau in achievable sidelobe depth. Additional validation using 1000-trail histograms and loop-back testing confirmed the robustness for the fixed MMF approach for higher time-bandwidth product stochastic waveforms. Where, overall, the results demonstrate that a fixed MMF strategy is feasible for stochastic waveforms when the time-bandwdith product and sidelobe region are sufficiently large. Furthermore, the Projection-based MMF provides a suboptimal alternative to the optimal MMF as it achieves comparable MMF performance when constrained to similar SNR-loss and may be desirable when the size of the domination eigenvalues is small relative to the filter length and can be efficiency obtained.