Model-based waveform design for optimal detection: A multi-objective approach to dealing with incomplete a priori knowledge.

This work considers the design of optimal, energy-constrained transmit signals for active sensing for the case when the designer has incomplete or uncertain knowledge of the target and/or environment. The mathematical formulation is that of a multi-objective optimization problem, wherein one can incorporate a plurality of potential targets, interference, or clutter models and in doing so take advantage of the wide range of results in the literature related to modeling each. It is shown, via simulation, that when the objective function of the optimization problem is chosen to maximize the minimum (i.e., maxmin) probability of detection among all possible model combinations, the optimal waveforms obtained are advantageous. The advantage results because the maxmin waveforms judiciously allocate energy to spectral regions where each of the target models respond strongly and each of the environmental models affect minimal detection performance degradation. In particular, improved detection performance is shown compared to linear frequency modulated transmit signals and compared to signals designed with the wrong target spectrum assumed. Additionally, it is shown that the maxmin design yields performance comparable to an optimal design matched to the correct target/environmental model. Finally, it is proven that the maxmin problem formulation is convex.