Locating the Few: Sparsity-Aware Waveform Design for Active Radar

Owing to the inherent sparsity of the target scene, compressed sensing (CS) has been successfully employed in radar applications. It is known that the performance of target scene recovery in CS scenarios depends highly on the coherence of the sensing matrix, which is determined by the radar transmit waveform. In this paper, we propose efficient transmit waveform optimization approaches for two different structures of the radar waveform, namely, the single-pulse and the more general pulse-train scenarios. By determining the identical coherence values associated with the sensing matrices of CS-based radars, the suggested methods provide a considerable reduction in the number of optimization variables. We show that, in the single-pulse scenario, fast Fourier transform operations can be used to improve the computation speed, whereas efficient power method-like iterations may be employed in the pulse-train scenarios. The effectiveness of the proposed algorithms is illustrated through several numerical examples.