Recovery guarantees for multifrequency chirp waveforms in compressed radar sensing

Abstract

Radar imaging systems transmit modulated wideband waveform to achieve high range resolution resulting in high sampling rates at the receiver proportional to the bandwidth of the transmit waveform. Analog processing techniques can be used on receive to reduce the number of measurements to N, the number of potential delay bins. If the scene interrogated by the radar is assumed to be sparse consisting of K point targets, results from compressive sensing suggest that number of measurements can be further reduced to scale with K logN for stable recovery of a sparse scene from measurements with additive noise. While unstructured random projectors guarantee successful recovery under sparsity constraints, they cannot be implemented in the radar hardware in practice. Recently, structured random Toeplitz and Circulant matrices that result from using stochastic waveforms in time delay estimation setting have been shown to yield recovery guarantees similar to unstructured sensing matrices. However, the corresponding transmitter and receiver structures have high complexity and large storage requirements. In this paper, we propose an alternative low complexity compressive wideband radar sensor which combines multitone signal chirp waveform on transmit with a receiver that utilizes an analog mixer followed with a uniform sub-Nyquist sampling stage. We derive the recovery guarantees for the resulting structured measurement matrix and sufficient conditions for the number of tones. The only random component of our design is the sparse tone spectrum implementable efficiently in hardware. Our analytical and empirical results show that the performance of our scheme is in par with unstructured random sensing matrices and structured Toeplitz and Circulant matrices with random entries.