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Recovery guarantees for high resolution radar sensing with compressive illumination

We present a compressive radar design that combines multitone linear frequency modulated (LFM) waveforms on transmit with classical stretch processor and sub-Nyquist sampling on receive. The proposed compressive illumination scheme has much fewer random elements compared to previously proposed compressive radar designs based on stochastic waveforms, resulting in reduced storage and complexity for implementation. We present bounds on the operator norm and mutual coherence of the sensing matrix of the proposed scheme and show that for sufficiently large number of modulating tones, high resolution range recovery is guaranteed for a sparse scene using sampling rates that scale linearly with the scene sparsity. Simulation results are presented to study recovery performance as a function of system parameters for targets both on and off the grid. In addition, we present experimental results using a high speed digital waveform generator and a custom designed analog stretch processor.