  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.
