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We propose a high-resolution imaging radar system to enable high-fidelity four-dimensional (4D) sensing for autonomous driving, i.e., range, Doppler, azimuth, and elevation, through a joint sparsity design in frequency spectrum and array configurations. To accommodate a high number of automotive radars operating at the same frequency band while avoiding mutual interference, random sparse step-frequency waveform (RSSFW) is proposed to synthesize a large effective bandwidth to achieve high range resolution profiles. To mitigate high range sidelobes in RSSFW radars, optimal weights are designed to minimize the peak sidelobe level such that targets with a relatively small radar cross section are detectable without introducing high probability of false alarm. We extend the RSSFW concept to multi-input multi-output (MIMO) radar by applying phase codes along slow time to synthesize a two-dimensional (2D) sparse array with hundreds of virtual array elements to enable high-resolution direction finding in both azimuth and elevation. The 2D sparse array acts as a sub-Nyquist sampler of the corresponding uniform rectangular array (URA) with half-wavelength interelement spacing, and the corresponding URA response is recovered by completing a low-rank block Hankel matrix. Consequently, the high sidelobes in the azimuth and elevation spectra are greatly suppressed so that weak targets can be reliably detected. The proposed imaging radar provides point clouds with a resolution comparable to LiDAR but with a much lower cost. Numerical simulations are conducted to demonstrate the performance of the proposed 4D imaging radar system with joint sparsity in frequency spectrum and antenna arrays.
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