Radar code design with a Peak to average power Ratio constraint: A randomized approximate approach

This paper considers the problem of radar waveform design in the presence of colored Gaussian disturbance under a Peak to Average power Ratio (PAR) and an energy constraint. Firstly, we focus on the selection of the radar signal optimizing the Signal to Noise Power Ratio (SNR) for a given target Doppler frequency (Algorithm 1). Then, we devise its phase quantized version (Algorithm 2), which forces the waveform phase to lie within a finite alphabet. Both the problems are formulated in terms of NP-hard non-convex quadratic optimization programs; in order to solve them, we resort to Semidefinite Programming (SDP) relaxation and randomization techniques, providing provable-quality sub-optimal solutions with a polynomial time computational complexity. Finally, we analyze the performance in terms of detection capability and robustness with respect to Doppler shifts.