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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, the authors focus on the selection of the radar signal optimizing the Signal to Noise Power Ratio (SNR) for a given target Doppler frequency (Algorithm1). Then, they 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; they resort to Semi Definite Programming (SDP) relaxation and randomization techniques, providing provable-quality sub-optimal solutions with a polynomial time computational complexity.
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