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Radar signal design in a spectrally crowded environment is currently a challenge due to the increasing requests for spectrum from both military sensing applications and civilian wireless services. The goal of this paper is to improve a previously devised algorithm for the synthesis of optimized radar waveforms fulfilling spectral compatibility with overlaid licensed radiators. The new technique achieves an enhanced spectral coexistence with the surrounding electromagnetic environment through a suitable modulation of the transmitted waveform energy, which was kept fixed at the maximum level in the previously devised algorithm. At the analysis stage, the waveform performance is studied in terms of trade-off among the achievable Signal to Interference Plus Noise Ratio (SINR), spectral shape, and the resulting Autocorrelation Function (ACF), also in situations where the previous technique cannot be applied.

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. First of all, we focus on the selection of the radar signal optimizing the signal-to-noise ratio (SNR) in correspondence of a given expected target Doppler frequency (Algorithm 1). Then, through a max-min approach, we make robust the technique with respect to the received Doppler (Algorithm 2), namely we optimize the worst case SNR under the same constraints as in the previous problem. Since Algorithms 1 and 2 do not impose any condition on the waveform phase, we also devise their phase quantized versions (Algorithms 3 and 4, respectively), which force the waveform phase to lie within a finite alphabet. All the problems are formulated in terms of non-convex quadratic optimization programs with either a finite or an infinite number of quadratic constraints. We prove that these problems are NP-hard and, hence, introduce design techniques, relying on semidefinite programming (SDP) relaxation and randomization as well as on the theory of trigonometric polynomials, providing high-quality suboptimal solutions with a polynomial time computational complexity. Finally, we analyze the performance of the new waveform design algorithms in terms of detection performance and robustness with respect to Doppler shifts

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