Designing practical spectrally constrained waveforms for HFSWR by successive convex approximations and projections

In this paper, we consider the design of practical transmit waveforms for a high frequency surface wave radar system operating in a congested spectral environment where the radar must adhere to strict regulations on the interference it can cause to on-going communications. The ideal waveform would be constant amplitude, and have low autocorrelation sidelobes, all while meeting the imposed spectral constraints; however, it is impossible to know a priori that such a waveform exists. We propose an algorithm based on alternating successive convex approximations and projections to design waveforms which meet strict spectral constraints and autocorrelation sidelobe constraints while minimizing amplitude modulation. In simulation, the proposed algorithm is found to converge rapidly and the resulting waveforms have better pulse compression properties than other similar methods from the relevant literature.