Comb waveform optimisation with low peak-to-average power ratio via alternating projection

The active sonar detection performance in shallow water is mainly restricted by the reverberation level. When target echoes are separable from reverberation according to Doppler shifts, comb waveforms with the bed-of-nails ambiguity function can achieve reverberation suppression. However, some comb waveforms present significantly low transmitting efficiency measured by the high peak-to-average power ratio (PAPR), which may severely affect the detection performance in a noise-limited scenario. In order to effectively improve their transmitting efficiency, the authors propose an approach of comb waveform optimisation with low PAPR via alternating projection in this study. The main idea is based on designing projection constraint sets and corresponding projection operators to achieve the shaping of comb spectra. Hence, the approach has the capability to make a compromise between the transmitting efficiency and reverberation suppression performance. The PAPR control of geometric comb waveforms is implemented in simulations, which prove the validity of the approach.