Multi-Unimodular Waveform Design With Low Peak Sidelobe Level Via Direct Phase Optimizations

In this paper, we propose an efficient algorithm for designing multi-unimodular waveforms with low peak sidelobe level (PSL) toward any time lags of interest, which differs from existing approaches. The generic PSL metric defined on the TLOI is formulated for minimization, and the phase values of waveforms are directly optimized. To be specific, we first convert the PSL-minimization based waveform design into an lp-norm based minimization problem. Then, we reformulate it into an unconstrained optimization problem with respect to the phase values of waveform elements, wherein the inherent waveform property of constant envelopes and a discrete Fourier transform matrix are both used. Our remaining contributions lie in deriving the complex gradient of the unconstrained objective and also elaborating its majorant via a Lipschitz-constant related quantity which is properly designed. A closed-form solution that updates the phase values through iterations is obtained by the majorization-minimization framework, and it boils down to a gradient descent regime. The fast implementation of our algorithm is also provided, whose performance improvements are verified.