Efficent Large-Scale Multi-Unimodular Waveform Design with Good Correlation Properties via Direct Phase Optimizations

In this paper, we propose an efficient algorithm for designing large-scale multi-unimodular waveforms with low correlations. Different from existing approaches that commonly involve repetitive projections of complex values into their constant-modulus approximations, we conduct optimizations directly on the phase values of waveform elements. Specifically, we optimize the weighted integrated sidelobe level of waveforms, and formulate such design into an unconstrained optimization problem with respect to phase values of waveform elements. Then, we derive the gradient of the newly formulated objective function, through which we subsequently elaborate its majorant with the support of a properly designed Lipschitz-constant related quantity. Our major contributions also lie in obtaining a closed-form update of phase values that boils down to a gradient-descent regime, and calculating the update with fast implementations. Simulation results verify the superiority of our algorithm over existing state-of-the-art methods.