Fast gradient descent for multi-objective waveform design

Gradient descent methods have not typically been applied to the design of phase coded sequences because their derivations require O(N2) computations. Previous papers have shown computational simplifications which reduce the number of computations for designing sequences with good autocorrelation and cross-correlation properties to O(N logN). In this paper, we present derivations and algorithms for designing sequences with specific autocorrelation, cross-correlation, and spectral properties, and show how sequences can be designed to also have these properties be good simultaneously. Sequences with autocorrelation and cross-correlation constraints meet the known bounds. Adding spectral constraints degrades the correlation properties of the designed sequences, and we quantify those effects by example.