Design of Single Unimodular Waveform With Good Correlation Level Via Phase Optimizations

In this paper, we focus on the unimodular waveform design with good correlation property, i.e., with low integrated sidelobe level (ISL). In contrast to existing approaches that commonly involve constraints on the moduli of waveform elements, we come up with the idea of designing the waveform via directly optimizing its phase values. Using this idea, the standard ISL-minimization based waveform design is converted as an unconstrained optimization problem with respect to the phase values of waveform elements, which avoids the repetitive procedure of projecting non-unimodular complex values into the best approximations of constant magnitudes. To this end, we first reformulate the ISL metric into a function of the phase values to be obtained for the waveform, and then solve the new unconstrained ISL-minimization-based waveform design using majorization-minimization techniques. The first-order gradient of the reformulated objective function is derived, by which the majorant of the objective is elaborated. Based on this, we finally tackle the design via iterations, at each of which we obtain a closed-form solution with fast implementations. An algorithm is proposed, with whose simpleness and effectiveness are verified by simulations.