Fast Algorithms for Designing Complementary Sets of Sequences Under Multiple Constraints

Complementary sets of sequences (CSSs) are widely used in many applications, such as active sensing and wireless communication. The construction of CSS has attracted considerable attention over the past few decades. In this paper, efficient and comprehensive computational algorithms for CSS design are proposed. We seek to minimize complementary integral sidelobe level (CISL) under multiple constraints, including unimodular, peak-to-average power ratio, discrete phase, and spectrum compatible constraint. The task of CSS design can be formulated as solving a nonconvex constraint optimization problem. As this problem is difficult to tackle directly, we resort to the general majorization-minimization (MM) method. By utilizing the inherent algebraic structure of the objective function, we construct the majorizing function via two consecutive applications of the MM method and obtain a closed-form solution by a couple of FFT operations at each iteration. The relationship between MM-based algorithms and derivative-based algorithms is revealed. Our algorithms are more flexible and widely applicable, and the numerical experiment results demonstrate the effectiveness and superiority over the existing state-of-art algorithms.