Doppler Resilient Complementary Sequences: Theoretical Bounds and Optimal Constructions

This paper studies Doppler resilient complementary sequences (DRCSs) whereby the ambiguity functions (AFs) of multiple element sequences are summed to attain low/zero AF values. We first derive a set of AF lower bounds for unimodular DRCS sets, which include the existing bounds on AFs as special cases. These bounds may be used as theoretical design guidelines to measure the optimality of DRCS sets against Doppler effect. In addition, we introduce some constructions of DRCS sets based on mathematical tools such as orthogonal matrices, circular Florentine rectangles and difference sets, which can generate the optimal DRCS set. Finally, we evaluate the feasibility of DRCSs for pulse train waveform design.