Doppler Resilient Complementary Waveform Design for Active Sensing

Active sensing systems prefer probing waveforms with good auto-correlation properties. Faced with the difficulty in getting individual sequences with impulse-like aperiodic auto-correlation functions, we resort to the temporal waveform diversity based on complementary sets of sequences (CSS). It seems an ideal solution, but has rarely been used due to the extreme sensitivity of CSS to Doppler shifts. This paper is devoted to applying numerical methods to the design of Doppler resilient complementary waveforms (DRCW) whose ambiguity functions are almost free of range sidelobes along modest Doppler shifts. We formulate the problem as minimizing the worst-case peak sidelobe level (PSL) with low peak-to-average power ratio (PAR) constraints, and then approximate the min-max problem by a ${l}_{p}$ -norm minimization problem. A hierarchical strategy is developed to tackle the phase optimization and the amplitude-phase optimization respectively. Correspondingly, two algorithms based on phase-gradient and Majorization-Minimization are proposed, both of which can be efficiently computed via FFT. Numerical experiments show our method is effective and superior to existing ones. The DRCWs thus obtained have their range sidelobes at all lags suppressed below −60dB, and are expected to bring significant performance improvements in active sensing. Two application examples, detecting weak targets in heavy clutter and estimating the high-resolution range profile of an extended target by active radars, are given.