Pulse Diversity Phase-Coded Waveform and Mismatched Filter Bank Design Via Periodic Ambiguity Function Shaping

Pulse diversity phase-coded (PDPC) waveform has received considerable attention recently because of its applications to obtain synthetic bandwidth, mitigate range-Doppler ambiguity, or suppress artificial repeat jamming and clutter. However, when applied to pulse-Doppler (PD) radar, high range-Doppler sidelobes will occur at the receiver, which cannot be improved by classical ambiguity function (AF) shaping methods. To address this problem, we first derive the discrete periodic AF (PAF) to characterize the range-Doppler processing of the PD radar. On this basis, we formulate a joint design problem for PDPC waveform and mismatched filter bank over the range-Doppler bins of interest under signal-to-noise ratio (SNR) loss and constant modulus constraints, which can be used to simultaneously suppress strong sidelobe interference and artificial repeat jamming. To solve the PAF shaping problem, which contains high-order polynomial constraints, we generalize and apply the maximum block improvement type algorithm with the help of the alternating direction method of multipliers and introducing auxiliary variables. In particular, a time-varying step-size strategy based on the dual theory is presented to enhance the convergence performance and refine the optimal solution. Several simulations are performed to show the effectiveness of the presented approach in improving the detection performance of PD radar, especially under low SNR scenarios.