Parameter Estimation of Hybrid LFM and MPSK Pulse Sequences Based on Sub-Nyquist Sampling

To accurately perceive pulse sequences containing linear frequency modulation (LFM) and M-ary phase shift keying (MPSK) signals, this article introduces a parameter measurement framework based on the finite rate of innovation (FRI) sampling theory. By following the radar reconnaissance approach of inter-pulse parameter estimation, pulse-type identification, and intra-pulse parameter estimation, we propose several measurement methods under the condition of sub-Nyquist sampling. These methods encompass hybrid pulse number estimation using singular value rectification (SVR), pulse-type identification through time-domain breakpoints and shift-invariant subspace (SIS) projection, and intra-pulse parameter estimation of hybrid sequences using linear modulation and interval matching. Our approach enables efficient sensing of hybrid sequences within a unified sampling framework, and through the utilization of FRI sampling theory, the efficiency of the parameter measurement process is significantly enhanced, thereby reducing the sampling pressure. Simulation and hardware experiments demonstrate substantial improvements in accuracy for both inter-pulse and intra-pulse parameter estimation in hybrid sequences when compared to classical methods.