In this paper we study the code design problem of a new form of linear frequency modulation phase-coded (LFM-PC) hybrid signal with wide Doppler tolerance based on a range-Doppler discrete ambiguity function (DAF) to get better detection performance and anti-jamming capability. The DAF of the LFM-PC inter pulse signal is derived within the Doppler tolerance. Two optimization models are established. One is single pulse sequence design (SSD) for Doppler tolerance extension based on minimum integral normalized sidelobe level (INSL); the other is multi pulse sequence set design (MSSD) for signal orthogonality based on the minimizing sum of the normalized DAF sidelobe (NDAFSL) and discrete cross ambiguity function (DCAF). Two low-complexity signal optimization methods based on alternating direction method of multiplier (ADMM) are proposed, respectively. The simulation results show that the optimized signals have either wide Doppler tolerance or good orthogonal performance, and the optimization methods (i.e., SSD-ADMM and MSSD-ADMM) have the characteristics of fast convergence speed and low operation amount.
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