Orthogonal anti-jamming waveform design with extended Doppler tolerance based on the LFM-PC signal

Abstract

Designing orthogonal waveforms based on linear frequency modulation and phase-coded (LFM-PC) signals with extended Doppler tolerance plays a vital role in multiple-input multiple-output (MIMO) radar systems. However, it is difficult to address the major problem of the mixed nonconvex unimodulus and nonlinear fourth-order polynomial constraints in sequence set design. In this paper, an orthogonal waveform based on the LFM-PC signal is designed for the discrete phase-coded sequence (DPCS) and continuous phase-coded sequence (CPCS). The hybrid alternating direction method of multipliers (ADMM) and coordinate descending (CD) algorithm are applied to the DPCS design. A novel method is designed with the approach of ADMM and the Lagrange programming neural network (LPNN) algorithm for the CPCS. The specific objective of this study is to propose new chirplike phase codes and a new algorithm framework that can separate the complex nonconvex and nonlinear constraints by ADMM, and we transfer the fourth-order polynomials from the nonlinear constraints into the Lagrange function. As a result, the optimized variables are updated in the ADMM-CD and ADMM-LPNN frameworks. Numerical simulation examples indicate the good performance of the proposed methods, and we compare these two effective methods.