Discrete Phase Coded Sequence Set Design for Waveform-Agile Radar Based on Alternating Direction Method of Multipliers

With increased degrees of freedom of the transmitter, a coherent waveform-agile radar system can change its interpulse waveform to enhance the capability against increasingly sophisticated jamming and spoofing threats. Furthermore, radar agile waveform can provide better detection performance than a single waveform. In this article, we consider discrete phase coded sequence set design (DPCSSD) problem based on range-Doppler discrete ambiguity function for coherent waveform-agile radar system. DPCSSD problem for optimizing discrete phase coded sequence set under constant module constraint with desired minimized sidelobes on range-Doppler plane, is a quartic function and the constraint is nonconvex. To solve this quartic optimization problem, we propose an effective algorithm based on alternating direction method of multipliers (ADMM), which is a powerful mathematical tool of the augmented Lagrangian scheme for dealing with separable objective functions. As the quartic optimization problem is hard to solve, majorization-minimization (MM) is also considered to introduce a quadratic auxiliary function which is the upperbound of the original function. By minimizing the auxiliary function, the original DPCSSD optimization problem can be solved through MM in an iterative way. Meanwhile, the problem of minimizing the quadratic auxiliary function with constraints can be solved through ADMM algorithm. In particular, fast implementation for the most computationally demanding step of matrix inversion is investigated. The effectiveness of the proposed approach is demonstrated via computer simulations.