Discrete-Phase Waveform Design to Quadratic Optimization via an ADPM Framework with Convergence Guarantee

This paper considers a quadratic optimization problem in radar discrete-phase waveform design under similarity and constant modulus constraints. A computationally efficient iterative algorithm based on the Alternating Direction Penalty Method (ADPM) framework is proposed. In each iteration, it converts the considered problem into two subproblems with closed-form solutions via an introduced auxiliary variable, while locally increasing the penalty factor involved in the ADPM framework. The proposed algorithm is proven to converge for any initialization under some mild conditions and avoids the non-convergence problem of the Alternating Direction Method of Multipliers (ADMM) when handling the NP-hard problems. Finally, numerical simulations demonstrate that the proposed algorithm can outperform their counterparts by providing better objective values.