A new approach for design of constant modulus discrete phase radar waveform with low WISL

Abstract

This paper deals with the constant modulus waveform design for a cognitive radar in an effort to achieve the desired Auto-Correlation Function (ACF). The Weighted Integrated Sidelobe Level (WISL) of ACF is considered as a figure of merit accounting for the finite alphabet constraint. By introducing an auxiliary variable, an Inexact Alternating Direction Penalty Method (IADPM) framework is developed to solve the resultant non-convex and, in general, NP-hard problem. In each iteration, it converts the original problem into two subproblems which are solved by an analytic technique and a fast Iterative Sequential Quartic Optimization (ISQO) method, respectively, while locally increasing the involved penalty factor. In particular, the developed procedure can well overcome the non-convergence issue of Alternating Direction Method of Multipliers (ADMM) as it is proved to be convergent for any initialization under some mild conditions. Finally, the WISL, auto-correlation performance, and convergence speed of the proposed technique are evaluated against the state-of-the-art methods. Results show that our proposal outperforms the competitive counterparts with reference to the achieved WISL value and provides the favorable performance-complexity balance.