Finite Alphabet Unimodular Sequence Design With Low WISL Via An Inexact ADPM Framework

This paper studies the unimodular sequence design with the finite alphabet case for a cognitive radar in order to achieve the desired auto-correlation. An iteration algorithm based on Inexact Alternating Direction Penalty Method (IADPM) framework is developed to minimize the Weighted Integrated Sidelobe Level (WISL). In each iteration, it splits the NP-hard problem into two subproblems via an introduced auxiliary variable, while locally increasing the penalty factor involved in the IADPM framework. The proposed algorithm is shown to converge for any initialization under some mild conditions and avoids the non-convergence problem of ADMM when handling the NP-hard problems. Finally, the auto-correlation performance and convergence speed of the proposed algorithm are evaluated against the state-of-the-art methods. Results show that our proposal outperforms the state-of-the-art competing methods while providing the favorable performance-complexity balance.