MaRLI: Attack on the Discrete-Phase WISL Minimization Problem

To facilitate target localization, active radar signals or sequences are designed to have low auto-correlation. This goal is typically achieved by the minimization of the auto-correlation integrated sidelobe level (ISL) metric, or the more general, weighted version of the ISL, known as the WISL metric. In this paper, we introduce two problem formulations to address unimodular quartic program, which arises in numerous applications, with WISL minimization being one of them. The first approach is almost equivalent, while the second scheme utilizes a bi-quadratic formulation, both of which simplify the main problem to a quadratic program. We propose efficient approaches to WISL minimization for unimodular sequence design that take advantage of the low-cost and easily implementable power method-like iterations (PMLI). Moreover, to design the discrete-phase unimodular sequences with low WISL, the $M$-ary unimodular sequence design via Relaxed PMLI (MaRLI) is proposed by changing and adopting the PMLI approach to tackle this challenging problem. Several numerical results and comparisons between MaRLI and other well-known sequence design algorithms are presented to illustrate the effectiveness of the proposed method. As we show, MaRLI appears to achieve a better suppression of the finite-alphabet autocorrelation levels compared to the state-of-the-art alternatives.