A Coordinate-Descent Framework to Design Low PSL/ISL Sequences

TL;DR

This paper introduces a coordinate descent framework for designing phase sequences with optimized autocorrelation properties, effectively handling non-convex, NP-hard problems for both continuous and discrete phases.

Contribution

It proposes a novel iterative coordinate descent method with specialized solutions for non-convex min-max problems in sequence design, including a heuristic initialization approach.

Findings

Outperforms existing methods in discrete phase sequence design

Produces sequences with lower PSL and ISL values

Effective for both continuous and discrete phase constraints

Abstract

This paper is focused on the design of phase sequences with good (aperiodic) autocorrelation properties in terms of Peak Sidelobe Level (PSL) and Integrated Sidelobe Level (ISL). The problem is formulated as a bi-objective Pareto optimization forcing either a continuous or a discrete phase constraint at the design stage. An iterative procedure based on the coordinate descent method is introduced to deal with the resulting optimization problems which are non-convex and NP-hard in general. Each iteration of the devised method requires the solution of a non-convex min-max problem. It is handled either through a novel bisection or an FFT-based method for the continuous and the discrete phase constraint, respectively. Additionally, a heuristic approach to initialize the procedures employing the lp-norm minimization technique is proposed. Simulation results illustrate that the proposed methodologies can outperform some counterparts providing sequences with good autocorrelation features especially in the discrete phase/binary case.