Waveform Design for Optimal PSL Under Spectral and Unimodular Constraints via Alternating Minimization

TL;DR

This paper introduces an alternating minimization method for designing unimodular waveforms that optimize peak side-lobe level while satisfying spectral constraints, outperforming existing methods and approaching theoretical bounds.

Contribution

It proposes a novel AM-based approach for waveform design with spectral and unimodular constraints, including a theoretical lower bound for PSL minimization.

Findings

The proposed method achieves lower PSL than existing algorithms.

Numerical results show PSL close to the theoretical lower bound.

Waveforms meet spectral and hardware constraints effectively.

Abstract

In an active sensing system, waveforms with good auto-correlations are preferred for accurate parameter estimation. Furthermore, spectral compatibility is required to avoid mutual interference between devices as the electromagnetic environment becomes increasingly crowded. Waveforms should also be unimodular due to hardware limits. In this paper, a new approach to generating a unimodular sequence with an approximately optimal peak side-lobe level (PSL) in auto-correlation and adjustable stopband attenuation is proposed. The proposed method is based on alternating minimization (AM) and numerical results suggest that it outperforms existing methods in terms of PSL. We also develop a theoretical lower bound for the PSL minimization problem under spectral constraints and unimodular constraints, which can be used for the evaluation of the results in various works about this waveform design problem. It is observed in the numerical results that the PSL of the proposed algorithm is close to the derived lower bound.