Reconstruction of Frequency Hopping Signals From Multi-Coset Samples

TL;DR

This paper proposes a segment-based reconstruction method for frequency hopping signals from Multi-Coset samples, utilizing compressive sensing techniques and DPSS dictionaries to address nonstationarity and reduce computational complexity.

Contribution

It introduces a novel segment-based framework for reconstructing frequency hopping signals from MC samples, contrasting with previous segment-less methods like MUSIC.

Findings

Effective reconstruction of frequency hopping signals demonstrated

DPSS dictionaries reduce computational complexity

Segment-based approach handles nonstationary signals better

Abstract

Multi-Coset (MC) sampling is a well established, practically feasible scheme for sampling multiband analog signals below the Nyquist rate. MC sampling has gained renewed interest in the Compressive Sensing (CS) community, due partly to the fact that in the frequency domain, MC sampling bears a strong resemblance to other sub-Nyquist CS acquisition protocols. In this paper, we consider MC sampling of analog frequency hopping signals, which can be viewed as multiband signals with changing band positions. This nonstationarity motivates our consideration of a segment-based reconstruction framework, in which the sample stream is broken into short segments for reconstruction. In contrast, previous works focusing on the reconstruction of multiband signals have used a segment-less reconstruction framework such as the modified MUSIC algorithm. We outline the challenges associated with segment-based recovery of frequency hopping signals from MC samples, and we explain how these challenges can be addressed using conventional CS recovery techniques. We also demonstrate the utility of the Discrete Prolate Spheroidal Sequences (DPSS's) as an efficient dictionary for reducing the computational complexity of segment-based reconstruction.