Efficient Sampling of Sparse Wideband Analog Signals

TL;DR

This paper introduces a novel analog front end for sparse wideband signals that enables sub-Nyquist sampling without requiring full-band exposure, leveraging compressive sampling principles for stable digital reconstruction.

Contribution

It proposes a new sampling architecture with lowpass filters and multipliers, avoiding full-band front ends, and demonstrates stable recovery using compressive sampling techniques.

Findings

The proposed method allows stable reconstruction of wideband sparse signals from low-rate samples.

Numerical experiments validate the theoretical guarantees of the sampling scheme.

Abstract

Periodic nonuniform sampling is a known method to sample spectrally sparse signals below the Nyquist rate. This strategy relies on the implicit assumption that the individual samplers are exposed to the entire frequency range. This assumption becomes impractical for wideband sparse signals. The current paper proposes an alternative sampling stage that does not require a full-band front end. Instead, signals are captured with an analog front end that consists of a bank of multipliers and lowpass filters whose cutoff is much lower than the Nyquist rate. The problem of recovering the original signal from the low-rate samples can be studied within the framework of compressive sampling. An appropriate parameter selection ensures that the samples uniquely determine the analog input. Moreover, the analog input can be stably reconstructed with digital algorithms. Numerical experiments support the theoretical analysis.