Xampling: Signal Acquisition and Processing in Union of Subspaces

TL;DR

Xampling is a comprehensive framework that enables efficient signal acquisition and processing in unions of subspaces, combining analog compression with nonlinear subspace detection for sub-Nyquist sampling.

Contribution

The paper introduces Xampling, a unified approach integrating analog compression and nonlinear detection for signals in unions of subspaces, with practical algorithms and comparisons.

Findings

Xampling effectively reduces bandwidth before sampling.

The framework compares different sub-Nyquist strategies like Rademacher and MWC.

Algorithms enable low-rate processing from sub-Nyquist samples.

Abstract

We introduce Xampling, a unified framework for signal acquisition and processing of signals in a union of subspaces. The main functions of this framework are two. Analog compression that narrows down the input bandwidth prior to sampling with commercial devices. A nonlinear algorithm then detects the input subspace prior to conventional signal processing. A representative union model of spectrally-sparse signals serves as a test-case to study these Xampling functions. We adopt three metrics for the choice of analog compression: robustness to model mismatch, required hardware accuracy and software complexities. We conduct a comprehensive comparison between two sub-Nyquist acquisition strategies for spectrally-sparse signals, the random demodulator and the modulated wideband converter (MWC), in terms of these metrics and draw operative conclusions regarding the choice of analog compression. We then address lowrate signal processing and develop an algorithm for that purpose that enables convenient signal processing at sub-Nyquist rates from samples obtained by the MWC. We conclude by showing that a variety of other sampling approaches for different union classes fit nicely into our framework.