Blind Multi-Band Signal Reconstruction: Compressed Sensing for Analog Signals

TL;DR

This paper introduces a novel compressed sensing-based method for perfect blind multi-band signal reconstruction from sub-Nyquist samples without prior knowledge of band locations, achieving minimal sampling rates.

Contribution

It develops a non-linear blind reconstruction scheme that leverages sparse frequency domain structure and formulates the problem as a finite-dimensional compressed sensing task.

Findings

Achieves perfect reconstruction at minimal sampling rates.

Provides a theoretical lower bound on sampling rate for blind recovery.

Demonstrates effectiveness through numerical experiments.

Abstract

We address the problem of reconstructing a multi-band signal from its sub-Nyquist point-wise samples. To date, all reconstruction methods proposed for this class of signals assumed knowledge of the band locations. In this paper, we develop a non-linear blind perfect reconstruction scheme for multi-band signals which does not require the band locations. Our approach assumes an existing blind multi-coset sampling method. The sparse structure of multi-band signals in the continuous frequency domain is used to replace the continuous reconstruction with a single finite dimensional problem without the need for discretization. The resulting problem can be formulated within the framework of compressed sensing, and thus can be solved efficiently using known tractable algorithms from this emerging area. We also develop a theoretical lower bound on the average sampling rate required for blind signal reconstruction, which is twice the minimal rate of known-spectrum recovery. Our method ensures perfect reconstruction for a wide class of signals sampled at the minimal rate. Numerical experiments are presented demonstrating blind sampling and reconstruction with minimal sampling rate.