Segmented compressed sampling for analog-to-information conversion: Method and performance analysis

TL;DR

This paper introduces a segmented compressed sampling method for analog-to-information conversion that enhances sampling efficiency and signal recovery performance by reusing sub-samples across segments, effectively extending the measurement matrix.

Contribution

The paper proposes a novel segmented sampling technique that reuses sub-samples to improve measurement matrix properties and signal recovery in AIC systems.

Findings

The extended measurement matrix satisfies the restricted isometry property with high probability.

Segmented AIC significantly improves signal recovery performance over conventional AIC.

Simulation results confirm the theoretical advantages of the proposed method.

Abstract

A new segmented compressed sampling method for analog-to-information conversion (AIC) is proposed. An analog signal measured by a number of parallel branches of mixers and integrators (BMIs), each characterized by a specific random sampling waveform, is first segmented in time into $M$ segments. Then the sub-samples collected on different segments and different BMIs are reused so that a larger number of samples than the number of BMIs is collected. This technique is shown to be equivalent to extending the measurement matrix, which consists of the BMI sampling waveforms, by adding new rows without actually increasing the number of BMIs. We prove that the extended measurement matrix satisfies the restricted isometry property with overwhelming probability if the original measurement matrix of BMI sampling waveforms satisfies it. We also show that the signal recovery performance can be improved significantly if our segmented AIC is used for sampling instead of the conventional AIC. Simulation results verify the effectiveness of the proposed segmented compressed sampling method and the validity of our theoretical studies.