# Minimum Rate Sampling and Spectrum Blind Reconstruction in Random Equivalent Sampling

## TL;DR

This paper investigates spectrum-blind multiband signal reconstruction from random equivalent sampling data, proposing a new sampling pattern and mathematical model that enable robust reconstruction with minimal acquisitions, leveraging compressive sensing techniques.

## Contribution

It introduces a novel RES sampling pattern and mathematical framework that guarantees well-conditioned multiband signal reconstruction with unknown spectral support, reducing the number of acquisitions needed.

## Key findings

- Reconstruction is feasible and robust for spectrum-blind sparse multiband signals.
- The proposed method reduces the minimum number of RES acquisitions needed.
- Experimental results validate the effectiveness of the reconstruction algorithm.

## Abstract

The random equivalent sampling (RES) is a well-known sampling technique that can be used to capture a high-speed repetitive waveform with low sampling rate. In this paper, the feasibility of spectrum-blind multiband signal reconstruction for data sampled from RES is investigated. We propose a RES sampling pattern and its corresponding mathematical model that guarantees well-conditioned reconstruction of multiband signal with unknown spectral support. We give the minimum number of RES acquisitions that hold overwhelming probability to successfully reconstruct original signal. We demonstrate that for signal with specific spectral occupation, the number of RES acquisitions and the minimum sampling rate could be approached. The signal reconstruction is studied in the framework of compressive sampling (CS) theory. The eigen-decomposition and minimum description length (MDL) criteria are adopted to adaptively estimate the dimension of signal, and the number of unknowns of reconstruction problem is reduced. Experimental results are reported to indicate that, for a spectrum-blind sparse multiband signal, the proposed reconstruction algorithm for RES is feasible and robust.

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Source: https://tomesphere.com/paper/1701.01831