Multi-Channel Sparse Data Conversion With a Single Analog-to-Digital Converter

Abstract

We address the problem of performing simultaneous analog-to-digital (A/D) conversion on multi-channel signals using a single A/D converter (ADC). Assuming that each input has an unknown sparse representation in known dictionaries, we find that multi-channel information can be sampled with a single ADC. The proposed ADC architecture consists of a mixed signal block and a digital signal processing (DSP) block. The channel inputs are sampled by switched-capacitor-based sample-and-hold circuits, and then mixed using sequences of plus or minus ones, leading to no bandwidth expansion. The resulting discrete-time signals are converted to digital sequences by a single ADC or quantizer. At the DSP block, each channel is separated from the digitized mixture through various separation algorithms that are widely used in compressive sensing. For this, we study several techniques for separating the mixture of the channel inputs into the sample number of digital sequences corresponding to each channel. We show that with an ideal ADC, perfect reconstruction of the signals is possible if the input signals are sufficiently sparse. We also show simulation results with a 16-bit ADC model, and the reconstruction is possible up to the accuracy of the ADCs.