Multichannel Modulo Sampling with Unlimited Noise

Abstract

Signal saturation represents a characteristic of practical analog-to-digital converters (ADCs) that leads to clipping and information loss. To prevent this, the signal can be "folded" at a given threshold using a modulo nonlinearity to match the ADC’s dynamic range. Existing recovery guarantees for single and multichannel modulo architectures require that the noise is significantly smaller than the modulo threshold. In this work, we introduce a new multichannel modulo architecture for improving noise robustness which has one single folding mechanism for all channels. We show that, by folding all channels at the same time, the modulo discontinuities are detectable under noise of arbitrary magnitude for the appropriate number of channels. We provide a noise independent sampling rate guarantee. Numerical studies validate the proposed method and show accurate input recovery for a wide range of SNRs including negative values.