On the Application of Modulo-ADCs for Compressed Sensing

Compressed sensing is an important tool for extending the capabilities of signal acquisition systems. The theoretical results available in the area generally work under the impractical assumption of the availability of measurements with infinite precision. In this paper, we consider the effect of finite dynamic range of the analog-to-digital converters (ADCs), and study the application of modulo-ADCs for compressed sensing, which counters the clipping effect by folding the signal crossing the range back to the dynamic range of ADCs via modulo arithmetic. For this setup with an additional constraint where the measurements span a given number of modulo periods, we present a convex relaxation algorithm and provide recovery guarantees. We then consider the effect of quantization, and empirically study the tradeoff between the number of modulo folds and quantization levels. We compare the NMSE and error probability performance of modulo-ADCs with traditional ADCs under saturated or scaled measurements. The simulation results show that modulo-ADCs offer the advantage of reduction in the number of bits compared to scaled measurements and better error probability compared to saturated measurements. The simulations and the recovery guarantee also provide a framework for characterizing the key tradeoffs involved, and plays an important role in the design and analysis of modulo-ADCs.