Threshold Sensitivity in Two-Channel Modulo ADCs: Analysis and Robust Reconstruction

This paper presents a comprehensive analysis of two-channel modulo analog-to-digital converters (ADCs) systems, focusing on the sensitivity of ADC thresholds. By exploiting analytic number theory, we first investigate the relationship among ADC threshold precision, maximum signal dynamic range, and error tolerance. Our analysis reveals that even slight deviations in ADC thresholds can substantially impact the maximum reconstructed signal dynamic range and error tolerance. To address these sensitivity issues, we propose a novel approach that strategically sacrifices signal dynamic range to stabilise error tolerance in the presence of slight ADC threshold variations. We also introduce a low-complexity reconstruction algorithm that exploits this trade-off, thereby enhancing system robustness. Simulation results validate the theoretical framework and confirm the efficiency of our proposed algorithm.