Modulo Sampling with 1-Bit Side Information: Performance Guarantees in the Presence of Quantization

In this work, we investigate the relationship between the dynamic range and quantization noise power in modulo analog-to-digital converters (ADCs). An algorithm to recover the original signal from quantized modulo observations with 1-bit side information is analyzed. We prove that an oversampling factor of OF > 3 and a quantizer resolution of b > 3 are sufficient for the modulo ADC to have better quantization noise suppression than a standard ADC without the modulo operator. Under this setting, the mean squared error (MSE) of a modulo ADC is O(1/OF3) whereas that of a standard ADC is only O(1/OF). Numerical results are presented to validate the derived performance guarantees.