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
$\mathcal{O}\left(\frac{1}{\text{OF}^{3}}\right)$
whereas that of a standard ADC is only
$\mathcal{O}\left(\frac{1}{\text{OF}}\right)$
. Numerical results are presented to validate the derived performance guarantees.