Sliding DFT-based Signal Recovery for Modulo ADC with 1-bit Folding Information

Abstract: The modulo analog-to-digital converter (ADC) is a promising solution to resolve the limited dynamic range (DR) issue of conventional ADCs and achieve an enhanced digital resolution given a fixed quantization bit budget. However, a modulo ADC requires an unfolding scheme to correct the nonlinear distortion introduced by the modulo operation. This paper presents a sliding discrete Fourier Transform (DFT)-based method for fast signal reconstruction given the modulo ADC output sequence and a 1-bit folding information sequence. In contrast to existing DFT-based signal recovery techniques for modulo ADCs, our proposed sliding DFT method reduces the required observation time and minimizes the spectral leakage effects via proper choice of window function parameters. A mean squared error (MSE) performance guarantee is established for the proposed signal recovery algorithm. More precisely, we derive sufficient conditions for the oversampling factor ($\mathrm{OF}$) and the number of quantization bits ($b$) to obtain a specific MSE performance. Our numerical results demonstrate that modulo ADCs equipped with our proposed recovery method can outperform conventional ADCs without modulo for $\mathrm{OF} \geq 4$ and $b \geq 4$. The impact of spectral leakage on the MSE performance of the proposed sliding DFT recovery method is also quantified.