2026 Vaghela Modulo ADC Symbol Detection

Modulo-folding ADCs are designed to minimize power consumption by constraining the dynamic range of the sampled signal prior to quantization, yet typically require an unfolding step to recover the true samples for further processing. This study demonstrates that the unfolding step can be bypassed entirely when it comes to symbol detection, even under realistic oversampled conditions where additive noise affects the signal pre-modulo and becomes correlated during the front-end filtering process of the receiver, compounded by independent quantization noise from the ADC itself. A derived residual—constructed from the folded and quantized observations alongside a candidate symbol hypothesis—cancels out the unknown integer wrap caused by folding, allowing the hypothesis likelihood to be determined by utilizing the density of the folded noise evaluated at that residual. We further establish that the wrap vector exhibits ternary and sparse characteristics at high probability, provided the folding threshold surpasses the noise standard deviation. Our resulting Mahalanobis maximum-likelihood detector operates directly on the folded samples, with a strategic block-structured search facilitating manageable detection for extended symbol sequences. Simulation results verify that our approach maintains accuracy comparable to conventional non-folding ADCs across various signal-to-noise ratios (SNRs), while traditional unfolding-based detection methods necessitate significantly higher oversampling to achieve similar performance.