Fold First, Detect Directly: Communication Symbol Detection Without Unfolding for Low-Bitrate Modulo-ADCs

Abstract

Modulo-folding analog-to-digital converters (MF-ADCs) enable low-dynamic-range quantizers to sample high-amplitude signals without clipping. However, downstream processing traditionally relies on waveform unfolding algorithms, which require high oversampling rates and are highly sensitive to noise. For communication receivers, where the goal is symbol detection rather than signal reconstruction, unfolding is a redundant intermediate step. In this paper, we propose an unfolding-free maximum-likelihood symbol-detection framework for oversampled MF-ADCs in the presence of joint channel and quantization noise. By leveraging modulo wrap cancellation, we derive an exact, single-term Mahalanobis-distance metric that operates directly on folded observations. To handle long sequences, we introduce a parallelized block search algorithm that reduces computational complexity to scale linearly with sequence length. Simulations show our detector significantly outperforms existing unfolding baselines and approaches unclipped conventional ADC performance.