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Analog-to-digital converters (ADCs) are crucial in signal processing but face challenges when handling high-dynamic-range signals. In radar systems, the coexistence of strong and weak targets can lead to significant information loss due to ADC limitations. Additionally, in unknown environments, ADC saturation can cause clipping, degrading downstream processing performance. To address these issues, modulo sampling (MS), also known as unlimited sampling (US), has been proposed recently, applying a modulo operator before sampling. However, its many-to-one mapping introduces challenges in signal identifiability and the development of effective recovery algorithms.

In this work, we first explore the identifiability of the IDFT sensing model under MS, which has applications in OFDM communication systems and periodic bandlimited signals. By leveraging techniques from abstract algebra, we establish necessary and sufficient conditions for unique signal recovery, offering key insights into the theoretical limits of modulo-based sampling and reconstruction. Next, we tackle the fundamental problem of line spectral estimation (LSE), which plays a crucial role in various signal processing applications. We propose a robust recovery algorithm that effectively mitigates noise in modulo-sampled signals. By integrating dynamic programming with orthogonal matching pursuit, our method achieves high-accuracy spectral estimation despite the nonlinear distortions introduced by modulo sampling. To further validate our approach, we design and implement a prototype modulo ADC and conduct real-world experiments, demonstrating the superior performance of our algorithm compared to existing methods. Finally, we extend our study to direction-of-arrival (DOA) estimation, a critical task in radar and sonar systems. Conventional ADC-based DOA estimation methods struggle in near-far scenarios, where strong and weak sources coexist, leading to significant information loss. To address this issue, we introduce a novel hybrid sampling framework that combines modulo sampling with one-bit quantization. We develop the one-bit-aided blind integerforcing (1bit-aided-BIF) algorithm, which leverages one-bit samples to estimate the covariance matrix and then applies integer-forcing decoder to unwrap modulo samples. Numerical experiments confirm that our approach significantly enhances DOA estimation accuracy in high-dynamic-range environments.

Qi Zhang received the BE degree in electronic information engineering and the ME degree in naval architecture and ocean engineering from Zhejiang University, Hangzhou, China, in 2017 and 2020, respectively. He is currently working toward the PhD degree in information systems technology and design with the Singapore University of Technology and Design, Singapore. His research interests include statistical signal processing, Bayesian compressed sensing, and modulo sampling.