Unlimited Sampling via One-Bit Quantization

Shannon’s sampling theorem plays a central role in the discrete-time processing of bandlimited signals. However, the infinite precision assumed by Shannon’s theorem is impractical because of the ADC clipping effect that limits the signal’s dynamic range. Moreover, the power consumption of an analog-to-digital converter (ADC) increases linearly with the sampling frequency and may be prohibitively high for a wide bandwidth signal. Recently, unlimited and one-bit sampling frameworks have been proposed to address these shortcomings. The former is a high-resolution technique that employs self-reset ADCs to achieve an unlimited dynamic range. The latter achieves relatively low cost and reduced power consumption at an elevated sampling rate. In this paper, we examine jointly exploiting the appealing attributes of both techniques. We propose unlimited one-bit (UNO) sampling, which entails a judicious design of one-bit sampling thresholds. This enables storing the distance between the input signal value and the threshold. We then utilize this information to accurately reconstruct the signal from its one-bit samples via a randomized Kaczmarz algorithm (RKA) which is considered to be a strong linear feasibility solver that selects a random linear equation in each iteration. The numerical results illustrate the effectiveness of RKA-based UNO over the state-of-the-art.