Unlimited Sampling via One-Bit Quantization

Arian Eamaz, Kumar Vijay Mishra, Farhang Yeganegi, Mojtaba Soltanalian

Abstract:

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.

Submission Type: Full Paper