ORKA: Accelerated Kaczmarz Algorithms for Signal Recovery from One-Bit Samples

Abstract

One-bit quantization with time-varying sampling thresholds has recently found significant utilization potential in statistical signal processing applications due to its relatively low power consumption and low implementation cost. In addition to such advantages, an attractive feature of one-bit analog-todigital converters (ADCs) is their superior sampling rates as compared to their conventional multibit counterparts. This characteristic endows one-bit signal processing frameworks with what we refer to as sample abundance. On the other hand, many signal recovery and optimization problems are formulated as (possibly non-convex) quadratic programs with linear feasibility constraints in the onebit sampling regime. We demonstrate, with a particular focus on the nuclear norm minimization, that the sample abundance paradigm allows for the transformation of such quadratic problems to merely a linear feasibility problem by forming a large-scale overdetermined linear system; thus removing the need for costly optimization constraints and objectives. To make this achievable, we propose enhanced randomized Kaczmarz algorithms to tackle these highly overdetermined feasibility problems. Several numerical results are presented to illustrate the effectiveness of the proposed methodologies.

L${}_{\text{2}}$min${}^{\text{2/2s}}$: Efficient Linear Reconstruction Filter for Incremental Delta-Sigma ADCs

“…which is costly to be implemented in digital circuits. Therefore, in this paper, we just focus on analyzing the performance of the L 2 min 2 filter expressed in (9). Meanwhile, only the generic modulator topologies are presented for conciseness, but the proposed filters are applicable to other modulator topologies/variants such as the cascade of integrators with feed-forward (CIFF) architecture, modulator with finite impulse response (FIR) feedback, modulator with signal scaling, etc.…”

“…FPGA and ASIC implementation results will also be discussed. Other implementations will also work if the filter kernel function (9) or ( 21) is satisfied.…”

“…In pursuit of this goal, various new quantization schemes have been reported. The recent pioneers in this field include unlimited sampling [2], [3] and one-bit quantization [3], [4], [5], [6], [7], [8], [9], which utilize advanced signal processing theories and powerful signal processing tools for signal Bo Wang and Jens Schneider are with the College of Science and Engineering, Hamad Bin Khalifa University, Doha 34110, Qatar (e-mail: bwang@hbku.edu.qa).…”

“…recovery. However, substantial computational resources are required (e.g., 0.3 ms computation time in a typical CPU [9]). Among the classical quantization schemes, delta-sigma (ΔΣ) ADC also relies on signal processing to reconstruct the input using the quantized one-bit or multi-bit output [1], [10].…”

“…However, its signal reconstruction process is more hardware-friendly to be integrated into standalone ADC chips. Meanwhile, compared to the emerging one-bit quantization scheme using time-varying thresholds drawn from a predefined distribution [3], [4], [5], [6], [7], [8], [9], the loop filter in a ΔΣ ADC can effectively generate uniform distancing time-varying thresholds, which recursively makes the threshold closer to the input signal, thus accurate signal recovery becomes possible using simple digital processing.…”