Signal Recovery From 1-Bit Quantized Noisy Samples via Adaptive Thresholding

Abstract

In this paper, we consider the problem of signal recovery from 1-bit noisy measurements. We present an efficient method to obtain an estimation of the signal of interest when the measurements are corrupted by white or colored noise. To the best of our knowledge, the proposed framework is the pioneer effort in the area of 1-bit sampling and signal recovery in providing a unified framework to deal with the presence of noise with an arbitrary covariance matrix including that of the colored noise. The proposed method is based on a constrained quadratic program (CQP) formulation utilizing an adaptive quantization thresholding approach, that further enables us to accurately recover the signal of interest from its 1-bit noisy measurements. In addition, due to the adaptive nature of the proposed method, it can recover both fixed and time-varying parameters from their quantized 1-bit samples.

ADMM-Based One-Bit Quantized Signal Detection for Massive MIMO Systems With Hardware Impairments

“…Signal estimation and detection from one-bit quantized samples have been studied outside the massive MIMO literature [12][13][14][15][16][17]. [12] con-This work was partially supported by ELLIIT and the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation. sidered estimation of an unknown single parameter in a wireless sensor network with multiple single-antenna nodes.…”

“…In this paper, we use the idea from [12] of casting the signal detection as an optimization problem to solve a multi-user QPSK detection by including modulation constraints. We reformulate the original non-convex problem to solve it with the powerful Alternating Direction Method of Multipliers (ADMM) algorithm [18] and we obtain closed-form updates.…”

“…Note that in [12], there is only one parameter to be estimated and the resulting convex problem is solved using standard numerical methods which do not take the specific problem structure into account. In this paper, we will exploit the additional structure of the data vector x in (3) and generalize the optimization problem in [12] for MIMO signal detection with hardware impairments by imposing more constraints. Then, an efficient formulation is proposed for the ADMM algorithm in order to obtain closed-form update equations.…”

One-Bit Radar Processing With Time-Varying Sampling Thresholds

“…The assumption of high-precision data is, however, not appropriate when the measurements are extremely quantized to very low bit-rates. Note that, the cost and the power consumption of ADCs grow exponentially with their number of quantization bits and sampling rate [37]. Such issues can be mitigated by a reduction in the number of quantization bits.…”

“…This can be achieved by repeatedly comparing the signal of interest with a time-varying threshold (reference) level. On the plus side, one-bit comparators can provide extremely high sampling rate and are very cheap and easy to manufacture [37]. Moreover, the one-bit ADCs operate on very low power and they can significantly reduce the data flow in the system, which further reduces the overall energy consumption.…”