Asymptotic Parameter Tracking Performance with Measurement Data of 1-bit Resolution

TL;DR

This paper investigates the performance of 1-bit resolution measurement data for signal parameter estimation and tracking, showing that incorporating channel evolution models can significantly reduce quantization loss, especially at low SNR.

Contribution

It introduces a Bayesian bound analysis demonstrating reduced quantization loss when channel dynamics are considered, supported by simulations in satellite and UWB applications.

Findings

Quantization loss is about 2/pi (-1.96 dB) for low SNR without channel dynamics.

Incorporating channel evolution reduces loss by a factor of two, approximately 0.98 dB.

Simulation results confirm the analytical predictions of improved tracking performance with 1-bit data.

Abstract

The problem of signal parameter estimation and tracking with measurement data of low resolution is considered. In comparison to an ideal receiver with infinite receive resolution, the performance loss of a simplistic receiver with 1-bit resolution is investigated. For the case where the measurement data is preprocessed by a symmetric hard-limiting device with 1-bit output, it is well-understood that the performance for low SNR channel parameter estimation degrades moderately by 2/pi (-1.96 dB). Here we show that the 1-bit quantization loss can be significantly smaller if information about the temporal evolution of the channel parameters is taken into account in the form of a state-space model. By the analysis of a Bayesian bound for the achievable tracking performance, we attain the result that the quantization loss in dB is in general smaller by a factor of two if the channel evolution is slow. For the low SNR regime, this is equivalent to a reduced loss of sqrt(2/pi) (-0.98 dB). By simulating non-linear filtering algorithms for a satellite-based ranging application (GPS) and a UWB channel estimation problem, both with low-complexity 1-bit analog-to-digital converter (ADC) at the receiver, we verify that the analytical characterization of the tracking error is accurate. This shows that the performance loss due to observations with low amplitude resolution can, in practice, be much less pronounced than indicated by classical results. Finally, we discuss the implication of the result for medium SNR applications like channel estimation in the context of mobile wireless communications.