Asymptotic Performance Analysis for 1-bit Bayesian Smoothing

TL;DR

This paper analyzes the asymptotic performance of 1-bit Bayesian smoothing, demonstrating that with additional delay, it can outperform ideal filtering systems in low-power, low-resolution signal processing.

Contribution

It extends existing analysis from Bayesian filtering to Bayesian smoothing, revealing that 1-bit systems can surpass infinite-bit filtering performance with delay.

Findings

1-bit Bayesian smoothing can outperform ideal infinite-bit filtering with delay.

Performance loss at low SNR is moderate, around -1 dB.

Smoothing with 1-bit ADC offers a promising low-power estimation approach.

Abstract

Energy-efficient signal processing systems require estimation methods operating on data collected with low-complexity devices. Using analog-to-digital converters (ADC) with $1$-bit amplitude resolution has been identified as a possible option in order to obtain low power consumption. The $1$-bit performance loss, in comparison to an ideal receiver with $\infty$-bit ADC, is well-established and moderate for low SNR applications ($2/\pi$ or $-1.96$ dB). Recently it has been shown that for parameter estimation with state-space models the $1$-bit performance loss with Bayesian filtering can be significantly smaller ($\sqrt{2/\pi}$ or $-0.98$ dB). Here we extend the analysis to Bayesian smoothing where additional measurements are used to reconstruct the current state of the system parameter. Our results show that a $1$-bit receiver performing smoothing is able to outperform an ideal $\infty$-bit system carrying out filtering by the cost of an additional processing delay $\Delta$.