Performance Analysis for Pilot-based 1-bit Channel Estimation with Unknown Quantization Threshold

TL;DR

This paper analyzes the impact of unknown quantization thresholds on pilot-based 1-bit channel estimation, revealing that threshold uncertainty causes additional information loss, especially at higher SNRs, but diminishes at low SNRs or near-zero offsets.

Contribution

It provides a theoretical analysis of the performance degradation caused by unknown quantization thresholds in 1-bit channel estimation using CRLB methods.

Findings

Unknown thresholds cause additional information loss.

Loss diminishes at low SNR or when offset is near zero.

Analysis uses CRLB and expected CRLB for random parameters.

Abstract

Parameter estimation using quantized observations is of importance in many practical applications. Under a symmetric $1$-bit setup, consisting of a zero-threshold hard-limiter, it is well known that the large sample performance loss for low signal-to-noise ratios (SNRs) is moderate ($\frac{2}{\pi}$ or $-1.96$dB). This makes low-complexity analog-to-digital converters (ADCs) with $1$-bit resolution a promising solution for future wireless communications and signal processing devices. However, hardware imperfections and external effects introduce the quantizer with an unknown hard-limiting level different from zero. In this paper, the performance loss associated with pilot-based channel estimation, subject to an asymmetric hard limiter with unknown offset, is studied under two setups. The analysis is carried out via the Cram\'{e}r-Rao lower bound (CRLB) and an expected CRLB for a setup with random parameter. Our findings show that the unknown threshold leads to an additional information loss, which vanishes for low SNR values or when the offset is close to zero.