Performance Analysis of Signal Detection using Quantized Received Signals of Linear Vector Channel

TL;DR

This paper analyzes the performance of optimal signal detection in large linear vector channels with quantized signals, revealing conditions for perfect detection and the impact of quantization on detection ability.

Contribution

It extends performance analysis to quantized signals in large linear channels using the replica method, providing new insights into detection limits.

Findings

Perfect detection in noiseless channels under certain conditions

Detection ability decreases with larger quantization step size in noisy channels

Analytical results derived using statistical mechanics techniques

Abstract

Performance analysis of optimal signal detection using quantized received signals of a linear vector channel, which is an extension of code-division multiple-access (CDMA) or multiple-input multiple-output (MIMO) channels, in the large system limit, is presented in this paper. Here the dimensions of channel input and output are both sent to infinity while their ratio remains fixed. An optimal detector is one that uses a true channel model, true distribution of input signals, and perfect knowledge about quantization. Applying replica method developed in statistical mechanics, we show that, in the case of a noiseless channel, the optimal detector has perfect detection ability under certain conditions, and that for a noisy channel its detection ability decreases monotonically as the quantization step size increases.