A High-Resolution Analysis of Receiver Quantization in Communication

TL;DR

This paper analyzes the limits and design considerations of high-resolution uniform quantization in communication systems, highlighting the importance of gain control and providing asymptotic results for optimal quantizer parameters.

Contribution

It derives an analytical achievable rate for high-resolution quantization with gain control, and characterizes the asymptotic behavior of rate loss due to overload and granular distortions.

Findings

Rate loss due to overload distortion decays exponentially with loading factor.

Rate loss due to granular distortion decays quadratically as step size decreases.

Optimal loading factor scales like 2√ln(2K) for a 2K-level quantizer.

Abstract

We investigate performance limits and design of communication in the presence of uniform output quantization with moderate to high resolution. Under independent and identically distributed (i.i.d.) complex Gaussian codebook and nearest neighbor decoding rule, an achievable rate is derived in an analytical form by the generalized mutual information (GMI). The gain control before quantization is shown to be increasingly important as the resolution decreases, due to the fact that the loading factor (normalized one-sided quantization range) has increasing impact on performance. The impact of imperfect gain control in the high-resolution regime is characterized by two asymptotic results: 1) the rate loss due to overload distortion decays exponentially as the loading factor increases, and 2) the rate loss due to granular distortion decays quadratically as the step size vanishes. For a $2K$-level uniform quantizer, we prove that the optimal loading factor that maximizes the achievable rate scales like $2\sqrt{\ln (2K)}$ as the resolution increases. An asymptotically tight estimate of the optimal loading factor is further given, which is also highly accurate for finite resolutions.