A High-Resolution Analysis of Receiver Quantization in Communication

2025-01-17

AI Summary

This work investigates the fundamental communication limits and receiver design for complex Gaussian channels under medium-to-high-resolution uniform quantization, focusing on the impact of overload and granular distortions on achievable rates when gain control is imperfect. Leveraging the generalized mutual information (GMI) framework with nearest-neighbor decoding, we derive a closed-form expression for the achievable rate. We establish, for the first time, the asymptotic scaling law $2sqrt{ln(2K)}$ for the optimal loading factor and provide a high-accuracy finite-resolution estimate. Rigorous analysis proves that overload distortion decays exponentially while granular distortion decays quadratically; we further characterize how the optimal quantization range scales with resolution. Numerical simulations confirm the high accuracy of our theoretical predictions. The results yield tight performance bounds and practical design guidelines for quantized communication systems.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

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 $2sqrt{ln 2K}$ as the resolution increases. An asymptotically tight estimate of the optimal loading factor is further given, which is also highly accurate for finite resolutions.

Problem

• Quantization Effects
• Communication Limits
• Optimal Quantization Range

Innovation

• Information Transmission Rate
• Gain Control in Quantization
• Optimal Quantization Interval