FDD CSI Feedback under Finite Downlink Training: A Rate-Distortion Perspective

2026-02-06

AI Summary

This study addresses the fundamental performance limits of channel state information (CSI) feedback in frequency-division duplexing (FDD) multi-antenna OFDM systems under limited downlink training. By leveraging rate-distortion theory and incorporating minimum mean square error (MMSE) channel estimation with Gaussian pilots, the work establishes, for the first time, a general rate-distortion function (RDF) for CSI feedback under finite training lengths. Theoretical analysis reveals non-asymptotic bounds on this RDF across arbitrary downlink signal-to-noise ratios, as well as its asymptotic convergence behavior: when the number of training symbols exceeds the antenna dimension, the overall RDF converges to the direct RDF achievable with perfect CSI, with a convergence rate inversely proportional to the training length. Simulations confirm the tightness of the derived bounds.

Technology Category

• Cognitive Modeling & Cognitive Systems: Other Foundations of Cognitive Modeling & Systems
• Machine Learning: Information Theory
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

This paper establishes the theoretical limits of channel state information (CSI) feedback in frequency-division duplexing (FDD) multi-antenna orthogonal frequency-division multiplexing (OFDM) systems under finite-length training with Gaussian pilots. The user employs minimum mean-squared error (MMSE) channel estimation followed by asymptotically optimal uplink feedback. Specifically, we derive a general rate-distortion function (RDF) of the overall CSI feedback system. We then provide both non-asymptotic bounds and asymptotic scaling for the RDF under arbitrary downlink signal-to-noise ratio (SNR) when the number of training symbols exceeds the antenna dimension. A key observation is that, with sufficient training, the overall RDF converges to the direct RDF corresponding to the case where the user has full access to the downlink CSI. More importantly, we demonstrate that even at a fixed downlink SNR, the convergence rate is inversely proportional to the training length. The simulation results show that our bounds are tight, and under very limited training, the deviation between the overall RDF and the direct RDF is substantial.

Problem

• FDD
• CSI feedback
• finite training
• rate-distortion
• channel estimation

Innovation

• Rate-Distortion Function
• FDD CSI Feedback
• Finite Training
• MMSE Channel Estimation
• Asymptotic Optimality