Fundamental Limits of CSI Compression in FDD Massive MIMO

TL;DR

This paper models FDD massive MIMO CSI feedback as a Gaussian mixture source, proposing a practical compression method that leverages latent geometry states, and derives fundamental limits showing near-optimal performance without neural networks.

Contribution

It introduces Gaussian-mixture transform coding (GMTC) for CSI compression, combining state inference with adaptive transform coding, and characterizes the fundamental rate-distortion limits for this model.

Findings

GMTC outperforms neural transform coding in RD tradeoff.

The optimal bit allocation follows a global reverse-waterfilling principle.

Simulations show GMTC requires less memory and complexity than neural approaches.

Abstract

Channel state information (CSI) feedback in frequency-division duplex (FDD) massive multiple-input multiple-output (MIMO) systems is fundamentally limited by the high dimensionality of wideband channels. In this paper, we model the stacked wideband CSI vector as a Gaussian-mixture source with a latent geometry state that represents different propagation environments. Each component corresponds to a locally stationary regime characterized by a correlated proper complex Gaussian distribution with its own covariance matrix. This representation captures the multimodal nature of practical CSI datasets while preserving the analytical tractability of Gaussian models. Motivated by this structure, we propose Gaussian-mixture transform coding (GMTC), a practical CSI feedback architecture that combines state inference with state-adaptive TC. The mixture parameters are learned offline from channel samples and stored as a shared statistical dictionary at both the user equipment (UE) and the base station. For each CSI realization, the UE identifies the most likely geometry state, encodes the corresponding label using a lossless source code, and compresses the CSI using the Karhunen-Loeve transform matched to that state. We further characterize the fundamental limits of CSI compression under this model by deriving analytical converse and achievability bounds on the rate-distortion (RD) function. A key structural result is that the optimal bit allocation across all mixture components is governed by a single global reverse-waterfilling level. Simulations on the COST2100 dataset show that GMTC significantly improves the RD tradeoff relative to neural transform coding approaches while requiring substantially smaller model memory and lower inference complexity. These results indicate that near-optimal CSI compression can be achieved through state-adaptive TC without relying on large neural encoders.