# Fundamental Limits of CSI Compression in FDD Massive MIMO

arXiv: https://arxiv.org/abs/2603.14325 · HTML: https://mlsanity.com/paper/2603.14325/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 43 references that are in the map.
- First posted on arXiv 15 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Lossy Image Compression with Conditional Diffusion Models](https://mlsanity.com/paper/2209.06950/) (2022)
- [Nonlinear Transform Coding](https://mlsanity.com/paper/2007.03034/) (2020)
- [Lossy Compression with Gaussian Diffusion](https://mlsanity.com/paper/2206.08889/) (2022)
- [Overview of Deep Learning-based CSI Feedback in Massive MIMO Systems](https://mlsanity.com/paper/2206.14383/) (2022)
- [Lightweight Convolutional Neural Networks for CSI Feedback in Massive MIMO](https://mlsanity.com/paper/2005.00438/) (2020)
- [Changeable Rate and Novel Quantization for CSI Feedback Based on Deep Learning](https://mlsanity.com/paper/2202.13627/) (2022)
- [Channel Vector Subspace Estimation from Low-Dimensional Projections](https://mlsanity.com/paper/1509.07469/) (2015)
- [Generative Diffusion Model-based Compression of MIMO CSI](https://mlsanity.com/paper/2503.03753/) (2025)
- [FDD Massive MIMO Without CSI Feedback](https://mlsanity.com/paper/2302.04398/) (2023)
- [Multi-Rate Variable-Length CSI Compression for FDD Massive MIMO](https://mlsanity.com/paper/2311.18172/) (2023)
- [Low-Complexity CSI Feedback for FDD Massive MIMO Systems via Learning to Optimize](https://mlsanity.com/paper/2406.16323/) (2024)

## Abstract (arXiv)

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.