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.

翻译：频分双工大规模多输入多输出系统中的信道状态信息反馈本质上受限于宽带信道的高维度特性。本文将堆叠的宽带CSI向量建模为具有潜在几何状态的高斯混合源，该几何状态表征不同的传播环境。每个混合分量对应一个局部平稳区域，其特征是具有自身协方差矩阵的相关复高斯分布。该表示方法既捕捉了实际CSI数据集的多模态特性，又保持了高斯模型的分析可处理性。基于此结构，我们提出高斯混合变换编码——一种结合状态推断与状态自适应变换编码的实用CSI反馈架构。混合参数通过信道样本离线学习，并作为共享统计字典存储在用户设备和基站两端。对于每个CSI实现，用户设备识别最可能的几何状态，使用无损信源编码对相应标签进行编码，并采用与该状态匹配的Karhunen-Loeve变换压缩CSI。我们进一步通过推导率失真函数的解析逆界与可达界，刻画了该模型下CSI压缩的基本极限。一个关键的结构性结论是：所有混合分量的最优比特分配由单一全局反注水水位决定。在COST2100数据集上的仿真表明，相较于神经变换编码方法，高斯混合变换编码显著改善了率失真权衡，同时所需模型存储量和推断复杂度大幅降低。这些结果表明，无需依赖大型神经编码器，通过状态自适应变换编码即可实现接近最优的CSI压缩。