In frequency division duplex massive multiple-input multiple-output systems, downlink channel state information must be fed back within a limited uplink budget. While transform coding with Karhunen-Loeve transform and reverse water-filling is rate-distortion optimal for Gaussian channels, its performance is limited by basis mismatch between the user and base station. We analyze this mismatch and propose a practical architecture separating long-term basis feedback from short-term coefficient quantization. Using a random vector quantization, we derive a closed-form end-to-end mean square error expression. This allows us to characterize the optimal rate split and identify a phase transition threshold for basis updates. Simulations on correlated Gaussian and COST2100 channels demonstrate near-optimal performance, robustness to update overhead, and significant complexity reduction compared to deep-learning-based autoencoders.

翻译：在频分双工大规模多输入多输出系统中，下行信道状态信息必须在有限的上行链路预算内进行反馈。虽然基于Karhunen-Loeve变换和逆向注水原理的变换编码对于高斯信道而言是率失真最优的，但其性能受限于用户与基站之间的基失配。我们分析了这一失配现象，并提出了一个将长期基反馈与短期系数量化相分离的实用架构。利用随机矢量量化方法，我们推导出了端到端均方误差的闭式表达式。由此可表征最优的率分配，并识别出基更新的相变阈值。在相关高斯信道及COST2100信道上的仿真表明，该方法具有接近最优的性能、对更新开销的鲁棒性，且与基于深度学习的自编码器相比复杂度显著降低。