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.

翻译：本文建立了在采用高斯导频的有限长度训练下，频分双工（FDD）多天线正交频分复用（OFDM）系统中信道状态信息（CSI）反馈的理论极限。用户采用最小均方误差（MMSE）信道估计，随后进行渐近最优的上行链路反馈。具体而言，我们推导了整体CSI反馈系统的一般率失真函数（RDF）。随后，在训练符号数量超过天线维度的条件下，我们给出了任意下行信噪比（SNR）下RDF的非渐近界和渐近缩放规律。一个关键发现是，在训练充分的情况下，整体RDF收敛于用户完全掌握下行CSI情况下的直接RDF。更重要的是，我们证明了即使在固定下行SNR下，收敛速率也与训练长度成反比。仿真结果表明，我们的界是紧致的，并且在训练非常有限的情况下，整体RDF与直接RDF之间存在显著偏差。