In this paper, we propose a precoding framework for frequency division duplex (FDD) integrated sensing and communication (ISAC) systems with multiple-input multiple-output (MIMO). Specifically, we aim to maximize ergodic sum spectral efficiency (SE) while satisfying a sensing beam pattern constraint defined by the mean squared error (MSE). Our method reconstructs downlink (DL) channel state information (CSI) from uplink (UL) training signals using partial reciprocity, eliminating the need for CSI feedback. To mitigate interference caused by imperfect DL CSI reconstruction and sensing operations, we adopt rate-splitting multiple access (RSMA). We observe that the error covariance matrix of the reconstructed channel effectively compensates for CSI imperfections, affecting both communication and sensing performance. To obtain this, we devise an observed Fisher information-based estimation technique. We then optimize the precoder by solving the Karush-Kuhn-Tucker (KKT) conditions, jointly updating the precoding vector and Lagrange multipliers, and solving the nonlinear eigenvalue problem with eigenvector dependency to maximize SE. The numerical results show that the proposed design achieves precise beam pattern control, maximizes SE, and significantly improves the sensing-communication trade-off compared to the state-of-the-art methods in FDD ISAC scenarios.

翻译：本文针对多输入多输出（MIMO）频分双工（FDD）集成感知与通信（ISAC）系统，提出了一种预编码框架。具体而言，我们的目标是在满足由均方误差（MSE）定义的感知波束方向图约束下，最大化遍历和频谱效率（SE）。该方法利用部分互易性，从上行链路（UL）训练信号中重构下行链路（DL）信道状态信息（CSI），从而无需CSI反馈。为了减轻由不完美的DL CSI重构和感知操作引起的干扰，我们采用速率分割多址接入（RSMA）。我们观察到，重构信道的误差协方差矩阵能有效补偿CSI的不完美性，并同时影响通信与感知性能。为此，我们设计了一种基于观测费希尔信息的估计技术。随后，我们通过求解Karush-Kuhn-Tucker（KKT）条件来优化预编码器，联合更新预编码向量和拉格朗日乘子，并求解具有特征向量依赖性的非线性特征值问题以最大化SE。数值结果表明，所提出的设计在FDD ISAC场景中实现了精确的波束方向图控制，最大化SE，并且相比现有最先进方法显著改善了感知-通信权衡。