In this paper, we investigate the fundamental limits of MIMO-OFDM integrated sensing and communications (ISAC) systems based on a Bayesian Cram\'er-Rao bound (BCRB) analysis. We derive the BCRB for joint channel parameter estimation and data symbol detection, in which a performance trade-off between both functionalities is observed. We formulate the optimization problem for a linear precoder design and propose the stochastic Riemannian gradient descent (SRGD) approach to solve the non-convex problem. We analyze the optimality conditions and show that SRGD ensures convergence with high probability. The simulation results verify our analyses and also demonstrate a fast convergence speed. Finally, the performance trade-off is illustrated and investigated.

翻译：本文基于贝叶斯克拉美-罗界（BCRB）分析，研究了MIMO-OFDM集成感知与通信（ISAC）系统的性能极限。我们推导了联合信道参数估计与数据符号检测的BCRB，并观察到两种功能之间的性能权衡。针对线性预编码器设计，我们构建了优化问题，并提出随机黎曼梯度下降（SRGD）方法以求解该非凸问题。通过分析最优性条件，证明了SRGD能以高概率确保收敛。仿真结果验证了我们的理论分析，并展示了较快的收敛速度。最后，对性能权衡进行了图示与探讨。