  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.
