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.
@article{arxiv.2308.12106,
title = {Optimal Linear Precoder Design for MIMO-OFDM Integrated Sensing and Communications Based on Bayesian Cram\'er-Rao Bound},
author = {Xinyang Li and Vlad Costin Andrei and Ullrich J Mönich and Holger Boche},
journal= {arXiv preprint arXiv:2308.12106},
year = {2023}
}