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Optimal Linear Precoder Design for MIMO-OFDM Integrated Sensing and Communications Based on Bayesian Cramér-Rao Bound
Xinyang Li, Vlad Costin Andrei, Ullrich J Mönich, Holger Boche
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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.
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