Optimal Linear Precoder Design for MIMO-OFDM Integrated Sensing and Communications Based on Bayesian Cram\'er-Rao Bound

TL;DR

This paper analyzes the fundamental limits of MIMO-OFDM integrated sensing and communications systems using Bayesian Cramér-Rao bounds, proposing an optimization approach for linear precoder design to balance sensing and communication performance.

Contribution

It introduces a novel BCRB-based analysis for joint estimation and detection, and develops a stochastic Riemannian gradient descent method for optimal precoder design in ISAC systems.

Findings

BCRB analysis reveals a trade-off between sensing and communication performance.

SRGD algorithm converges rapidly and with high probability.

Simulation results confirm theoretical insights and effectiveness of the proposed method.

Abstract

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.