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On the Asymptotic MSE-Optimality of Parametric Bayesian Channel Estimation in mmWave Systems (2504.16710v1)
Published 23 Apr 2025 in eess.SP
Abstract: The mean square error (MSE)-optimal estimator is known to be the conditional mean estimator (CME). This paper introduces a parametric channel estimation technique based on Bayesian estimation. This technique uses the estimated channel parameters to parameterize the well-known LMMSE channel estimator. We first derive an asymptotic CME formulation that holds for a wide range of priors on the channel parameters. Based on this, we show that parametric Bayesian channel estimation is MSE-optimal for high signal-to-noise ratio (SNR) and/or long coherence intervals, i.e., many noisy observations provided within one coherence interval. Numerical simulations validate the derived formulations.