Efficient Off-Grid Bayesian Parameter Estimation for Kronecker-Structured Signals

TL;DR

This paper introduces an efficient off-grid Bayesian estimation method for Kronecker-structured signals, improving accuracy and speed in applications like IRS-aided channel estimation by leveraging structure decomposition and sparse Bayesian learning.

Contribution

The work presents a novel off-grid sparse Bayesian learning algorithm that exploits Kronecker structure for improved parameter estimation in multidimensional signals.

Findings

Enhanced estimation accuracy in IRS-aided channel scenarios

Reduced computational complexity compared to existing methods

Demonstrated denoising benefits and convergence of the proposed approach

Abstract

This work studies the problem of jointly estimating unknown parameters from Kronecker-structured multidimensional signals, which arises in applications like intelligent reflecting surface (IRS)-aided channel estimation. Exploiting the Kronecker structure, we decompose the estimation problem into smaller, independent subproblems across each dimension. Each subproblem is posed as a sparse recovery problem using basis expansion and solved using a novel off-grid sparse Bayesian learning (SBL)-based algorithm. Additionally, we derive probabilistic error bounds for the decomposition, quantify its denoising effect, and provide convergence analysis for off-grid SBL. Our simulations show that applying the algorithm to IRS-aided channel estimation improves accuracy and runtime compared to state-of-the-art methods through the low-complexity and denoising benefits of the decomposition step and the high-resolution estimation capabilities of off-grid SBL.