In this paper, we propose an inversion method based on the firefly particle swarm optimization (FA-PSO) algorithm to estimate the permittivity, conductivity, and thickness of building materials using the free-space method. To improve convergence efficiency and robustness, an adaptive firefly algorithm (FA) is employed to systematically optimize the hyperparameters of the particle swarm optimization (PSO). By optimizing the parameters of the Gaussian distribution used for population initialization, the accuracy of parameter estimation is gradually improved. Furthermore, we derive the Cramer-Rao lower bound (CRLB) for the permittivity, conductivity, and thickness under a complex Gaussian noise model, which serves as a theoretical benchmark for evaluating the estimation accuracy of the FA-PSO algorithm. Numerical results indicate that for relatively thin materials, the estimation accuracy of the proposed method approaches this theoretical lower bound, confirming the effectiveness of the inversion framework. This study accurately extracts the electromagnetic properties of building materials, providing strong support for evaluating their wireless performance.

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