Bayesian Self-Calibration and Parametric Channel Estimation for 6G Antenna Arrays

Accurate channel estimation is essential for both high-rate communication and high-precision sensing in 6G wireless systems. However, a major performance limitation arises from calibration mismatches when operating phased-array antennas under real-world conditions. To address this issue, we propose to integrate antenna element self-calibration into a variational sparse Bayesian learning (VSBL) algorithm for parametric channel estimation. We model antenna gain and phase deviations as latent variables and derive explicit update equations to jointly infer these calibration parameters and the channel parameters: the model order, complex amplitudes, delays, angles, and the noise variance. The resulting algorithm operates online and adapts in real time to hardware-induced mismatches. We assess its performance in terms of the root mean square error (RMSE) and the optimal subpattern-assignment (OSPA) metric, demonstrating consistent improvements over conventional VSBL without calibration. Our results demonstrate that embedding self-calibration within Bayesian inference significantly enhances the robustness of channel estimation.