Hierarchical expectation propagation for semi-blind channel estimation in cell-free networks

In this work, we study uplink communication in cell-free (CF) massive multiple-input multiple-output (MaMIMO) systems, a promising architecture for next-generation networks. To address the challenge of pilot contamination, we employ semi-blind transmission structures that enable joint channel and data symbol estimation. However, Bayesian estimation in such semi-blind frameworks leads to intractable bilinear problems. To tackle this, we propose a simplified, distributed method based on Expectation Propagation (EP) for efficient semi-blind channel estimation. Notably, we identify that if the data constellation set can be decomposed into multiple sub-constellation sets with identical amplitudes, this structure can be leveraged to significantly reduce computational complexity. This approach is particularly advantageous for managing large constellation sizes, ensuring scalability and efficiency in practical systems. Additionally, approximations based on the Central Limit Theorem are incorporated to further simplify computations.