Expectation propagation based analysis of semi-blind channel estimation in cell-free systems

In this work, we investigate the uplink communi-cation in cell-free (CF) massive multiple-input multiple-output (MaMIMO) systems. One of the major problems in CF MaMIMO systems is pilot contamination, i.e., the number of users is larger than the length of the pilot sequences. Researchers have proposed a semi-blind approach to overcome this problem. The semi-blind joint estimation of the channel and the data leads to a bilinear problem. We propose a vector-level Expectation Propagation (EP) method to avoid the high-dimensional intractable integrals of Bayesian posterior distributions and estimate both the multi-user data sequences and channels. We exploit the property of orthogonal pilots to decompose the pilot measurement into multiple smaller, mutually independent equivalent measurements. We also assume the data sequences to be randomly chosen from a codebook (possibly with structure) of finite alphabet codewords.