color:#002060">In this thesis, message-passing-based algorithms for the uplink of Cell-Free Massive Multiple-Input Multiple-Output (CF-MaMIMO) communications are investigated. In CF networks, all user equipments (UEs) within a region are simultaneously served by all access points (APs). As a result, the number of users may exceed the length of pilot sequences, leading to pilot contamination. To address this issue, semi-blind methods are required, in which APs jointly estimate channel coefficients and UE data symbols. Pilot-based channel estimation can be formulated as a linear estimation problem, while data-based estimation leads to a bilinear estimation problem. Exact Bayesian inference involves high-dimensional integrals and is NP-hard. Therefore, iterative approximation methods, such as message-passing algorithms, are essential for practical CF communication systems.
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color:#002060">The close relationship between constrained Bethe Free Energy (BFE) optimization and message-passing algorithms is analyzed. Pilot-based channel estimation is generalized as a sparse signal recovery problem under a generalized linear model (GLM), which is a fundamental problem in signal processing. The approximate posterior, along with the corresponding equivalent Gaussian prior and noise, is obtained using Expectation Propagation (EP) on a loop-free factorization of the GLM. A constrained BFE formulation that shares the same stationary points as the corresponding EP algorithm is studied. Furthermore, an alternative derivation of the large-system-limit (LSL) approximation of the BFE is presented. Based on this LSL approximation, a provably convergent iterative method is proposed.
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color:#002060">In the second part, this thesis focuses on bilinear estimation problems. A hybrid method combining Expectation Maximization (EM) and EP (EM-EP) is proposed, where EP mitigates multi-user interference and EM converts the single-user bilinear estimation into two linear estimation problems. By employing a loop-free factorization scheme, EM-EP converges rapidly to a stationary point. To exploit discrete constellations, a decentralized EP-based algorithm is developed and further simplified using LSL approximations. To reduce the computational complexity of EP caused by constellation size, a hybrid Variational Bayes (VB) and EP method (VB-EP) is proposed. While VB-EP follows a similar design philosophy to EM-EP and variable-level EP (VL-EP), it introduces additional constraints that may degrade performance from the perspective of BFE optimization. In contrast, hierarchical EP avoids introducing new constraints and reduces computational complexity by exploiting the hierarchical structure of $4^M$-QAM constellations.
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color:#002060">Motivated by emerging machine-type communications in 6G systems, grant-free (GF) CF networks are also investigated. A distributed iterative maximum likelihood algorithm is proposed for user activity detection.
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color:#002060">EP serves as the core framework for both linear and bilinear estimation in this thesis. A fundamental challenge in EP is the presence of non-integrable beliefs. In bilinear estimation, this issue arises when computing Gaussian-equivalent messages for Gaussian mixture model (GMM) messages. To address this, an EP-based algorithm is proposed to approximate the mean and variance of a random variable whose distribution is given by a product of GMMs. Two approaches are developed to preserve non-integrable messages while preventing non-integrable beliefs. These approaches are further generalized into an EP framework capable of handling more complex factorization structures, such as those encountered in CF communication systems.
