Multiple-Input-Multiple-Output (MIMO) systems can improve the performance of wireless communication systems. They consist of multiple transmitter and multiple receiver antennas. This means however, that efficient algorithms are needed, that can decode the transmitted signals at the receiver side. Since the complexity of the Maximum Likelihood (ML) algorithm increases exponentially with the number of transmitter antennas, approximating algorithms are needed for large Multiple-Input-Multiple-Output (MIMO) systems. This work focuses on graphical methods that aim at approximating the MIMO detection problem. Firstly, the mathematical description of the MIMO detection problem is shown. Then, a short introduction to graphical models and the belief propagation (BP) algorithm is provided, as well as its application for the MIMO detection problem. Additionally, a description of the maximum spanning tree (MST), edge dropout (ED) and junction tree algorithm (jTA) is provided. A short description of the Ising model is provided as well. The first experiments in this work examine how the removal of edges from a fully-connected graph affects the performance of the BP algorithm and the development of the marginal probabilities. Moreover, a modified BP message update rule, in this work referred to as damping, is examined. The impact of initializing the BP algorithm with different messages is examined as well. Some metrics regarding the initial and final values of the marginal probabilities and the convergence ratios of the BP algorithm are calculated.

Furthermore, the performance of a method is evaluated, which keeps the initial marginal probabilities in case the BP algorithm doesn’t converge. A modified structure for the MST is proposed and the performance of the BP algorithm when evaluating this type of spanning tree is examined. Next, it was examined how the BP algorithm performs when evaluating models with linear exponents in the local potentials compared to when evaluating models with a quadratic term in the exponents of the local potentials. Finally, the impact of the absolute value of the exponents of the pairwise potentials on the performance and convergence properties of the BP algorithm for models with linear exponents in their local potentials was examined.