Group Information Geometry Approach for Ultra-Massive MIMO Signal Detection

We propose a group information geometry approach (GIGA) for ultra-massive multiple-input multiple-output (MIMO) signal detection. The signal detection task is framed as computing the approximate marginals of the a posteriori distribution of the transmitted data symbols of all users. With the approximate marginals, we perform the maximization of the {\textsl{a posteriori}} marginals (MPM) detection to recover the symbol of each user. Based on the information geometry theory and the grouping of the components of the received signal, three types of manifolds are constructed and the approximate a posteriori marginals are obtained through m-projections. The Berry-Esseen theorem is introduced to offer an approximate calculation of the m-projection, while its direct calculation is exponentially complex. In most cases, more groups, less complexity of GIGA. However, when the number of groups exceeds a certain threshold, the complexity of GIGA starts to increase. Simulation results confirm that the proposed GIGA achieves better bit error rate (BER) performance within a small number of iterations, which demonstrates that it can serve as an efficient detection method in ultra-massive MIMO systems.