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.

翻译：本文提出了一种面向超大规模多输入多输出（MIMO）信号检测的群信息几何方法（GIGA）。该信号检测任务被构建为计算所有用户发送数据符号的后验分布的近似边缘分布。利用这些近似边缘分布，我们执行最大后验边缘（MPM）检测以恢复每个用户的符号。基于信息几何理论以及对接收信号分量的分组，我们构建了三种类型的流形，并通过m投影获得了近似后验边缘分布。引入Berry-Esseen定理以实现m投影的近似计算，而其直接计算具有指数级复杂度。在大多数情况下，分组越多，GIGA的复杂度越低。然而，当分组数量超过特定阈值时，GIGA的复杂度开始增加。仿真结果证实，所提出的GIGA在少量迭代次数内即可实现更优的误码率（BER）性能，这表明其可作为超大规模MIMO系统中一种高效的检测方法。