  In this paper, we propose a unified framework based on equivariance for the
design of artificial intelligence (AI)-assisted technologies in multi-user
multiple-input-multiple-output (MU-MIMO) systems. We first provide definitions
of multidimensional equivariance, high-order equivariance, and multidimensional
invariance (referred to collectively as tensor equivariance). On this basis, by
investigating the design of precoding and user scheduling, which are key
techniques in MU-MIMO systems, we delve deeper into revealing tensor
equivariance of the mappings from channel information to optimal precoding
tensors, precoding auxiliary tensors, and scheduling indicators, respectively.
To model mappings with tensor equivariance, we propose a series of
plug-and-play tensor equivariant neural network (TENN) modules, where the
computation involving intricate parameter sharing patterns is transformed into
concise tensor operations. Building upon TENN modules, we propose the unified
tensor equivariance framework that can be applicable to various communication
tasks, based on which we easily accomplish the design of corresponding
AI-assisted precoding and user scheduling schemes. Simulation results
demonstrate that the constructed precoding and user scheduling methods achieve
near-optimal performance while exhibiting significantly lower computational
complexity and generalization to inputs with varying sizes across multiple
dimensions. This validates the superiority of TENN modules and the unified
framework.
