  Optimization theory assisted algorithms have received great attention for
precoding design in multiuser multiple-input multiple-output (MU-MIMO) systems.
Although the resultant optimization algorithms are able to provide excellent
performance, they generally require considerable computational complexity,
which gets in the way of their practical application in real-time systems. In
this work, in order to address this issue, we first propose a framework for
deep-unfolding, where a general form of iterative algorithm induced
deep-unfolding neural network (IAIDNN) is developed in matrix form to better
solve the problems in communication systems. Then, we implement the proposed
deepunfolding framework to solve the sum-rate maximization problem for
precoding design in MU-MIMO systems. An efficient IAIDNN based on the structure
of the classic weighted minimum mean-square error (WMMSE) iterative algorithm
is developed. Specifically, the iterative WMMSE algorithm is unfolded into a
layer-wise structure, where a number of trainable parameters are introduced to
replace the highcomplexity operations in the forward propagation. To train the
network, a generalized chain rule of the IAIDNN is proposed to depict the
recurrence relation of gradients between two adjacent layers in the back
propagation. Moreover, we discuss the computational complexity and
generalization ability of the proposed scheme. Simulation results show that the
proposed IAIDNN efficiently achieves the performance of the iterative WMMSE
algorithm with reduced computational complexity.
