This paper studies the problem of linear precoding for multiple-input
multiple-output (MIMO) communication channels employing finite-alphabet
signaling. Existing solutions typically suffer from high computational
complexity due to costly computations of the constellation-constrained mutual
information. In contrast to existing works, this paper takes a different path
of tackling the MIMO precoding problem. Namely, a data-driven approach, based
on deep learning, is proposed. In the offline training phase, a deep neural
network learns the optimal solution on a set of MIMO channel matrices. This
allows the reduction of the computational complexity of the precoder
optimization in the online inference phase. Numerical results demonstrate the
efficiency of the proposed solution vis-\`a-vis existing precoding algorithms
in terms of significantly reduced complexity and close-to-optimal performance.

本文提出基于深度学习的多输入多输出通信信道中有限字母信号的线性预编码方法，采用线下训练方式，大大降低在线推理阶段的预编码复杂度，并以数值实验验证了该方法在复杂度和性能上的优势。

基于深度学习的 MIMO 有限字母信号线性预编码

Deep-Learning Based Linear Precoding for MIMO Channels with  Finite-Alphabet Signaling

We study the optimality of linear precoding for the two-receiver
multiple-input multiple-output (MIMO) Gaussian broadcast channel (BC) with
confidential messages. Secret dirty-paper coding (SDPC) is optimal under an
input covariance constraint, but there is no computable secrecy capacity
expression for the general MIMO case under an average power constraint. In
principle, for this case, the secrecy capacity region could be found through an
exhaustive search over the set of all possible matrix power constraints.
Clearly, this search, coupled with the complexity of dirty-paper encoding and
decoding, motivates the consideration of low complexity linear precoding as an
alternative. We prove that for a two-user MIMO Gaussian BC under an input
covariance constraint, linear precoding is optimal and achieves the same
secrecy rate region as S-DPC if the input covariance constraint satisfies a
specific condition, and we characterize the corresponding optimal linear
precoders. We then use this result to derive a closed-form sub-optimal
algorithm based on linear precoding for an average power constraint. Numerical
results indicate that the secrecy rate region achieved by this algorithm is
close to that obtained by the optimal S-DPC approach with a search over all
suitable input covariance matrices.

研究了两个接收器多输入多输出高斯广播通道下线性预编码的最优性和机密能力，证明了如果满足特定条件的输入协方差约束，线性预编码可以实现与 S-DPC 相同的机密速率区域，并得到相应的最优线性预编码器。这个结果被应用于平均功率约束下的封闭式次优算法的导出。