Forward channel state information (CSI) often plays a vital role in
scheduling and capacity-approaching transmission optimization for massive
multiple-input multiple-output (MIMO) communication systems. In frequency
division duplex (FDD) massive MIMO systems, forwardlink CSI reconstruction at
the transmitter relies critically on CSI feedback from receiving nodes and must
carefully weigh the tradeoff between reconstruction accuracy and feedback
bandwidth. Recent studies on the use of recurrent neural networks (RNNs) have
demonstrated strong promises, though the cost of computation and memory remains
high, for massive MIMO deployment. In this work, we exploit channel coherence
in time to substantially improve the feedback efficiency. Using a Markovian
model, we develop a deep convolutional neural network (CNN)-based framework
MarkovNet to differentially encode forward CSI in time to effectively improve
reconstruction accuracy. Furthermore, we explore important physical insights,
including spherical normalization of input data and convolutional layers for
feedback compression. We demonstrate substantial performance improvement and
complexity reduction over the RNN-based work by our proposed MarkovNet to
recover forward CSI estimates accurately. We explore additional practical
consideration in feedback quantization, and show that MarkovNet outperforms
RNN-based CSI estimation networks at a fraction of the computational cost.

本文介绍了一种基于 Markovian 模型的深度卷积神经网络框架 MarkovNet，用于对前向通道状态信息 (CSI) 进行编码、传输和恢复，以提高 CSI 的重建精度和反馈效率。与基于递归神经网络 (RNN) 的方法相比，MarkovNet 在保证重建准确性的前提下，能显著降低成本和复杂度，尤其在反馈量化方面表现优异。

基于马尔科夫模型的深度学习框架用于大规模 MIMO CSI 反馈

A Markovian Model-Driven Deep Learning Framework for Massive MIMO CSI  Feedback

Acyclic directed mixed graphs (ADMGs) are graphs that contain directed
($\rightarrow$) and bidirected ($\leftrightarrow$) edges, subject to the
constraint that there are no cycles of directed edges. Such graphs may be used
to represent the conditional independence structure induced by a DAG model
containing hidden variables on its observed margin. The Markovian model
associated with an ADMG is simply the set of distributions obeying the global
Markov property, given via a simple path criterion (m-separation). We first
present a factorization criterion characterizing the Markovian model that
generalizes the well-known recursive factorization for DAGs. For the case of
finite discrete random variables, we also provide a parameterization of the
model in terms of simple conditional probabilities, and characterize its
variation dependence. We show that the induced models are smooth. Consequently,
Markovian ADMG models for discrete variables are curved exponential families of
distributions.

研究了无向边和有向边混合，并且无向边形成无环图的 acyclic directed mixed graphs (ADMGs) 及其概率模型，提出了一种基于简单路径判据的全局马尔科夫性标准 ——m-separation，并得到了该模型的因子分解准则及离散随机变量的参数化表示，验证了该模型的光滑性，从而证明了马尔科夫性 ADMG 模型是曲率指数族。