This paper presents a deep learning-aided iterative detection algorithm for
massive overloaded multiple-input multiple-output (MIMO) systems where the
number of transmit antennas $n$ is larger than that of receive antennas $m$.
Since the proposed algorithm is based on the projected gradient descent method
with trainable parameters, it is named the trainable projected
gradient-detector (TPG-detector). The trainable internal parameters, such as
the step-size parameter, can be optimized with standard deep learning
techniques, i.e., the back propagation and stochastic gradient descent
algorithms. This approach is referred to as data-driven tuning, and ensures
fast convergence during parameter estimation in the proposed scheme. The
TPG-detector mainly consists of matrix-vector product operations whose
computational cost is proportional to $m n$ for each iteration. In addition,
the number of trainable parameters in the TPG-detector is independent of the
number of antennas. These features of the TPG-detector result in a fast and
stable training process and reasonable scalability for large systems. Numerical
simulations show that the proposed detector achieves a comparable detection
performance to those of existing algorithms for massive overloaded MIMO
channels, e.g., the state-of-the-art IW-SOAV detector, with a lower computation
cost.

本论文介绍了一个基于深度学习的迭代检测算法，用于具有传输天线数大于接收天线数的大规模超载 MIMO 系统的检测，该算法能够快速有效地收敛参数估计，计算成本低，可扩展性强。

用于海量超载 MIMO 信道的可训练投影梯度检测器：数据驱动调整方法

Trainable Projected Gradient Detector for Massive Overloaded MIMO  Channels: Data-driven Tuning Approach

In this paper, we propose a model-driven deep learning network for
multiple-input multiple-output (MIMO) detection. The structure of the network
is specially designed by unfolding the iterative algorithm. Some trainable
parameters are optimized through deep learning techniques to improve the
detection performance. Since the number of trainable variables of the network
is equal to that of the layers, the network can be easily trained within a very
short time. Furthermore, the network can handle time-varying channel with only
a single training. Numerical results show that the proposed approach can
improve the performance of the iterative algorithm significantly under Rayleigh
and correlated MIMO channels.

本文提出了一种基于模型驱动的深度学习网络用于多输入多输出（MIMO）检测，通过深度学习技术优化网络的可训练参数以提高检测性能；由于网络可训练变量的数量等于层数，因此可以在很短的时间内轻松训练网络，并且网络可以处理时变信道，通过数值结果表明该方法可以显著提高 Rayleigh 和相关 MIMO 信道下迭代算法的性能。

面向 MIMO 检测的模型驱动深度学习网络

A Model-Driven Deep Learning Network for MIMO Detection

We consider a general framework for reducing the number of trainable model
parameters in deep learning networks by decomposing linear operators as a
product of sums of simpler linear operators. Recently proposed deep learning
architectures such as CNN, KFC, Dilated CNN, etc. are all subsumed in this
framework and we illustrate other types of neural network architectures within
this framework. We show that good accuracy on MNIST and Fashion MNIST can be
obtained using a relatively small number of trainable parameters. In addition,
since implementation of the convolutional layer is resource-heavy, we consider
an approach in the transform domain that obviates the need for convolutional
layers. One of the advantages of this general framework over prior approaches
is that the number of trainable parameters is not fixed and can be varied
arbitrarily. In particular, we illustrate the tradeoff of varying the number of
trainable variables and the corresponding error rate. As an example, by using
this decomposition on a reference CNN architecture for MNIST with over 3x10^6
trainable parameters, we are able to obtain an accuracy of 98.44% using only
3554 trainable parameters.

通过将线性操作分解为较简单线性操作之和的乘积，我们提出了一种可以减少深度神经网络可训练模型参数数量的通用框架，用于各类神经网络结构，并展示了基于该框架的算法在 MNIST 和 Fashion MNIST 数据集上的表现。此外，我们探究了一种新的卷积层变换方法，不再需要卷积操作，这种方法可以任意改变可训练参数数量，并通过使用该框架在 MNIST 数据集上的实验验证了可用更少的参数获得更高的准确率的优点。