Foreword

Depth communication network column | from the encoder: Finishing 2018--2019 annual use neural network communications system from paper encoder, a little humble opinion, if biased, please keep, when Shun Chung-kei.

Articles central idea

Advantage of OFDM systems is a simple single-path equalization for the sampling synchronization error is more robust. This article from the encoder to expand the application to an OFDM system, the single carrier system, in conjunction with the SDR simulation results show in multipath channel, the neural network implemented from the encoder than traditional methods to better performance loss compensation caused by hardware (e.g. synchronization, nonlinear problems of the amplifier).

Full overview

System Model

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The s input autoencoder coding end (a single information s ∈ M , the OFDM system W _{an FFT} subcarriers, the sequence s ∈ M ^{$ 12.70} ), a neural network side transmits encoded into a s n / 2 complex symbols x (sequence s ∈ M ^{$ 12.70} , the output sequence X ∈ C ^{n-/ 2 * $ 12.70} ), after the IFFT transform the OFDM signal in the time domain after the CP is added through the channel, the use of CP doing correlation operation for frame synchronization, obtain an OFDM time-domain output, after the FFT results receiving end afferent neural network, the neural network outputs the detected signal on each subcarrier.

Network configuration Parameter Description

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Simulation results

Reference curve is QPSK encoded using an MMSE equalization on a single subcarrier $\hat{h}_{i}=\frac{y_{i} \cdot p^{*}}{|p|^{2}+\sigma^{2}}$
其中p为导频，每两个s插入一个导频p（也就是认为在发送两个符号的时间间隔中，信道不变），y_i为第i个子载波上接收的信号

均衡

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信道模型：信道为5径随机信道，加高斯噪声

一点说明：文章使用平均功率归一化
$\|\mathrm{x}\|^{2} \leq n$

结果分析：蓝线为自编码器+传统MMSE均衡，这是OFDM自编码器的性能上界。当去掉传统MMSE均衡时（红线），自编码器性能并未下降，比传统方法（绿线）好2db。值得一提的是，当无传统MMSE均衡，无导频时，自编码器依旧能实现比传统方法更好的性能，这说明神经网络在无任何先验信息的情况下，能实现单径信道的均衡。

那么问题来了，在无导频的情况下，神经网络是如何实现均衡的？
上图对比了有无导频情况下，神经网络编码的结果。分析得出自编码器可以通过改变星座点的中心从所有符号中学习到叠加导频。
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作者原文：The autoencoder is able to learn some kind of superimposed-piloting over all symbols by shifting the center of the constellations.
我的疑问：我没怎么看得懂画出来的星座图，这些点是如何得到的，怎么理解作者所说的 superimposed-piloting？我做过单径瑞利信道下用神经网络实现预编码，当神经网络知道h时能补偿h，旋转星座点，但当神经网络不知道h，也不提供pilot时，神经网络束手无策。这个结果与作者分析的结论**“神经网络在无任何先验信息的情况下，能实现单径信道的均衡”**是不符合的。