Deep-Waveform: A Learned OFDM Receiver Based on Deep Complex Convolutional Networks 译文（I.-III.）

I. INTRODUCTION

Despite the great success of Deep Learning in a number of fields, its application in wireless communication, especially the physical layer (PHY), was explored only very recently [1]–[9]. Many considered that phenomenons in the physical layer of over-the-air wireless communication, such as noise, fading, channel impairment, etc, have been understood, and addressed by well-established theories of signal and coding. On the other hand, although some progresses, such as signal classification, have been achieved in recent works [1]–[9], it is yet unclear if Deep Learning (DL), known as a black box approach good at structured tasks those are easy for human while hard for traditional analytical approaches, would be able to outperform white-box approaches, such as signal and coding theories.

尽管深度学习在许多领域取得了巨大的成功，但其在无线通信中的应用，尤其是物理层（PHY）的应用是最近才被探索出来的[1]-[9]。许多人认为，空中无线通信物理层的现象，如噪声、衰落、信道损伤等，已经被理解，并由成熟的信号和编码理论解决。另一方面，虽然在最近的工作中取得了一些进展，如信号分类[1]-[9]，但深度学习(Deep Learning，DL)作为一种黑盒方法，擅长于人类容易而传统分析方法难以完成的结构化任务，是否能够胜过信号和编码理论等白盒方法，目前还不清楚。

Currently, the applications of DL in wireless communications are mostly focused on enhancing certain functionalities [7], [10]. Above the PHY level, DL is applied in resource management, such as traffic prediction on network level [11], interference alignment [12], as well as decision makings such as power control and spectrum sharing [13]. Among the researches of DL in PHY, many works focus on enhancing certain components in wireless system [7], such as signal classification [1], [2], detection [8], channel coding [3], [5], channel estimation [8], [14], [15], Direction-of-Arrival (DoA) estimation [14], or control problems such as antenna titling. Another thread of researches attempt to establish a novel, end-to-end, communication architecture entirely based on Deep Neuron Networks (DNN) [4], [6], [7].

目前，DL在无线通信中的应用多集中在增强某些功能上[7]、[10]。在PHY层以上，DL应用于资源管理，如网络层的流量预测[11]、干扰配准[12]，以及功率控制和频谱共享等决策[13]。在物理场域DL的研究中，许多工作集中在增强无线系统的某些组件[7]，如信号分类[1]、[2]、检测[8]、信道编码[3]、[5]、信道估计[8]、[14]、[15]、到达方向(DoA)估计[14]或控制问题如天线滴定。另一条研究线索是试图建立一个完全基于深度神经元网络（DNN）的新型端到端通信架构[4]，[6]，[7]。

Among these efforts, building a DL-based end-to-end wireless communication architecture is the most aggressive attempt that could potentially transform the field that is largely based on expert knowledge and models. In [4], [6], the end-to-end wireless PHY is viewed as an autoencoder (AE), as illustrated in Fig. 1. Compared to a typical AE in the DL field that processes structured data such as image and natural language, as shown in Fig. 1, a communication AE has two unique characters: First, the objective of communication AE is to find latent coding that can carry information over detrimental wireless channel, generally by increasing the redundancy, while typical AE is intended to find compact representations of structured data in lower-dimensional latent space without concern of pollution of the code. Second, communication AE is designed to learn the inherit behaviors of channel rather than the structure of data. Data in a communication AE–input and output bits–is considered unstructured and incompressible. Therefore, an communication AE should be trained over a set of channel(s) with random data.

在这些努力中，构建基于DL的端到端无线通信架构是最积极的尝试，它有可能改变这个主要基于专家知识和模型的领域。在[4]、[6]中，端到端无线PHY被看作是一个自动编码器（AE），如图1所示。与DL领域典型的处理图像、自然语言等结构化数据的AE相比，通信AE具有两个独特的特点，如图1所示。第一，通信AE的目标是寻找能够在不利的无线信道上携带信息的隐藏编码，一般是通过增加冗余度来实现，而典型AE的目的是在低维的潜伏空间中寻找结构化数据的紧凑表示，而不担心编码的污染。其次，通信AE的目的是学习信道的继承行为，而不是数据的结构。通信AE中的数据--输入和输出位--被认为是非结构化和不可压缩的。因此，通信AE应该在一组随机数据的通道上进行训练。

Numerical and experimental evaluations in [4], [6] demonstrate the capability of DNN in learning key PHY functionalities all together, e.g. channel coding, modulation, carrier synchronization. QAM-like constellations different from those designed by experts are created by their AEs. However, none of these works have shown the ability of DNN in mastering advanced waveforms in modern wireless networks, such as the family of Orthogonal Frequency Division Modulation (OFDM). Furthermore, AEs in [4], [6] have not outperformed expert-designed wireless communication systems.

在[4]、[6]中的数值和实验评估证明了DNN在学习关键的PHY功能方面的能力，例如信道编码、调制、载波同步等。由其AE创建了不同于专家设计的QAM-like星图。然而，这些工作都没有显示出DNN在掌握现代无线网络中高级波形的能力，如正交频分调制系列 (OFDM)。此外，[4]、[6]中的AE也没有优于专家设计的无线通信系统。

Building an DNN that work with OFDM signal without using explicit Discrete Fourier Transform (DFT) module is a clear demonstration of the capability of DL in learning (and potentially creating) advanced waveforms. Waveform generation relies on various complex convolutions, such as filter and DFT, on digital base-band signal that is typically represented as complex number–the In-Phase and Quadrature (IQ) data. However, complex convolution is not currently supported by  popular Deep Learning platforms, such as TensorFlow [16], Keras [17]. On the other hand, due to the lack of theoretical guidance on using non-linear activations, the extensive usages of Rectified Linear Unit (Relu) [4], [6], [8] seems to contradict with existing, generally linear, signal processing techniques.

在不使用明确的离散傅里叶变换(DFT)模块的情况下，建立一个能处理OFDM信号的DNN是DL在学习(和潜在的创造)高级波形方面的能力的一个明显证明。波形的生成依赖于各种复杂的卷积，如滤波器和DFT，在数字基带信号上，通常以复数表示--同相和正交（IQ）数据。然而，目前流行的深度学习平台并不支持复杂卷积，如TensorFlow[16]、Keras[17]。另一方面，由于缺乏使用非线性激活的理论指导，线性修正单元（Relu）[4]、[6]、[8]的大量使用似乎与现有的、一般线性的信号处理技术相矛盾。

In this paper, an OFDM receiver entirely based on Deep Complex Convolutional Network (DCCN) is developed without using any FFT/IFFT modules. The DCCN receiver contains a basic OFDM receiver and a separated channel equalizer. Following the principle of signal processing, the developed DCCN model is significantly different from existing works [4], [6], [8] that only use Fully-Connected hidden layers with Rectified Linear Unit (Relu) activation. Our model contains both dense and convolutional layers which are mostly linearactivated, and new structures of residual and skip connections. Moreover, complex convolutional layer is implemented within Tensorflow [16] to process complex IQ data, instead of treating it as two independent real numbers. The DCCN-based OFDM receiver achieves similar bit error rate (BER) of an expert receiver on 2,4,8, and 16 QAMs in AWGN channel, and learns to exploit the Cyclic Prefix to outperform an LMMSE channel estimator with prior channel information in Rayleigh channels over low to middle SNRs. This work shows the capabilities of Deep Learning in complex signal transformations that are key to master waveforms and channel behaviors.

本文在不使用任何FFT/IFFT模块的情况下，开发了一种完全基于深度复杂卷积网络(DCCN)的OFDM接收机。DCCN接收器包含一个基本的OFDM接收器和一个分离的信道均衡器。遵循信号处理的原理，所开发的DCCN模型与现有的作品[4]、[6]、[8]仅使用线性修正单元(Relu)激活的全连接隐藏层有很大不同。我们的模型包含了稠密层和卷积层，而卷积层大多是线性激活的，同时还包含了residual connections 和 skip connections的新结构。此外，复杂卷积层是在Tensorflow[16]内实现的，用于处理复杂的IQ数据，而不是将其作为两个独立的实数处理。在AWGN信道中，基于DCCN的OFDM接收机在 2,4,8和16 QAMs上实现了与专家接收机相似的误码率(BER)，并且学会了利用循环前缀，在中低信噪比的Rayleigh信道中优于使用事先信道信息的LMMSE信道估计器。这项工作显示了深度学习在复杂信号变换中的能力，而这是主波形和信道行为的关键。

The rest of this paper is organized as follows: Related work is discussed in Section II. OFDM communication system is introduced in Section III. In Section IV, the model and training approaches of DCCN receiver and equalizer are introduced. Numerical evaluation results are presented in Sections V. Finally, the paper is concluded in Section VI.

本文其余部分组织如下:  第二节讨论了相关工作。第三节介绍了OFDM通信系统。在第四节中，介绍了DCCN接收器和均衡器的模型和训练方法。数值评估结果在第五节中介绍，最后，第六节对本文做了总结。

II. RELATED WORK

A. Deep Learning in PHY of Wireless Communications

Deep learning for wireless communication in physical layeremerged only lately. In surveys [7], [10], it is pointed out that Deep learning could be used for modulation recognition, channel decoding, and detection to enhance existing wireless communication system, and can also be used to construct novel communication architecture, extend existing expert knowledge, for multi-user and MIMO. In [1], a convolutional (Conv) network is developed to classify the modulation of radio signal. In [2], a Radio Transformer Network (RTN) based on Conv and FC layers with Relu activations is developed for parametric estimation and recover signal, e.g. from Carrier Frequency Offset (CFO). Despite Complex Convolutional (CConv) layer is introduced in [2], it is not used in RTN, in which complex number is represented by power and phase but real and imaginary parts. For many tasks, this representation could be problematic as the phases of two nearby samples may jump from m π to π. An end-to-end wireless communication architecture based entirely on DNN is introduced in [4], where the entire PHY is viewed as an autoencoder trained by unsupervised learning. The Deep Learning PHY is expanded to multiple-input multiple output (MIMO) system in [5] by introducing spatial-temporal coding. The DNN models in [4], [5] are both based on dense (Fully-Connected (FC)) layers, normalization, and activations such as Relu and Softmax. Channel State Information (CSI) is estimated in [5] via FC layers with Relu activation at the receiver. In [3], Deep Learning based channel encoding is explored in AWGN channel with impairment. Comparison in [3] shows that DNN networks (Fully-Connected Layers) always outperform or equal to CNN networks (network with Convolutional (Conv) layers). In [6], an DL based end-to-end communication system is developed, where dense layers with Relu are used at both transmitter and receiver. However, the resulted BER performance in [6] underperforms existing DQPSK in both AWGN simulation and real channels. In [18], an OFDM end-to-end autoencoder based on FC layers and DFT/IDFT is claimed to outperform the QPSK with MMSE channel estimation in block error rate (BLER). However, to the best of our knowledge, learning advanced waveforms have not been addressed in all those works.

深度学习在物理层无线通信中的应用是最近才出现的，在调查[7]，[10]中指出深度学习可以用于调制识别、信道解码和检测，增强现有的无线通信系统，也可以用于构建新型的通信架构。在调查[7]、[10]中指出，深度学习可用于调制识别、信道解码和检测，以增强现有的无线通信系统，也可用于构建新颖的通信架构，扩展现有的专家知识，用于多用户和MIMO。在[1]中，开发了卷积(Conv)网络来对无线电信号的调制进行分类。在[2]中，开发了一个基于Conv和FC层的包含Relu激活的无线电变换网络(RTN)，用于参数化估计和恢复信号，例如从载波频率偏移(CFO)。尽管在[2]中引入了复数卷积层(Convolutional, CConv)，但它并没有在RTN中使用，在RTN中，复数是由功率和相位来表示的，而是由实部和虚部来表示的。对于许多任务来说，这种表示方式可能会有问题，因为附近两个样本的相位可能会从mπ跳到π。 [4]中介绍了一种完全基于DNN的端到端无线通信架构，整个PHY被看作是一个由无监督学习训练的自动编码器。在[5]中，通过引入空间-时间编码，将深度学习PHY扩展为多输入多输出（MIMO）系统。[4]、[5]中的DNN模型都是基于密集(Fully-Connected，FC)层、归一化和激活，如Relu和Softmax。在[5]中，信道状态信息(CSI)是通过FC层与接收机的Relu激活来估计的。在[3]中，探讨了基于深度学习的信道编码在AWGN信道中的损伤。在[3]中的比较表明，DNN网络(全连接层)的性能总是优于或等于CNN网络(带有卷积(Conv)层的网络)。在[6]中，开发了一种基于DL的端到端通信系统，在发射机和接收机上都使用了Relu的密集层。然而，[6]中得到的误码率性能在AWGN模拟和实际信道中都低于现有的DQPSK。在[18]中，一种基于FC层和DFT/IDFT的OFDM端到端自动编码器被认为在块误差率(BLER)方面优于带MMSE信道估计的QPSK。然而，据我们所知，所有这些工作中都没有解决学习高级波形的问题。

B. OFDM System and Its Enhancements

OFDM system is the most popular system in modern wireless communication. In [19], [20], the OFDM physical layer and various channel estimation approaches are introduced. Any improvements on OFDM system would significant impact the existing wireless system. Several enhancements is proposed to improve OFDM system, such as , Filter Bank MultiCarrier (FBMC), UFMC, GFDM [21] for next generation communication system such as 5G. These new waveforms are generally modifications of OFDM for better characteristics with regards to various interferences. An constellation enhancement approach [22] and DL-based coding system [23] are proposed to reduce the Peak to Average Power Ratio (PAPR) of OFDM waveform.

OFDM系统是现代无线通信中最流行的系统。在[19]、[20]中，介绍了OFDM物理层和各种信道估计方法。对OFDM系统的任何改进都会对现有的无线系统产生重大影响。提出了几种改进OFDM系统的方法，如 ，滤波器组多载波(FBMC)、UFMC、GFDM [21]，用于5G等下一代通信系统。这些新的波形一般都是OFDM的修改，以获得对各种干扰更好的特性。提出了一种星座增强方法[22]和基于DL的编码系统[23]，以降低OFDM波形的峰均功率比（PAPR）。

At the receiver side, several works explored the use of Cyclic Prefix (CP) to enhance the performance of OFDM receiver [24]–[27]. CP is a redundancy of time-domain OFDM symbol which is necessary to mitigate intersymbol interference (ISI), but takes up a portion of spectrum resource in time domain. A key of exploiting CP is to determine the unpolluted length in CP. Our work is a complementary of existing analytical approaches, such as Maximum Likelihood [24], [26], Factor Graph [25], [27] in exploiting CP.

在接收端，有几项工作探讨了使用循环前缀(CP)来提高OFDM接收机的性能[24]-[27]。CP是时域OFDM符号的冗余，它是缓解符号间干扰(ISI)所必需的，但会占用时域的部分频谱资源。利用CP的一个关键是确定CP中的未污染长度。我们的工作是对现有分析方法的补充，如最大似然[24]，[26]，因子图[25]，[27]为对CP的利用。

Several recent works focus on DL-based enhancements of OFDM receiver [8], [9]. In [8], an 5-layer DNN-based OFDM receiver simultaneously implements channel estimation and modulation symbol recovery. Their model uses Relu activation for hidden layers, and sigmoid for output, and equalization and recovery are trained in 2 stages. However, channel equalizer and receiver are separated in this paper, and our receiver directly output bits instead of IQ data. Moreover, [8] only studies QPSK with a block type pilot, of which could not be replicated for higher order modulation with direct bit output. A DL-based OFDM receiver in [9] is claimed outperforming LMMSE channel estimator by initialized to known model. However, explicit usage of FFT/IFFT [9], [18], [23] could not demonstrate the ability of DNN in learning waveforms.

最近的几项工作都集中在基于DL的OFDM接收器的增强上[8]，[9]。在[8]中，基于DNN的5层OFDM接收机同时实现了信道估计和调制符号恢复。他们的模型对隐藏层使用Relu激活，对输出使用sigmoid，并且均衡和恢复分2个阶段进行训练。然而，在本文中，信道均衡器和接收器是分开的，我们的接收器直接输出位而不是IQ数据。此外，[8]仅研究具有块型导频的QPSK，其中对于直接位输出的高阶调制无法复制。。在[9]中，一种基于DL的OFDM接收机据称性能优于前者。LMMSE信道估计器通过对已知模型进行初始化。然而，FFT/IFFT[9]、[18]、[23]的明确使用无法实现。展示DNN在学习波形方面的能力。

III. OFDM COMMUNICATION SYSTEM

The physical layer (PHY) of OFDM communication is introduced in this section. Specifically, the transmitter, receiver, channel process, and channel equalization in expert system are introduced to serve as the baseline of this paper.

本节将介绍OFDM通信的物理层（PHY）。具体介绍了专家系统中的发射机、接收机、信道过程和信道均衡，作为本文的基线。

A. Physical Layer

The block diagram of the PHY of OFDM communication system is illustrated in Fig. 2(a). Input bits of the OFDM transmitter is first encoded (with redundancy) to reduce errors in specific channels, the encoded bits are mapped into constellation on the In-Phase and Quadrature (IQ) plane via modulation, the resulted IQ data is represented as complex number. Pilot and guard bands are inserted to the IQ data to form frequency-domain OFDM symbol. The frequencydomain OFDM symbol is then transformed into time-domain via Inverse Discrete Fourier Transformation (IDFT), and then converted in to 1 dimensional (1D) via Parallel to Serial (P/S) conversion. Cyclic Prefix (CP), which is a section of timedomain IQ data from the end, is copied to the beginning of time-domain IQ data to form a full time-domain OFDM symbol, as shown in Fig. 2(b). The base-band IQ data stream is then up-converted to radio frequency (RF) and broadcast over-the-air by RF frontend. The radio wave propagated over wireless channel is received and down-converted into baseband digital IQ data by the RF frontend of receiver. A carrier synchronizer recovers time-domain OFDM symbols, and send it to base-band receiver. At the receiver, CP is first removed and rest of the IQ data is transformed to frequency domain via FFT. A channel equalizer estimates the responses of channel, and equalize the received IQ data distorted by the fading channel. Next, the equalized frequency-domain IQ data is demodulated to soft bits (float numbers), which are further decoded by channel decoder into binary bits. The output bit stream is sent to next layer and recovered into packets. Note that channel equalization is for fading rather than AWGN channel. Moreover, channel coding is ignored in this paper in order to focus on the lower PHY.

OFDM通信系统的PHY框图如图2(a)所示。OFDM发射机的输入位首先要进行编码（有冗余），以减少特定信道的误差，编码后的位通过调制在相位和正交（IQ）平面上映射成星座，得到的IQ数据用复数表示。在IQ数据中插入导频和保护频带，形成频域OFDM符号。频域OFDM符号通过反离散傅里叶变换(IDFT)转化为时域，再通过并行到串行(P/S)的转换转化为一维(1D)。循环前缀(Cyclic Prefix，CP)，是将时域IQ数据从末尾的一段复制到时域IQ数据的开头，形成一个完整的时域OFDM符号，如图2(b)所示。然后，基带IQ数据流被向上转换为射频(RF)，并通过RF前端进行空中广播。通过无线信道传播的无线电波被接收机的射频前端接收并下变频为基带数字IQ数据。载波同步器回收时域OFDM符号，并将其发送到基带接收器。在接收机上，首先去除CP，其余的IQ数据通过FFT转换到频域。信道均衡器估计信道的响应，并对接收到的被衰落信道扭曲的IQ数据进行均衡。接下来，经过均衡的频域IQ数据被解调为软位（浮点数），再由信道解码器将其进一步解码为二进制位。输出的比特流被送到下一层，并回收成数据包。请注意，信道均衡是针对衰减而不是加性高斯白噪声（AWGN）信道的。此外，为了关注下层PHY，本文忽略了信道编码。

OFDM communication system is usually based on physical frame composed by multiple OFDM symbols, as illustrated by an example in Fig. 2(b). The notations of parameters in a OFDM frame are defined as follows: OFDM symbol contains N subcarriers, where N is the size of IDFT at transmitter. Among these N subcarriers, there are total of G guard subcarriers at the center (DC guard band) and edge (edge guard band). A OFDM frame contains multiple consecutive OFDM symbols, which is denoted as F. A resource cell refers to a subcarrier of an OFDM symbol. For each OFDM frame, there are P cells allocated as training signals (pilot) known by both transmitter and receiver, and the rest D cells allocated to modulated IQ data. Moreover, in time domain, cyclic prefix (CP), which is a copy of a section of time-domain OFDM symbol, is added to the beginning of each OFDM symbol. As a result, the total length of time-domain OFDM symbol will be increased from N to S. These parameters are usually prescribed according to channel characteristics, such as coherence time, coherence bandwidth, and total channel bandwidth. Meanwhile, for m-ary modulation, each constellation points contains m bits, and there are 2^m constellation points.

OFDM通信系统通常基于由多个OFDM符号组成的物理帧，如图2(b)所示的一个例子。OFDM帧中参数的符号定义如下。OFDM符号包含N个子载波，其中N是发射机处IDFT的大小。在这N个子载波中，中心（DC保护带）和边缘（边缘保护带）共有G个保护子载波。一个OFDM帧包含多个连续的OFDM符号，它被表示为F，资源单元指的是一个OFDM符号的子载波。对于每个OFDM帧，有P个单元被分配为发射机和接收机都知道的训练信号(先导)，其余D个单元被分配为调制IQ数据。此外，在时域中，循环前缀（CP）是时域OFDM符号的一段副本，它被添加到每个OFDM符号的开头。因此，时域OFDM符号的总长度将从N增加到S，这些参数通常是根据信道特性规定的，如相干时间、相干带宽、总信道带宽等。同时，对于m进制调制，每个星座点包含m位，有2的m次方个星座点。

B. Wireless Channel

From the perspective of digital base-band, the wireless channel not only include over-the-air propagation between transmit and receive antennas, but also everything on the RF frontend. However, in this paper, we only consider a wireless channel with fading and noise processes, as a well accepted simplification [20]. The wireless channel is modeled as:

从数字基带的角度来看，无线信道不仅包括发射天线和接收天线之间的空中传播，还包括射频前端的一切。然而，在本文中，我们只考虑了一个有衰减和噪声过程的无线信道，这是一个公认的简化[20]。无线信道的模型为：

where vectors x and y are time-domain transmitted and received signals, vector h is time domain channel coefficient, vector n is time domain white noise, and ∗ stands for convolution. (1) can also be represented in frequency domain as:

其中向量x和y为时域的发送和接收信号，向量h为时域信道系数，向量n为时域白噪声，∗代表卷积。(1)在频域中也可以表示为：

where the vector X, Y , H, and are frequency domain transformation of x, y, h, and n, e.g. X = DF T(x).  is still white noise.  
stands for element wise production. Fading channel is modeled as a tapped delay line, in which channel responses, h, are a train of impulse responses [20]:

其中向量X、Y、H、是x、y、h、n的频域变换，如X=DF T(x)。仍旧是白噪声。 代表按元素相乘（两个向量的第i个元素分别相乘）。衰落信道被建模为一条分接延时线，其中信道响应h是一列脉冲响应[20]：

where the ith tap, , is a complex number representing amplitude and phase of the ith path of signal propagation, and . The fading coefficients varies by radio environments. Fading is called slow fading if the channel coefficients keep relatively constant within a frame, vise versa fast fading. Although theoretically, channel coefficient can also change within an OFDM symbol, this situation is usually not considered based on the assumption that the OFDM frame parameters are carefully selected before hand based on prior knowledge of wireless channel.

其中，第i个抽头是一个复数，代表信号传播第i条路径的振幅和相位，并且满足。衰减系数因无线电环境不同而不同。如果在一帧内信道系数保持相对恒定，则称为慢速衰减，反之则为快速衰减。虽然从理论上讲，信道系数也可以在OFDM符号内变化，但通常不考虑这种情况，因为假设OFDM帧参数是基于对无线信道的先验知识事先精心选择的。

K in (3) stands for number of propagation paths in the channel. For an OFDM symbol, if K = 1, channel coefficients would be constant across all the sub-carriers, the channel is flat fading. If K > 1 (multipath), channel coefficients may vary across sub-carriers, the channel is frequency selective. In Rayleigh channel, the real and imaginary parts of  follow identically independent Gaussian distributions, and follows Rayleigh distribution. The effects of different fading on OFDM frame in frequency domain are illustrated in Fig. 3. Note that only noise and fading are considered, while channel impairment for channel coding is left for future works.

(3)中K代表信道中的传播路径数。对于一个OFDM符号，如果K=1，则所有子载波的信道系数将是恒定的，信道是平坦的衰减。如果K>1(多径)，各子载波的信道系数可能不同，信道具有频率选择性。在Rayleigh信道中，的实部和虚部遵循完全独立的高斯分布，循Rayleigh分布。频域内不同的衰落对OFDM帧的影响如图3所示。需要注意的是，这里只考虑了噪声和衰落，而信道编码的信道损伤则留待以后的工作。

The multipath propagation introduces Inter-Symbol Interference (ISI) at the receiver, as shown in Fig. 2(b). To mitigate ISI, proper length of Cyclic Prefix is selected such that ISI from OFDM symbol i only stays in the CP of OFDM symbol i+1 in the worst cases. CP is usually dropped out at the OFDM receiver to eliminate ISI. However, not all the CP is polluted by ISI in most cases, therefore, the CP, as a redundancy of main signal, can be exploited to improve the receiver performance. This work shows that except existing analytical approaches [24]–[27], exploiting the CP to enhance receiver performance can be learned by DCCN.

如图2（b）所示，多径传播在接收机处引入了符号间干扰（ISI）。 为了减轻ISI，选择适当的循环前缀长度，使得来自OFDM符号i的ISI在最坏的情况下仅停留在OFDM符号i + 1的CP中。 通常会在OFDM接收器中丢弃CP，以消除ISI。 但是，在大多数情况下，并非所有CP都被ISI污染，因此，可以利用CP作为主信号的冗余来改善接收机性能。 这项工作表明，除了现有的分析方法[24]-[27]，DCCN可以学习利用CP来增强接收机性能。

C. Channel Estimation and Equalization

In communication system, training signal (pilot) is inserted to the frames so that the receiver could estimate the channel responses, based on the assumption that pilot and data are distorted similarly. A proper pilot pattern is designed to meet such assumption. Typical pilot patterns in OFDM system are: block, comb, and scattered, as shown in Fig. 4 [20]. The pilots could be a constant value on IQ plane, or known sequence with low auto-correlation (e.g. LTE system). The simplest channel equalization in OFDM system is based on Least Square (LS) estimator [19], [20]:

在通信系统中，将训练信号（导频）插入帧中，以便接收器可以根据导频和数据类似地失真的假设来估计信道响应。 设计了一种适当的导频模式来满足这种假设。 OFDM系统中的典型导频模式为：块，梳状和分散式，如图4所示[20]。 导频可以是IQ平面上的恒定值，也可以是具有低自相关的已知序列（例如LTE系统）。 OFDM系统中最简单的信道均衡是基于最小平方（LS）估计器[19]，[20]：

where and are transmitted and received pilots in frequency domain, respectively, and and are received data and recovered transmit data, respectively. The channel coefficients of data cells are obtained by interpolation, , of channel estimates on pilot . Common interpolations include linear, spline, low-pass-filter, and DFT [19], [20]. Other estimators, such as Minimum Mean Square Error (MMSE), Linear MMSE (LMMSE), Maximal likelihood, and parametric channel modeling-based (PCMB) estimator, are based on LS estimation and/or prior channel knowledge [19], [20].

其中和分别在频域中发送和接收导频，和分别是接收数据和恢复的发送数据。通过导频上信道估计的插值获得数据单元的信道系数。常见的插值包括线性插值、样条插值、低通滤波和DFT[19]、[20]。其他估计器，如最小均方误差（MMSE）、线性MMSE（LMMSE）、最大似然和基于参数信道建模（PCMB）的估计器，基于LS估计和/或先验信道知识[19]、[20]。