I Introduction
Many of our daily communication services rely on the digital communication technology, a block diagram of which is depicted in Fig. 1. While the technologies in this system are quite mature, individual blocks therein are separately designed, often with different assumptions and objectives, making it difficult if not impossible to ascertain global optimality of the system. In addition, the channel propagation is expressed in an assumed mathematical model embedded in the design. The assumed model may not be correctly reflected in the actual transmission scenario, thereby compromising the system performance.
Recently, deep learning has been utilized for improving the performance of the traditional blockstructure communication system, including the multipleinput and multipleoutput (MIMO) detection
[1], channel decoding [2], and channel estimation
[3]. In addition, deep learning based methods also show potential improvement by jointly optimizing the processing blocks, including joint channel estimation and detection [4], joint channel encoding and source encoding [5].Besides enhancing the traditional communication blocks, deep learning provides a new paradigm of the communication system. As a pure datadriven method, the features and the parameters of a deep learning model can be learned directly from the data without handcraft or adhoc designs by optimizing an endtoend loss function. Inspired by this methodology, endtoend learning based communication systems have been investigated in several prior works
[6, 7, 8, 9] where both the transmitter and the receiver are represented as deep neural networks (DNNs) and can be interpreted as an autoencoder and an autodecoder, respectively.The structure of the endtoend learning based communication system is depicted in Fig. 2. As shown in the figure, the transmitter learns to encode the transmitted symbols into encoded data, , which is then sent to the channel, while the receiver learns to recover the transmitted symbols based on the received signal, , from the channel.
The weights of the model are trained in a supervised learning manner to optimize the endtoend recovery accuracy. This idea is first proposed in
[6] and has been shown to have a similar performance as the traditional approaches with block structures under the additive white Gaussian noise (AWGN) channel. In [7], the endtoend method has been extended to handle the various hardware imperfection. In [8], an endtoend learning method is adopted within the orthogonal frequencydivision multiplexing (OFDM) system.Despite these applications, a major limitation of the above endtoend design paradigm is the instantaneous channel state information (CSI), , or the channel transfer function,
, must be known when optimizing the transmitter. As is well known, the weights of the DNN are usually updated using stochastic gradient descent (SDG) with the computed error gradients propagated from the output layer back to the input layer. However, when the channel in unknown, the backpropagation of the gradients is blocked by the unknown channel, preventing the overall learning of the endtoend network. The channel transfer function may be assumed, but any such assumption would bias the learned weights, repeating the pitfalls caused by the likely discrepancy between the assumed model and the actual channel. In addition, in real communication systems, an accurate instantaneous CSI is hard to obtain in advance because the endtoend channel often includes several types of random effects, such as channel noise and varying, which may be unknown or can not be expressed analytically. As a result, it is desirable to develop a channel agnostic endtoend learning based communication system, where different types of channel effects can be automatically learned without knowing the specific channel transfer function.
In order to achieve this goal, two major challenges should be addressed. First, since the backpropagation is blocked by of the unknown channel, one needs to attempt to train the transmitter with surrogate gradients or without gradients. Second, in many communication systems, the channels may vary with time and location but the instantaneous CSI is vital for coherent detection. Recently, reinforcement learning has been employed in
[9] to optimize an endtoend transmitter without knowing the channel transfer function, where the channel and the receiver are considered as the environment when training the transmitter. But some prior information of the channel is still needed to achieve a competitive performance.In this article, we propose a channel agnostic endtoend learning based communication system where the distribution of channel output can be learned through a conditional generative adversarial net (GAN) [10]. The conditioning information is the encoded signals from the transmitter along with the received pilot information used for estimating the channel. By iteratively training the conditional GAN, the transmitter, and the receiver, the endtoend loss can be optimized in a supervised way. A concurrent work [11] has modeled the channel effects with a GAN and is similar to our work in that sense. But we build an endtoend model and our proposed approach can be applied to more realistic timevarying channels, which is significantly different from the existing work.
Our main contributions are threefolded. First, we use the conditional GAN to model the channel conditional distribution, , so that the channel effects can be learned based on the data instead of expert knowledge about the channel. Second, by adding the pilot information as a part of the conditioning information for the timevarying channels, the conditional GAN can generate more specific samples for the current channel. Third, an endtoend learning based communication system is developed, where the gradients of the endtoend loss can be propagated to the transmitter through the conditional GAN.
The rest of the paper is organized as follows. In Section II, the conditional GAN based channel modeling approach is introduced. In Section III, the training for the endtoend system is presented in detail. In Section IV, the simulation results are presented and the conclusions are drawn in Section V.
Ii Modeling Channel with Conditional GAN
The endtoend communication system learns the implements of the transmitter and the receiver using DNNs. However, the backpropagation, which is used to train the weights of DNNs, is block by the channel, preventing the overall learning of the endtoend network. To address the issue, we use a conditional GAN to learn the channel effects and the learned model can act as a bridge for the gradients to pass through. In this section, the conditional GAN is introduced and the how to use the conditional GAN to model the channel effects is presented.
Iia Conditional GAN
GAN is a new class of generative methods for distribution learning, where the objective is to learn a model that can produce samples close to some target distribution, . In our system, a GAN is applied to model the distribution of the channel output and the learned model is then used as a surrogate of the real channel when training the transmitter so that the gradients can pass through to the transmitter.
The structure of the GAN is shown in Fig. 3, where a minmax two players game is introduced between a generator, , and a discriminator, . The discriminator, , learns to distinguish between the data generated by the generator and the data from the real dataset while the generator, , learns to generate samples to fool the discriminative networks into making mistakes.
During the training, the generator maps an input noise, , with prior distribution, , to a sample. Then the samples from the real data and the samples generated from the generator, , are collected to train the discriminator, , to maximize the ability to distinguish between the two categories. If the discriminator,
, is successful at classifying the samples of the two sources, then its success can be used to generate a feed back to the generator,
, so that the generator, , will learn to produce samples more similar to the real samples. The training procedure will end when reaching the equilibrium, where the discriminator, , can do no better than random guessing to distinguish the real samples and the generated fake samples.Both the generator, , and the discriminator, , are represented by a DNN, with parameters and , respectively, and the objective for optimization is
(1) 
The object of the discriminator, , is to give a high value when the input belongs to the real dataset and a low value when the input is generated by the generator, , while the object of generator, , is to maximize the output of the discriminator, , given the generated samples, .
The GAN can be extended to a conditional model if both the generator, , and the discriminator, , are conditioned on some extra information, . The structure of the conditional GAN is shown in Fig. 4. We only need to feed the conditioning information, , into both the generator, , and discriminator, , as the additional input. Therefore, the output of the generator, , will be and the output of discriminator, , will be . The minmax optimization objective becomes
(2) 
The conditional GAN is employed in our endtoend system to model the channel output distribution with given conditioning information on the encoded signal and the received pilot data.
IiB Modeling Channels
GAN is a powerful tool in learning distribution and the channel output, , given input, , is determined by the conditional distribution, . Therefore, a conditional GAN can be employed for learning the output distribution of a channel by taking the as the condition information. The generator will try to produce the samples similar to the output of the real channel while the discriminator will try to distinguish data coming from the real channel and the data coming from the generator.
The instantaneous CSI, , can be regarded as a sample from a large channel set, and is also vital coherent detection of the data at the receiver. In order to obtain the CSI, a common practice is to send some pilot information to the receiver so that the channel information is inferred based on the received pilot information, . In our proposed method, the received pilot information, , can be added as a part of the conditioning information so that the output samples follow the distribution of give the and the received pilot data, .
Iii EndtoEnd Communication System
With the conditional GAN, the gradients can be backpropagated to the transmitter. Following the previous works[6], the transmit symbol drawn from a finite discrete set of size
is converted into a onehot vector,
, of length and the endtoend transmission is treated as a class classification problem. The output of the receiver,, is a probability vector over the
possible classes. The crossentropy loss is computed at the receiver, which is defined as(3) 
where and represent the th elements of and , respectively.
The training and testing of the proposed endtoend communication system are shown in Fig. 5. During the training, the data are obtained, where the transmitted symbols are randomly generated and the instantaneous CSI is sampled randomly from the channel set. Based on the training data, the transmitter, the receiver, and the channel generator in the conditional GAN can be trained iteratively and when training one component, the parameters of the others remain fixed. When training the receiver and the transmitter, the object is to minimize the endtoend loss. The object is to minimize the minmax optimization objective when training the conditional GAN for generating the channel. In the testing stage, the endtoend reconstruction performance is evaluated on the learned transmitter and the receiver with real channels.
Iiia Training Receiver
The receiver can be trained easily since the loss function is computed at the receiver, thus the gradients of the loss can be easily obtained. The input of the DNN will be the received signal, , and the receive pilot data, . For the timevarying channels, by directly put the received signal, , and the receive pilot data, , together as the input, the receiver can automatically infer the channel condition and perform the channel estimation and detection simultaneously without explicitly estimating the channel.
IiiB Training Transmitter
With the channel generator being a surrogate channel, the training of the transmitter will be similar to the training of the receiver. The endtoend crossentropy loss is computed at the receiver, and the gradients are propagated back the transmitter through the conditional GAN. The weights of the transmitter will be updated based on SGD while the weights of the conditional GAN and the receiver remain fixed.
IiiC Training Channel Generator
The channel generator is trained with the discriminator together. With the learned transmitter, the real data can be obtained with the encoded signal from the transmitter going through the real channel while the fake data is obtained from the encoded data going through the channel generator. The objective function to optimize is shown in Equation (2).
Iv Experiments
In this section, simulation results on the AWGN channel and the Rayleigh fading channel are provided. We compare our channel agnostic learning based approach with the traditional methods, which are designed based on the channel transfer functions.
The structures and parameters of each model are listed in Table I. The weights are updated by Adam [13] and the batch size for training is 320.
Parameters  Values 

Transmitter hidden layers  32, 32 
Learning rate  0.001 
Receiver hidden layers  32, 32 
Learning rate  0.001 
Generator hidden layers  128, 128, 128 
Discriminator hidden layers  32, 32, 32 
Learning rate  0.0001 
Iva AWGN Channel
The proposed method is first applied in the AWGN channel, where the output of the channel, , is the summation of the input signal, , and Gaussian noise, , that is, . In this case, there is no need for channel estimation. Thus the conditioning information is only the encoded signal from the transmitter.
We first test the ability of the conditional GAN in learning the channel output distribution. Fig. 6 shows the output of the channel generator with the standard 16 QAM modulation as the conditioning information. From the figure, the synthetic samples produced by the generator are very similar to the output from the AWGN channel.
The endtoend recovering performance on the AWGN channel is shown in Fig. 7. At each time, four information bits are transmitted and the length of the transmitter output is set to be seven. From the figure, the blockerror rate (BLER) of learning based approach is similar to Hamming (7,4) code with maximumlikelihood decoding (MLD).
IvB Rayleigh Fading Channel
In the case of the Rayleigh fading channels, the channel output is determined by , where . Since the channel is timevarying, additional conditional information is added to the channel generator and the receiver. We can use real for coherent detection task or received pilot data, , for joint channel estimation and detection (the pilot is assumed to be 1).
We first test the effectiveness of conditional GAN in learning the distribution of the channel with standard 16 QAM as the encoded symbols. Fig. 8 shows generated samples with different channel values added to the conditioning information. From the figure, the conditional GAN is able to produce the samples with various means according to conditioning information.
The endtoend reconstruction results are shown in Fig. 9, where the learning based endtoend approach shows a similar performance to the traditional methods in both tasks.
V Conclusions
DNN has been used to develop endtoend communication systems, where both the transmitter and the receiver are represented by DNNs. The accurate instantaneous channel transfer function is necessary to compute the gradients for optimizing the transmitter. However, in many communication systems, the channel transfer function is hard to obtain and varies with time and location. In this article, we show that the conditional distribution of the channel can be modeled by the conditional GAN, which enables the endtoend learning of a communication system without prior information of the channel. In addition, by adding the pilot information into the condition information, the conditional GAN can generate data corresponding to the specific instantaneous channel.
The endtoend pipeline consists of DNNs for the transmitter, the channel generator, and the receiver. By iteratively training these networks, the endtoend loss can be optimized in a supervised way. The simulation results confirm the effectiveness of the proposed method, by showing similar performance with traditional approaches based on expert knowledge and channel models.
Our method provides a new way for the endtoend learning system. Although the simulation is only based on the AWGN and the Rayleigh fading channels, it can be easily extended to other channels, therefore opens a new door for building the pure datadriven communication systems.
References
References
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