Abstract
Deep learning has been applied in physical-layer communications systems in recent years and has demonstrated fascinating results that were comparable or even better than human expert systems. In this paper, a novel convolutional neural networks (CNNs)-based autoencoder communication system is proposed, which can work intelligently with arbitrary block length, can support different throughput and can operate under AWGN and Rayleigh fading channels as well as deviations from AWGN environments. The proposed generalized communication system is comprised of carefully designed convolutional neural layers and, hence, inherits CNN’s breakthrough characteristics, such as generalization, feature learning, classification, and fast training convergence. On the other hand, the end-to-end architecture jointly performs the tasks of encoding/decoding and modulation/demodulation. Finally, we provide the numerous simulation results of the learned system in order to illustrate its generalization capability under various system conditions.
近年來，深度學習被應用於物理層通信系統中，並顯示出與人類專家系統相當甚至更好的迷人效果。本文提出了一種新型的基於卷積神經網絡(CNNs)的自動編碼器通信系統，該系統可以在任意塊長的情況下智能工作，可以支持不同的吞吐量，並且可以在AWGN和Rayleigh漸變信道以及偏離AWGN的環境下工作。 所提出的泛化通信系統由精心設計的卷積神經層組成，因此，繼承了CNN的泛化、特徵學習、分類和快速訓練收斂等突破性特徵。另一方面，端到端架構共同完成編碼/解碼和調製/解調的任務。最後，我們提供了學習系統的大量仿真結果，以說明其在各種系統條件下的泛化能力。
I. INTRODUCTION
In the past, conventional methods optimize the modules of communication system separately, such as encoder, modulator, to achieve the better transmission quality [1] [2]. Deep Learning has experienced fast development in the past decade and it also possesses great potential in wireless communication. There have been lots of model-driven applications based on Deep Learning [3], such as massive MIMO [4] and OFDM [5].
以往傳統的方法是將通信系統的各個模塊分別進行優化，如編碼器、調製器，以達到較好的傳輸質量[1][2]。深度學習在過去十年中經歷了快速發展，在無線通信領域也擁有巨大的潛力。基於深度學習[3]的模型驅動應用已經很多，如大規模MIMO[4]和OFDM[5]。
One important application of Deep Learning is to view communication system as an end-to-end autoencoder, in which the modules can be optimized jointly. The result in [6] has shown that autoencoders can readily match the performance of nearoptimal existing baseline modulation and coding schemes by learning the system during training. The transmitter maps a one-hot vector to particular constellation symbols for transmission. The signals distorted by channel are used to reconstruct the original vector. The authors of [7] have proved that an end-to-end structure need a differential channel model to optimize the transceiver. However, one-hot transmission scheme is limited because all information bits are only used to transmit one symbol, which decreases transmission efficiency seriously.
深度學習的一個重要應用是將通信系統看作是一個端到端的自動編碼器，在這個系統中，各模塊可以聯合優化。在[6]中的結果已經表明，自動編碼器通過在訓練過程中學習系統，可以很容易地匹配現有基線調製和編碼方案中接近最佳的性能。發射機將一個one-hot vector 映射到特定的星座符號上進行傳輸。用通道失真的信號來重建原始向量。作者[7]已經證明了端到端結構需要一個差分信道模型來優化收發器。但是，one-hot 傳輸方案由於所有信息位只用來傳輸一個符號，傳輸效率嚴重下降，因此受到限制。
Opposite to one-hot transmission scheme, block scheme is a transmission scheme which allows parallel inputs. It enables communication systems to transmit a stream of information bits instead of bits for one symbol [8]. In [9], block scheme [10] is introduced in autoencoder to deal with the transmission of batches of sequences. This structure supports arbitrary length of binary sequences as input, but its performance is not good enough for practical use.
與獨熱編碼傳輸方案相對應，塊方案是一種允許並行輸入的傳輸方案。它使通信系統能夠傳輸信息位流，而不是一個符號的位[8]。在[9]中，在自動編碼器中引入了塊方案[10]來處理批量序列的傳輸。這種結構支持任意長度的二進制序列作爲輸入，但其性能在實際使用中還不夠好。
In this paper, we build up an end-to-end autoencoder with block transmission scheme. In order to improve its perfor mance, we also introduce memory mechanism into the neural networks. Our contributions are following:
- We propose a novel autoencoder structure based on neural networks. It introduces block scheme to deal with sequences in the form of blocks and allows arbitrary input length, which improves transmission efficiency. With the memory mechanism of recurrent neural networks (RNN), the autoencoder explores potential relationships between blocks for modulating. Through optimizing the transmitter and receiver jointly, the constellation diagram can be learned automatically for particular modulation mode.
- We train and test the model under different channel models. The performance of the proposed model is better than other autoencoder-based communication systems under typical channels [9]. At the same time, the simulation result shows that lower code rate leads to a lower bit error rate (BER).
在本文中，我們建立了一個端到端的自動編碼器，並採用了 塊傳輸方案。爲了提高其性能，我們還在神經系統中引入了記憶機制。網絡。我們的貢獻如下：
- 我們提出了一種基於神經網絡的新型自動編碼器結構。它引入塊方案，以塊的形式處理序列，並允許任意輸入長度，提高了傳輸效率。藉助於循環神經網絡（RNN）的記憶機制，自動編碼器探索區塊之間的潛在關係進行調製。通過發射機和接收機的共同優化，可以自動學習特定調製模式的星座圖。
- 我們在不同的通道模型下對模型進行訓練和測試。在典型信道下，所提出的模型的性能優於其他基於自動編碼器的通信系統[9]。同時，仿真結果表明，較低的碼率會導致較低的誤碼率（BER）。
II. DEEP NEURAL NETWORK STRUCTURES
III. SYSTEM MODEL
We build up an end-to-end communication system using neural networks feeding with block data, which enables us to complete joint optimization of transceiver.
我們使用輸入塊數據的神經網絡建立了端到端通信系統，這使我們能夠完成收發器的聯合優化。
A. Network Structure
The structure of block autoencoder is shown in Fig.2. It consists several parts as following.
- The input is a stream of bits. To solve the problem of block transmission, we set the number of blocks to M, and each block has S bits to be modulated, so the total length of input bits is S × M.
- In the first layer, we adopt a convolutional neural network to compress input bits into M blocks. The output is sent to several LSTM layers to produce the modulated M complex symbols. We combine the time distributed layer with LSTM layer in order to introduce some linear relationship between symbols. To satisfy power constraint, we normalize the output symbols at the end of the transmitter. The detailed parameters of our autoencoder are shown in table I.
- Since we add the operation of encoding into the network through adjusting output dimension of time-distributed layers, the number of complex symbols should be M' instead of M, which is dependent on the code rate we set.
塊狀自動編碼器的結構如圖2所示。它包括以下幾個部分：
- 輸入是一個比特流。爲了解決塊傳輸的問題，我們設置塊數爲M，每個塊有S個位要調製，所以輸入位的總長度爲S×M。
- 在第一層，我們採用卷積神經網絡將輸入位壓縮成M個塊。輸出送至多個LSTM層，得到已調製的M個複數符號。我們將時間分佈層與LSTM層結合起來，以引入符號之間的一些線性關係。爲了滿足功率約束，我們對發射機末端的輸出符號進行歸一化處理。我們的自動編碼器的詳細參數如表I所示。
- 由於我們通過調整時間分佈層的輸出維度，在網絡中加入了編碼的操作，所以複數符號的數量應該是M'而不是M，這取決於我們設定的碼率。
Following the encoding and modulating operation, the coded sequence z is transmitted over the communication channel by I and Q components of digital signal. In our model, the communication channel is non-trainable, which can be represented as h(z).
經過編碼和調製操作後，編碼序列z由數字信號的I和Q分量在通信信道上傳輸。在我們的模型中，通信通道是不可訓練的，可以用h(z)表示。
The distorted signal 
is demodulated and decoded by the receiver. These layers reconstruct the input sequence. Each trainable layer of proposed autoencoder is followed by a batch normalization layer so that the training process will converge more quickly.
失真信號由接收機解調和解碼。這些層重建輸入序列。所提出的自動編碼器的每個可訓練層後面都有一個BN層，這樣訓練過程將更快地收斂。
B. Channel model
- First we consider AWGN channel models. AWGN channel is used to train and test our autoencoder. We add zero mean complex Gaussian noise to the transmitted symbol z. The variance of noise is calculated by given
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and block size S. - In wireless communication, frequency selective fading is a radio propagation anomaly caused by partial cancellation of a radio signal by itself. The signal arrives at the receiver by several different paths. There exists intersymbol interference (ISI) that influences the signal to be received. For generalization, we also do experiments under frequency selective fading channels. Traditional methods add protective interval to avoid or decrease ISI. However, our autoencoder is an end-to-end system, so we simply increase the number of symbols instead of introducing extra artificial symbols into the end of transmitter. We train and test the models under two multipath channels. The channel models we use are shown in Fig.3. Channel A has two fading paths and the zero-delayed path is strong. Different from channel A, channel B has three fading paths, including a weak zero-delayed one.
- 首先我們考慮AWGN信道模型。AWGN信道用於訓練和測試我們的自動編碼器。我們在傳輸的符號z中加入零均值復高斯噪聲，噪聲的方差由給定的
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和塊大小S計算。 - 在無線通信中，頻率選擇性衰落是由無線電信號自身的部分消除引起的一種無線電傳播異常。信號通過幾種不同的路徑到達接收機。存在符號間干擾(ISI)，影響了信號的接收。爲了便於推廣，我們還做了頻率選擇性衰落信道下的實驗。傳統的方法是通過增加保護間隔來避免或減少ISI。然而，我們的自動編碼器是一個端到端系統，所以我們只是增加了符號的數量，而不是在發射端引入額外的人工符號。我們在兩個多徑信道下對模型進行了訓練和測試。我們使用的信道模型如圖3所示。信道A有兩條衰落路徑，零延遲路徑很強。與信道A不同的是，信道B有三條衰落路徑，包括一條弱的零延遲路徑。
IV. EXPERIMENTS
In order to obtain the performance of proposed autoencoder, we train and test the model in different scenarios. Bit error rate (BER) is a measure of the number of bit errors that occur in a given number of bit transmissions under all scenarios. For generalization, we simply select AWGN channel model. In fact, under the scenario of wireless communication, the channel would be more complex because signals arrive at the receiver through different paths which leads to ISI between symbols.
爲了獲得所提出的自動編碼器的性能，我們在不同的場景下對模型進行了訓練和測試。誤碼率（BER）是在所有情況下，在給定數量的比特傳輸中發生的比特錯誤數量的度量。爲了推廣，我們只選擇AWGN信道模型。事實上，在無線通信的情況下，由於信號通過不同的路徑到達接收機，導致符號之間的ISI，信道會變得更加複雜。
A. Settings
For simulation, we set the block size to 6 and block number to 400. So the autoencoder acts like a joint coding and modulating 64-QAM system. We compare the learned autoencoder with conventional coding and modulating method. The data sets are generated by random distributed {0, 1}. The number of samples is 40000 for training and 10000 for testing. We set batch size to 64 and use Adam optimizer with learning rate 0.001. We need to train the autoencoder under an SNR fixed channel. Through several experiments, we find the best training 
is 12dB.
仿真時，我們設置塊大小爲6，塊數爲400。所以自動編碼器的作用就像一個聯合編碼和調製的64-QAM系統。我們將學習的自動編碼器與傳統的編碼和調製方法進行比較。數據集由隨機分佈的{0，1}生成。訓練樣本數爲40000，測試樣本數爲10000。我們設置批次大小爲64，使用Adam優化器，學習率爲0.001。我們需要在SNR固定的信道下訓練自動編碼器。通過多次實驗，我們發現最佳訓練爲12dB。
B. AWGN Channel
The performance of the autoencoder under AWGN channel is shown in Fig.4. We also implement the autoencoder in [9] for comparison. We add redundant information to resist the influence of channel through increasing the number of symbols. The way that we adjust the code rate is to set different dimension to the time-distributed layer and the convolutional layer in the decoder. When code rate is set to 1, which means the sequence is uncoded, our autoencoder performs very closely to conventional MMSE decoding method. Clearly as shown in Fig.5, our block autoencoder gives better performance than autoencoder in [9]. When we decrease the code rate to 2/3, which means we add redundant information to the encoded sequence, the autoencoder’s performance is improved rationally. When code rate is set to 1/2, we compare it with Viterbi hard decoding method in 64QAM. We can find that our autoencoder performs far beyond Viterbi hard decoding method in low SNR situation. It requires lower power to reach the same BER as Viterbi’s method.
自動編碼器在AWGN信道下的性能如圖4所示。我們還實現了[9]中的自動編碼器進行比較。我們通過增加符號數來增加冗餘信息，以抵抗信道的影響。我們調整碼率的方法是對解碼器中的時間分佈層和卷積層設置不同的維度。當碼率設置爲1，即序列未編碼時，我們的自動編碼器的性能與傳統的MMSE解碼方法非常接近。顯然，如圖5所示，我們的塊狀自動編碼器的性能比[9]中的自動編碼器更好。當我們將碼率降低到2/3，即在編碼序列中加入冗餘信息時，自動編碼器的性能得到了合理的提高。當碼率設置爲1/2時，我們將其與64QAM中的Viterbi硬解碼方法進行比較。我們可以發現，在低信噪比情況下，我們的自動編碼器的性能遠遠超過了Viterbi硬解碼方法。它需要更低的功率才能達到與Viterbi方法相同的誤碼率。
We draw the constellation diagram of the trained autoencoder in Fig.5. We can see that the symbols plotted in complex plane are distributed in 64 clusters. In actual deployment, it is easy to transfer symbols through inphase and quadrature component according to the constellation diagram.
我們在圖5中畫出經過訓練的自動編碼器的星座圖。 我們可以看到，繪製在複雜平面上的符號分佈在64個簇中。 在實際部署中，很容易根據星座圖通過同相和正交分量傳輸符號。
C. Fading Channel
The performance under two chosen channels is shown in Fig.6. We set the code rate to 1/2 and training to 20dB. Our autoencoder performs well in the noise ranging from -5dB to 10dB but faces an error floor when is more than 15dB. Compared with channel A, channel B’s BER is higher because it contains a weaker zero-delay path is weaker.
在兩個選擇的信道下的性能如圖6所示。我們將編碼速率設置爲1/2，將訓練爲20dB。我們的自動編碼器在-5dB到10dB的噪聲範圍內表現良好，但當大於15dB時會面臨錯誤的下限，很難繼續降低。與信道A相比，信道B的誤碼率更高，因爲它包含的零延遲路徑較弱。
To improve the autoencoder’s performance, we continue to decrease the code rate. As shown in Fig.7, its BER decreases when we amplify the number of symbols under the same channel B when we set training BER to 12dB. However, this will reduce the transmission efficiency so that the system is hard to be deployed on hardware. So trade-off strategy is important.
爲了提高自動編碼器的性能，我們繼續降低碼率。如圖7所示，當我們將訓練誤碼率設爲12dB時，放大同一信道B下的符號數，其誤碼率會降低。但這樣會降低傳輸效率，使系統難以在硬件上部署。所以權衡策略很重要。