目前已快速發展的多輸入多輸出 (Multi-input multi-output，簡稱 MIMO) 通訊系統技術，是藉由發射端和接收端使用多個天線來提高用戶之間的傳輸效率，然而這樣的技術會使研究人員面臨性能和計算複雜度之間的折衷問題，為了對上述問題提出解決方案，本論文在 MIMO 的空間多樣性 (Spatial diversity) 和空間多路復用 (Spatial multiplexing) 上，針對兩者的訊息檢測 (Data detection) 問題和過去研究中未涉及的通道估測 (Channel estimation) 問題作改善，因此本論文基於自編碼 (Autoencoder) 架構提出了四種模型，每種模型都使用端到端學習 (End-to-end learning) 的訓練方式來進行訓練。本論文對最常見的通道環境進行評估，也就是瑞利衰落 (Rayleigh fading) 和高斯白雜訊 (Additive white gaussian noise，簡稱 AWGN)，所有結果顯示基於深度學習的模型效能皆優於 MIMO 傳統普遍使用的基線法 (Baseline method)。在接收端接收到完美的通道狀態資訊 (Channel state information at receiver side，簡稱CSIR) 情況下，在訊號檢測方面，所提出的模型在訊雜比為22.5dB時位元錯誤率可以幾乎達到 〖10〗^(-5)，而在通道估測方面，即使模型只傳送兩個導頻訊號，效能依然能超越基線法。

Multiple Input Multiple Output (MIMO) communication system, a system implementing multiple antennas at the transmitter and receiver, has been developed rapidly in order to improve the effectiveness of communication among users. However, trade-off phenomenon between performance and computational complexity always become the hugest dilemma suffered by researchers. As an alternative solution to the aforementioned problem, this research proposes an optimization in both of spatial diversity and spatial multiplexing MIMO communication system using end-to-end learning-based model, specifically, it adapts autoencoder model. Four models are introduced in this thesis which each two of them address a problem about data detection task and channel estimation task that has not been addressed in the previous research. The proposed models were evaluated in one of the most common channel impairment which is Rayleigh fading with additional Additive White Gaussian Noise (AWGN). The results show that these deep learning based models for MIMO communication system result in very promising results by outperforming the baseline methods (methods widely used in conventional MIMO communication). In perfect CSIR (Channel State Information in Receiver side) case, the proposed models achieve BER nearly 〖10〗^(-5) at SNR 22.5 dB. While in the channel estimation case, the proposed models can exceed the baseline performance even by only transmitting 2 pilots.

Table of Contents

Acknowledgement i
摘要 ii
ABSTRACT iii
Table of Contents iv
List of Tables vii
List of Figures viii
List of Abbreviations x
1. Introduction 1
1.1 Background 1
1.2 Motivation 3
1.3 Objective 4
1.4 Thesis Organization 4
2. Related Theory 6
2.1 Deep Learning 6
2.1.1 Deep Feed Forward Network 6
2.1.2 Backpropagation 7
2.1.3 Autoencoder 9
2.1.4 Activation Function 10
2.1.4.1 PReLU (Parametric Rectified Linear Unit) 10
2.1.4.2 Softmax 12
2.1.4.3 Linear 12
2.1.5 Batch Normalization 13
2.1.6 Optimizer 13
2.1.6.1 Adam 13
2.1.7 Loss Function 14
2.1.7.1 Log-cosh 15
2.1.7.2 Categorical Cross Entropy 16
2.2 Baseline Method 16
2.2.1 Alamouti 16
2.2.2 Maximum Likelihood (ML) Detector 19
3. Design of Deep Learning Based Model 21
3.1 Overview of Proposed Method 21
3.2 Spatial Diversity Model 23
3.2.1 Previous research 23
3.2.2 Proposed Model 24
3.2.2.1 Data Detection with Perfect CSIR 24
3.2.2.2 Channel Estimation 27
3.3 Spatial Multiplexing Model 31
3.3.1 Data Detection with Perfect CSIR 31
3.3.2 Channel Estimation 32
4. Result and Discussion 36
4.1 Spatial Diversity MIMO Communication 36
4.1.1 Data Detection with Perfect CSIR 36
4.1.2 Channel Estimation 37
4.2 Spatial Multiplexing MIMO Communication 39
4.2.1 Data Detection with Perfect CSIR 39
4.2.2 Channel Estimation 41
5. Conclusion 43
References 44

[1] Oestges, Claude, and Bruno Clerckx. MIMO wireless communications: From real-world propagation to space-time code design. Academic Press, 2010, pp.1-5.
[2] Biglieri, Ezio, Robert Calderbank, Anthony Constantinides, Andrea Goldsmith, Arogyaswami Paulraj, and H. Vincent Poor. MIMO wireless communications. Cambridge university press, 2007, pp.1-8.
[3] LeCun, Yann, Bernhard Boser, John S. Denker, Donnie Henderson, Richard E. Howard, Wayne Hubbard, and Lawrence D. Jackel. "Backpropagation applied to handwritten zip code recognition." Neural computation 1, no. 4 (1989), pp.541-551.
[4] Krizhevsky, Alex, Ilya Sutskever, and Geoffrey E. Hinton. "Imagenet classification with deep convolutional neural networks." In Advances in neural information processing systems, 2012, pp. 1097-1105.
[5] Goodfellow, Ian, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. "Generative adversarial nets." In Advances in neural information processing systems, pp. 2672-2680. 2014.
[6] Hinton, Geoffrey E., Simon Osindero, and Yee-Whye Teh. "A fast learning algorithm for deep belief nets." Neural computation 18, no. 7 (2006), pp.1527-1554.
[7] O’Shea, Timothy, and Jakob Hoydis. "An introduction to deep learning for the physical layer." IEEE Transactions on Cognitive Communications and Networking 3, no. 4 (2017), pp.563-575.
[8] Dörner, Sebastian, Sebastian Cammerer, Jakob Hoydis, and Stephan ten Brink. "Deep learning based communication over the air." IEEE Journal of Selected Topics in Signal Processing 12, no. 1 (2018), pp.132-143.
[9] Baldi, Pierre. "Autoencoders, unsupervised learning, and deep architectures." In Proceedings of ICML Workshop on Unsupervised and Transfer Learning, 2012, pp. 37-49.
[10] Gruber, Tobias, Sebastian Cammerer, Jakob Hoydis, and Stephan ten Brink. "On deep learning-based channel decoding." In Information Sciences and Systems (CISS), 2017 51st Annual Conference on. IEEE, 2017, pp. 1-6
[11] Ye, Hao, Geoffrey Ye Li, and Biing-Hwang Juang. "Power of deep learning for channel estimation and signal detection in OFDM systems." IEEE Wireless Communications Letters 7, no. 1 (2018), pp.114-117.
[12] Goodfellow, Ian, Yoshua Bengio, Aaron Courville, and Yoshua Bengio. Deep learning. Vol. 1. Cambridge: MIT press, 2016.
[13] Mikolov, Tomáš, Martin Karafiát, Lukáš Burget, Jan Černocký, and Sanjeev Khudanpur. "Recurrent neural network based language model." In Eleventh Annual Conference of the International Speech Communication Association. 2010.
[14] He, Kaiming, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. "Delving deep into rectifiers: Surpassing human-level performance on imagenet classification." In Proceedings of the IEEE international conference on computer vision, 2015, pp. 1026-1034.
[15] Duan, Kaibo, S. Sathiya Keerthi, Wei Chu, Shirish Krishnaj Shevade, and Aun Neow Poo. "Multi-category classification by soft-max combination of binary classifiers." In International Workshop on Multiple Classifier Systems, Springer, Berlin, Heidelberg, 2003, pp. 125-134.
[16] Ioffe, Sergey, and Christian Szegedy. "Batch normalization: Accelerating deep network training by reducing internal covariate shift." arXiv preprint arXiv:1502.03167 (2015).
[17] Kingma, Diederik P., and Jimmy Ba. "Adam: A method for stochastic optimization." arXiv preprint arXiv:1412.6980(2014).
[18] Duchi, John, Elad Hazan, and Yoram Singer. "Adaptive subgradient methods for online learning and stochastic optimization." Journal of Machine Learning Research 12, no. Jul (2011), pp.2121-2159.
[19] Tieleman, T. and Hinton, G. Lecture 6.5 - RMSProp, COURSERA: Neural Networks for Machine Learning. Technical report, 2012.
[20] Neuneier, Ralph, and Hans Georg Zimmermann. "How to train neural networks." In Neural networks: tricks of the trade, Springer, Berlin, Heidelberg, 1998, pp. 373-423.
[21] Cho, Yong Soo, Jaekwon Kim, Won Young Yang, and Chung G. Kang. MIMO-OFDM wireless communications with MATLAB. John Wiley & Sons, 2010, pp.294-298, pp.327-329
[22] Alamouti, Siavash M. "A simple transmit diversity technique for wireless communications." IEEE Journal on selected areas in communications 16, no. 8 (1998), pp.1451-1458.
[23] F. Chollet, “keras,” https://github.com/fchollet/keras, 2015
[24] Abadi, Martín, Paul Barham, Jianmin Chen, Zhifeng Chen, Andy Davis, Jeffrey Dean, Matthieu Devin et al. "Tensorflow: a system for large-scale machine learning." In OSDI, vol. 16, pp. 265-283. 2016
[25] Ng, Andrew. "Machine learning course." Coursera. org Backpropagation Lecture, https://www.coursera.org/learn/machine-learning/lecture/1z9WW/backpropagation-algorithm (2012).
[26] Fausett, Laurene V. Fundamentals of neural networks: architectures, algorithms, and applications. Vol. 3. Englewood Cliffs: Prentice-Hall, 1994.
[27] O'Shea, Timothy J., Tugba Erpek, and T. Charles Clancy. "Deep learning based MIMO communications." arXiv preprint arXiv:1707.07980 (2017).