本文擴展了 [1] 中的研究，其中提出了一種用於下行鏈路多基地台系統的深度學習協調預編碼方法。[1] 探討了使用黑盒子神經網絡架構在基地台之間在有限信息交換下的通道狀態資訊實現協調預編碼的可能性。其主要目的旨在最大化多基地台網絡中所有用戶的加權和率（WSR）。然而，所提的用於預編碼的方法需要大量的數據進行訓練，而且非常耗時。這是因為在整體的結構設計中很少包含對數學的獨到見解。

在本文中，我們提出了幾種方法來進一步降低訓練複雜度並加強 [1] 中提出的方法的可擴展性。我們首先嘗試使用卷積神經網絡 (CNN) 和全連接 (FC) 網絡的黑盒子神經網絡模型。但是，這種方法需要在不同的基地台上對模型進行訓練，因此無法擴展到具有多個基地台的網絡。為了解決這個問題，採用了環繞機制 (wrap around mechanism) 和相關的訓練策略。 基地台的環繞機制具有置換同變性，這意味著我們可以將每一個基地台視為一張圖中的一個節點。因此，我們提出了一種新的基於 GNN 的可擴展性神經網絡模型，以充分利用置換同變性。然而，這些模型仍然難以分析並且需要大量數據進行訓練。受加權最小均方誤差（WMMSE）算法本身[2]的啟發，我們提出了一種基於WMMSE算法迭代結構的神經網絡模型。在模型中，需要進行一些數學計算，因此必須仔細設計神經網絡的一些輸出。例如，該模型中估計的權重矩陣必須限制在大於 1 的範圍。該 WMMSE 啟發模型的更多詳細設計將在第 6 章中討論。

In this thesis, we extend up on the work in [1] where a deep learning coordinated precoding method was proposed for downlink multicell systems. In particular, [1] explored the possibility of using a black-box neural network architecture to achieve coordinated precoding under limited channel state information (CSI) exchange among base-stations (BSs). The proposed method aims to maximize the weighted sum rate (WSR) of all users in the multicell network. However, the proposed black-box method for precoding requires a huge amount of data for training and is time-consuming since little mathematical insight is used in the architecture design.

In this thesis, we present several approaches to further reduce the training complexity and improve the scalability of the method proposed in [1]. We first attempt a black-box neural network model with convolutional neural network (CNN) and fully connected (FC) network. However, this approach requires joint training of the models at different BSs and, thus, is not scalable to networks with many BSs. To solve this problem, the wrap-around mechanism and related training strategy is adopted. The wrap-around mechanism of BSs has permutation equivariance property, which means we can consider each BS as a node in the concept of a graph. Thus, we propose a new neural network model for scalability based on GNN to make good use of the permutation equivariance. However, these models are still hard to analyze and require lots of data for training. Inspired by the weighted minimum mean square error (WMMSE) algorithm itself [2], we propose a neural network model based on the iterative structure of the WMMSE algorithm. In the model, some mathematical calculation is required and so some output from the neural network must be carefully designed. For example, the weight matrix estimated in this model must be limited to a range bigger than 1. A more detailed design of this WMMSE-inspired model will be discussed in chapter 6.

[1] A.-A. Lee, “Deep csi compression and coordinated precoding for multicell downlink systems,” Master’s thesis, National Tsing Hua University, 2021.
[2] Q. Shi, M. Razaviyayn, Z. Luo, and C. He, “An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel,” IEEE Trans.Signal Process., vol. 59, pp. 4331–4340, Sept 2011.
[3] H. Huang, W. Xia, J. Xiong, J. Yang, G. Zheng, and X. Zhu, “Unsupervised learning-based fast beamforming design for downlink MIMO,” IEEE Access, vol. 7, pp. 7599–7605, 2019.
[4] J. Kim, H. Lee, S.-E. Hong, and S.-H. Park, “Deep learning methods for universal miso beamforming,” IEEE Wireless Communications Letters, vol. 9, no. 11, pp. 1894–1898, 2020.
[5] H. Huang, Y. Peng, J. Yang, W. Xia, and G. Gui, “Fast beamforming design via deep learning,” IEEE Transactions on Vehicular Technology, vol. 69, no. 1, pp. 1065–1069, 2020.
[6] W. Xia, G. Zheng, Y. Zhu, J. Zhang, J. Wang, and A. P. Petropulu, “A deep learning framework for optimization of MISO downlink beamforming,” IEEE Transactions on Communications, vol. 68, no. 3, pp. 1866–1880, 2020.
[7] S. Lu, S. Zhao, and Q. Shi, “Learning-based massive beamforming,” in GLOBECOM 2020 - 2020 IEEE Global Communications Conference, pp. 1–6, 2020.
[8] J. Jang, H. Lee, I.-M. Kim, and I. Lee, “Deep learning for multi-user mimo systems: Joint design of pilot, limited feedback, and precoding,” IEEE Transactions on Communications, vol. 70, no. 11, pp. 7279–7293, 2022.
[9] Q. Hu, Y. Cai, Q. Shi, K. Xu, G. Yu, and Z. Ding, “Iterative algorithm induced deep-unfolding neural networks: Precoding design for multiuser mimo systems,” IEEE Transactions on Wireless Communications, vol. 20, no. 2, pp. 1394–1410, 2021.
[10] L. Pellaco, M. Bengtsson, and J. Jald ́en, “Deep weighted mmse downlink beamforming,” in ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 4915–4919, 2021.
[11] L. Schynol and M. Pesavento, “Deep unfolding in multicell mu-mimo,” in 2022 30th European Signal Processing Conference (EUSIPCO), pp. 1631–1635, 2022.
[12] A. Chowdhury, G. Verma, C. Rao, A. Swami, and S. Segarra, “Unfolding wmmse using graph neural networks for efficient power allocation,” IEEE Transactions on Wireless Communications, vol. 20, no. 9, pp. 6004–6017, 2021.
[13] A. Balatsoukas-Stimming and C. Studer, “Deep unfolding for communications systems: A survey and some new directions,” in 2019 IEEE International Workshop on Signal Processing Systems (SiPS), pp. 266–271, IEEE, 2019.
[14] L. Pellaco, M. Bengtsson, and J. Jald ́en, “Deep unfolding of the weighted mmse beamforming algorithm,” arXiv preprint arXiv:2006.08448, 2020.
[15] L. Pellaco, M. Bengtsson, and J. Jald ́en, “Matrix-inverse-free deep unfolding of the weighted mmse beamforming algorithm,” IEEE Open Journal of the Communications Society, vol. 3, pp. 65–81, 2022.
[16] Y. Ma, X. Yu, J. Zhang, S. Song, and K. B. Letaief, “Augmented deep unfolding for downlink beamforming in multi-cell massive mimo with limited feedback,” arXiv preprint arXiv:2209.01436, 2022.
[17] C. Zhang, P. Patras, and H. Haddadi, “Deep learning in mobile and wireless networking: A survey,” IEEE Communications Surveys Tutorials, vol. 21, no. 3, pp. 2224–2287, 2019.
[18] M. Zhang, J. Gao, and C. Zhong, “A deep learning-based framework for low complexity multiuser mimo precoding design,” IEEE Transactions on Wireless Communications, vol. 21, no. 12, pp. 11193–11206, 2022.
[19] W. Lee, M. Kim, and D. Cho, “Deep power control: Transmit power control scheme based on convolutional neural network,” IEEE Commun. Lett., vol. 22, pp. 1276–1279, Jun 2018.
[20] F. Liang, C. Shen, W. Yu, and F. Wu, “Towards optimal power control via ensembling deep neural networks,” IEEE Transactions on Communications, vol. 68, no. 3, pp. 1760–1776, 2020.
[21] Y. Zhao, I. G. Niemegeers, and S. M. H. De Groot, “Dynamic power allocation for cell-free massive mimo: Deep reinforcement learning methods,” IEEE Access, vol. 9, pp. 102953–102965, 2021.
[22] M. Eisen, C. Zhang, L. F. Chamon, D. D. Lee, and A. Ribeiro, “Learning optimal resource allocations in wireless systems,” IEEE Transactions on Signal Processing, vol. 67, no. 10, pp. 2775–2790, 2019.
[23] T. Van Chien, E. Bjornson, and E. G. Larsson, “Sum spectral efficiency maximization in massive mimo systems: Benefits from deep learning,” in ICC 2019-2019 IEEE International Conference on Communications (ICC), pp. 1–6, IEEE, 2019.
[24] A. Chowdhury, G. Verma, C. Rao, A. Swami, and S. Segarra, “Efficient power allocation using graph neural networks and deep algorithm unfolding,” in ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 4725–4729, 2021.
[25] A. Chowdhury, F. Gama, and S. Segarra, “Stability analysis of unfolded wmmse for power allocation,” in ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 5298–5302, 2022.
[26] Y. Shen, Y. Shi, J. Zhang, and K. B. Letaief, “A graph neural network approach for scalable wireless power control,” in 2019 IEEE Globecom Workshops (GC Wkshps), pp. 1–6, 2019.
[27] M. Zhang and M. Chen, “Power allocation in multi-cell system using distributed deep neural network algorithm,” in 2019 International Conference on Wireless and Mobile Computing,
Networking and Communications (WiMob), pp. 1–4, 2019.
[28] F. Meng, P. Chen, L. Wu, and J. Cheng, “Power allocation in multi-user cellular networks: Deep reinforcement learning approaches,” IEEE Transactions on Wireless Communications, vol. 19, no. 10, pp. 6255–6267, 2020.
[29] I. Hubara, M. Courbariaux, D. Soudry, R. El-Yaniv, and Y. Bengio, “Binarized neural networks,” in Advances in neural information processing systems, 2016.
[30] M. Courbariaux, I. Hubara, D. Soudry, R. El-Yaniv, and Y. Bengio, “Binarized neural networks: Training deep neural networks with weights and activations constrained to +1 or -1,” arXiv preprint arXiv:1602.02830, 2016.
[31] J. Wang, Y. Wang, Z. Yang, L. Yang, and Y. Guo, “Bi-gcn: Binary graph convolutional network,” 2021.
[32] A.-A. Lee, Y.-S. Wang, and Y.-W. P. Hong, “Deep csi compression and coordinated precoding for multicell downlink systems,” in GLOBECOM 2020 - 2020 IEEE Global Communications Conference, pp. 1–6, 2020.
[33] T. Jiang, H. V. Cheng, and W. Yu, “Learning to reflect and to beamform for intelligent reflecting surface with implicit channel estimation,” IEEE Journal on Selected Areas in Communications, vol. 39, no. 7, pp. 1931–1945, 2021.