在本文中，我們在可重構智慧反射板之通訊系統中探索主動與被動式波束成型設計的問題，由於單一可重構智慧反射板不足以服務多個使用者，我們考慮兩個可重構智慧反射板並且將使用者分為兩群，藉由從各群中選出一個使用者，我們專注於雙可重構智慧反射板系統的波束設計同時服務兩個使用者，對於通道強度較強的使用者，我們利用一個可重構智慧反射板服務該使用者並且利用另一個可重構智慧反射板消除干擾; 至於通道強度較弱的使用者，我們採用兩個可重構智慧反射板同時服務該使用者並且在訊雜比維持在一定程度上最小化傳送端的傳輸功率。因為兩個使用者的波束成型最佳化問題都是非凸優的型式，我們使用一些方法將其轉換成具有凸優特性的問題，並且找到基於交換最佳化方法之主動與被動波束成型設計的最佳解。接下來，由於通道強度較弱的用戶訊號品質較差，我們對其考慮強韌主動波束成型設計，並考慮兩種不同數學模型的通道錯誤，第一類是由量化錯誤造成的有邊界的通道錯誤，另一種是由通道估計造成的無邊界的通道錯誤，最後以模擬結果驗證所提方法的效能比現行常用波束成型效能更好。

In this work, we explore the joint design problem of active and passive beamforming for reconfigurable intelligent surface (RIS) assisted communications. Since a single RIS may not be sufficient to serve multiple users, we consider two RISs and divide the users into two groups. By choosing one user from each group, we focus on the beamforming design for two users assisted by double RISs. Customized design strategies are considered for the two users, respectively. For the user with a stronger channel gain, we use one RIS to maximize the signal strength and the other to suppress interference. As to the user with a weaker channel gain, two RISs are used simultaneously to improve the signal-to-interference-plus-noise ratio using the minimal transmission power. Since
the optimization problems for the two users are both non-convex, we introduce several relaxation techniques to transform the problems into convex ones that permit the optimization of the active and passive beamforming based on alternating optimization (AO). Next, we consider the robust active beamforming design for the far user because it's received signal quality is relatively poor. Two CSI error models are considered. The first one models the bounded CSI errors caused by the quantization process. The other one handles the unbounded CSI errors caused by the estimation process. Simulation results demonstrate that the proposed beamforming design outperforms existing beamforming strategies.

[1] E. Basar, M. D. Renzo, J. D. Rosny, M. Debbah, M. Alouini, and R. Zhang, “Wireless communications through reconfigurable intelligent surfaces,” IEEE Access, vol. 7, pp. 116 753–116 773, 2019.
[2] W. Wang, M. Z. Chen, X. Chen, J. Y. Dai, Y. Han, M. Di Renzo, Y. Zeng, S. Jin, Q. Cheng, and T. J. Cui, “Wireless communications with reconfigurable intelligent surface: Path loss modeling and experimental measurement,” IEEE Trans. Wireless Commun., vol. 20, no. 1, pp. 421–439, Jan. 2021.
[3] Q. Wu and R. Zhang, “Intelligent reflecting surface enhanced wireless network via
joint active and passive beamforming,” IEEE Trans. Wireless Commun., vol. 18,
no. 11, pp. 5394–5409, Nov. 2019.
[4] D. Gesbert, S. Hanly, H. Huang, S. Shamai Shitz, O. Simeone, and W. Yu, “Multi-cell mimo cooperative networks: A new look at interference,” IEEE Journal on Selected Areas in Communications, vol. 28, no. 9, pp. 1380–1408, 2010.
[5] Z.-Q. Luo, W.-K. Ma, A. M.-C. So, Y. Ye, and S. Zhang, “Semidefinite relaxation of quadratic optimization problems,” IEEE Signal Processing Magazine, vol. 27, no. 3, pp. 20–34, 2010.
[6] G. Zhou, C. Pan, H. Ren, K. Wang, and A. Nallanathan, “A framework of robust transmission design for irs-aided miso communications with imperfect cascaded channels,” IEEE Transactions on Signal Processing, vol. 68, pp. 5092–5106, 2020.
[7] C. Huang, A. Zappone, G. C. Alexandropoulos, M. Debbah, and C. Yuen, “Reconfigurable intelligent surfaces for energy efficiency in wireless communication,” IEEE Trans. Wireless Commun., vol. 18, no. 8, pp. 4157–4170, Aug. 2019.
[8] Q. Wu and R. Zhang, “Beamforming optimization for wireless network aided by intelligent reflecting surface with discrete phase shifts,” IEEE Trans. Commun., vol. 68, no. 3, pp. 1838–1851, Mar. 2020.
[9] B. Zheng, C. You, and R. Zhang, “Intelligent reflecting surface assisted multi-user OFDMA: Channel estimation and training design,” IEEE Trans. Wireless Commun., vol. 19, no. 12, pp. 8315–8329, Dec. 2020.
[10] Y. Yang, B. Zheng, S. Zhang, and R. Zhang, “Intelligent reflecting surface meets OFDM: Protocol design and rate maximization,” IEEE Trans. Commun., vol. 68, no. 7, pp. 4522–4535, Jul. 2020.
[11] Q. Wu and R. Zhang, “Joint active and passive beamforming optimization for intelligent reflecting surface assisted SWIPT under QoS constraints,” IEEE J. Select. Areas Commun., vol. 38, no. 8, pp. 1735–1748, Aug. 2020.
[12] Y. Han, S. Zhang, L. Duan, and R. Zhang, “Cooperative double-IRS aided communication: Beamforming design and power scaling,” IEEE Wireless Commun. Lett., vol. 9, no. 8, pp. 1206–1210, Aug. 2020.
[13] G. C. Alexandropoulos, S. Samarakoon, M. Bennis, and M. Debbah, “Phase configuration learning in wireless networks with multiple reconfigurable intelligent surfaces,” in 2020 IEEE Globecom Workshops (GC Wkshps), 2020, pp. 1–6.
[14] Q. Cao, H. Zhang, Z. Shi, H. Wang, Y. Fu, G. Yang, and S. Ma, “Outage performance analysis of Harq-aided multi-ris systems,” in Proc 2021 IEEE Wireless Communications and Networking Conference (WCNC), 2021, pp. 1–6.
[15] C. Pan, H. Ren, K. Wang, W. Xu, M. Elkashlan, A. Nallanathan, and L. Hanzo, “Multicell mimo communications relying on intelligent reflecting surfaces,” IEEE Trans on Wireless Commun, vol. 19, no. 8, pp. 5218–5233, 2020.
[16] X. Li, J. Fang, F. Gao, and H. Li, “Joint active and passive beamforming for intelligent reflecting surface-assisted massive MIMO systems,” CoRR, vol. abs/ 1912.00728, 2019. [Online]. Available: http://arxiv.org/abs/1912.00728
[17] Y. Liu, L. Liu, and C. Xu, “Spectrum underlay-based water-filling algorithm in cognitive radio networks,” in Proc 2011 International Conference on Electric Information and Control Engineering, 2011, pp. 2614–2617.
[18] Z.-Q. Luo and W. Yu, “An introduction to convex optimization for communications and signal processing,” IEEE J. Select. Areas Commun, vol. 24, no. 8, pp. 1426–1438, 2006.
[19] M. Min and A. Chinchuluun, Optimization in Wireless Networks. Boston, MA: Springer US, 2006, pp. 891–915.
[20] H. Zhang, B. Di, Z. Han, H. V. Poor, and L. Song, “Reconfigurable intelligent surface assisted multi-user communications: How many reflective elements do we need?” IEEE Wireless Commun. Lett.
[21] P. Mursia, V. Sciancalepore, A. Garcia-Saavedra, L. Cottatellucci, X. C. Perez, and D. Gesbert, “RISMA: Reconfigurable intelligent surfaces enabling beamforming for iot massive access,” IEEE J. Select. Areas Commun., vol. 39, no. 4, pp. 1072–1085, Apr. 2021.