臺灣博碩士論文加值系統

未來之通訊系統如5G advanced和6G中為了滿足逐漸增長的資料傳輸需求，皆使用 6GHz 以上之更高頻帶以滿足顯著成長中的傳輸需求。而名為智慧反射平面之技術在近年逐漸興起並被廣泛地認為是具有潛力的有效解決方案之一以解決在高頻率中傳輸時巨幅成長之衰減和路徑損耗進而使得傳輸服務之覆蓋範圍有限之議題。

智慧反射平面主要由大量稱為相位偏移器之被動元件組成並用來中繼由接取點發送之信號，其被動元件特性擁有低成本和低功率消耗等優勢。由於其被動元件之特性使得智慧反射平面在負擔成本的考量下適合被大量建置於各種環境中，如行動載具、大樓外部和室內之天花板與壁面，得以在成本昂貴且數量有限的基站部屬下擴大傳輸服務範圍。藉由調節智慧反射平面上亦被稱作相位偏移器的每一個被動元件使得接收信號之相位產生偏移後實現建設性干涉形成被動波束成型，進而使其朝期望方向反射至被障礙遮蔽之用戶設備。換言之，智慧反射平面為無線通訊環境中創造一個可操控性的通道環境。

在本作中，假設智慧反射平面被設置在一無人飛行載具上，稱為空中智慧反射平面。本作中考慮一空中智慧反射平面輔助之下行多輸入單輸出系統並含有多個接取點和多個用戶設備且每個用戶設備僅被單一接取點透過空中智慧反射平面服務。其中接取點與用戶設備之間之配對假設已在傳輸前完成且由於障礙遮蔽使接取點和用戶設備間之直接路徑不存在。藉由空中智慧反射平面之機動性，本作聚焦於以限制成對瞬時洩漏干擾功率下最大化各用戶設備之總接收信號功率以共同設計接取點和空中智慧反射平面之主動和被動波束成型與空中智慧反射平面之位置。

由於此問題為非凸最佳化問題，本作利用了連續凸近似 (successive convex approximation)、交替方向乘子法 (Alternative Direction Method of Multiplier) 和 Generalized Benders Decomposition (GBD)提出了 SCA-ADMM-GBD (SAG) 演算法。 儘管沒有收斂性的保證，透過使用梯度上升結合動量 (Gradient ascent with momentum)使得SAG演算法得以在所有模擬實驗中達成收斂。

儘管SAG演算法能夠得到空中智慧反射平面三度空間中之最佳位置，由於時間條件的限制下難以完成比較基準之窮舉搜尋算法之模擬，在模擬中僅比較與1D- 和 2D-SAG之模擬結果表現。然而空中智慧反射平面基於不同高度下使用SAG演算法之頻譜效率仍在模擬結果中展示。總結來說，在基於頻譜效率標準下，1D-和 2D-SAG之表現得以逼近窮舉搜尋算法，此外，SAG演算法之表現亦優於文獻中所提出之空中智慧反射平面位置最佳化算法。最後，本作討論梯度上升結合動量方法得以幫助收斂之分析。

關鍵詞 - 智慧反射平面(IRS)、 多輸入多輸出(MIMO)、主動波束成型(active beamforming)、被動波束成型(passive beamforming)、第六代行動通訊系統 (6G)

In future communication system such as 5G advanced and 6G, will exploit higher frequency bands above 6GHz to satisfy the significantly growing demand on transmission rate. An emerging technology called intelligent reflecting surface (IRS) or reconfigurable intelligent surface (RIS) has been viewed as a promising technology to deal with the incredibly increasing attenuation and path loss at high frequencies that results in limited service coverage.

The IRS consists of large number of passive elements called phase shifters that can relay the transmit signal from any access points (APs) and have many advantages over active systems such as low cost and low power consumption. Its passive nature allows it to be widely deployed with affordable costs in various wireless environment, for example, mobile vehicle, buildings or walls and ceilings in indoor environment to achieve coverage extension with limited number of costly base station (BS). By adjusting the phase of the received signal on each element of the phase shifters, IRS has the capability of creating constructive interference so the impinging signals are beamformed and reflected into a desired direction to reach user equipment (UE) located in shadow area that is unreachable in the direct path between the transmitters and the receivers due to blockage. In other words, IRS provides a manipulable channel environment in wireless communication.

In this work, we consider a downlink MISO system with multiple APs and UEs that each AP can serve via an aerial IRS (AIRS), where an IRS is mounted on an unmanned aerial vehicle (UAV). It is assumed that the AP-UE pairing is done prior to transmission and the direct paths from APs to UEs are absent due to blockage. With the mobility given by the AIRS, this work aims to jointly design the passive and active beamformers at the APs and the AIRS, respectively, and the AIRS' position by maximizing the total received power for all UEs while constraining the pairwise instantaneous leakage interference power. However, the formulated problem is highly non-convex since the active and passive beamformer are coupled in both the objective and the constraints, both of which are also non-convex function in the AIRS position.

Due to nonconvexity of the problem, this work proposed the SCA-ADMM-GBD (SAG) algorithm, which utilizes successive convex approximation (SCA), alternating direction of method of multipliers (ADMM), and the Generalized Benders Decomposition (GBD). Despite lack of guaranteed convergence, using gradient ascent with momentum (GAM) in part of the SAG algorithm allows it to converge in all of the simulations.

Despite the SAG's ability to optimally determine the 3D coordinates of the AIRS, due to simulation time constraint of the exhaustive search algorithm that benchmarks the SAG, performance of only the 1D- and 2D-SAG is shown. However, spectral efficiency results are shown using the SAG when the AIRS are at different heights. In summary, in terms of spectral efficiency, 1D- and 2D-SAG perform extremely close to that of the exhaustive search. Moreover, the proposed SAG method outperforms another AIRS positioning method in literature. Finally, an analysis of why the GAM performs better than gradient ascent is given.

Keywords - Intelligent Reflecting Surface(IRS)、 Multiple-Input-Multiple-Output(MIMO)、active beamforming、passive beamforming、6G

Abstract (Chinese) i
Abstract (English) iii
Symbols and abbreviations viii
Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
List of Figures xiv
List of Tables xv
List of Algorithms xvi
1 Introduction 1
1.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Previous Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Backgrounds 6
2.1 Intelligent Reflecting Surface . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Generalized Benders Decomposition . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Successive Convex Approximation . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 Alternating Direction Method of Multipliers . . . . . . . . . . . . . . . . . 20
2.4.1 Dual Ascent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.2 Dual Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.3 Augmented Lagrangian and Method of Multipliers . . . . . . . . . . 22
2.4.4 ADMM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3 SAG Algorithm for Joint Beamforming and Aerial IRS Positioning Design 29
3.1 System Model & Problem Formulation . . . . . . . . . . . . . . . . . . . 29
3.2 GBD-based Algorithm for Joint Beamforming Design . . . . . . . . . . . . 31
3.2.1 Subproblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.2 Relaxed Master Problem . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Spatial Correlation Model for AIRS Positioning . . . . . . . . . . . . . . . 34
3.4 Constraint Reformulation via SCA . . . . . . . . . . . . . . . . . . . . . . 37
3.5 ADMM-based Algorithm for AIRS Positioning . . . . . . . . . . . . . . . . 38
3.5.1 a-step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5.2 ℓ-step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.5.3 s-step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.5.4 λ-step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.6 Overall SAG Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4 Simulation 44
4.1 Simulation parameters and Channel Generation . . . . . . . . . . . . . . . 44
4.2 SAG Algorithm for Joint Beamforming and Aerial IRS Positioning Design 46
4.2.1 Convergence behavior of SAG algorithm . . . . . . . . . . . . . . . 49
4.2.2 Comparison of 1D and 2D cases . . . . . . . . . . . . . . . . . . . 49
4.2.3 Comparison of different initial point of the AIRS . . . . . . . . . . 54
4.2.4 Comparison of different height of the AIRS . . . . . . . . . . . . . . 55
4.2.5 Comparison of different number of APs . . . . . . . . . . . . . . . . 55
4.2.6 Discussions on GAM for non-convex Problem . . . . . . . . . . . . 59
5 Conclusion and Future Works 62
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

[1] F. Liu, A. Pitilakis, M. S. Mirmoosa, O. Tsilipakos, X. Wang, A. C. Tasolamprou,
S. Abadal, A. Cabellos-Aparicio, E. Alarc ́on, C. Liaskos, N. V. Kantartzis, M. Kafe-
saki, E. N. Economou, C. M. Soukoulis, and S. Tretyakov, “Programmable metasur-
faces: State of the art and prospects,” in 2018 IEEE International Symposium on
Circuits and Systems (ISCAS), 2018, pp. 1–5.

[2] H. Li, S. Shen, and B. Clerckx, “Beyond diagonal reconfigurable intelligent surfaces:
From transmitting and reflecting modes to single-, group-, and fully-connected ar-
chitectures,” IEEE Transactions on Wireless Communications, vol. 22, no. 4, pp.
2311–2324, 2023.

[3] Q. Wu and R. Zhang, “Intelligent reflecting surface enhanced wireless network: Joint
active and passive beamforming design,” in 2018 IEEE Global Communications Con-
ference (GLOBECOM), 2018, pp. 1–6.

[4] S. Zeng, H. Zhang, B. Di, Z. Han, and L. Song, “Reconfigurable intelligent surface
(ris) assisted wireless coverage extension: Ris orientation and location optimization,”
IEEE Communications Letters, vol. 25, no. 1, pp. 269–273, 2020.

[5] H. Lu, Y. Zeng, S. Jin, and R. Zhang, “Enabling panoramic full-angle reflection
via aerial intelligent reflecting surface,” in 2020 IEEE International Conference on
Communications Workshops (ICC Workshops). IEEE, 2020, pp. 1–6.

[6] T. Zhou, K. Xu, X. Xia, W. Xie, and J. Xu, “Achievable rate optimization for
aerial intelligent reflecting surface-aided cell-free massive mimo system,” IEEE Ac-
cess, vol. 9, pp. 3828–3837, 2021.

[7] Y. Su, X. Pang, S. Chen, X. Jiang, N. Zhao, and F. R. Yu, “Spectrum and energy
efficiency optimization in irs-assisted uav networks,” IEEE Transactions on Commu-
nications, vol. 70, no. 10, pp. 6489–6502, 2022.

[8] X. Song, Y. Zhao, Z. Wu, Z. Yang, and J. Tang, “Joint trajectory and communica-
tion design for irs-assisted uav networks,” IEEE Wireless Communications Letters,
vol. 11, no. 7, pp. 1538–1542, 2022.

[9] Y. Cai, Z. Wei, S. Hu, D. W. K. Ng, and J. Yuan, “Resource allocation for power-
efficient irs-assisted uav communications,” in 2020 IEEE International Conference
on Communications Workshops (ICC Workshops), 2020, pp. 1–7.

[10] S. Jiao, F. Fang, X. Zhou, and H. Zhang, “Joint beamforming and phase shift design
in downlink uav networks with irs-assisted noma,” Journal of Communications and
Information Networks, vol. 5, no. 2, pp. 138–149, 2020.

[11] K. Li, K. Zhao, M. F. Khan, P.-H. Ho, and L. Peng, “Uav-mounted intelligent re-
flecting surface (irs) miso communications,” in 2022 International Conference on
Networking and Network Applications (NaNA), 2022, pp. 62–66.

[12] O. E. Ayach, R. W. Heath, S. Abu-Surra, S. Rajagopal, and Z. Pi, “The capacity op-
timality of beam steering in large millimeter wave mimo systems,” in 2012 IEEE 13th
International Workshop on Signal Processing Advances in Wireless Communications
(SPAWC), 2012, pp. 100–104.

[13] S. Shen, B. Clerckx, and R. Murch, “Modeling and architecture design of reconfig-
urable intelligent surfaces using scattering parameter network analysis,” IEEE Trans-
actions on Wireless Communications, vol. 21, no. 2, pp. 1229–1243, 2021.

[14] J. Xu, Y. Liu, X. Mu, J. T. Zhou, L. Song, H. V. Poor, and L. Hanzo, “Simultane-
ously transmitting and reflecting (star) intelligent omni-surfaces, their modeling and
implementation,” arXiv preprint arXiv:2108.06233, 2021.

[15] R. Fletcher and S. Leyffer, “Solving mixed integer nonlinear programs by outer ap-
proximation,” Mathematical Programming, vol. 66, pp. 327–349, 1995.

[16] A. M. Geoffrion, “Generalized benders decomposition,” Journal of optimization the-
ory and applications, vol. 10, pp. 237–260, 1972.

[17] C. Floudas, “Nonlinear and mixed-integer optimization: Fundamentals and applica-
tions,” 1995.

[18] S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein, et al., “Distributed optimization
and statistical learning via the alternating direction method of multipliers,” Founda-
tions and Trends® in Machine learning, vol. 3, no. 1, pp. 1–122, 2011.

[19] 3GPP, ““section 7.3: Reference sensitivity”, 5G, NR, User Equipment (UE) radio
transmission and reception; Part 1: Range 1 Standalone (3GPP TS 38.101-1 version
16.5.0 Release 16) ,” 2020.

[20] V. Kumar, Z. Ding, and M. F. Flanagan, “On the performance of downlink noma
in underlay spectrum sharing,” IEEE Transactions on Vehicular Technology, vol. 70,
no. 5, pp. 4523–4540, 2021.

[21] L. Dai, B. Wang, Y. Yuan, S. Han, I. Chih-lin, and Z. Wang, “Non-orthogonal mul-
tiple access for 5g: solutions, challenges, opportunities, and future research trends,”
IEEE Communications Magazine, vol. 53, no. 9, pp. 74–81, 2015.

[22] M. Grant and S. Boyd, “CVX: Matlab software for disciplined convex programming,
version 2.1,” http://cvxr.com/cvx, Mar. 2014.

[23] 3GPP, “5g study on channel model for frequencies from 0.5 to 100 ghz (3gpp tr
38.901 version 16.1.0 release 16),” Nov. 2020.