臺灣博碩士論文加值系統

本論文設計了在頻分雙工（Frequency-Division Duplex）巨量天線（Massive MIMO）系統架構之下行波束成型，同時在僅有部分下行通道資訊（Partial CSIT）和個別天線功率限制（Per-Antenna Power Constraints）之下進行。
因在頻分雙工巨量天線系統之基地台（Base Station）取得下行（Downlink）通道資訊困難，團隊過去所構想的一個有效的部分通道資訊回授方式可有效降低取得通道資訊之成本，以提升頻分雙工巨量天線系統的可實現性。部分通道資訊在此論文中的形式為下行傳輸時的訊號發射角度以及被選中路徑之通道增益。利用下行傳輸發射角與上行（Uplink）傳輸訊號接收角度之間的互惠性（Reciprocity），基地台在獲得接收角與發射角度資訊後，向每位使用者要求估測、並回傳一特定路徑之通道增益。

此外，我們考慮到每根傳送天線所裝載功率放大器皆有其線性工作區間，若於線性區間之外操作會導致訊息失真，為避免失真天線配置上必須花費更大成本使用較昂貴之功率放大器。因此本論文亦加入個別天線功率限制(Per-Antenna Power Constraints)，設計更符合現實考量之波束成型。
之後我們亦分析、推導波束成型之訊號與干擾之效能與通道資訊需求之關係、取捨。

隨後分析過去的波束成型設計之最佳化問題，因受部分通道資訊之條件限制，而大幅度限侷限波束成型設計最佳化問題之可行性。
此論文並引入上、下行通道增益之相關性，基地台在獲得上行通道增益之振幅後能得知下行通道增益振幅之條件機率密度函數。我們將此資訊加入波束成型之設計以放寬處理雜訊之限制，提高最佳化問題之可行性。

In a previous work [1], multi-user beamforming design problem has been studied for frequency-division duplex (FDD) massive MIMO systems that uses only partial downlink (DL) channel state information at transmitter (CSIT), which requires very little overhead for CSI acquisition, under a total power constraint, where the partial CSIT is in the form of DL angles of departure(AoDs) and the amplitudes of the strongest paths of each user equipment(UE).

In this thesis, we consider the problem under an additional per-antenna power constraints (PAPCs) criterion, which makes the problem more practical especially when cost on power amplifiers (PAs) is of concerns. And New relaxation techniques are developed toward the goal to solve the new problem with PAPC. On the whole, not only the feasibility of FDD massive MIMO systems is greatly enhanced but low-cost antenna elements are required. Simulation results show the effectiveness of the proposed method and verify that the PAPCs only cause a very slight performance decrease compared to total power constraints.

Afterwards, we analyze the beamforming designs of this and previous work, and the feasibility of the optimization problem solving the beamformers. Due to the lack of full CSIT, base station (BS) has to excessively limit and narrow the feasible set of potential candidate of beamformers that might have stronger equivalent channel gains.
So we found that beamforming designs with PAPCs fail if no surplus of spatial degrees of freedom exists. Hence, we also introduce the correlation between uplink (UL) and DL channel. The BS can obtain the conditional probability density function of the magnitude of the DL path gains given the magnitude of UL path gains. A beamforming design with statistical CSI is considered to relax the constraints on the interference to release the feasible set of candidate beamformers from overly strict limits.

Contents

口試委員會審定書 i

誌謝 ii

摘要 iii

Abstract v

1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2
1.2 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 System Model 5
2.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
2.3 Existing Beamformers Using Partial CSIT . . . . . . . . . . . . . . . . . 10
2.3.1 Interference-Nulling Beamforming . . . . . . . . . . . . . . . . . . . . . .13
2.3.2 Robust Interference-Suppressing Beamforming . . . . . . . . . . .15
2.4 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17
2.4.1 Per-Antenna Power Constraints . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.2 Feasibility Analysis and Inspiration from Statistical CSI . . . . .18

3 Proposed Methods 21
3.1 Interference-Nulling Beamforming with PAPCs . . . . . . . . . . . . . .22
3.2 Robust Interference-Suppressing Beamforming with PAPCs . . .24
3.3 Idea of Beamforming Design Using Statistical CSI . . . . . . . . . . .26
3.3.1 Formulation of relaxed problem . . . . . . . . . . . . . . . . . . . . . . . .26
3.3.2 Short discussion on the beamforming designs . . . . . . . . . . . . 27

4 Simulation Results 30
4.1 Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32

5 Conclusion 35

Bibliography 38

[1]M.-F. Tang, S.-Y. Wang, and B. Su, “Beamforming Designs for Multiuser Transmis-sions in FDD Massive MIMO Systems Using Partial CSIT,” in2016 IEEE SensorArray and Multichannel Signal Processing Workshop (SAM), July 2016.
[2]Q. Spencer, A. Swindlehurst, and M. Haardt, “Zero-forcing methods for downlinkspatial multiplexing in multiuser MIMO channels,”IEEE Trans. Signal Process.,vol. 52, no. 2, pp. 461–471, Jan. 2004.
[3]A. Wiesel, Y. C. Eldar, and S. Shamai, “Linear precoding via conic optimization forfixed MIMO receivers,”IEEE Trans. Signal Process., vol. 54, no. 1, pp. 161–176,Jan. 2006.
[4]D. Gesbertet al., “Shifting the MIMO Paradigm,”IEEE Signal Process. Mag.,vol. 24, no. 5, pp. 36–46, Sept. 2007.
[5]E.Larssonet al.,“MassiveMIMOfornextgenerationwirelesssystems,”IEEE Com-mun. Mag., vol. 52, no. 2, pp. 186–195, Feb. 2014.
[6]F. Ruseket al., “Scaling Up MIMO: Opportunities and Challenges with Very LargeArrays,”IEEE Signal Process. Mag., vol. 30, no. 1, pp. 40–60, Jan. 2013.
[7]T. Marzetta, “Noncooperative Cellular Wireless with Unlimited Numbers of BaseStation Antennas,”IEEE Trans. Wireless Commun., vol. 9, no. 11, pp. 3590–3600,Nov. 2010.
[8]3GPP,“StudyonElevationBeamforming/Full-Dimension(FD)MIMOforLTE(Re-lease 13),” TR 36.897 V13.0.0, June 2015
[9]U. Ugurluet al., “A Multipath Extraction-Based CSI Acquisition Method for FDDCellular Networks With Massive Antenna Arrays,”IEEE Trans. Wireless Commun.,vol. 15, no. 4, pp. 2940–2953, Apr. 2016.
[10]W. Yu and T. Lan, “Transmitter Optimization for the Multi-Antenna Downlink WithPer-Antenna Power Constraints,”IEEE Trans. Signal Process., vol. 55, no. 6, pp.2646–2660, June 2007.
[11]S. Zhang, R. Zhang, and T. J. Lim, “Massive MIMO with per-antenna power con-straint,” in2014 IEEE Global Conference on Signal and Information Processing(GlobalSIP), Dec. 2014, pp. 642–646.
[12]P.L.Caoet al., “OptimalTransmitStrategyforMISO ChannelsWithJointSum andPer-Antenna Power Constraints,”IEEE Trans. Signal Process., vol. 64, no. 16, pp.4296–4306, Aug. 2016.
[13]C.-W. Hsu, M.-F. Tang, and Borching, “Power Allocation for Downlink Path-BasedPrecoding in Multiuser FDD Massive MIMO Systems Without CSI Feedback,” inIEEE Asilomar Conference on Signals, Systems and Computers (ACSSC),Mar.2017.
[14]Y.-R. Jwo, M.-F. Tang, and B. Su, “Beamforming Designs for Per-Antenna PowerConstrained Downlink MISO Using Partial CSIT,” in2017 IEEE Signal ProcessingAdvances in Wireless Communications Workshop (SPAWC), May 2017.
[15]D. Tse and P. Viswanath,Fundamentals of Wireless Communication. CambridgeUniversity Press, 2005.
[16]S. Shakeri, D. Ariananda, and G. Leus, “Direction of arrival estimation using sparserulerarraydesign,”in2012 IEEE 13th International Workshop on Signal ProcessingAdvances in Wireless Communications (SPAWC), June 2012, pp. 525–529.
[17]M. Viberg, B. Ottersten, and A. Nehorai, “Performance analysis of direction findingwith large arrays and finite data,”IEEE Trans. Signal Process., vol. 43, no. 2, Feb.1995.
[18]S. Boyd and L. Vandenberghe,Convex optimization. Cambridge university press,2004.
[19]Z. L. Yuet al., “Robust Adaptive Beamformers Based on Worst-Case Optimiza-tionandConstraintsonMagnitudeResponse,”IEEE Trans. Signal Process., vol.57,no. 7, pp. 2615–2628, July 2009.
[20]A. Papoulis,Signal analysis. McGraw-Hill, 1977, vol. 191.
[21]M. Grant and S. Boyd, “CVX: Matlab Software for Disciplined Convex Program-ming, version 2.1,” http://cvxr.com/cvx, Mar. 2014.