適用於大量多輸入多輸出毫米波正交分頻多工通訊之基於改進塔克分解混合式波束成型設計及實作

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研究生：	何虹毅 Ho, Hung-Yi
論文名稱：	適用於大量多輸入多輸出毫米波正交分頻多工通訊之基於改進塔克分解混合式波束成型設計及實作 Modified Tucker2-based Hybrid Beamforming Design and Implementation for Millimeter Wave OFDM Massive MIMO Communications
指導教授：	黃元豪 Huang, Yuan-Hao
口試委員:	沈中安 Shen, Chung-An 蔡佩芸 Tsai, Pei-Yun
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 通訊工程研究所 Communications Engineering
論文出版年：	2023
畢業學年度：	111
語文別：	英文
論文頁數：	91
中文關鍵詞：	混合波束成型、毫米波、多輸入多輸出、塔克分解
外文關鍵詞：	Hybrid Beamforming, millimeter wave (mmWave), MIMO, Tucker decomposition
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由於移動數據大爆炸時代的到來，頻譜緊縮和高數據傳輸需求成為主要問題。毫米波通信提供了大量的頻寬和更高的數據傳輸速率，以克服這些挑戰。然而，毫米波信號具有顯著的路徑損耗和衰減。幸運的是，混合波束成型（HBF）和大規模多輸入多輸出（massive MIMO）是第五代（5G）和下一代通信的關鍵技術之一，可以減輕這些不利的傳播效應。混合波束成型結合了低維的數位波束成型和高維的類比波束成型。此外，混合波束成型通過減少射頻鏈的數量，保持了降低功耗和成本的優勢。
本研究提出了一種改進的混合波束成型設計，旨在提高毫米波OFDM系統的可實現總速率。類比波束成型可以被視為一個Tucker2分解問題。Tucker2分解的主要想法是在找出一個因子矩陣解的時候固定其他因子矩陣。因此，考慮到通道是張量的形式，可以通過利用交替最小二乘法（ALS）獲得類比波束成型。此外，數位波束成型可以通過對每個子載波基底上的有效基帶通道進行奇異值分解（SVD）來確定。模擬結果表明，在各種場景下，改進的Tucker2算法在平均總速率方面具有比其他方法更好的效能。此外，改進的Tucker2算法還在TSMC 40奈米製程技術中進行了設計和實現。該提出的架構支持64個天線和4個數據流，並配備4個射頻鏈。沒有並行計算的版本中，可以在200 MHz的工作頻率下實現每秒918.31k矩陣的運算並消耗4860 mW的功耗。而有部分進行並行計算的版本中，可以在184.5 MHz的工作頻率下實現每秒13.222M矩陣的運算並消耗10100 mW的功耗。

Due to the era of the mobile data deluge, spectrum crunch and high data transmission demands become the main problem. Millimeter wave (mmWave) communication provides large bandwidths and higher data rates to overcome these challenges. However, the signals in mmWave have significant path loss and attenuation. Fortunately, hybrid beamforming (HBF) and massive MIMO are two of the key enabling technologies for the fifth-generation (5G) and the next-generation to mitigate these unfavorable propagation effects. Hybrid beamforming combines a low-dimensional digital beamforming and a high-dimensional analog beamforming. What's more, Hybrid beamforming preserves the reduced power consumption and cost by virtue of the decreased number of RF chains.
This study proposes a modified hybrid beamforming design aiming to improve the achievable sum-rate of mmWave OFDM systems. The analog beamforming can be regarded as a Tucker2 decomposition problem. The main idea behind Tucker2 decomposition is to solve one of the factor matrices and fix the others at the same time. Therefore, taking the channel tensor into consideration, the analog beamforming can be obtained from utilizing the alternate least square (ALS) method. Furthermore, the digital beamforming can be decided by the singular value decomposition (SVD) of the effective baseband channel on each subcarrier basis. The simulation results demonstrate that the modified Tucker2 algorithm has better performance than other methods in terms of average sum-rate in various scenarios. In addition, the modified Tucker2 algorithm was also designed and implemented in TSMC 40-nm process technology. The proposed architecture supports 64 antennas and 4 data streams with 4 RF chains. It can achieve 918.31k matrices per second and consume 4860 mW at 200 MHz operating frequency without parallel computation. It can achieve 13.222M matrices per second and consume 10100 mW at 184.5 MHz operating frequency with some parallel computation.

Abstract
Contents
Introduction 1
1 Millimeter Wave MIMO Systems . . . . . . . . . . . . . . . . . . . . . . 1
2 Beamforming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3 Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
5 Organization of This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 6
6 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Hybrid Beamforming for Millimeter Wave MIMO Systems 7
1 SVD-based Precoder and Combiner . . . . . . . . . . . . . . . . . . . . . 7
2 SVD-based Hybrid Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Constrained-SVD-based Hybrid Beamforming . . . . . . . . . . . . . . . 12
3.1 Analog Precoder and Combiner . . . . . . . . . . . . . . . . . . . 13
3.2 Digital Precoder and Combiner . . . . . . . . . . . . . . . . . . . 14
Tucker2-based Hybrid Beamforming 17
1 Basic Definitions of Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.1 Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.2 Rank-1 Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.3 Matrix Representation of a Tensor . . . . . . . . . . . . . . . . . 20
1.4 N-mode product . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2 Tucker2 Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3 System Model and Problem Formulation . . . . . . . . . . . . . . . . . . 25
3.1 Extend Saleh Valenzuela Channel Model . . . . . . . . . . . . . . 25
3.2 Achievable Sum-Rate over All Subcarriers . . . . . . . . . . . . . 27
4 Analog Precoder and Combiner Design . . . . . . . . . . . . . . . . . . . 28
5 Digital Precoder and Combiner Design . . . . . . . . . . . . . . . . . . . 31
Proposed Modified Tucker2-based Hybrid Beamforming Design 33
1 Proposed Tensor-based Hybrid Beamforming . . . . . . . . . . . . . . . . 33
1.1 Revision of convergence . . . . . . . . . . . . . . . . . . . . . . . 33
1.2 Modified Tucker2 I . . . . . . . . . . . . . . . . . . . . . . . . . . 40
1.3 Modified Tucker2 II . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2 Proposed Digital Beamforming Design . . . . . . . . . . . . . . . . . . . 45
Simulation Results and Analysis 47
1 Simulation Environmental Parameters . . . . . . . . . . . . . . . . . . . 47
2 Computational Cost Analysis . . . . . . . . . . . . . . . . . . . . . . . . 48
3 Spectral Efficiency and Achievable sum-rate . . . . . . . . . . . . . . . . 51
4 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5 Fixed-Point Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
VLSI Architecture 65
1 Hardware Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2 Analog Precoder and Combiner . . . . . . . . . . . . . . . . . . . . . . . 67
2.1 Matrix Multiplication Processor . . . . . . . . . . . . . . . . . . . 67
2.2 Normalization Processor . . . . . . . . . . . . . . . . . . . . . . . 70
3 Power Method Processor . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4 Synthesis Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.1 Timing Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.2 Synthesis Result . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Conclusion 85
References 87
                                

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