用於混合式波束成形正交分頻多工系統之高維度通道張量估測演算法

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姓名

柯翔展(Hsiang-Chan Ke) 查詢紙本館藏

畢業系所

電機工程學系

論文名稱

用於混合式波束成形正交分頻多工系統之高維度通道張量估測演算法
(Higher-Order Tensor-Based Channel Estimation in Hybrid Beamforming MIMO-OFDM Systems)

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至系統瀏覽論文 (2029-7-31以後開放)

摘要(中)

本論文主要對於高維度通道張量估測演算法進行研究，使用的系統模型為單使用者多輸入多輸出(multi-input multi-output, MIMO)正交分頻多工(orthogonal frequency-division multiplexing, OFDM)與採用均勻矩形天線陣列(uniform rectangular array, URA)之混和式波束成形(hybrid beamforming)的架構，並且對於所構成的5維的通道張量進行估測。首先我們對於均勻矩形陣列的天線擺放方式提出了兩種依據角度分析方式不同的波束成形架構，並比較兩種架構下通道估測演算法的表現及複雜度差異。此外我們提出了干擾消除演算法，解決了旋轉張量正交匹配追蹤(Tensor-Orthogonal Matching Pursuit with Rotation, T-OMP-R)演算法中，鄰近路徑間的相互干擾問題，使演算法的估測精準度有著非常大的提升。再來我們提出了不需要繁雜的偽逆運算(pseudo inverse)路徑增益計算方式，加上以階層式離散傅立葉轉換碼簿(hierarchical discrete Fourier transform codebook)取代原先的循序搜尋法，在維持演算法表現的同時大幅度地節省了運算複雜度。為了進一步確保演算法的正確性及表現，我們對於提出的兩種波束成形架構下的演算法均進行克拉馬－羅下限(Cramer-Rao Bound, CRB)以及正規化平均平方誤差(normalized mean square error, NMSE)的分析，分析不同的信號雜訊比(signal-to-noise ratio, SNR)下對於演算法的影響，並與相關通道張量估測演算法進行比較，比較不同的優化方式對於運算複雜度的影響。最後我們對於我們所提出之演算法進行硬體實現上的評估與運算化簡，節省了約41%的實數乘法次數以及約95%的所需時脈。

摘要(英)

This thesis studies higher-order tensor-based channel estimation, in single-user hybrid beamforming multi-input multi-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems with uniform rectangular array (URA) at the transmitter and the receiver. Two hybrid beamforming patterns are proposed for channel estimation. Additionally, we introduce an interference cancellation algorithm to address the issue of mutual interference between adjacent paths in the Tensor-Orthogonal Matching Pursuit with Rotation (T-OMP-R) algorithm, the proposed algorithm significantly improves the accuracy. We further propose a pseudo-inverse free path gain calculation method, which eliminate about 10% computation complexity. Furthermore, by replacing the original sequential searching with a hierarchical discrete Fourier transform codebook, we substantially reduce the arithmetic complexity while maintaining the algorithm performance. To ensure the validity and performance of the proposed algorithm, we conduct analysis using the Cramer-Rao bound (CRB) to examine the estimation performance of the algorithms. Compared to some prior works applied in 5D tensor-based channel estimation, our proposed algorithm achieves similar performance with much reduced complexity. Moreover, the hardware architecture is also designed and evaluated. With computation reduction scheme, 41% multiplication operations and 95% computation cycles can be saved.

關鍵字(中)

★ 通道估測
★ 正交匹配追蹤
★ 克拉馬－羅下限
★ 混和式波束成形
★ 多輸入多輸出正交分頻多工系統

關鍵字(英)

★ channel estimation
★ orthogonal matching pursuit (OMP)
★ Cramer-Rao bound
★ hybrid beamforming
★ MIMO-OFDM

論文目次

摘要 i
Abstract ii
目錄 iii
表目錄 vi
圖目錄 vii
第一章緒論 1
1.1 研究動機 1
1.2 研究方法 2
1.3 論文組織 2
第二章張量運算與張量系統模型 3
2.1 張量乘法 3
2.1.1 向量與矩陣[1] 3
2.1.2 張量 4
2.2 張量分解 5
2.2.1 CANDECOMP/PARAFAC (CP)分解 5
2.2.2 唯一性(Uniqueness) [4] 6
2.2.3 Tucker分解[1] 7
2.2.4 矩陣展開 8
2.3 張量系統模型 10
2.3.1 五維通道張量模型 11
2.3.2 離散傅立葉轉換碼簿(Discrete Fourier Transform (DFT) Codebook) 13
2.3.3 雙一維相移器設計 14
2.3.4 二維相移器設計 16
2.3.5 OFDM領航子載波擺放方式 18
2.3.6 接收信號 20
第三章高維度正交匹配追蹤干擾消除演算法 22
3.1 壓縮感知(Compressive Sensing)[8] 22
3.2 虛擬通道張量表示法 24
3.2.1 稀疏基底 24
3.2.2 稀疏基底解析度提高方法 25
3.3 應用於雙一維架構之正交匹配追蹤演算法 28
3.3.1 高維度張量正交匹配追蹤演算法 28
3.3.2 階層式搜尋法 32
3.3.3 應用於雙一維架構之正交匹配追蹤演算法 36
3.4 應用於二維架構之正交匹配追蹤演算法 44
3.5 干擾消除演算法(Interference Cancellation) 49
3.5.1 路徑間的相互干擾 49
3.5.2 干擾消除演算法 51
第四章模擬結果 56
4.1 模擬參數 56
4.2 相關高維度通道張量估測演算法介紹 60
4.2.1 CP - Alternating Least Squares (CP-ALS)演算法 60
4.2.2 Structured CP Decomposition (SCPD)演算法 65
4.3 克拉馬－羅下限(Cramer-Rao Bound, CRB) 70
4.3.1 雙一維架構下的CRB 70
4.3.2 二維架構下的CRB 81
4.4 演算法NMSE分析 85
4.4.1 階層式DFT Codebook層數選擇 85
4.4.2 干擾消除演算法優化結果 88
4.4.3 不同演算法效能比較 90
4.5 運算複雜度分析 93
4.5.1 偽逆運算移除複雜度分析 93
4.5.2 階層式DFT Codebook複雜度分析 94
4.5.3 完整複雜度分析 95
第五章硬體評估 99
5.1 延遲維度單纖維(Single-Fiber)複雜度優化 99
5.2 硬體架構評估 103
5.2.1 延遲維度硬體架構評估 103
5.2.2 T-OMP-R完整硬體架構評估 109
第六章結論 113
參考文獻 114

參考文獻

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指導教授

蔡佩芸(Pei-Yun Tsai)

審核日期

2024-8-14

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