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姓名 儲志平(Chih-Ping Chu) 查詢紙本館藏 畢業系所 通訊工程學系 論文名稱 基於拉格朗日法之適應性數位預失真方法
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摘要(中) 因為功率放大器產生的振幅(AM/AM) 和相位(AM/PM) 非線性效應，會導致調變訊號的誤差向量幅度(error vector magnitude, EVM)擴大和頻帶外的頻譜增生，以致於干擾鄰近通道的傳輸訊號。為了有效解決此一問題，本論文研究了預失真技術。傳統上，在過去的文獻中，預失真器通常設計為一多項式模型，基於極座標法(polar form)，產生兩路的輸出訊號，分別對功率放大器的振福和相位進行線性化的補償。本篇論文先將真實功率放大器的模型表示成一多項式通式，藉由最小平方近似法(Least-square approximation method, LSA) 統一功率放大器的模型表示後，設計者可以更容易觀察諧波失真的嚴重度。再應用拉格朗日乘子法(Lagrange multiplier method)同時對功率放大器的非線性振幅和相位進行限制，期望使用單一路徑輸出的預失真訊號，就能達成高度的線性化補償。模擬結果顯示在固定的調變訊號(如：64QAM)和回退率環境下，功率放大器可以操作在接近飽和點的位置，仍舊保有高度的功率因素(power factor)。同時，帶外頻譜也可以有效的被抑制，使得接收端的錯誤率十分逼近線性的通道表現。
摘要(英) The nonlinear effect of a power amplifier (PA) due to the AM/AM and AM/PM characteristics usually leads to a significant error vector magnitude (EVM) and out-of-band spectral regrowth, which interferes the signals in adjacent transmission channels. To solve this problem, we study a pre-distortion scheme for the PA based on the Lagrange multiplier method. According to previous research in the literature, the PA’s pre-distorter used to utilize a polynomial model and the polar form to produce the compensating signals for AM/AM and AM/PM effects. Without following this routine work, we first establish the polynomial models for PA characteristics by the least-square approximation method. Through these models, we can easily calculate the harmonic distortion due to the PA. Then, the adaptive Lagrange multiplier method is developed to find the compensating signals for amplitude and phase. Simulation results show that the compensated PA output can achieve the high power factor even when the PA works almost close to the saturation region with a constant modulation type such as 64-ary QAM and the same back-off condition. Besides, the out-of-band spectrum can be suppressed effectively so that the bit error rate performance of the proposed pre-distortion method is almost as good as the result obtained in the linear channel.
關鍵字(中) ★ 功率放大器
★ 適應性預失真
★ 線性化
★ 頻帶增生
★ 均方誤差
★ 割線法
★ 次梯度法
★ 拉格朗日乘子法
★ 誤差向量幅度
★ 預失真關鍵字(英) ★ power amplifier (PA)
★ predistortion
★ Lagrange multiplier method
★ Sub-gradient method
★ Secant method
★ mean squared error (MSE)
★ adaptive predistorter
★ EVM
★ spectral regrowth
★ linearization論文目次 目錄
中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
致謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I
圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III
表目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V
第1 章序論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 前言. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 章節架構介紹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
第2 章功率放大器介紹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 功率放大器的訊號表示法和模型. . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 功率放大器的訊號表示. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 功率放大器的模型種類. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.2.1 多項式(Polynomial) 模型. . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2.2 沙雷(Saleh) 模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.2.3 葛邦尼(Ghorbani) 模型. . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.2.4 瑞普(Rapp) 模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.2.5 懷特(White) 模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.3 功率放大器的失真效應. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.3.1 功率放大器對單音訊號的振幅影響. . . . . . . . . . . . . . . . 20
2.1.3.1.1 增益壓縮與增益擴張. . . . . . . . . . . . . . . . . . . . . . 21
2.1.3.1.2 諧波失真. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.1.3.2 功率放大器對多音以及調變訊號產生的非線性失真
效應. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.3.2.1 交互調變失真. . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.1.3.2.2 相鄰通道功率比. . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.1.3.2.3 雜訊功率比. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1.3.2.4 多音交互調變比. . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2 功率放大器輸出的線性化. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
第3 章系統模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.1 傳輸訊號模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 預失真器模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 接收訊號模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
第4 章功率放大器非線性效應的補償演算法. . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.1 使用拉格朗日乘子法(Lagrange multiplier method) 實現訊號的
預失真. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2 拉格朗日函數的解法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.3 拉格朗日乘子的疊代. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4 拉格朗日函數的解. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.4.1 數值求根法(Numerical root finding methods) . . . . . . . . . . . . 52
4.4.2 應用割線法(Secant method) 求解拉格朗日函數. . . . . . . . . . 53
4.5 預失真演算法的疊代流程. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.6 引入適應性技術改善預失真器效能. . . . . . . . . . . . . . . . . . . . . . . 58
4.6.1 適應性演算法的複雜度比較. . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.6.2 最小均方演算法(Least Mean Square algorithm) . . . . . . . . . . 59
4.6.3 適應性預失真器架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
第5 章數值結果與效能分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.1 單載波環境(Single-carrier environment) . . . . . . . . . . . . . . . . . . . 64
5.1.1 符元錯誤率(Symbol error rate) . . . . . . . . . . . . . . . . . . . . . . . . 66
5.1.2 總體性能衰退(total degradation, TD) . . . . . . . . . . . . . . . . . . . 69
5.1.3 功率頻譜密度(Power spectral density) . . . . . . . . . . . . . . . . . . 71
5.1.4 均方誤差(mean squared error, MSE) . . . . . . . . . . . . . . . . . . . . 76
5.2 多載波環境(Multi-carrier environment) . . . . . . . . . . . . . . . . . . . . 77
5.2.1 總體性能衰退(total degradation, TD) . . . . . . . . . . . . . . . . . . . 80
5.2.2 功率頻譜密度(Power spectral density) . . . . . . . . . . . . . . . . . . 81
5.3 與過去文獻的比較. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
第6 章結論與展望. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
附錄A：拉格朗日限制式滿足凸函數之條件證明. . . . . . . . . . . . . . . . . . . . . . . . 93
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