Chi等人提出了快速峰度最大化演算法(fast kurtosis maximization algorithm, FKMA)與渦輪式訊號源分離演算法(turbo source separation algorithm, TSSA)，兩者均是要設計一個空間干擾消除濾波器來分離量測訊號中內含的訊號源，而利用分離出來的訊號源與量測訊號之間的交錯相關性，我們可以估測出此訊號源所對應的通道估測值，此通道估測方法稱為輸入輸出交錯相關性(input-output cross-correlation, IOCC)方法，是由Tugnait所提出的。最後再藉由Tugnait所提出的多階段消除程序(multistage successive cancellation, MSC)，我們便可將整體系統(針對無記憶性通道)估測出來。但由於IOCC方法並沒有考慮訊號源與量測訊號中的雜訊效應，所以其是一個偏移的估測器(biased estimator)。有鑑於上述的問題，我們在本篇論文中，基於FKMA與TSSA兩演算法個別提出了一個成立於有限的訊雜比(signal-to-noise ratio, SNR)下的時域HV關係式，其均可適用於時間上獨立的訊號源或時間上具有色彩的訊號源。進一步地，基於這兩個關係式，我們在本論文中提出了兩個盲敝系統鑑別(blind system identification, BSI)演算法來估測多輸入多輸出(multi-input multi-output, MIMO)系統，其效能優於Tugnait的輸入輸出交錯相關性(input-output cross-correlation, IOCC)方法與一些基於二階統計量(second-order statistics, SOS)的演算法(AMUSE與SOBI)。額外地，由於本論文所提出的BSI演算法對訊號源的頻譜並沒有任何條件限制，所以其比大部分基於二階統計量的現存演算法來的有彈性。這可藉由本文章中所展示的數個模擬結果來獲得驗證。

Chi et al. proposed a fast kurtosis maximization algorithm (FKMA) and a turbo source separation algorithm (TSSA), respectively have been widely used for blind source separation. Based on FKMA and TSSA, respectively we drive two rela-
tionships which holds true for finite SNR in time domain with temporally independent or temporally colored source signal. Then based on the two relationships, two iterative blind system identification (BSI) algorithms for multiple-input multiple-output system
are proposed in this thesis, which work well with better performance than Tugnait's
input-output cross-correlation (IOCC) method and some existing second-order stati-
stics (SOS) based algorithms. Besides, the proposed two iterative BSI algorithms dose
not require any condition on the spectra of the sources signals and is thus more flexi-
ble then SOS based algorithms. Some simulation results are presented to support the efficacy of the proposed BSI algorithms.

中文摘要 Ⅰ
英文摘要 Ⅲ
誌謝 Ⅴ
目錄 Ⅵ
第一章 簡介 1
第二章 盲敝訊號源分離演算法與系統鑑別演算法之回顧 4
2-1 訊號模型與假設 4
2-2 快速峰度最大化演算法(FKMA)與渦輪式訊號源分離 5
演算法(TSSA)之回顧
2-2a. 快速峰度最大化演算法(FKMA)之回顧 5
2-2b. 渦輪式訊號源分離演算法(TSSA)之回顧 7
2-3 輸入輸出交錯相關性(IOCC)通道估測方法與多階段消除 9
(multistage successive cancellation, MSC)程序
第三章 新的盲蔽系統鑑別演算法 11
3-1含多輸入多輸出系統與最佳空間干擾消除濾波器 11
的關係式
3-1a. 基於FKMA所求出之關係式 11
3-1b. 基於TSSA所求出之關係式 12
3-2基於FKMA-HV與TSSA-HV 關係式的盲敝系統鑑別演算法 14
3-2a. 基於FKMA-HV關係式的盲敝系統鑑別演算法 15
3-2b. 基於TSSA-HV關係式的盲敝系統鑑別演算法 15
附錄
3-A FKMA-HV關係式之證明 18
3-B TSSA-HV關係式之明 21
3-C 空間干擾消出濾波器的初始條件值 24
第四章 模擬結果 26
4-1 Example 1：混和矩陣固定且輸入訊號是時間上具有 27
色彩的訊號源
4-2 Example 2：混和矩陣隨機產生且輸入訊號是時間上具 28
有色彩的訊號源
4-3 Example 3：時間上具有色彩的訊號源之間的頻譜差異 29
程度對演算法的影響
第五章 結論 33
參考書目 34

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