本論文提出頻域-空間結構之多重訊號區別法(MUltiple SIgnal Classification, MUSIC)估測無線通道之路徑延遲時間。在室內定位系統中,基於訊號抵達時間法為最常被使用的幾何定位技術。因此,準確的估測通道中第一個路徑(直視傳播路徑)的傳播時間為主要的議題。然而,室內多重路徑干擾嚴重,其他路徑會造成第一個路徑的估測錯誤。此時,超寬頻訊號的良好時間解析度正好提供了定位上的需求。
故本論文使用超寬頻(Ultra-wideband)訊號作為傳送訊號,並利用高解析度演算法-MUSIC演算法中的頻域形式,參考時域-空間-時域的結構,
進而提出頻域-空間MUSIC演算法,並結合空間平滑法改善演算法的效能,於兩條多重路徑通道模型中,模擬分析演算法的路徑解析能力和訊號抵達時間的估測錯誤方差。由電腦模擬分析可以看出頻域-空間MUSIC演算法具有解析路徑延遲時間非常接近時的能力。此外,因頻域作法之導引向量形式的性質可加入空間平滑技術,相較於時域上來說,
更具有改善的可能性。從MUSIC演算法特徵分解子空間的角度來看,
頻域MUSIC演算法於超寬頻訊號應用上只擷取了一半的點數,運算上更為省時,且利用廣義特徵分解而使效能要比時域MUSIC演算法更佳,此為選擇頻域MUSIC演算法的主要原因。利用天線陣列估測訊號抵達角度的優勢,可以解析出更為接近的路徑,為時間延遲估測上提供了更好的解析能力。頻域-空間MUSIC演算法的優勢在於可利用本身導引向量的特性,結合空間平滑技術,可再一次的改善效能。

In this thesis, an algorithm based on frequency-space domain MUSIC method is presented for estimating the propagation delay of a wireless multipath channel.For indoor geolocation systems, the time-of-arrival (TOA) is the most popular technique for accurate positioning system. The basic idea in TOA-based techniques is to accurately estimate the propagation delay of the radio signal arriving from the direct line-of-sight (DLOS) path. However, dense multipath environments may cause unresolved paths, and yield an error in the estimation of the DLOS path. UWB (Ultra-wideband) technology provides an excellent means for wireless positioning due to its high resolution capability in the time domain. Its ability to resolving multipath components makes it possible to obtain accurate location estimates. In this thesis, we investigate the use of UWB signals in positioning and combine frequency-domain MUSIC algorithm. At the same time, the structure of time-space-time method is studied.
In addition, we propose a frequency-space domain MUSIC algorithm, called FSF-MUSIC algorithm, and use the spatial smoothing technique to improve the performance of the algorithm. For a two-multipath case, analysis and simulation results of multipath resolvability and the variance of estimation errors of signal arrival time are discussed.

1 緒論1
1.1 研究背景. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 論文結構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 超寬頻系統及其訊號4
2.1 系統簡介. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 基本脈衝訊號. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 超寬頻多重路徑通道. . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 訊號抵達時間估測12
3.1 接收訊號模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 傳統估測方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3 高解析度演算法. . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3.1 最大概似法. . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.3.2 時域MUSIC 演算法. . . . . . . . . . . . . . . . . . . . . . 18
3.3.3 訊號子空間逼進法. . . . . . . . . . . . . . . . . . . . . . . 21
4 MUSIC演算法的其他作法24
4.1 頻域MUSIC 演算法. . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.1.1 Wiener 濾波器. . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1.2 空間平滑法. . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 聯合估測訊號抵達時間及角度之MUSIC 演算法. . . . . . . . . . . 31
4.2.1 通道模型修正. . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2.2 時域-空間-時域MUSIC 演算法. . . . . . . . . . . . . . . . 32
4.3 解析機率. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5 頻域-空間MUSIC 演算法37
5.1 頻域-空間MUSIC 演算法. . . . . . . . . . . . . . . . . . . . . . . 37
5.2 頻域-空間MUSIC 演算法結合空間平滑技術. . . . . . . . . . . . . 40
6 電腦模擬分析與討論42
6.1 頻域MUSIC 演算法. . . . . . . . . . . . . . . . . . . . . . . . . . 43
6.2 頻域MUSIC 演算法與時域MUSIC 演算法的比較. . . . . . . . . . 49
6.3 頻域MUSIC 演算法加入空間平滑技術. . . . . . . . . . . . . . . . 50
6.4 TST-MUSIC演算法效能. . . . . . . . . . . . . . . . . . . . . . . 53
6.5 FSF-MUSIC演算法效能. . . . . . . . . . . . . . . . . . . . . . . . 55
6.6 FSF-MUSIC演算法與TST-MUSIC 演算法的效能比較. . . . . . . 62
7 結論與建議65
7.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.2 建議. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
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