正交分頻多工技術（orthogonal frequency division multiplexing，OFDM）在現今的無線通訊領域被廣泛應用。正交分頻多工技術普及的主要原因之一是其子載波間的正交性（orthogonality）使得它比傳統系統減少將近一半的頻寬。在信號在傳送時會受到都普勒效應（Doppler effects）和本地振盪器間的誤差所造成的載波頻率偏移（carrier frequency offset，CFO），載波頻率偏移會破壞正交分頻多工系統的正交性，形成載波間干擾（Intercarrier Interference，ICI）。載波間干擾將導致系統位元錯誤率下降。因此我們必須精準的估測到載波頻率偏移量，並利用估測做頻率補償來移除載波間干擾。H. Liu和 U. Tureli在1998提出多重信號分類頻率偏移估測法（Multiple Signal Classification，MUSIC）[ 11 ]。多重信號分類在盲蔽式（Blind）載波頻率偏移估測方面擁有十分高的精準度，但此估測法只能用在以循環字首（cyclic prefix，CP）為保護區間的正交分頻多工系統。
在本篇論文中，我們提出了一個適用於以零點填充（zero padding，ZP）為保護區間的正交分頻多工系統的多重信號分類頻率偏移估測法。我們將零點填充正交分頻多工的接收信號做適當的疊合後，會得到與循環字首正交分頻多工接收信號排列相同的資料，再將迴旋褶積特性的多重信號分類頻率偏移估測法應用在零點填充正交分頻多工系統上。並根據系統模型修改了只適用在子載波滿載的情況下的奇異值分解通道估測（singular value decomposition，SVD），使之能夠使用在有空載波配置的零點填充正交分頻多工系統下。
模擬結果証實多重信號分類頻率偏移估測用在零點填充正交分頻多工是可行的。其頻偏估測的效能與搜尋及補償的間隔大小有關，當頻率補償間隔愈，效能就愈好。而奇異值分解通道估測的模擬亦顯示了有配置空載波的零點填充正交分頻多工系統有更好的估測方均根差。而奇異值分解通道估測效能只與通道根數有關，而不受通道能量分布的影響。

Orthogonal Frequency Division Multiplexing (orthogonal frequency division multiplexing, OFDM) has been widely applied in today's wireless communications. One major reason for the popularity of OFDM systems is that almost half of bandwidth can be saved from traditional systems with subcarriers' orthogonality. The transmitted signals may suffer Carrier Frequency Offsets (CFO), caused by Doppler effects and misadjustment of transmit and receive oscillators, and the orthogonality will be destroyed. The CFO will result Intercarrier Interference (ICI) and degrade the system performance. Therefor, CFO must be estimated accurately to remove the ICI. In 1998, H. Liu and U. Tureli proposed a CFO estimation algorithm based on Multiple Signal Classification (MUSIC)[ 11 ]. This method is blind and can provide hight accuracy. However, it only works in cyclic prefix (CP) OFDM system.
In this thesis, we propose a MUSIC CFO estimation which can be used in zero padding (ZP) OFDM. After appropriate superposition of ZP-OFDM received signals, a CP-like signal can be obtained. Such that the MUSIC algorithm can be applied to ZP-OFDM.A modified singular value decomposition (SVD) channel estimation for ZP-OFDM with full-loaded subcarriers is also proposed in this thesis.
From simulation results, the MUSIC CFO estimation for ZP-OFDM is workable. The performance of CFO estimation depends on the searching interval of the minimization process. Smaller searching results better. In SVD channel estimation, ZP-OFDM with null subcarriers can provide better root-mean-square error performance. The performance of SVD channel estimation is only related to the length of channel path.

第一章 簡介 1
第二章 正交分頻多工系統 3
2.1　正交分頻多工技術 3
2.1.1　正交分頻多工的基本架構與信號模型 4
2.1.2　守護頻帶：虛擬載波 6
2.1.3　守護區間：循環字首與零點填充 7
2.2　通道問題描述 10
2.3　頻率偏移估測與通道估測的子空間方法 12
2.3.1　循環字首正交分頻多工系統接收端架構與接收信號表示式 12
2.3.2　循環字首正交分頻多工的頻偏移估測 15
2.3.3　循環字首正交分頻多工的通道估測 18
2.3.4　零點填充正交分頻多工接收端架構與接收信號表示式 20
2.3.5　零點填充正交分頻多工的通道估測 22
2.3.6　零點填充正交分頻多工的頻率通道估測 23
第三章 零點填充正交分頻多工系統的頻偏估測演算法 24
3.1　演算法概念與接收端架構 24
3.2　系統模型 25
3.3　零點填充正交分頻多工使用多重信號分類頻偏估測演算法 27
3.4　零點填充正交分頻多工的奇異值分解通道估測演算法 30
第四章 系統模擬 32
4.1　多重信號分類法頻率偏移估測之模擬 32
4.1.1　零點填充與循環字首正交分頻多工系統之多重信號分類頻偏估測效能比較 33
4.1.2　不同載波頻率偏移值對多重信號分類頻偏估測效能的影響 34
4.1.3　搜尋間隔大小對多重信號分類法估測效能的影響 35
4.1.4　符際間干擾對多重信號分類法估測效能的影響 36
A、當通道階數大於守護區間長度 36
B、當接收端取樣有誤差 37
4.2　奇異值分解通道估測之模擬 39
4.2.1　 有配置空載波與滿載之奇異值分解估測效能比較 40
4.2.2　不同通道對奇異值分解通道估測效能的影響 41
4.2.3　符際間干擾對奇異值分解通道估測效能的影響 44
A、通道階數大於守護區間長度 44
B、當接收端取樣有誤差 45
4.3　系統結合之模擬 46
第五章 結論 48

[ 1 ]　T. Cui and C. Tellambura, “Joint frequency offset and channel estimation for OFDM systems using pilot symbols and virtual carriers,” IEEE Trans. Wireless Commun., vol. 6, no. 4, pp. 1193-1202, Apr. 2007.

[ 2 ]　S. Roy and C. Li, “A subspace blind channel estimation method for OFDM systems without cyclic prefix,” IEEE Trans. Commun., vol. 1, no. 4, pp. 572–580, Oct. 2002.

[ 3 ]　B. Muquet, M. Courville, and P. Duhamel, “Subspace-based blind and semi-blind channel estimation for OFDM systems,” IEEE Trans. Signal Processing, vol. 50, no. 7, pp. 1699–1712, July 2002.

[ 4 ]　Y. Zeng and T. S. Ng, “A proof of the identifiability of a subspace-based blind channel estimation for OFDM systems,” IEEE Signal Processing Letters, vol. 11, no. 9, pp. 756–759, Sept. 2004.

[ 5 ]　C. Li and S. Roy, “Subspace-based blind channel estimation for OFDM by exploiting virtual carrier,” IEEE Trans. Commun., vol. 2, no. 1, pp. 141–150, Jan. 2003.

[ 6 ]　F. Gao, A. Nallanathan, and C. Tellambura, “Blind channel estimation for cyclic-prefixed single-carrier systems by exploiting real symbol characteristics,” IEEE Trans. Vehicular Technology, vol.56, no.5, pp. 2487-2497, Sep. 2007.

[ 7 ]　X. G. Doukopoulos and G. V. Moustakides, “Blind adaptive channel estimation in OFDM systems,” IEEE Trans. Wireless Commun., vol. 5, no. 7, pp. 1716–1725, July 2006.

[ 8 ]　S. Barbarossa, A. Scaglione, and B. Giannakis, “Performance analysis of a deterministic channel estimator for block transmission systems with null guard intervals,” IEEE Trans. Signal Processing, vol. 50, no. 3, pp. 684–695, Mar. 2002.

[ 9 ]　J. Zhu and W. Lee, “Carrier Frequency Offset Estimation for OFDM Systems With Null Subcarriers,” IEEE Trans. Veh. Technol., VOL. 55, NO. 5, pp. 1677–1690, Sep 2006.

[ 10 ]　X. Ma, C. Tepedelenlioglu, G. B. Giannakis, and S. Barbarossa, “Non data-aided carrier offset estimators for OFDM with null subcarriers: Identifiability, algorithms and performance,” IEEE J. Sel. Areas Commun., vol. 19, no. 12, pp. 2504–2515, Dec. 2001.

[ 11 ]　H. Liu, and U. Tureli “A High-Efficiency Carrier Estimator for OFDM Communication,” IEEE Commun. Letters, vol. 2, no. 4, pp. 104-106, Apr. 1998.

[ 12 ]　U. Tureli, H. Liu, and M. D. Zoltowski “OFDM Blind Carrier Offset Estimation: ESPRIT,” IEEE Trans. Commum., vol. 48, no. 9, pp. 1459-1461, Sep. 2000.

[ 13 ]　C. Li, M. Pun and S. Roy, ”Low Complexity Blind Frequency-Offset Estimator for OFDM systems over ISI channels,” in Proc. IEEE GLOBECOM '02., Vol. 1, pp. 249–253, Nov. 2002.

[ 14 ]　U. Tureli, P. J. Honan, and H. Liu “Low-Complexity Nonlinear Least Squares Carrier Offset Estimator for OFDM: Identifiability, Diversity and performance,” IEEE Trans. Signal Process, vol. 52, no. 9, pp. 2441–2452, Sep. 2004.

[ 15 ]　Roman, T. and Koivunen V., “Subspace method for blind CFO estimation for OFDM systems with constant modulus constellations ” in Proc. Vehicular Technology Conference, 2005. Vol. 2, pp. 1253-1257, June 2005.

[ 16 ]　X. Ma, G. B. Giannakis, and S. Barbarossa, “Non-data-aided frequency offset and channel estimation in OFDM and related block transmissions,” in Proc. Int. Conf. Communications, vol. 6, Helsinki, Finland, June 11–15, 2001, pp. 1866–1870.

[ 17 ]　T. Roman, S. Visuri, and V. Koivunen “Blind frequency synchronization in OFDM via diagonality criterion,” IEEE Trans. Signal Process, vol. 54, no. 8, pp. 3125–3135, Aug. 2006.