現今無線通訊系統中，多輸入多輸出（Multiple Input Multiple Output, MIMO）正交分頻多工調變（Orthogonal Frequency Division Multiplexing, OFDM）技術已成為現今行動通訊的技術標準之一。

MIMO技術是在傳輸（Transmitter）和接收端（Receiver）各設置多根天線，提供空時分集（Space Time Diversity），藉以提升通訊速率或提高無線通訊系統資料傳輸量。OFDM技術具有高頻譜使用效率和對抗多重路徑衰落通道（Multipath Fading Channel）的效應，因此MIMO-OFDM技術一直是許多專家學者所研究的熱門議題。雖然OFDM技術具有高頻譜使用率與對抗通道衰落的能力，但OFDM對於載波頻率偏移（Carrier Frequency Offset, CFO）和相位偏移（Phase Shift）非常敏感，這些現象皆可能破壞子載波（Subcarrier）間彼此的正交性，造成載波間干擾（Inter Carrier Interference, ICI），使得位元錯誤率（Bit Error Rate, BER）提升，甚至使整個系統失能（Breakdown）。

許多關於MIMO-OFDM之CFO與通道響應（Channel Response）估計演算法已被提出，但其大多數的演算法必須事先知道通道階數(Channel Order, CO)；在論文[12]所提的方法中，雖能有效解決需預先知道通道階數的問題，但其演算法複雜度過高。

有鑑於此，本論文中，吾人提出改良型低複雜度不需預先知道通道階數之CFO與通道響應估計演算法。經由電腦模擬驗證，所提的方法相較於傳統不需預先知道通道階數演算法，可以更加達到與最佳演算法最大似然法則（Maximum Likelihood, ML）估測（假設通道階數已知）效能相仿之效能。

Nowadays, in wireless communication system, the multiple input multiple output（MIMO）orthogonal frequency division multiplexing（OFDM）becomes a standard in wireless communications.

The MIMO technique is delivering (Transmitter) and receiving (Receiver), both of them establish several antennae, it provides space time diversity, by promoting communication velocity or the exaltation wireless communication system data transmission quantity. OFDM technique has many advantages including high bandwidth efficiency and resist the effect of the multipath fading channel. Therefore the MIMO-OFDM technique has been the popular subject for many experts and scholars. Although OFDM has high bandwidth efficiency and resist to the multipath fading channel, OFDM is very sensitive about carrier frequency offset（CFO）and the phase shift. These phenomena may break the orthogonality between subcarriers and cause inter carrier interference （ICI）, destroy the bit error rate （BER）,and even cause the system breakdown.

Many approaches about the CFO and channel response estimation for MIMO-OFDM systems have been proposed, but all of these algorithms require a priori knowledge about channel order（CO）. In [12], a technique can effectively solve this problem, but this technique complexity is very high.

In this thesis, I propose a low complexity estimator which jointly estimates the CFO and channel response without a priori knowledge about channel order for a MIMO-OFDM systems. Imitate the identification through the computer, the method suggested, comparing to tradition, not knowing the channel order algorithm in advance, and it can achieve similar performance as the optimal estimator（ML）.

[1]J. Chuang, N. Sollenberger, “Beyond 3G：Wideband Wireless Data Access Based on OFDM and Dynamic Packet Assignment,” IEEE Commun. Mag., vol.32, no.1, pp.78-87, 2000.
[2]H. B Lcskei, R. W. Health, Jr. and A. J. Paulraj, “Blind Channel Identification and Equalization in OFDM-Based Multi-Antenna Systems,” IEEE Trans. Signal Process., vol.50, pp.96-109, 2002.
[3]E. Dahlman, S. Parkvall and J. Skold, 4G LTE/LTE-Advanced for Mobile Broadband., Academic Press, 2011.
[4]H. Minn, Al-Dhahi, and Y. Li, “Optimal training signals for MIMO OFDM channel estimation in the presence of frequency offset and phase noise systems,” IEEE Trans. Commun., vol.54, no.10, pp.1754-1759, 2006.
[5]W.Y. Zou, Yiyan Wu, “COFDM：An overview,” IEEE Trans. on Broadcasting., vol.41, no.1, pp.1-8, 1995.
[6]O. Besson, P. Stoica, “On parameter estimation of MIMO flat-fading channels with frequency offsets,“ IEEE Trans. Signal Process., vol.51, no.3, pp.602-613, 2003.
[7]H. Sampath, S. J. Talwar, V. Tellado, and A. Paulray, “A fourth generation MIMO-OFDM: Broadband wireless system: Design, performance, and field trial results,” IEEE Commun. Mag., vol.40, no.9, pp.143-149, 2002.
[8]I. Ziskind, M. Wax, “Maximum likelihood localization of multiple sources by alternating projection ,” IEEE Trans. Signal Process., vol.36, no.10, pp.1553-1560, 1988.
[9]S. Salari, M. Heydarzadeh, and J.P. Cances, “Joint maximum-likelihood frequency synchronization and channel estimation in MIMO-OFDM systems with timing ambiguity,” Proc. ISWCS, pp.954-958, 2012.
[10]B.Hu, X.Wang, “Low-complexity ML estimator for carrier and sampling frequency offsets in OFDM systems,” IEEE Commun. Lett., vol.18, no.3, pp.503-506, 2014.
[11]Z. Cao, U. Tureli, Yu-Dong Yao and P. Honan, “Frequency Synchronization for Generalized OFDMA Uplink,” IEEE Trans. Commun., vol.2, pp.1071-1075, 2004.
[12]T.T. Lin, F.H. Hwang , “On the CFO/Channel estimation technique for MIMO-OFDM systems without using a prior knowledge of channel length,” EURASIP Journal on Wireless Communications and Networking, 2015.
[13]S. S. Haykin, Communication systems4thEdition., Wiley, 2001.
[14]J. Proakis, Digital Communications 5th Edition., McGraw-Hill, 2007.
[15]G.L. Stuber, Principles of Mobile Communications 2th Edition., Kluwer Academic, 2001.
[16]M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Sel. Areas Commun., vol.16, no.8, pp.1451-1458, 1998.
[17]H. Lin, G. Li, OFDM-Based Broadband Wireless Networks., Wiley, 2005.
[18]L. Litwin, “The principles of OFDM,” RF Design., pp.30-48, 2001.
[19]Weile Zhang, QinyeYin , “Linear Receiver for OFDMA Uplink with both CFOs and IQ Imbalances,” IEICE Trans. Commun., vol.E95-B, no.2, pp.1-2, 2012.
[20]T.T. Lin, F.H. Hwang , “A Simple Joint Channel and CFO Estimation Technique for MIMO-OFDM Systems without Using Exhaustive Search,” ICIC Express Letters, vol.8, pp.459-466, 2014.