在無線通訊系統中，是利用大氣環境作為媒介來傳遞訊號，因此在傳遞的過程中，會有許多的干擾，如多路徑效應、通道衰減、都卜勒效應、路徑損失、遮蔽效應、高斯雜訊等的通道效應而使訊號失真。除了通道的影響外，電路本身也會產生非理想的效應，如載波頻率的漂移、取樣頻率的偏差等，而使訊號失真。在OFDM系統中，是利用數位電路的方式，在基頻部分進行非理想效應的估測及補償，而使接收端能精確的還原傳送端的訊號。在ODFM系統的同步過程中，首先會在時域做封包偵測來判斷是否接收到訊號，接著進行頻率漂移的估測以及OFDM訊號邊界的估測。經過FFT運算後，在頻域進行通道估測與補償，以及載波頻率追蹤，上述這些工作都是由內接收器(inner receiver)所完成。經過這些運算後，使得非理想效應的影響大幅縮減，再經過Reed Solomon，Viterbi等錯誤更正運算後，可以重建原本的資訊。本論文的目標，是設計用來進行同步運算的內接收器，首先經過理論探討整個內接收器所需之演算法後以MATLAB軟體模擬同步過程所需的演算法，分析同步的效能並加以調整，最後將這些演算法以硬體電路的方式實現，並利用FPGA驗證其設計的正確性，來評估此同步電路設計的可行性，實驗結果證明所設計的內接收器在功能及速度上確實達到Wimax規格的要求。

In wireless communication system, air is the medium of signal propagation. There are many channel effects in signal propagation that distort transmitted signal, such as multi-path, fading, Doppler effect, path-loss, shadowing, AWGN, and so on. Except channel effects, the hardware circuit itself has some effects in distorting the transmitted signal such as carrier frequency offset, sampling frequency drift, etc. We can recover the transmitted signal from the received distorted signal precisely with some estimation and compensation, which is developed by digital signal processing in base-band, at the receiver. In the synchronization process, the receiver performs packet detection in time domain to judge whether the signal is received or not. Then the receiver precedes the estimation of frequency offset and OFDM symbol boundary. After FFT operations, the receiver estimates and compensates for the channel effect in frequency domain, and tracks the carrier phase. These works described above are completed by the inner receiver. After these operations, the non-ideal channel effects are reduced substantially. Moreover, the original information can be reconstructed by error correcting code, such as Reed Solomon and Viterbi. In this thesis, our goal is to design and implement the inner receiver for signal synchronization. First, we investigate theoretically the algorithms for inner receiver. Then, we simulate the algorithms for synchronization, analyze the performance and adjust the algorithms by using MATLAB. Finally, we implement these algorithms by hardware circuit, verify the design and evaluate the synchronization performance with FPGA. The experimental results verify that our design of inner receiver actually achieves the WiMAX specification in function and speed.

[1].http://www.ieee802.org/
[2].http://www.intel.com/standards/case/case_wimax.htm
[3].http://www.intel.com/netcomms/technologies/wimax/
[4].http://www.wimaxforum.org/home/
[5].IEEE Std 802.16-2004(Revision of IEEE Std 802.16-2001), “IEEE Standard for Local and metropolitan area networks,” 3 Park Avenue, New York, NY 10016-5997, USA.
[6].“IEEE Standard for Local and metropolitan area networks Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems Amendment 2: Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands and Corrigendum 1,” IEEE Std 802.16e-2005 and IEEE Std 802.16-2004/Cor 1-2005 (Amendment and Corrigendum to IEEE Std 802.16-2004)2006, pp.0_1-822.
[7].J.D.Parsons, “The Mobile Radio Propagation Channel,” Halsted Press, New York, 1992.
[8].T A Wilkinson, “channel model and link simulation studies for the DECT test bed program,” The University of Leeds, UK, 1999.
[9].Juha Heiskala, John Terry, “OFDM Wireless LANs : A Theoretical and Pratical Guide ,” SAMS.
[10].H. Meyr, M. Moeneclaey, S. Fechtel, “Digital Communication Receivers : Synchronization, Channel Estimation, and Signal Processing,” Wiley, 1997.
[11].R. V. Nee and R. Prasad, “OFDM for Wireless Multimedia Communications,” Artech House, 2000.
[12].Bernard Sklar, “Digital Communications,” 2nd Ed., Prentice Hall, 2001.
[13].John G. Proakis, “Digital Communications,” McGraw Hill, 2001.
[14].Baoguo Yang, Letaief, K. B., Cheng. R. S., Zhigang Cao, “Timing recovery for OFDM transmission,” Selected Areas in Communications, IEEE Journal on Volume 18, Issue 11, Nov. 2000 pp-2278 – 2291.
[15].K. Wang, M. Faulkner, J. Singh, and I. Tolochko, “Timing Synchronization for 802.11a under Multipath Channels,” to appear in the proceedings of Australian Telecommunications, Networks and Applications Conference, Melbourne, 2003.
[16].T. M. Schmidl and D. C. Cox, ”Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun., vol. 45, 1997, pp.1613-1621.
[17].Bo Ai, Zhi-xing Yang, Chang-yong Pan, Jian-hua Ge, Yong Wang, Zhen Lu, “On the Synchronization Techniques for Wireless OFDM Systems,” IEEE Transactions on Broadcasting, vol. 52, No. 2, June 2006, pp.236-244.
[18].Jie-Ping Xu, Bo-Ran Guan, “An efficient timing synchronization scheme for OFDM systems in IEEE 802.16d,” Microwave Conference Proceedings, 2005. APMC 2005. Asia-Pacific Conference Proceedings vol. 1, 4-7 Dec. 2005.
[19].M. Speth, S. A. Fechtel, G. Fock & H. Meyr, “Optimum Receiver Design for Wireless Broad-Band Systems Using OFDM – Part II : A case study,” IEEE Transactions on Communications, vol. 49, no. 4, April 2001.
[20].T. Pollet, M. van Bladel, M. Moeneclaey, “BER Sensitivity of OFDM Systems to Carrier Frequency Offsetand Wiener Phase Noise,” IEEE Transactions on Communications, Vol. 43, Issue 2, Part 3, February, March, April 1995, pp.191-193.
[21].T. M. Schmidl, D. C. Cox, “Low-Overhead, Low-Complexity [burst] Synchronization for OFDM,” International Conference on Communications, Vol. 3., 1996, pp 1301–1306.
[22].Alan V. Oppenheim, Ronald W. Schafer, “Discrete-Time Signal Processing,” Prentice Hall.
[23].C. S. Burrus, “Index mappings for multidimensional formulation of the DFT and convolution,” IEEE Trans., vol. ASSP-25, June 1977, pp. 239-242.
[24].IEEE 802.16.3, “Channel Models for Fixed Wireless.”
[25].Sreeraman Rajan, Sichun Wang, Robert Inkol, and Alain Joyal, “Efficient Approximations for the Arctangent Function,” IEEE SIGNAL PROCESSING MAGAZINE, May 2006, pp.108-111.
[26].Jun Wu, Qun Zhou, Cheng, K.K.M., “The adaptive algorithm of symbol timing and carrier phase estimation in OFDM systems,” Communications, 2001. ICC 2001. IEEE International Conference on vol. 1, 11-14 June 2001, pp.156 - 160.
[27].Johansson, S., Nilsson, M., Nilsson, P., “An OFDM timing synchronization ASIC,” Electronics, Circuits and Systems, 2000. ICECS 2000. The 7th IEEE International Conference on vol. 1, 17-20 Dec. 2000, pp.324 - 327.
[28].Gu Y.J., Li Y., Ren. W., Chen K.S., “FPGA Implementation of the Timing Synchronization in Preamble Based OFDM System,” Mobile Technology, Applications and Systems,” 2005 2nd International Conference on 15-17 Nov. 2005, pp.1-4.
[29].Fort, A., Weijers, J.-W., Derudder, V., Eberle, W., Bourdoux, A., “A performance and complexity comparison of auto-correlation and cross-correlation for OFDM burst synchronization,” Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03). 2003 IEEE International Conference on Volume 2, 6-10 April 2003, pp.II-341-4.
[30].Taehyeun Ha, Seongjoo Lee, Jaseok Jim, “Low-complexity correlation system for timing synchronization in IEEE802.11a wireless LANs,” Radio and Wireless Conference, 2003. RAWCON '03. Proceedings, 10-13 Aug. 2003, pp.51 - 54.
[31].Yi-Lin Li, Hsin-Hung Chen, Yi Chen, Hsien-Po Shiang, Yumin Lee, “Low-complexity receiver design for OFDM packet transmission with mobility support,” Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE Volume 1, 17-21 Nov. 2002, pp.599 - 604.
[32].Wang, K., Singh, J., Faulkner, M., “FPGA implementation of an OFDM-WLAN synchronizer,” Electronic Design, Test and Applications, 2004. DELTA 2004. Second IEEE International Workshop on 28-30 Jan. 2004, pp.89 - 94.
[33].Ching-Hsien Chang, Chin-Liang Wang, Yu-Tai Chang, “A novel memory-based FFT processor for DMT/OFDM applications,” IEEE International Conference on Acoustics, Speech, and Siganl, 15-19 March 1999, pp.1921-1924.
[34].Chin-Liang Wang, Ching-Hsien Chang, “A new memory-based FFT processor for VDSL transceivers,” IEEE Int. Symp. On Circuits and Systems, vol. 4, May 2001, pp.670-673.
[35].Sang-Chul Moon, Ln-Cheol Park, “Area-Efficient Memory-Based Architecture for FFT Processing,” IEEE Int. Symp. On Circuits and Symstems, 25-28 May 2003, pp.101-104.
[36].Suvra S Das, Ratnam V. Rajakumar, Muhammad I. Rahman, Arpan Pal, Frank H.P.Fitzek, Ole Olsen, Ramjee Prasad, “Low Complexity Residual Phase Tracking Algorithm for OFDM-based WLAN Systems,” CSNDSP Symposium 2004, Fourth International Symposium 20-22 July 2004, Newcastle, UK, Juli, 2004, pp.128-131.