利用多個簡單天線所排成的陣列來接收訊號，而藉不同的相位(phase)可以控制最大增益出現的方向，並藉由演算法來計算所接收的訊號，進而得到一權重以提高訊號對干擾雜訊功率比(SINR)，以增加頻道容量，提高通訊品質及消除多重路徑效應。所謂pre-DFT beamformer(波束構成器)是將接收的時域(time domain)訊號做完波束構成的權重計算後，然後再將合成訊號送進DFT運算器，那麼這樣只需用到一個DFT運算器就可以達成，因此pre-DFT的運算複雜度較低;而post-DFT beamformer是將接收訊號先經過DFT運算器，然後再將頻域(frequency domain)訊號做波束構成的權重計算，這樣就會需要多個DFT運算器，所以post-DFT的運算複雜度較高，不過它會比pre-DFT有更好且穩定的效能，本篇論文將會針對post-DFT和pre-DFT波束構成器在OFDM系統上做一個效能的比較及分析說明。也利用三種演算法(MVDR﹑GSC和Eigenvector)來分析在DFT前或DFT後的效能，另外也比較所要訊號的路徑到達角度之間隔、多路徑數量及不同干擾訊號強度所影響的程度。

We use an antenna array to receive signals and control the direction of the maximum gain via different phase adjustment. The received signal is computed through beamforming algorithms which improve the SINR (Signal Interference Noise Ratio), increase the channel capacity, and enhance the quality of the communication. It also eliminates the effect of the multi-path through beamforing weights.In the pre-DFT beamformer, the received signal in the time domain is calculated by beamforming algorithms before DFT (Discrete Fourier Transform). Therefore, the complexity of computation will be lower because the DFT is only applied once.In the post-DFT beamformer, the processing of received signals is performed by beamforming algorithms after DFT. In this way, the complexity of post-DFT beamformer will be higher. However, its performance is much better than pre-DFT. In this thesis, we will analyze and compare post-DFT and pre-DFT beamformers for OFDM systems.We use three algorithms (MVDR, GSC, and Eigenvector) before DFT or after DFT, to analyze the performance. Finally, we will make the performance comparison with different angle of arrivals, numbers of multi-paths, and degree of interference signal strength.

【1】William Y.Zou, Yiyan Wu, “COFDM: AN OVERVIEW”, IEEE Trans-
actions on Broadcasting, Vol.41, No.1, pp.1-8, March 1995.
【2】IEEE Std 802.16TM-2004, IEEE Standard for Local and Metropolitan Area Networks-part 16：Air Interface for Fixed Broadband Wireless Access Systems. New York, IEEE, June 2004.
【3】IEEE Std 802.16TM-2001, IEEE Standard for Local and Metropolitan Area Networks-part 16：Air Interface for Fixed Broadband Wireless
【4】S. Haykin, “Adaptive Filter Theory”, 4th edition, Prentice Hall, New Jersey 1996.
【5】Muhammad Imadur Rahman, Klaus Witrisal, Suvra Sekhar Das, Fra- nk H.P. Fitzek, Ole Olsen, Ramjee Prasad,“Optimum Pre-DFT Combi- ning with Cyclic Delay Diversity for OFDM Based WLAN Systems”, Ve- hicular Technology Conference, 2004.VTC 2004-Spring. 2004 IEEE 59th, vol.4, pp.1844-1848, 2004.
【6】G.-S. Liu and C.-H. Wei, “A new variable fractional sample delay filter with nonlinear interpolation”, IEEE Trans.Circuits and Systems, vol.39, No.3, pp.123-126, February 1992.
【7】Y. (Geoffrey) Li, “Pilot-symbol-aided channel estimation for OFDM in wireless systems”, IEEE Transactions on Vehicular Technology, vol.49, pp.1207-1215, July 2000.
【8】Muhammad Imadur Rahman, Suvra Sekhar Das, Frank H.P. Fitzek, Ramjee Prasad, “Pre- and Post-DFT Combining Space Diversity Rec- eiver forWideband Multi-Carrier Systems”, International Symposium on Wireless Personal Multimedia Communications (WPMC''05)
【9】Zhongding Lei and Francois P.S. Chin“Post and Pre-FFT Beamform- ing in an OFDM System”, Vehicular Technology Conference, 2004. VTC 2004-Spring. 2004 IEEE 59th, vol.1, pp39-43, 2004.
【10】Yung-Fang Chen, Chih-Peng Li,“Adaptive Beamforming Schemes for Interference Cancellation in OFDM Communication Systems”,Vehic- ular Technology Conference, 2004.VTC 2004-Spring.2004 IEEE 59th, vol.1, pp.103-107, 2004.
【11】Bing-Leung Patrick Cheung , “Simulation of Adaptive Array Algor- ithms for OFDM and Adaptive Vector OFDM Systems”,September 2002.