正交分頻多工技術是目前通訊系統的關鍵技術，例如數位音訊廣播、數位視訊廣播和數位高畫質電視。利用正交的頻率通道來提升傳輸資料的速率，並且能有效的抵抗多重路徑干擾。但是，當用戶有移動速度的時候，其產生的都普勒擴展會使得系統中各個子載波失去彼此之間的正交性，使得載波之間互相干擾。如果接收端能夠準確地估測都普勒擴展，就可以消除在解調時因正交性被破壞產生的干擾，增進偵測訊號的準確度。因此，如何在正交分頻多工系統下估測都普勒擴展是相當重要的。我們提出利用時域上收集到的訊號來做最大似然都普勒擴展的估測，並藉由適當的設計領航訊號，可以使接收訊號有特別的統計特性，進而將整段訊號分成幾個子組群來降低運算上的複雜度。另一方面，當需要收集更多的OFDM訊號做估測時，我們提出了兩個方法，一是假設不同OFDM訊號彼此之間是沒有相關性的，加總各個訊號各自對應的最大似然函數之後做估測，二是考慮了不同OFDM訊號之間的相關性，先將各個訊號做加總得到一個新的訊號，再用這個新的訊號對應的最大似然函數做估測，兩種方法的表現在不同的訊雜比下有其差異，也各有其優缺點。最後我們跟兩種基於相關性的方法來做比較，由模擬的結果發現，我們提出的方法在短的估測時間下有較好的表現。

Bibliography
[1]R. V. Nee and R. Prasad, OFDM Wireless Multimedia Communications, Norwood, MA: Artech House, 2000.

[2]H. Sari, G. Karam, and J. Janclaude, “Transmission techniques for digital TV broadcasting,” IEEE Commun. Mag., vol. 36, pp. 100-109, Feb. 1995.

[3]M. Russell and G. Stuber, “Interchannel interference analysis of OFDM in a mobile environment,” in Proc. IEEE Vehicular Technology Conf., vol. 2, pp. 820-824, 1995.

[4]W. Sheng and S. D. Blostein, “SNR-independent velocity estimation for mobile cellular communications systems,” in Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing (ICASSP),May 13–17, 2002, vol. 3, pp. 2469–2472.

[5]C. Tepedelenlio˘glu, “Performance analysis of velocity (Doppler) estimators in mobile communications,” in Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing (ICASSP),May 13–17, 2002, vol. 3, pp.2201–2204.

[6]G. Park, S. Nam, T.Yu,D. Hong, and C. Kang, “A modified covariancebased mobile velocity estimation method for Rician fading channels,” IEEE Commun. Lett., vol. 9, no. 8, pp. 706–708, Aug. 2005.

[7]M. D. Austin and G. L. Stüber, “Velocity adaptive handoff algorithms for microcellular systems,” IEEE Trans. Veh. Technol., vol. 43, no. 3, pt. 1–2, pp. 549–561, Aug. 1994.

[8]G. Park, D. Hong, and C. Kang, “Level crossing rate estimation with Doppler adaptive noise suppression technique in frequency domain,” in Proc. IEEE 58th Veh. Technol. Conf. (VTC 2003-Fall), Oct. 6–9, 2003, vol. 2, pp. 1192–1195.

[9]C. Juncker, P. Toft, and N. Mørch, “Speed estimation for WCDMA based on the channel envelope derivative,” in Proc. 4th IEEEWorkshop on Signal Processing Advances in Wireless Commun. (SPAWC 2003), Jun. 15–18, 2003, pp. 527–531.

[10]S. Mohanty, “VEPSD: A novel velocity estimation algorithm for nextgeneration wireless systems,” IEEE Trans. Wireless Commun., vol. 4, no. 6, pp. 2655–2660, Nov. 2005.

[11]J. P. Cai, W. T. Song and Z. Li, ”Doppler spread estimation for mobile OFDM systems in Rayleigh fading channels,” IEEE Trans. Consum. Electron, vol. 49 no. 4, pp. 973-977, November 2003.

[12]W. Zhou and W. H. Lam, ” A novel method of Doppler shift estimation for OFDM systems,” MIL.COM. 2008

[13]Y.-S. Choi, O. C. Ozdural, H. P. Liu and S. Alamouti., “A maximum likelihood Doppler frequency estimator for OFDM systems,” proceedings, IEEE ICC, vol. 10, pp. 4572-4576, 2006.

[14]G. L. Stüber, principle of mobile communication, 2nd ed., Boston, MA: Kluwer Academic Publishers, 2001.

[15]L. Krasny, H. Arslan, D. Koilpillai, and S. Chennakeshu, “Doppler spread estimation in mobile radio systems,” IEEE Commun. Lett., vol. 5, no. 5, pp. 197–199, May 2001.

[16]R.Ware and F. Lad. “Approximating the distribution for sums of products of normal variables.” Tech. rep., University of Canterbury,2003.

[17]S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice Hall PTR, 1993