通道估測在無線通訊系統中一直是個很重要的議題。基於對通道增益的了解，我們可處理許多無線通訊上的問題，例如：信號偵測和傳輸功率控制。這篇論文提出了一個在多入多出正交分頻多工調變（MIMO-OFDM）系統中藉由（Takagi-Sugeno）TS模糊（Fuzzy）卡曼濾波器（Kalman filter） 的方法對一個速度隨時變的通道做估測。我們考慮一個由自回歸（autoregressive）隨機程序來做通道模型的正交空時區碼（OSTBC）多入多出系統。所提出的TS卡曼濾波器在多輸入多輸出正交分頻多工調變系統中可藉由內插許多根據不同移動端速度的線性參數系統來逼近非線性系統近而同時估測自回歸程序的參數和通道增益達到強健性的非線性參數估測和預測。在快速衰減的通道下直接偵測通道追蹤設計是個有效的方法，而直接偵測方法本質上的延遲問題可藉由模糊卡曼濾波器的預測方法來補償。而且，強健性的最小均方誤差等化器設計可藉由考慮通道預測誤差的協方差來改善信號的偵測。為了確立所提出的方法的效果，在模擬的部分會與其他方法做比較。由於在多入多出正交分頻多工系統中考慮移動端的隨時變速度，藉由TS卡曼濾波器強化後的等化器跟傳統的等化器相比有較低的信號偵測誤差。

Channel estimation is an important issue for wireless communication system.
A Channel estimation scheme using Takagi-Sugeno (T-S) fuzzy-based Kalman filter under the time-varying velocity of mobile station in a multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) system is proposed in this paper.
We consider the orthogonal space time block coding (OSTBC) scheme of MIMO system where the mobile radio channel is modeled as an autoregressive (AR) random process.
The parameters of the AR process and the channel gain are simultaneously estimated by the proposed T-S fuzzy-based Kalman filter to achieve robust nonlinear parameter estimation and prediction by interpolating several linear parameter systems at different mobile speeds to approximate the nonlinear parameter systems in MIMO-OFDM communication.
It is useful for the decision-directed channel tracking design, especially in fast fading channel due to time-varying velocity of mobile station.
The inherent delay problem of decision-directed scheme can also be compensated by a fuzzy Kalman-based channel prediction method.
Further, the robust MMSE equalization design can be achieved by the consideration of channel prediction error to improve the performance of symbol detection.
To confirm the performance of proposed method, several simulation results are given in comparison with other methods.
With consideration of time-varying velocity of the mobile station communicated in the MIMO-OFDM system, the enhanced equalizer based on the T-S fuzzy-based Kalman filter performs better than those based on the conventional channel estimators in symbol error rate.

[1] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-time block codes from orthogonal designs,” IEEE Trans. Inform. Theory, vol. 45, no. 5, pp. 1456–1467, July 1999.
[2] S. M. Alamouti, “A simple transmit diversity technique for wireless communication,” IEEE J. Sel. Areas Commun., vol. 16, no. 8, pp. 1451–1458, Oct. 1998.
[3] D. Gesbert, M. Shafi, D. Shiu, P. J. Smith, and A. Naguib, “From theory to practice: An overview of MIMO space-time coded wireless systems,” IEEE J. Sel. Areas Commun., vol. 21, no. 3, pp. 281–302, April 2003.
[4] A. J. Paulraj, D. A. Gore, R. U. Nabar, and H. Bolcskei, “An overview of MIMO communications–a key to gigabit wireless,” Proc. IEEE, vol. 92, no. 2, pp. 198–218, February 2004.
[5] R. N. A. J. Paulraj and D. Gore, Introduction to space-time wireless
communications. Cambridge University Press, 2003.
[6] H. Bocskei and A. J. Paulraj, Multiple-input multiple-output (MIMO) wireless systems. Cambridge University Press, 2003.
[7] G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment using multiple antennas,” Wireless Personal Commun., vol. 6, no. 3, pp. 311–355, 1998.
[8] H. A. Suraweera and J. Armstrong, “Alamouti coded OFDM in rayleigh fast fading channels - receiver performance analysis,” IEEE Region 10 TENCON, pp. 1–5, Nov. 2005.
[9] M. Uysal, N. Al-Dhahir, and C. N. Georghiades, “A space-time blockcoded OFDM scheme for unknown frequency-selective fading channels,” IEEE Commun. Lett., vol. 5, no. 10, pp. 393–395, Oct. 2001.
[10] B. Lu, X. Wang, and Y. G. Li, “Iterative receivers for space-time blockcoded OFDM systems in dispersive fading channels,” IEEE Trans. Wireless Commun., vol. 1, no. 2, pp. 213–225, April 2002.
[11] R. S. Blum, Y. G. Li, J. Winters, and Q. Yan, “Improved space-time coding for MIMO OFDM wireless communications,” IEEE Trans. Commun., vol. 49, no. 11, pp. 1873–1878, November 2001.
[12] V. Richard and P. Ramjee, OFDM Wireless Multimedia Communications. Artech House, 2000.
[13] L. Li, H. Li, H. Yu, B. Yang, and H. Hu, “A new algorithm for MIMO channel tracking based on Kalman filter,” IEEE Wireless Communications and Networking Conference (WCNC ’07), pp. 164–168, March 2007.
[14] T.-J. Ho and B.-S. Chen, “Tracking of dispersive DS-CDMA channels: an AR-embedded modified interacting multiple-model approach,” IEEE Trans. Wireless Commun., vol. 6, no. 1, pp. 166–174, January 2007.
[15] Y. Li and S. Seshadri, N. ; Ariyavisitakul, “Channel estimation for OFDM systems with transmitter diversity in mobile wireless channels,” IEEE J. Sel. Areas Commun., vol. 17, no. 3, pp. 461–471, Mar 1999.
[16] G. Stuber, J. Barry, S. McLaughlin, Y. Li, M. Ingram, and T. Pratt, “Broadband MIMO-OFDM wireless communications,” Proceedings of the IEEE, vol. 92, no. 2, pp. 271–294, Feb 2004.
[17] B. Balakumar, S. Shahbazpanahi, and T. Kirubarajan, “Joint MIMO channel tracking and symbol decoding using Kalman filtering,” IEEE Trans. Signal Process., vol. 55, no. 12, pp. 5873–5879, December 2007.
[18] J. Yue, K. J. Kim, J. Gibson, and R. Iltis, “Channel estimation and data detection for MIMO-OFDM systems,” Global Telecommunications Conference, vol. 2, pp. 581–585, Dec. 2003.
[19] C. Min, N. Chang, J. Cha, and J. Kang, “MIMO-OFDM downlink channel prediction for IEEE802.16e systems using kalman filter,” Proc. IEEE WCNC’07, Kowloon, pp. 942–946, March 2007.
[20] Z. Liu, X. Ma, and G. B. Giannakis, “Space-time coding and Kalman filtering for time-selective fading channel,” IEEE Trans. Commun., vol. 50, no. 2, pp. 183–186, February 2002.
[21] D. Schafhuber, G. Matz, and F. Hlawatsch, “Kalman tracking of timevarying channels in wireless MIMO-OFDM systems,” 36th Asilomar Conference, Signals, Systems and Computers, vol. 2, pp. 1261–1265, November 2003.
[22] W.-G. Song and J.-T. Lim, “Channel estimation and signal detection for MIMO-OFDM with time varying channels,” IEEE Communications Letters, vol. 10, no. 7, pp. 540–542, July 2006.
[23] I. Barhumi, G. Leus, and M. Moonen, “Optimal training sequences for channel estimation in MIMO-OFDM systems in mobile wireless channels,” in Int. Zurich Symp. Broadband Communications, Feb. 2002, pp. 44–1 – 44–6, 2002.
[24] M. Shin, H. Lee, and C. Lee, “Enhanced channel-estimation technique for MIMO-OFDM systems,” IEEE Trans. Vech. Technol., vol. 53, no. 1, pp. 261–265, Jan. 2004.
[25] E. Karami and M. Shiva, “Blind multi-input multi-output channel tracking using decision-directed maximum-likelihood estimation,” IEEE Trans. Vech. Technol., vol. 56, no. 3, pp. 1447–1454, May 2007.
[26] D. N. Kalofonos, M. Stojanovic, and J. G. Proakis, “Performance of adaptive MC-CDMA detectors in rapidly fading rayleigh channels,” IEEE Trans. wireless Communications, vol. 2, no. 2, pp. 1375–1387, March 2003.
[27] L. Lindbom, “Simplified Kalman estimation of fading mobile radio channels: highperformance at LMS computational load,” Acoustics, Speech, and Signal Processing, 1993. ICASSP-93, vol. 3, pp. 352–355, Apr. 1993.
[28] B.-S. Chen, C.-L. Tsai, and C.-S. Hsu, “Robust adaptive MMSE/DFE multiuser detection in multipath fading channel with impulse noise,” IEEE Trans. Signal Process., vol. 53, no. 1, pp. 306–317, January 2005.
[29] S. Haykin, Adaptive Filter Theory 4rd Edition. Prentice-Hall, 2002.
[30] B. S. Chen, C. S. Tseng, and H. J. Uang, “Mixed H2=H1 fuzzy output feedback control design for nonlinear dynamic systems: An LMI approach,” IEEE Trans. Fuzzy Syst., vol. 8, pp. 249–265, June 2000.
[31] C. S. Tseng, B. S. Chen, and H. J. Uang, “Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model,” IEEE Trans. Fuzzy Syst., vol. 9, pp. 381–392, June 2001.
[32] ——, “H1 fuzzy estimation for a class of nonlinear discrete-time dynamic systems,” IEEE Trans. Signal Process., vol. 49, pp. 2605–2619, Nov 2001.
[33] L.-X. Wang and J. Mendel, “Fuzzy adaptive filters, with application to nonlinear channel equalization,” IEEE Trans. Fuzzy Syst., vol. 1, pp. 161–170, Aug 1993.
[34] Q. Liang and J. Mendel, “Equalization of nonlinear time-varying channels using type-2 fuzzy adaptive filters,” IEEE Trans. Fuzzy Syst., vol. 8, pp. 551–563, Oct 2000.
[35] B. S. Chen, C. L. Tsai, and D. S. Chen, “Robust H1 and mixed H2=H1 filter for equalization designs of nonlinear communication systems: Fuzzy interpolation approach,” IEEE Trans. Fuzzy Syst., vol. 11, no. 3, pp. 384–398, June 2003.
[36] T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Trans. Syst., Man, Cybern., vol. SMC-15, pp. 116–132, 1985.
[37] E. G. Larsson and P. Stoica, Space-Time Block Coding for Wireless Communications. New York : Cambridge University Press, 2003.
[38] H. Jafarkhani, “A quasi-orthogonal space-time block code,” IEEE Trans. Commun., vol. 49, no. 1, pp. 1–4, Januay 2001.
[39] P. H.-Y. Wu and A. Duel-Hallen, “Multiuser detectors with disjoint Kalman channel estimation for synchronous CDMA mobile radio channels,” IEEE Trans. Commun., vol. 48, no. 5, pp. 752–756, May 2000.
[40] J. Proakis, Digital Communication, 4th ed. McGRAW-HILL, 2001.
[41] C. C. Wong and C. C. Chen, “A clustering-based method for fuzzy modelingm,” IEICE Trans. Inform. Syst, vol. E82-D, no. 6, pp. 1058–1065, Jun 1999.
[42] T. S. Rappaport, Wireless communications: Principles and Practice. Prentice Hall PTR, 2002.