Capon提出的傳統式最小變異無失真響應（minimum variance distortionless response, MVDR）演算法用於盲蔽式波束成型與訊號源抵達方向（direction-of-arrival, DOA）之估測，以及Schmidt提出的多重訊號源分類（multiple signals classification, MUSIC）演算法用於DOA的估測，已被廣泛地用於陣列訊號處理領域。這兩個演算法所做的基本假設為所有未知的訊號源皆為廣義穩態（wide-sense stationary）且彼此在統計上是互相獨立的。波束成型（beamforming）被考慮在多用戶正交分頻多工（orthogonal frequency division multiplexing, OFDM）系統的上傳模式（mplink）中，而上述的假設只對前置快速傅立葉轉換波束成型架構（pre-FFT beamforming structure）是成立的，然而由於缺乏路徑分集（path diversity），不管是MVDR演算法或是MUSIC演算法所得到的波束成型效能都會受到限制。
對於多用戶OFDM系統的上傳模式之後置快速傅立葉轉換波束成型架構（post-FFT beamforming structure），適當地建立離散時間多輸入多輸出訊號模型，再以子載波平均取代統計平均用於估測訊號的相關矩陣，MVDR與MUSIC演算法可以被證明是可應用的（也就是上述的基本假設能夠解除）。接著，我們提出一個基於子載波平均的半盲蔽通道估測演算法，其只須要一個OFDM區塊伴隨著少量的導引子載波（Pilot Subcarriers）。此提出的演算法基本上包含MUSIC演算法用於DOA的估測、MVDR演算法用於訊號源抽取、每個DOA所對應的時間延遲與路徑增益的估測、以及它們的分類（與每個使用者相關聯）與每個使用者的通道還原。最後，我們將呈現一些模擬結果以支持所提出的半盲蔽通道估測演算法之功效。

The conventional minimum variance distortionless response (MVDR) algorithm proposed by Capon for blind beamforming and direction-of-arrival (DOA) estimation, and the multiple signals classification (MUSIC) algorithm proposed by Schmidt only for DOA estimation have been widely used in array signal processing areas. A fun-damental assumption made by the two algorithms is that all the unknown source sig-nals are wide-sense stationary and mutually statistically independent. Beamforming has been considered in the uplink of a multiuser orthogonal frequency division multi-plexing (OFDM) system, while this assumption is only valid for the pre-FFT beam-forming structure. However, the resultant beamforming performance of either MVDR algorithm or MUSIC algorithm is limited due to lack of path diversity.
By properly formulating a discrete-time multi-input multi-output signal model for the post-FFT beamforming structure of the uplink of a multiuser OFDM system, MVDR and MUSIC algorithms can be shown to be applicable if ensemble average for estimating data correlation matrices is replaced by subcarrier average (i.e., the above fundamental assumption can be relaxed). Then a semi-blind channel estimation algorithm by subcarrier averaging is proposed which needs only one OFDM block with few pilot subcarriers. The proposed algorithm basically consists of DOA estima-tion through using MUSIC algorithm, source extraction through using MVDR algo-rithm, estimation of time delay and fading gain of each DOA, and their classification (associated with each user) as well as channel recovery of each user. Finally, some simulation results are presented to support the effectiveness of the proposed semi-blind channel estimation algorithm.

參考文獻

[1] R. V. Nee and R. Prasad, OFDM for Wireless Multimedia Communications . Boston:
Artech House, 1999.

[2] Hongwei Yang, Alcatel Shanghai Bell Co., and Ltd., “A road to future broadband wireless access: MIMO-OFDM-based air interface,” IEEE Communications Magazine, pp. 53-60, Jan. 2005.

[3] Montree Budsabathon, Yoshitaka Hara, and Shinsuke Hara, Member, “Optimum beamforming for pre-FFT OFDM adaptive antenna array,” IEEE Trans. Vehicular Technology, vol. 53, no. 4, pp. 945-955, July 2004.

[4] Shinsuke Hara, Montree Budsabathon, and Yoshitaka Hara, “A pre-FFT OFDM adaptive antenna array with eigenvector combining,” Proc. IEEE International Conference on Communication., vol. 4, pp. 2412-2416, June. 2004.

[5] Yung-Fang Chen and Chih-Peng Li, “Adaptive beamforming schemes for interference cancellation in OFDM communication systems,” Proc. IEEE 59th Vehicular Technology Conference, vol. 1, Milan, Italy, May 17-19, 2004, pp. 103- 107.

[6] Qinghai Yang, Shaoyi Xu, Jong Kyoung Lim and Kyung Sup Kwak, “Pilot-aided channel estimation for multiuser MIMO-OFDM systems,” Proc. IEEE International Symposium on Communications and Information Technology, vol 2, Beijing, China, Italy, Oct. 12-14, 2005, pp. 1005 – 1008.

[7] Fred W. Vook and Kevin L. Baum, “Adaptive antennas for OFDM,” Proc. IEEE 48th Vehicular Technology Conference, vol. 1, Ottawa, Ont., May 18-21, 1998, pp. 606-610.

[8] Chan Kyu Kim, Kwangchun Lee, and Yong Soo Cho, “Adaptive Beamforming Algorithm for OFDM Systems with Antenna Arrays,” IEEE Trans. Consumer Electronics, vol. 46, no. 4, pp. 1052-1058, Nov. 2000.

[9] Hidehiro Matsuoka and Hiroki Shoki, “Comparison of pre-FFT and post-FFT processing adaptive arrays for OFDM systems in the presence of co-channel interference,” Proc. IEEE 14th International Symposium on Personal, Indoor and Mobile Radio Communications, vol. 2, Beijing, China, Sept. 7-10, 2003, pp. 1603-1607.

[10] Zhongding Lei and Francois P.S. Chin, “Post and pre-FFT beamforming in an OFDM system,” Proc. IEEE 59th Vehicular Technology Conference, vol. 1, Milan, Italy, May 17-19, 2004, pp. 39-43.

[11] Matthias Munster and Lajos Hanzo, “Performance of SDMA multi-user detection techniques for Walsh-Hadamard-Spread OFDM schemes,” Proc. IEEE 54th Vehicular Technology Conference, vol. 4, Atlantic City, NJ, USA, Oct. 7-11, 2001, pp. 2219-2323.

[12] Samir Kapoor, Daniel J. Marchok, and Yih-Fang Huang, “Adaptive interference suppression in multiuser wireless OFDM systems using antenna arrays,” IEEE Trans. Signal Processing, vol. 47, no. 12, pp. 3381-3391, Dec. 1999.

[13] Ralph O. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Trans. Antennas and Propagation, vol. AP-34, no. 3, pp. 276-280, Mar. 1986.

[14] L. C. Godara, “Application of antenna arrays to mobile communications, Part II: Beam-forming and direction-of-arrival considerations,” IEEE Proceedings, vol. 85, no. 8, pp 1195-1245, Aug. 1997.

[15] Ernesto L. Santos and Michael D. Zoltowski, “Spatial power spectrum estimation based on a MVDR-MMSE-MUSIC hybrid beamformer,” IEEE Trans. Antennas and Propagation, vol. AP-34, No. 3, pp. 276-280, Mar. 1986.

[16] Chandra Vaidyanathan and Kevin M. Buckley, “Performance analysis of the MVDR spatial spectrum estimator,” IEEE Trans. Signal Processing, vol. 43, No. 6, pp. 1427-1437, June. 1995.

[17] Bassem R. Mahafza and Atef Z. Elsherbeni, Matlab Simulations for Radar Systems Design. Chapman & Hall CRC, 2000.

[18] Shenghao Yang and Yuping Zhao, “Channel estimation method for 802.11a WLAN with multiple-antenna,” Proc. 5th International Symposium on Multi-Dimensional Mobile Communications, 29 Aug.-1 Sept, 2004, pp. 297-300.

[19] Daofeng Xu, Luxi Yang, and Zhenya He “Superimposed training aided channel estimation in OFDM system,” IEEE Trans. Communications, vol. 44, pp. 1009-1020, Aug. 1996.

[20] Yonghong Zeng and Tung-Sang Ng, “A semi-blind channel estimation method for multiuser multiantenna OFDM systems,” IEEE Trans. Signal Processing, vol. 52, no. 5, pp. 1419-1429, May 2004.

[21] Mounir Ghogho and Ananthram Swami, “Blind channel identification for OFDM systems with receive antenna diversity,” IEEE Trans. Signal Processing, vol. 45, pp. 137-147, Jan. 1997.

[22] Wei Bai, Chen He, Ling-ge Jiang, and Hong-wen Zhu, “Blind channel estimation in MIMO-OFDM systems,” Proc. IEEE International Symposium on Signal Processing and Information Technology, Darmstadt, Germany, Dec. 14-17, 2003, pp. 498-501.

[23] Farrokh Rashid-Farrokhi, K. J. Ray Liu, and Leandros Tassiulas, “Transmit beamforming and power control for cellular wireless systems,” IEEE Journal on Selected Areas in Communications, vol. 16, no. 8, pp. 1437-1450, Oct. 1998.

[24] Jihoon Choi, Robert W. Heath, and Jr., “Interpolation based transmit beamforming for MIMO-OFDM with limited feedback,” IEEE Trans. Signal Processing, vol. 53, no. 11, pp. 4125-4135, Nov. 2005.

[25] Shiann-Shiun Jeng, Garret Toshio Okamoto, Guanghan Xu, Hsin-Piao Lin, and Wolfhard J. Vogel, “Experimental evaluation of smart antenna system performance for wireless communications,” IEEE Trans. Antennas and Propagation, vol. 46, no. 6, pp. 749-757, June 1998.

[26] Derek Gerlach and Arogyaswami Paulraj, “Adaptive transmitting antenna arrays with feedback,” IEEE Signal Processing Letters, vol. 1, no. 10, pp. 150-152, Oct. 1994.

[27] Kai-Kit Wong, Roger S.-K. Cheng, Khaled Ben Letaief, and Ross D. Murch, “Adaptive antennas at the mobile and base stations in an OFDM/TDMA system,” IEEE Trans. Signal Processing, vol. 49, no. 1, pp. 195-206, Jan. 2001.