近年來，合作式通訊已受到許多關注。而合作式通訊的概念，在於利用無線傳輸為廣播形式的特點，透過鄰近節點將收到的訊號經過處理後轉傳給接收端，以補強點對點的傳輸可能受到通道衰減的不足，這樣的概念就好像將原本在傳送端的數根傳送天線拆開散置於網路中，透過這些散佈的天線之間的合作，可以達成等同於 MIMO 的效果，提供了小型用戶裝置受限體積無法容納多天線的解決之道。藉由傳送的通道資訊，接收端可決定多樣性結合的方式，來改善系統的效能。而一些通道資訊簡化及有效率回傳的演算法已經陸續被提出。一般回傳方法為接收端利用通道響應之外，還須回傳通道振幅至傳送端，勢必大幅提高回傳量。
為了更有效率的傳送通道資訊，我們基於Karhunen–Loève Expansion(KLE)，提出回傳估測的通道響應制傳送端的方法。我們將KLE的係數當作通道響應重見的參數。而KLE係數的個數比起通道響應的數量少很多，這是很有效率的資料壓縮。這些係數為高斯分佈，在合作式正交分頻多工調變的系統下，為了有效的傳送係數，我們使用高斯量化來減少量化誤差。模擬結果顯示了利用傳送的通道資訊的合作式正交頻多工調變系統及時變且頻率選擇性的通道環境下，我們所提出的演算法擁有很低的傳送負載，並且有很好的錯誤率效能。

In recent years, cooperative communications have received much attention. The concept of cooperative communications is to let un-used mobile units help the transmission of other users. Through the neighbor nodes, the transmitted signal can be relayed to the destination. Cooperative communications can reinforce the point-to-point transmission channel. Based on the cooperative communications, we attain a scenario that is like there are several transmit antennas at the transmitter, and this achieves the effect of multiple-input multiple-output (MIMO) system. In fact, the transmitter needs the forward channel state information (CSI) to improve the performance of system. Sometimes, the transmitter needs to estimate the channel responses (CRs) and/or channel amplitude, and forward these CRs to the receiver, and this increases the forward load.
In order to efficiently forward the CSI, we propose an efficient method that forward the estimated channel responses (CRs) to the receiver based on the Karhunen-Loève Expansion (KLE). The coefficients of the KLE are used as the parameters for rebuilding the CRs. The number of coefficients of the KLE is much fewer than the size of the original block of CRs, and the KLE leads to efficient compression. These coefficients are Gaussian distribution and nearly uncorrelated. To efficiently forward the coefficients for the cooperative OFDM system, we use the Gaussian quantization (GQ) to reduce the quantization error. The simulation results show that the proposed algorithms can attain good error performance for the cooperative OFDM systems with low forward load in time-varying and frequency-selective channels.

[1] J. N. Laneman, D.N.C. Tse, and G. W. Wornell. “Cooperative diversity in wireless networks: Efficient protocols and outage behavior’’. IEEE Trans. On Inf Theory,50(12):3062-3080,Dec. 2004.
[2] A. K. Sadek, W. su, and K. J. R. liu. “Multinode cooperative communication in wireless networks’’. IEEE Trans. Signal Process.,vol. 55, no. 1 , pp. 341-355, Jan.2007
[3] A. Sendonaris, E. Erkip, and B. Aazhang. “User cooperation diversity. Part ii. Implementation aspects and performance analysis’’. IEEE Trans. on Commun.,51(11):1939-1948,Nove 2003.
[4] A. Ribeiro, X. Cai, and G.B. Giannakis. “Symbol error probabilities for general cooperative links’’. IEEE Trans. on wireless Commun., 4(3):1264-1273, May 2005.
[5] T. Wang, A. Cano, G. B. Giannakis, and J. N. Laneman. “High-performance cooperative demodulation with decode-and-forward relays’’. IEEE Trans. on Commun., 55(7):1427-1438, July 2007
[6] Y. Li, and X Huang, “The simulation of Independent Rayleigh Faders,’’ IEEE Trans. Commun.,vol. 50, No. 9,pp.1503-1514,Sept.2002.
[7] A. Kuhne, “throughput analysis of multi-user OFDMA-systems using imperfect CQI
feedback and diversity techniques,” IEEE J. Select. Areas Commun., vol. 26, no. 8,pp. 1440 - 1450, October 2008.
[8] S.Guharoy, N.B. Mehta, “Joint Evaluation of Channel Feedback Schemes, Rate
Adaptation, and Scheduling in OFDMA Downlinks With Feedback Delays,” IEEE
Trans. Veh. Technol., vol. 62, No. 4, pp. 1719-1731, May 2013.
[9] S. Zhou, G. B. Giannakis, “Optimal transmitter eigen-beamforming and space-time block coding based on channel mean feedback,” IEEE Trans. Signal Processing, vol. 50, no. 10, pp. 2599-2613 ,Oct. 2002.
[10] Sheng-Lun Chiou, Kuo-Wang Hsieh, and Ming-Xian Chang, “CSI Reduction of
MIMO-OFDM Systems by Parameterization,” in Proc. IEEE International
Symposium on Personal, Indoor and Mobile Radio Communications, 15-18. Sept.
2008
[11] Ren-Shian Chen and Ming-Xian Chang, “CSI Feedback for closed-loop
MIMO-OFDM systems based on B-splines,” in Proc. IEEE Globe Com Workshop
2010.
[12] M. X. Chang and Y. T. Su, “Model-based channel estimation for OFDM signals in
Rayleigh fading,” IEEE Trans. Commun., vol. 50, pp. 540-544, Apr. 2002.
[13] D.J. Love, R.W. Heath. Jr., W. Santipach, M.L. Honig, “What is the value of limited
feedback for MIMO channels” IEEE Commun. Mag vol. 42, No. 10, pp. 54-59, Oct.
2004.
[14] Tao Cui, “Blind Receiver Design for OFDM Systems Over Doubly Selective
Channels,” IEEE Trans. Commun., vol. 55, no.5, pp. 906 - 917, May 2007.
[15] H. Zhang, Y. Li, V. Stolpman, and N. V. Waes, “A reduced CSI feedback approach
for precoded MIMO-OFDM systems,” IEEE Trans. Wireless Commun., vol. 6, no. 1,
pp. 55-58, Jan. 2007
[16] Channel State Information (CSI) Reduction in Frequency and Time Domain for
Close-loop MIMO-OFDM Systems.