在此論文中我們研究多信源(source)多中繼站(relay)的上行CDMA網路，在此網路中，各信源將利用不同之展頻序列(spreading sequences)同時存取通道，並在各中繼站競爭頻寬，而有限頻寬的中繼站將接收的資訊作放大再傳輸(amplify-and-forward)的動作傳至接收端，目標是使得接收端接收訊號與信源訊號誤差最小。
在中繼站的傳輸維度有限並低於信源數的前提下，我們提出了一種降秩多用戶中繼（Reduced-Rank Multiuser Relaying）方法。在此系統中每個中繼站會將從各信源接收到的資料壓縮到較低的維度，再傳輸至接收端。在本文中，我們首先提出了兩種集中式的預編碼和解碼技術：其一是疊代處理(iterative procedure)；另一方法為次佳閉型方法(suboptimal closed-form solution)。其次，在考慮到訊源至中繼站和中繼站至接收端通道估計誤差的問題，我們設計了強健型(robust)預編碼和解碼技術來使估計通道的均方誤差最小。最後，在實際應用中，我們又提出了一種分散式設計稱為「最小均方誤差主要成分分析」（MMSE-PCA）的方法。我們證明了MMSE-PCA方法等效於在忽略其他中繼站存在的情況下，所計算出的最佳中繼站預編碼方法。通過數值模擬比較，我們證明了我們所提出的疊代處理方法優於文獻中其它的上行CDMA系統的中繼方法，而我們所提出的次佳閉型方法通過犧牲檢測準確性來降低計算複雜度。當中繼站和接收端都有通道估計誤差時，該誤差將嚴重影響接收端的檢測準確性。

We study a cooperative uplink CDMA network with multiple sources and multiple relays. The sources simultaneously access the channel using different spreading sequences and compete for the bandwidth at the relays, and the bandwidth-limited relays then forward the information from the sources to the destination. Under the assumption that the transmission dimension at relays is limited and less than the number of sources, we propose a reduced-rank multiuser
relaying (RR-MUR) scheme where the data received from sources are first compressed into lower dimensions before being retransmitted. Specifically, we employ linear precoders at relays and a decoder at the destination to minimize the mean square error (MSE) of the estimate at the destination. In this paper, we propose a centralized methods to devise the precoders and decoder with global channel state information (CSI). Moreover, by taking into consideration the channel estimation error at both relays and the destination, we devise the robust precoders and decoder that minimize the MSE under the presence of channel estimation error. For practical considerations, a decentralized scheme is then proposed: the Minimum Mean Square Error Principle Component Analysis (MMSE-PCA) method. We show that the MMSE-PCA scheme is equivalent to the optimal decentralized design where each relay's precoder is computed separately by neglecting the presence of other relays. Through the numerical comparison, we show that the proposed iterative procedure outperforms the other existing relaying methods for uplink CDMA systems. When the relays and the destination have channel estimation error, the presence of error dramatically degrades the detection
accuracy at the destination.

[1] A. Sendonaris, E. Erkip, and B. Aazhang, “User Cooperation Diversity – Part I: System
Description,” IEEE Trans. on Commun., vol. 51, no. 11, pp. 1927-1938, Nov. 2003.
[2] A. Sendonaris, E. Erkip, and B. Aazhang, “User Cooperation Diversity – Part II: Implementation
Aspects and Performance Analysis,” IEEE Trans. on Commun., vol. 51,
no. 11, pp. 1939-1948, Nov. 2003.
[3] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative Diversity in Wireless
Networks: Efficient Protocols and Outage Behavior,” IEEE Trans. on Inform. Theory,
vol. 50, no. 12, pp. 3062-3080, Dec. 2004.
[4] A. Scaglione and Y.-W. Hong, “Opportunistic Large Arrays: Cooperative Transmission
in Wireless Multihop Ad Hoc Networks to Reach Far Distances,” IEEE Trans. on Signal
Processing, vol. 51, NO. 8, pp. 2082-2092, August 2003.
[5] Y.-W. Hong, W.-J. Huang, F.-H. Chiu, and C.-C. J. Kuo, “Cooperative Communications
in Resource-Constrained Wireless Networks,” IEEE Signal Processing Mag.,
vol. 24, no. 3, pp. 47-57, May 2007.
[6] Y. Cao and B. Vojcic, “MMSE Multiuser Detection for Cooperiave Diversity CDMA
Systems,” Proceedings of the Wireless Communications and Networking Conference
(WCNC), pp. 42-47, 2004
[7] L. Venturino, X.Wang, and M. Lops, “Multiuser detection for cooperative networks and
performance analysis,” IEEE Trans. on Signal Processing, vol. 54, no. 9, pp. 3315-3329,
Sep. 2006
[8] W.-J. Huang, Y.-W. P. Hong, and C.-C. J. Kuo, “Relay-Assisted Decorrelating Multiuser
Detector (RAD-MUD) for Cooperative CDMA Networks,” IEEE J. Select. Areas
Commun., vol. 26, no. 3, pp. 550-560, April 2008
[9] Chengwen Xing, Shaodan Ma and Y.-C. Wu, “Robust Joint Design of Linear Relay
Precoder and Destination Equalizer for Dual-Hop Amplify-and-Forward MIMO Relay
Systems,” IEEE Trans. on Signal Processing, Vol. 58, issue 4, pp. 2273-2283, 2010
[10] M. Dong and L. Tong, “Optimal Design and Placement of Pilot Symbols for Channel
Estimation,” IEEE Trans. on Signal Processing , vol. 50, no. 12, pp. 3055-3069, Dec.
2002
[11] A. Scaglion, G.B. Giannakis, and S. Barbarossa, “Redundant Filterbank Precoders and
Equalizers - Part I: Unification and Optimal Designs,” IEEE Trans. on Signal Processing,
vol. 47, no. 7, pp. 1998-2006, Jul. 1999
[12] D. P. Palomar, J. M. Cioffi, and M. A. Lagunas, “Joint Tx-Rx Beamforming Design for
Multicarrier MIMO Channels: A Unified Framework for Convex Optimization,” IEEE
Trans. on Signal Processing, vol. 51, no. 9, pp. 2381-2401, Sept. 2003