對無線通訊系統而言，由於其向四面八方傳播的特性，如何對其傳送的資訊加以保密，是個很值得研究的問題，除了利用應用層的加密技術之外，在文獻中亦有實體層保密(physical layer secrecy)技術之相關探討，其重點在於如何利用實體層通道的傳輸特性，在竊聽者無法竊取資料的前提下，使得合法傳輸者之間所獲得的資訊量最大化，讓合法的傳輸更加可靠。本文考慮一個放大後傳送(amplify-and-forward, AF)多重輸入輸出(multiple-input multiple-output, MIMO)的合作式傳輸網路，網路中有一個多天線的不可靠中繼點(untrusted relay, UR)，並將預編碼器(precoder)布置在訊號源(source)、中繼點(relay)以及目的端(destination)上，中繼點是扮演著訊號源與目的端(destination)之間溝通的橋梁角色，然而在本文中，我們假設中繼點是不可靠的，可能會在未經許可的狀況下，竊取訊號源的訊息。有鑑於此，在尋求不可靠的中繼點幫助傳送的同時，也要避免中繼點成功竊聽，因此在中繼點接收訊號的同時，由目的端產生一個人工雜訊(artificial noise, AN)，以期破壞中繼點對來源訊號的解碼，因為人工雜訊由目的端產生，所以其接收到中繼點傳送的訊號時，可自行消除人工雜訊的部分，不至於影響正常通訊，我們在訊號源、中繼點與目的端各佈置一個預編碼器(precoder)，在各節點的功率限制下，欲達到保密容量(secrecy capacity)的最大化，利用各通道的奇異值分解(singular value decomposition, SVD)及不等式關係，將矩陣的最佳化問題簡化為功率分配最佳化問題，最後以遞迴方式處理最佳化問題，使保密容量最大化。

For wireless communication systems, due to broadcasting nature of wireless medium, how to keep eavesdroppers from wiretapping messages is worth investigated. In addition to encryption techniques applied in application layer, physical layer secrecy techniques have been studied in literature. Under the premise that eavesdropper cannot steal any information, physical layer secrecy focus on maximizing the capacity of legal transmission, and make it more reliable by using physical properties of wireless channel. This thesis considers an amplify-and-forward (AF) multiple-input multiple-output (MIMO) cooperative communication network with an untrusted relay (UR), and linear precoders are employed at source, relay, and destination. The relay here serves as a bridge of transmission 1 between the source and the destination. However, assume that the untrusted relay may wiretap information from the source without authorization. In order to prevent relay from wiretapping information, the destination generates artificial noise (AN) to interfere the relay, when the relay is receiving information from the source. Since AN is generated by the destination, the destination can eliminate AN by itself after receiving signal from the relay without corrupting signals of legal transmission. We propose precoder design for source, relay and destination to maximize secrecy capacity under the power constraint of three nodes. By utilizing singular value decomposition (SVD) of all channel matrices and Hadamard inequality, we simplify the optimization problem of precoding matrices to scalar optimization problem, and optimization can be accomplished recursively.

論文審定書………………………………………………….i
誌謝……………........……………………………….….......ii
摘要……....………………………………………….…......iii
Abtract……………………………………………………...iv
第一章 簡介………………………………………………1
第二章 文獻探討…………………………………………3
2-1 使用人工干擾的保密 …………………………...……4
2-2 不可靠中繼點的保密 ………………..………….……6
2-3 多天線合作式系統的保密 ……………………...……8
第三章 系統模型 …………………………………………13
第四章 預編碼器設計......………………………...………18
4-1 給定訊號源與目的端預編碼器求解中繼點預編碼器.....................21
4-2 給定訊號源與中繼點預編碼器求解目的端預編碼器………….…23
4-3 給定中繼點與目的端預編碼器求解訊號源預編碼器…….………28
4-4 預編碼器的最佳化演算法…………………......…….30
第五章 模擬結果......……………...………………………32
第六章 結論……………………………….………………35
參考文獻 ……………………………..……………………36
附錄…………………………………………………...……38

[1] 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, Feb. 2004.
[2] A. Nosratinia and A. Hedayat, “Cooperative communication in wireless networks,” IEEE Commun. Mag., vol. 42, no. 10, pp. 74–80, Oct. 2004.
[3] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity–Part I: System description,” IEEE Trans. Commun., vol. 51, no. 11, pp. 1927–1938, Nov. 2003.
[4] —, “User cooperation diversity—Part II: Implementation aspects and performance analysis,” IEEE Trans. Commun., vol. 51, no. 11, pp. 1939–1948, Nov. 2003.
[5] T. E. Hunter and A. Nosratinia, “Cooperation diversity through coding,” in Proc. IEEE Int. Symp. Information Theory, Lausanne, Switzerland, July 2002, p. 220.
[6] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans. Inf. Theory, vol. 50, no. 12, pp. 3062–3080, Dec. 2004.
[7] S. Goel and R. Negi, “Guaranteeing secrecy using artifical noise,” IEEE Trans. Wireless Commun., vol. 7, no. 6, pp. 2180–2189, Jun. 2008.
[8] Z. Li, R. D. Yates, and W. Trappe, “Secure communication with a fading eavesdropper channel,” in Proc. IEEE Int. Symp. Information Theory, Nice, France, Jun. 2007, pp. 1296–1300.
[9] X. He and A. Yener, “Cooperation with an untrusted relay: A secrecy perspective,” IEEE Trans. Inf. Theory, vol. 56, no. 8, pp. 3801–3827, Aug. 2010.
[10] X. He and A. Yener, “Two-hop secure communication using an untrusted relay: A case for cooperative jamming,” in Proc. IEEE Globecom, New Orleans, USA, Dec. 2008.
[11] Z. Li, R. Yates, and W. Trappe, “Achieving secret communication for fast rayleigh fading channels,” IEEE Trans. Wireless Commun., vol. 9, no. 9, pp. 2792–2799, Sep. 2010.
[12] Z. Li, W. Trappe, and R. Yates, “Secret communication via multiantenna transmission,” in Proc. CISS ’07, Baltimore, MD, pp. 905-910, Mar. 2007.
[13] C. Jeong, I. Kim, and D. Kim “Joint secure beamforming design at the source and the relay for an amplify-and-forward MIMO untrusted relay system,” IEEE Trans. Signal Processing, vol. 60, no. 1, pp.310–325, Jan. 2012.