臺灣博碩士論文加值系統

在本篇論文中，我們考慮一個衰退通道實體安全傳輸之系統。在此系統中，假設傳送端知道合法接收端之通道資訊以及只知道竊聽者通道之統計特性。我們利用人工雜訊來增加系統之傳輸速度，而人工雜訊第一個是被Goel和Negi所提出來。我們證明Goel和Negi提出來人工雜訊的選法不是最佳；我們提出在多輸入多輸出且竊聽者只有一根天線之系統中，將人工雜訊放在所有方向上以干擾竊聽者來改進Goel和Negi方法的效能。我們證明在上述條件下最佳傳輸方式是波束合成。同時，我們亦證明在選擇波束方向與合法接收端通道同方向下，所有落在波束方向之零空間之人工雜訊之功率是均勻分布。此外，我們亦提供最佳人工雜訊之共變異數矩陣滿秩之必要條件。模擬結果顯示我們所提出之人工雜訊選法優於Goel和Negi之選法，尤其當合法接收端通道品質相對於竊聽者通道非常差時。利用我們所提出之人工雜訊選擇方式，傳輸速度非零之區域將被放大，此性質可用於改善安全網路的可連通性。

In this thesis we consider the secure transmission in fading channels with only the statistics of the eavesdropper’s channel state information known at the transmitter. We optimize the celebrated artificial-noise (AN) assisted beamforming, which was studied by Goel and Negi using heuristically selected AN and beamforming directions. We find that Goel and Negi’s AN selection is strictly sub-optimal. On the contrary, one may inject AN to the beam direction of the message to improve the secrecy rate performance. We prove that for a multiple-input, single-output, single-eavesdropper antenna system, the optimal transmission scheme is a beamformer. With the selected beamformer in the direction of main channel, we then prove that for the AN projecting in the null space of the legitimate channel, uniformly allocating power is optimal. We also provide the necessary condition for the proposed AN selection to be optimal. Simulation results show that our AN selection outperforms Goel and Negi’s, especially when the legitimate channel is poor. In particular, the regime with non-zero secrecy rate is enlarged, which can significantly improve the connectivity of the secure network when the AN assisted beamforming is applied.

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Chapters:
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Cryptography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 CDMA and frequency hopping techniques . . . . . . . . . . . . . . . . 2
1.3 Information theoretic security . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.5 Fading Wiretap Channel . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.6 Channels with side information . . . . . . . . . . . . . . . . . . . . . . 8
1.7 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2. System model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1 Secrecy Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 The analysis of the proposed signaling . . . . . . . . . . . . . . . . . . . 15
2.4 The necessary condition for the covariance matrix of AN to be full rank . 23
2.5 The iterative algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.6 Asymptotic analysis under high SNR . . . . . . . . . . . . . . . . . . . 34
2.7 Asymptotic analysis of large nT . . . . . . . . . . . . . . . . . . . . . . 36
3. MIMOSE system model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.1 The analysis of the proposed signaling for MIMOSE . . . . . . . . . . . 39
3.2 The suboptimal signaling by singular value decomposition . . . . . . . . 41
4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.1 The performance analysis with additional GPC . . . . . . . . . . . . . . 43
4.2 Both the legitimate receiver’s and the eavesdropper’s channels are fading 45
5. Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Appendices:
A. Simplification of I(U;Z|G) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
B. Proof of Theorem 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

[1] M. Abramowitz and I. A. Stegun. Handbook of Mathematical Functions with For-
mulas, Graphs, and Mathematical Tables. Dover, New York, 9th printing edition,
1972.
[2] S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press,
2004.
[3] M. H. M. Costa. Writing on dirty paper (corresp.). IEEE Trans. Inform. Theory,
29(3):439–441, May. 1983.
[4] I. Csisz′ar and J. K‥orner. Broadcast channels with confidential messages. IEEE Trans.
Inform. Theory, 24(3):339–348, May. 1978.
[5] S. I. Gelfand and M. S. Pinsker. Coding for channel with random parameters. Prob-
lems of control and information theory, 9(1):19–31, 1980.
[6] S. Goel and R. Negi. Guaranteeing secrecy using artificial noise. IEEE Trans.Wireless
Commun., 7(6):2180–2189, Jun. 2008.
[7] P. K. Gopala, L. Lai, and H. El-Gamal. On the secrecy capacity of fading channels.
IEEE Trans. Inform. Theory, 54(10):4687–4698, Oct. 2008.
[8] M. T. Heath. Scientific computing: an introductory survey. McGraw-Hill, New York,
2002.
[9] R. A. Horn and C. R. Johnson. Matrix analysis. Cambridge university press, Cam-
bridge, UK, 1985.
[10] A. V. Kusnetsov and B. S. Tsybakov. Coding in a memory with defective cells. Probl.
Pered. Inform., 10(2):53–60, Apr.-Jun. 1974.
[11] S. K. Leung-Yan-Cheong and M. E. Hellman. The gaussian wire-tap channel. IEEE
Trans. Inform. Theory, 24(4):451–456, Jul. 1978.
[12] J. Li and A. Petropulu. Transmitter optimization for achieving secrecy capacity in
gaussian mimo wiretap channels. http://arxiv.org/abs/0909.2622, Sep. 2009.
[13] J. Li and A. Petropulu. On ergodic secrecy rate for gaussian miso wiretap channels.
IEEE Trans. Wireless Commun., 10(4):1176 –1187, April 2011.
[14] Z. Li, R. Yates, and W. Trappe. Secret communication with a fading eavesdropper
channel. In Information Theory, 2007. ISIT 2007. IEEE International Symposium on,
pages 1296–1300, Jun. 2007.
[15] Z. Li, R. Yates, and W. Trappe. Achieving secret communication for fast rayleigh
fading channels. IEEE Trans. Wireless Commun., 9(9):2792–2799, Sep. 2010.
[16] Z. Li, R. D. Yates, andW. Trappe. Secrecy capacity of independent parallel channels.
In 44th Annual Allerton Conference on Communications, Control and Computing,
Sep. 2006.
[17] Y. Liang, H. V. Poor, and S. Shamai. Secure communication over fading channels.
IEEE Trans. Inform. Theory, 54(6):2470–2492, Jun. 2008.
[18] S. C. Lin, T. H. Chang, Y. L. Liang, Y. P. Hong, and C. Y. Chi. On the impact of
quantized channel feedback in guaranteeing secrecy with artificial noise: The noise
leakage problem. IEEE Trans. Wireless Commun., 10(3):901–915, Mar. 2011.
[19] C. Mitrpant, A.J.H. Vinck, and Y. Luo. An achievable region for the gaussian wiretap
channel with side information. IEEE Trans. Inform. Theory, 52(5):2181 –2190, May.
2006.
[20] R. L. Rivest, A. Shamir, and L. Adleman. A method for obtaining digital signatures
and public-key cryptosystems. Commun. ACM, 21:120–126, Feb. 1978.
[21] C. E. Shannon. Communication theory of secrecy systems. B.S.T.J, 28(4):656–715,
Oct. 1949.
[22] C. E. Shannon. Channels with side information at the transmitter. IBM J. Res. Devel.,
2:289–293, 1958.
[23] P. W. Shor. Polynomial-time algorithms for prime factorization and discrete loga-
rithms on a quantum computer. SIAM J.SCI.STATIST.COMPUT., 26:1484, 1997.
[24] A. D. Wyner. The wire-tap channel. Bell. Syst. Tech. J., 54(8):1355–1387, Jan. 1975.