Abstract
This paper considers a two-user multiple-input single-output (MISO) interference channel with confidential messages (IFC-CM), where the beamforming vectors at the two transmitters are jointly optimized using the closed-form Pareto-optimal parameterization. We prove that artificial noise cannot improve the secrecy rate performance, and coordinated beamforming is secrecy-rate optimal which is achieved by agreeing on the parameters between the two transmitters. We analyze the feasible set of the beamforming parameters that guarantees positiveness of the secrecy rates when the transmitters know only statistical CSI, and then analysis in the ergodic secrecy rate region is discussed. More importantly, we derive the closed form of the ergodic secrecy rates and illustrate the Pareto-optimal structure of the beamforming vectors.
摘要
本文考虑两用户多输入单输出的带有安全信息的干扰信道, 采用闭式帕累托最优参数法来联合优化发送端的波束成形向量。 其次, 证明加入人为噪声不能提高安全速率, 且对发送端参数的一致性调整可获得协作波束成形的最优安全速率。 当发送端已知信道的统计信息时, 通过分析波束成形参数的可行集来保证安全速率的正定性, 进而得到遍历安全速率域。 最后, 提出遍历安全速率的闭式解, 并阐明波束成形向量的帕累托最优解的结构。
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References
Wyner A D. The wire-tap channel. Bell Syst Tech J, 1975, 54: 1355–1387
Leung-Yan-Cheong S, Hellman M E. The Gaussian wire-tap channel. IEEE Trans Inf Theory, 1978, 24: 451–456
Csiszár I, Korner J. Broadcast channels with confidential messages. IEEE Trans Inf Theory, 1978, 24: 339–348
Cui Q, Huang X Q, Luo B, et al. Capacity analysis and optimal power allocation for coordinated transmission in MIMO-OFDM systems. Sci China Inf Sci, 2012, 55: 1372–1387
Shu F, Berber S, Wang D M, et al. ML integer frequency offset estimation for OFDM systems with null subcarriers: estimation range and pilot design. Sci China Inf Sci, 2010, 53: 2567–2575
You X, Wang D, Zhu P, et al. Cell edge performance of cellular mobile systems. IEEE J Sel Area Comm, 2011, 29: 1139–1150
Xu X D, Wang D, Tao X F, et al. Resource pooling for frameless network architecture with adaptive resource allocation. Sci China Inf Sci, 2013, 56: 83–94
Zhang Z, Long K, Wang J. Self-organization paradigms and optimization approaches for cognitive radio technologies: a survey. IEEE Wirel Commun, 2013, 20: 36–42
Wang D, Ji C, Sun S, et al. Spectral efficiency of multi-cell multi-user DAS with pilot contamination. In: Proceedings of Wireless Communications and Networking Conference (WCNC), Shanghai, 2013. 3208–3212
Goel S, Negi R. Guaranteeing secrecy using artificial noise. IEEE Trans Wirel Commun, 2008, 7: 2180–2189
Pei M, Wei J, Wong K K, et al. Masked beamforming for multiuser MIMO wiretap channels with imperfect CSI. IEEE Trans Wirel Commun, 2012, 11: 544–549
Khisti A, Wornell G W. Secure transmission with multiple antennas I: the MISOME wiretap channel. IEEE Trans Inf Theory, 2010, 56: 3088–3104
Lai L, El Gamal H. The relay-eavesdropper channel: cooperation for secrecy. IEEE Trans Inf Theory, 2008, 54: 4005–4019
Zheng G, Choo L C, Wong K K. Optimal cooperative jamming to enhance physical layer security using relays. IEEE Trans Signal Process, 2011, 59: 1317–1322
He X, Yener A. Cooperation with an untrusted relay: a secrecy perspective. IEEE Trans Inf Theory, 2010, 56: 3807–3827
Liu R, Maric I, Spasojevic P, et al. Discrete memoryless interference and broadcast channels with confidential messages: secrecy rate regions. IEEE Trans Inf Theory, 2008, 54: 2493–2507
Li Z, Yates R D, Trappe W. Secrecy capacity region of a class of one-sided interference channel. In: Proceedings of IEEE International Symposium on Information Theory, Toronto, 2008. 379–383
Koyluoglu O O, El Gamal H, Lai L, et al. Interference alignment for secrecy. IEEE Trans Inf Theory, 2011, 57: 3323–3332
He X, Yener A. The Gaussian many-to-one interference channel with confidential messages. IEEE Trans Inf Theory, 2011, 57: 2730–2745
Zhu J, Mo J, Tao M. Cooperative secret communication with artificial noise in symmetric interference channel. IEEE Commun lett, 2010, 14: 885–887
Jorswieck E A, Mochaourab R. Secrecy rate region of MISO interference channel: Pareto boundary and non-cooperative games. In: Proceedings of International ITG Workshop on Smart Antennas, Berlin, 2009
Jorswieck E A, Larsson E G, Danev D. Complete characterization of the Pareto boundary for the MISO interference channel. IEEE Trans Signal Process, 2008, 56: 640–649
Fakoorian S A A, Swindlehurst A L. MIMO interference channel with confidential messages: achievable secrecy rates and precoder design. IEEE Trans Inf Foren Sec, 2011, 6: 640–649
Xing C, Ma S, Wu Y C. Robust joint design of linear relay precoder and destination equalizer for dual-hop amplifyand-forward MIMO relay systems. IEEE Trans Signal Process, 2010, 58: 2273–2283
Zhang Z S, Huang F W, Long K P, et al. On the designing principles and optimization approaches of bio-inspired self-organized network: a survey. Sci China Inf Sci, 2013, 56: 1–28
Vishwanath S, Jindal N, Goldsmith A. Duality, achievable rates, and sum-rate capacity of gaussian MIMO broadcast channels. IEEE Trans Inf Theory, 2003, 49: 2658–2668
Lindblom J, Karipidis E, Larsson E G. Closed-form parameterization of the Pareto boundary for the two-user MISO interference channel. In: Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, Prague, 2011. 3372–3375
Lindblom J, Larsson E G, Jorswieck E A. Parametrization of the MISO IFC rate region: the case of partial channel state information. IEEE Trans Wirel Commun, 2010, 9: 500–504
Lindblom J, Karipidis E, Larsson E G. Selfishness and altruism on the MISO interference channel: the case of partial transmitter CSI. IEEE Commun Lett, 2009, 13: 667–669
Mallik R K, Win M Z, Shao J W, et al. Channel capacity of adaptive transmission with maximal ratio combining in correlated Rayleigh fading. IEEE Trans Wirel Commun, 2004, 3: 1124–1133
Abramowitz M, Stegun I A. Handbook of mathematical functions with formulas, graphs, and mathematical tables. Appl Math, 1972
Ding M, Zhang Q T. Stochastic precoding for MISO interference channels with channel mean feedback. IEEE Trans Commun, 2012, 60: 1082–1090
Lindblom J, Larsson E G, Jorswieck E A. Parameterization of the MISO interference channel with transmit beamforming and partial channel state information. In: Proceedings of Asilomar Conference on Signals, Systems Computers, Pacific Grove, 2008. 1103–1107
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Fei, Z., Ni, J., Zhao, D. et al. Ergodic secrecy rate of two-user MISO interference channels with statistical CSI. Sci. China Inf. Sci. 57, 1–14 (2014). https://doi.org/10.1007/s11432-014-5098-4
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DOI: https://doi.org/10.1007/s11432-014-5098-4