Optimal power allocation for achieving perfect secrecy capacity in MIMO wire-tap channels

In this paper, we investigate optimal power allocation to achieve perfect secrecy capacity in Gaussian MIMO wire-tap channels. The number of antennas in the MIMO wire-tap channel is arbitrary at the transmitter, the intended receiver, and the eavesdropper. For this challenging non-convex optimization problem, we design a novel global optimization algorithm called branch-and-bound with reformulation and linearization technique (BB/RLT). As opposed to convex programming methods that only yield local optimal solutions, our proposed BB/RLT method guarantees finding a global optimal solution. The main contribution in this paper is that our proposed BB/RLT algorithm is the first method that solves the optimal power allocation problem for achieving perfect secrecy capacity problem in MIMO wire-tap channels. Numerical examples are also given to demonstrate the efficacy of the proposed algorithm.

[1]  Frédérique E. Oggier,et al.  The secrecy capacity of the MIMO wiretap channel , 2007, 2008 IEEE International Symposium on Information Theory.

[2]  Martin E. Hellman,et al.  The Gaussian wire-tap channel , 1978, IEEE Trans. Inf. Theory.

[3]  Roy D. Yates,et al.  The Discrete Memoryless Multiple Access Channel with Confidential Messages , 2006, 2006 IEEE International Symposium on Information Theory.

[4]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[5]  A. D. Wyner,et al.  The wire-tap channel , 1975, The Bell System Technical Journal.

[6]  Sennur Ulukus,et al.  Achievable Rates in Gaussian MISO Channels with Secrecy Constraints , 2007, 2007 IEEE International Symposium on Information Theory.

[7]  Rohit Negi,et al.  Guaranteeing Secrecy using Artificial Noise , 2008, IEEE Transactions on Wireless Communications.

[8]  Warren P. Adams,et al.  A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems , 1998 .

[9]  Roy D. Yates,et al.  Secret Communication via Multi-antenna Transmission , 2007, 2007 41st Annual Conference on Information Sciences and Systems.

[10]  Ender Tekin,et al.  The General Gaussian Multiple-Access and Two-Way Wiretap Channels: Achievable Rates and Cooperative Jamming , 2007, IEEE Transactions on Information Theory.

[11]  Ender Tekin,et al.  Achievable Rates for the General Gaussian Multiple Access Wire-Tap Channel with Collective Secrecy , 2006, ArXiv.

[12]  H. Vincent Poor,et al.  Multiple-Access Channels With Confidential Messages , 2008, IEEE Transactions on Information Theory.

[13]  Alfred O. Hero,et al.  Secure space-time communication , 2003, IEEE Trans. Inf. Theory.

[14]  Imre Csiszár,et al.  Broadcast channels with confidential messages , 1978, IEEE Trans. Inf. Theory.