DocumentCode :
31586
Title :
An Algorithm for Global Maximization of Secrecy Rates in Gaussian MIMO Wiretap Channels
Author :
Loyka, Sergey ; Charalambous, Charalambos D.
Author_Institution :
Sch. of Electr. Eng. & Comput. Sci., Univ. of Ottawa, Ottawa, ON, Canada
Volume :
63
Issue :
6
fYear :
2015
fDate :
Jun-15
Firstpage :
2288
Lastpage :
2299
Abstract :
Optimal signaling for secrecy rate maximization in Gaussian MIMO wiretap channels is considered. While this channel has attracted a significant attention recently and a number of results have been obtained, including the proof of the optimality of Gaussian signalling, an optimal transmit covariance matrix is known for some special cases only and the general case remains an open problem. An iterative custom-made algorithm to find a globally-optimal transmit covariance matrix in the general case is developed in this paper, with guaranteed convergence to a global optimum. While the original optimization problem is not convex and hence difficult to solve, its minimax reformulation can be solved via the convex optimization tools, which is exploited here. The proposed algorithm is based on the barrier method extended to deal with a minimax problem at hand. Its convergence to a global optimum is proved for the general case (degraded or not) and a bound for the optimality gap is given for each step of the barrier method. The performance of the algorithm is demonstrated via numerical examples. In particular, 20 to 40 Newton steps are already sufficient to solve the sufficient optimality conditions with very high precision (up to the machine precision level), even for large systems. Even fewer steps are required if the secrecy capacity is the only quantity of interest. The algorithm can be significantly simplified for the degraded channel case and can also be adopted to include the per-antenna power constraints (instead or in addition to the total power constraint). It also solves the dual problem of minimizing the total power subject to the secrecy rate constraint.
Keywords :
Gaussian channels; MIMO communication; Newton method; convex programming; covariance matrices; minimax techniques; wireless channels; Gaussian MIMO wiretap channel; Newton method; convex optimization tool; globally-optimal transmit covariance matrix; iterative custom-made algorithm; minimax reformulation; optimal Gaussian signaling; per-antenna power constraint; secrecy rate maximization; Convergence; Covariance matrices; MIMO; Newton method; Optimization; Receivers; Signal to noise ratio; MIMO; optimization; secrecy capacity; wiretap channel;
fLanguage :
English
Journal_Title :
Communications, IEEE Transactions on
Publisher :
ieee
ISSN :
0090-6778
Type :
jour
DOI :
10.1109/TCOMM.2015.2424235
Filename :
7088600
Link To Document :
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