3 research outputs found
An Algorithm for Global Maximization of Secrecy Rates in Gaussian MIMO Wiretap Channels
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 \textit{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.Comment: accepted by IEEE Transactions on Communication