20 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
Algorithms for Globally-Optimal Secure Signaling over Gaussian MIMO Wiretap Channels Under Interference Constraints
Multi-user Gaussian MIMO wiretap channel is considered under interference
power constraints (IPC), in addition to the total transmit power constraint
(TPC). Algorithms for \textit{global} maximization of its secrecy rate are
proposed. Their convergence to the secrecy capacity is rigorously proved and a
number of properties are established analytically. Unlike known algorithms, the
proposed ones are not limited to the MISO case and are proved to converge to a
\textit{global} rather than local optimum in the general MIMO case, even when
the channel is not degraded. In practice, the convergence is fast as only a
small to moderate number of Newton steps is required to achieve a high
precision level. The interplay of TPC and IPC is shown to result in an unusual
property when an optimal point of the max-min problem does not provide an
optimal transmit covariance matrix in some (singular) cases. To address this
issue, an algorithm is developed to compute an optimal transmit covariance
matrix in those singular cases. It is shown that this algorithm also solves the
dual (nonconvex) problems of \textit{globally} minimizing the total transmit
power subject to the secrecy and interference constraints; it provides the
minimum transmit power and respective signaling strategy needed to achieve the
secrecy capacity, hence allowing power savings.Comment: accepted for publicatio
Solutions for the MIMO Gaussian Wiretap Channel with a Cooperative Jammer
We study the Gaussian MIMO wiretap channel with a transmitter, a legitimate
receiver, an eavesdropper and an external helper, each equipped with multiple
antennas. The transmitter sends confidential messages to its intended receiver,
while the helper transmits jamming signals independent of the source message to
confuse the eavesdropper. The jamming signal is assumed to be treated as noise
at both the intended receiver and the eavesdropper. We obtain a closed-form
expression for the structure of the artificial noise covariance matrix that
guarantees no decrease in the secrecy capacity of the wiretap channel. We also
describe how to find specific realizations of this covariance matrix expression
that provide good secrecy rate performance, even when there is no non-trivial
null space between the helper and the intended receiver. Unlike prior work, our
approach considers the general MIMO case, and is not restricted to SISO or MISO
scenarios