178 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
Transmit design for MIMO wiretap channel with a malicious jammer
In this paper, we consider the transmit design for multi-input multi-output
(MIMO) wiretap channel including a malicious jammer. We first transform the
system model into the traditional three-node wiretap channel by whitening the
interference at the legitimate user. Additionally, the eavesdropper channel
state information (ECSI) may be fully or statistically known, even unknown to
the transmitter. Hence, some strategies are proposed in terms of different
levels of ECSI available to the transmitter in our paper. For the case of
unknown ECSI, a target rate for the legitimate user is first specified. And
then an inverse water-filling algorithm is put forward to find the optimal
power allocation for each information symbol, with a stepwise search being used
to adjust the spatial dimension allocated to artificial noise (AN) such that
the target rate is achievable. As for the case of statistical ECSI, several
simulated channels are randomly generated according to the distribution of
ECSI. We show that the ergodic secrecy capacity can be approximated as the
average secrecy capacity of these simulated channels. Through maximizing this
average secrecy capacity, we can obtain a feasible power and spatial dimension
allocation scheme by using one dimension search. Finally, numerical results
reveal the effectiveness and computational efficiency of our algorithms.Comment: 2015 IEEE 81st Vehicular Technology Conference (VTC Spring
On the Secrecy Capacity of MIMO Wiretap Channels: Convex Reformulation and Efficient Numerical Methods
This paper presents novel numerical approaches to finding the secrecy
capacity of the multiple-input multiple-output (MIMO) wiretap channel subject
to multiple linear transmit covariance constraints, including sum power
constraint, per antenna power constraints and interference power constraint. An
analytical solution to this problem is not known and existing numerical
solutions suffer from slow convergence rate and/or high per-iteration
complexity. Deriving computationally efficient solutions to the secrecy
capacity problem is challenging since the secrecy rate is expressed as a
difference of convex functions (DC) of the transmit covariance matrix, for
which its convexity is only known for some special cases. In this paper we
propose two low-complexity methods to compute the secrecy capacity along with a
convex reformulation for degraded channels. In the first method we capitalize
on the accelerated DC algorithm which requires solving a sequence of convex
subproblems, for which we propose an efficient iterative algorithm where each
iteration admits a closed-form solution. In the second method, we rely on the
concave-convex equivalent reformulation of the secrecy capacity problem which
allows us to derive the so-called partial best response algorithm to obtain an
optimal solution. Notably, each iteration of the second method can also be done
in closed form. The simulation results demonstrate a faster convergence rate of
our methods compared to other known solutions. We carry out extensive numerical
experiments to evaluate the impact of various parameters on the achieved
secrecy capacity
On the Interference Alignment Designs for Secure Multiuser MIMO Systems
In this paper, we propose two secure multiuser multiple-input multiple-output
transmission approaches based on interference alignment (IA) in the presence of
an eavesdropper. To deal with the information leakage to the eavesdropper as
well as the interference signals from undesired transmitters (Txs) at desired
receivers (Rxs), our approaches aim to design the transmit precoding and
receive subspace matrices to minimize both the total inter-main-link
interference and the wiretapped signals (WSs). The first proposed IA scheme
focuses on aligning the WSs into proper subspaces while the second one imposes
a new structure on the precoding matrices to force the WSs to zero. When the
channel state information is perfectly known at all Txs, in each proposed IA
scheme, the precoding matrices at Txs and the receive subspaces at Rxs or the
eavesdropper are alternatively selected to minimize the cost function of an
convex optimization problem for every iteration. We provide the feasible
conditions and the proofs of convergence for both IA approaches. The simulation
results indicate that our two IA approaches outperform the conventional IA
algorithm in terms of average secrecy sum rate.Comment: Updated version, updated author list, accepted to be appear in IEICE
Transaction
Outage Constrained Robust Secure Transmission for MISO Wiretap Channels
In this paper we consider the robust secure beamformer design for MISO
wiretap channels. Assume that the eavesdroppers' channels are only partially
available at the transmitter, we seek to maximize the secrecy rate under the
transmit power and secrecy rate outage probability constraint. The outage
probability constraint requires that the secrecy rate exceeds certain threshold
with high probability. Therefore including such constraint in the design
naturally ensures the desired robustness. Unfortunately, the presence of the
probabilistic constraints makes the problem non-convex and hence difficult to
solve. In this paper, we investigate the outage probability constrained secrecy
rate maximization problem using a novel two-step approach. Under a wide range
of uncertainty models, our developed algorithms can obtain high-quality
solutions, sometimes even exact global solutions, for the robust secure
beamformer design problem. Simulation results are presented to verify the
effectiveness and robustness of the proposed algorithms
Physical Layer Service Integration in 5G: Potentials and Challenges
High transmission rate and secure communication have been identified as the
key targets that need to be effectively addressed by fifth generation (5G)
wireless systems. In this context, the concept of physical-layer security
becomes attractive, as it can establish perfect security using only the
characteristics of wireless medium. Nonetheless, to further increase the
spectral efficiency, an emerging concept, termed physical-layer service
integration (PHY-SI), has been recognized as an effective means. Its basic idea
is to combine multiple coexisting services, i.e., multicast/broadcast service
and confidential service, into one integral service for one-time transmission
at the transmitter side. This article first provides a tutorial on typical
PHY-SI models. Furthermore, we propose some state-of-the-art solutions to
improve the overall performance of PHY-SI in certain important communication
scenarios. In particular, we highlight the extension of several concepts
borrowed from conventional single-service communications, such as artificial
noise (AN), eigenmode transmission etc., to the scenario of PHY-SI. These
techniques are shown to be effective in the design of reliable and robust
PHY-SI schemes. Finally, several potential research directions are identified
for future work.Comment: 12 pages, 7 figure
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