A Low-Complexity Algorithm for Achieving Secrecy Capacity in MIMO Wiretap Channels

Abstract

We consider a secure transmission including a transmitter, a receiver and an eavesdropper, each being equipped with multiple antennas. The aim is to develop a low-complexity and scalable method to find a globally optimal solution to the problem of secrecy rate maximization under a total power constraint at the transmitter. In principle, the original formulation of the problem is nonconvex. However, it can be equivalently translated into finding a saddle point of a minimax convex-concave program. An existing approach finds the saddle point using the Newton method, whose computational cost increases quickly with the number of transmit antennas, making it unsuitable for large scale antenna systems. To this end, we propose an iterative algorithm based on alternating optimization, which is guaranteed to converge to a saddle point, and thus achieves a globally optimal solution to the considered problem. In particular, each subproblem of the proposed iterative method admits a closedform solution. We analytically show that the iteration cost of our proposed method is much cheaper than that of the known solution. As a result, numerical results demonstrate that the proposed method remarkably outperforms the existing one in terms of the overall run time.

Efficient Numerical Methods for Secrecy Capacity of Gaussian MIMO Wiretap Channel

“…For Algorithm 2 we plot the objective f (Q n , X n ) in ( 4). We also plot the convergence of the outer loop of [11,Algorithm 2] for comparison. It is clearly seen that the proposed algorithms converge very fast and all algorithms converge to the same objective.…”

“…Update Q n+1 according to (14) 5: end for 6: Output: X n We remark that the iterative method presented in [11] also aims to find the saddle-point of (4). However, it is a doubleloop algorithm where a lower bound of f (Q n , X) is used for the X-update.…”

“…Power minimization and secrecy rate maximization for MIMO WTC was studied in [10] using a difference of convex functions algorithm (DCA). More recently, a lowcomplex solution for Gaussian MIMO WTC was proposed in [11] using the equivalent convex-concave reformulation of the secrecy capacity problem.…”

“…The idea of PBRA is to find a saddle point of the concave-convex problem, for which efficient numerical methods are also derived. We remark that the method presented in [11] is a double-loop iterative algorithm, while the proposed PBRA in this paper only requires a single loop.…”

Achievable Physical-Layer Secrecy in Multi-Mode Fiber Channels using Artificial Noise

“…where the step from ( 15) to ( 16) is done using Jensen's inequality. Solving for Q, based on [19], in (16) will result in a more "pessimistic" ergodic secrecy rate.…”