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IEEE Asia-Pacific Conference on Antennas and Propagation

Iterative precoding for MIMO wiretap channels using successive convex approximation

Bing Fang, Zuping Qian, Zhong Wei, Wei Shao

Published Jun 1, 2015• 10 citations
Publisher

Abstract

In this paper, we study the precoding problem for physical layer security in a general multiple-input multiple-output (MIMO) wiretap channel. Since the resultant secrecy capacity maximization (SCM) problem is nonconvex in general, we solve it by employing a successive convex approximation method, where the nonconvex part of the formulated problem is approximated by its first-order Taylor expansion. Thus, the SCM problem can be iteratively solved through convex programming of its convexified version. Finally, an iterative precoding algorithm with provable convergence is presented. Numerical simulations are also provided to verify the proposed algorithm.

DOI
10.1109/apcap.2015.7374273

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In this paper, we study the precoding problem for physical layer security in a general multiple-input multiple-output (MIMO) wiretap channel. Since the resultant secrecy capacity maximization (SCM) problem is nonconvex in general, we solve it by employing a successive convex approximation method, where the nonconvex part of the formulated problem is approximated by its first-order Taylor expansion. Thus, the SCM problem can be iteratively solved through convex programming of its convexified version. Finally, an iterative precoding algorithm with provable convergence is presented. Numerical simulations are also provided to verify the proposed algorithm.
In this paper, we study the energy-efficient secrecy precoding problem for a general multiple-input multiple-output multiple-eavesdropper (MIMOME) wiretap channel. The system model considered here consists of a common transmitter, a legitimate receiver, and multiple eavesdroppers, all mounted with multiple antennas. In order to improve the energy efficiency (EE) performance of the proposed system, an artificial noise (AN)-aided precoding scheme is adopted. Because the formulated EE maximization problem is of huge nonconvex complexity, we solve it by employing a two-tier optimization structure. Although the outer-tier optimization problem is quite simple and can be efficiently solved by the famous golden section searching method, the inner-tier optimization problem turns out to be nonconvex and cannot be easily solved. To solve it, we relax it to a secrecy rate maximization (SRM) problem, which naturally constitutes a difference convex (DC)-type programming problem and can be iteratively solved by employing a successive convex approximation (SCA) method. Numerical simulations are further provided to demonstrate the proposed algorithms. Results show that our algorithms can converge fast to a near-optimal solution.
In this paper, we study the precoder design problem for secrecy rate maximization in a decode-and-forward (DF)-based multiple-input multiple-output (MIMO) relay network. The system model considered here consists of a source, a trusted relay, a legitimate receiver and an eavesdropper, all mounted with multiple antennas. Our objective is to maximize the achievable secrecy rate of this DF-based MIMO relay wiretap system subject to a total transmit power constraint. Since the formulated secrecy rate maximization (SRM) problem is nonconvex in general, we solve it by employing a successive convex approximation (SCA) method. With the SCA method, the nonconvex part of the formulated problem is linearized to its first-order Taylor expansion. Then, the nonconvex SRM problem can be iteratively solved through successive convex programming of its convexified version, and thus an iterative precoding algorithm is developed. Moreover, the theoretical result is further extended to the case when multiple eavesdroppers are simultaneously present. Finally, numerical simulations are provided to evaluate the performance of the proposed algorithm. Results show that our algorithm can converge fast to a near-optimal solution.
In this letter, we study energy-efficient precoder design in a three-node MIMO wiretap channel. Different from previous works in this area that mainly focus on secrecy rate maximization or power minimization problems, here, we aim to maximize the energy efficiency (EE) of the system subject to the secret rate and transmit power constraints, which is a nonconvex optimization and hard to tackle. To solve it, we first transform it into an equivalent parameterized polynomial subtractive form and then approximate the nonconvex equivalent problem into a convex optimization problem by means of Taylor series expansion. Based on that, an iterative algorithm with proved convergence is proposed, and this algorithm is also extended to an imperfect-channel-state-information case. Numerical results show that the proposed algorithm outperforms traditional design methods in terms of EE.
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.
In this letter, we study the secrecy precoding problem for simultaneous wireless information and power transfer (SWIPT) in a cognitive multiple-input multiple-output (MIMO) broadcast channel. We adopt an artificial noise (AN)-aided precoding scheme and formulate the problem as a secrecy rate maximization (SRM) problem, which is subject to both an interference power constraint imposed to protect the primary user (PU) and an energy harvesting constraint required by the secondary energy receiver (SER). Since the formulated SRM problem constitutes a difference convex (DC)-type programming problem, we solve it by employing a successive convex approximation (SCA) method. With the SCA method, the nonconvex part of the SRM problem can be locally linearized to its first-order Taylor expansion. Then, relying on solving a series of convexified optimization problems, an iterative precoding algorithm is developed. Numerical simulations are also provided to demonstrate the proposed algorithm. Results show that our algorithm can achieve a near-optimal performance with guaranteed convergence.