Secrecy capacity of single- and multi-antenna channels with simple helpers

Secrecy can be achieved on the physical layer in fading channels by smart resource allocation and transmit optimization. In this work, simple helper nodes creating artificial noise are applied to improve the secrecy of a point-to-point link. In the single-antenna case, the channel parameters and SNR determine whether a helper can increase the secrecy capacity. We derive a necessary and sufficient condition for optimality of a helper. The single-antenna helper provides only limited support for the single-antenna link. Therefore, we compute the optimal beamforming vectors of the transmitter in closed form for the multiple antenna link under ideal assumption of perfectly informed transmitters. The optimal beamforming vectors of the helpers are characterized and an algorithm is proposed which jointly optimizes transmitter and helper beamformers. It is shown that with increasing number of helpers the secrecy capacity approaches the capacity of the peaceful multiple-antenna link without secrecy constraints. Finally, numerical simulations illustrate the secrecy capacity gain by these simple helpers.Secrecy can be achieved on the physical layer in fading channels by smart resource allocation and transmit optimization. In this work, simple helper nodes creating artificial noise are applied to improve the secrecy of a point-to-point link. In the single-antenna case, the channel parameters and SNR determine whether a helper can increase the secrecy capacity. We derive a necessary and sufficient condition for optimality of a helper. The single-antenna helper provides only limited support for the single-antenna link. Therefore, we compute the optimal beamforming vectors of the transmitter in closed form for the multiple antenna link under ideal assumption of perfectly informed transmitters. The optimal beamforming vectors of the helpers are characterized and an algorithm is proposed which jointly optimizes transmitter and helper beamformers. It is shown that with increasing number of helpers the secrecy capacity approaches the capacity of the peaceful multiple-antenna link without secrecy constraints. Finally, numerical simulations illustrate the secrecy capacity gain by these simple helpers.

Apr 15, 201028 citations

Secrecy Capacity of a Class of Broadcast Channels with an Eavesdropper

Ersen Ekrem, Şennur Ulukuş

Jan 1, 20091 citation

Secrecy Capacity of Independent Parallel Channels

Zang Li, Roy D. Yates, Wade K. Trappe

Springer eBooksJan 1, 2009173 citations

On the Secrecy Capacity of a MIMO Gaussian Wiretap Channel with a Cooperative Jammer

Lingxiang Li, Zhi Chen, Jun Fang +1 more

We study the secrecy capacity of a helper-assisted Gaussian wiretap channel with a source, a legitimate receiver, an eavesdropper and an external helper, where each terminal is equipped with multiple antennas. Determining the secrecy capacity in this scenario generally requires solving a nonconvex secrecy rate maximization (SRM) problem. To deal with this issue, we first reformulate the original SRM problem into a sequence of convex subproblems. For the special case of single-antenna legitimate receiver, we obtain the secrecy capacity via a combination of convex optimization and one-dimensional search, while for the general case of multi-antenna legitimate receiver, we propose an iterative solution. To gain more insight into how the secrecy capacity of a helper-assisted Gaussian wiretap channel behaves, we examine the achievable secure degrees of freedom (s.d.o.f.) and obtain the maximal achievable s.d.o.f. in closed-form. We also derive a closed-form solution to the original SRM problem which achieves the maximal s.d.o.f.. Numerical results are presented to illustrate the efficacy of the proposed schemes.We study the secrecy capacity of a helper-assisted Gaussian wiretap channel with a source, a legitimate receiver, an eavesdropper and an external helper, where each terminal is equipped with multiple antennas. Determining the secrecy capacity in this scenario generally requires solving a nonconvex secrecy rate maximization (SRM) problem. To deal with this issue, we first reformulate the original SRM problem into a sequence of convex subproblems. For the special case of single-antenna legitimate receiver, we obtain the secrecy capacity via a combination of convex optimization and one-dimensional search, while for the general case of multi-antenna legitimate receiver, we propose an iterative solution. To gain more insight into how the secrecy capacity of a helper-assisted Gaussian wiretap channel behaves, we examine the achievable secure degrees of freedom (s.d.o.f.) and obtain the maximal achievable s.d.o.f. in closed-form. We also derive a closed-form solution to the original SRM problem which achieves the maximal s.d.o.f.. Numerical results are presented to illustrate the efficacy of the proposed schemes.

arXiv:1509.04624Sep 15, 20152 citations

Secrecy-Enhancing Channel Estimation in Multi-Antenna Wireless Systems

Y.-W. Peter Hong, Pang-Chang Lan, C.‐C. Jay Kuo

Springer briefs in electrical and computer engineeringSep 26, 20130 citations

On Secrecy Capacity of the Helper-Assisted Gaussian Wiretap Channel with Multi-Antennas

Lingxiang Li, Zhi Chen, Duo Zhang +1 more

We investigate the secrecy capacity of Gaussian wiretap channel with a source, an external helper, an eavesdropper and a single-antenna legitimate receiver where the former three terminals are equipped with $N_a$ , $N_j$ and $N_e$ antennas, respectively. Generally, an analytical form of the secrecy capacity in this scenario is difficult to obtain. Instead, we recast the original nonconvex secrecy rate maximization (SRM) problem into a sequence of convex optimization problems. In doing so, the secrecy capacity can be obtained using a combination of convex optimization and a one-dimensional search. On the other hand, to gain more insight into how the secrecy capacity behaves, we study the secure degrees of freedom (s.d.o.f.) and quantify its connection with system parameters, where our result proves that the s.d.o.f. equal to 1 can be achieved if and only if N_e<N_a+N_j-1. As a by-product, we give a suboptimal but closed-form solution to the original SRM problem for the scenario where N_e<N_a+N_j-1.Numerical results are presented to validate the theoretical findings and illustrate the efficacy of the proposed schemes.We investigate the secrecy capacity of Gaussian wiretap channel with a source, an external helper, an eavesdropper and a single-antenna legitimate receiver where the former three terminals are equipped with $N_a$, $N_j$ and $N_e$ antennas, respectively. Generally, an analytical form of the secrecy capacity in this scenario is difficult to obtain. Instead, we recast the original nonconvex secrecy rate maximization (SRM) problem into a sequence of convex optimization problems. In doing so, the secrecy capacity can be obtained using a combination of convex optimization and a one-dimensional search. On the other hand, to gain more insight into how the secrecy capacity behaves, we study the secure degrees of freedom (s.d.o.f.) and quantify its connection with system parameters, where our result proves that the s.d.o.f. equal to 1 can be achieved if and only if N_e<N_a+N_j-1. As a by-product, we give a suboptimal but closed-form solution to the original SRM problem for the scenario where N_e<N_a+N_j-1.Numerical results are presented to validate the theoretical findings and illustrate the efficacy of the proposed schemes.

GlobecomDec 1, 20150 citations

N_a

N_j

and

N_e

antennas, respectively. Generally, an analytical form of the secrecy capacity in this scenario is difficult to obtain. Instead, we recast the original nonconvex secrecy rate maximization (SRM) problem into a sequence of convex optimization problems. In doing so, the secrecy capacity can be obtained using a combination of convex optimization and a one-dimensional search. On the other hand, to gain more insight into how the secrecy capacity behaves, we study the secure degrees of freedom (s.d.o.f.) and quantify its connection with system parameters, where our result proves that the s.d.o.f. equal to 1 can be achieved if and only if N_e<N_a+N_j-1. As a by-product, we give a suboptimal but closed-form solution to the original SRM problem for the scenario where N_e<N_a+N_j-1.Numerical results are presented to validate the theoretical findings and illustrate the efficacy of the proposed schemes.