Secrecy Capacity of Space Keying with Two Antennas

Alessio Zappone, Pin-Hsun Lin, Eduard Axel Jorswieck

Energy-efficient resource allocation in multiple-antenna wiretap channels is investigated, subject to maximum power and minimum secrecy capacity/rate constraints. Two energy-efficient metrics are optimized, namely the secrecy energy efficiency, defined as the ratio between the system secrecy capacity and the consumed power, and the secret-key energy efficiency, defined as the ratio between the system secret-key capacity and the consumed power. If the legitimate receiver and the eavesdropper have a single antenna, and the transmitter has multiple antennas, the global solution can be expressed by a simple formula that requires negligible complexity to be computed. Instead, if all nodes have multiple-antennas, provably convergent and computationally-friendly iterative algorithms are provided, which are able to determine the global maximum of the secret-key energy efficiency and candidate solutions of the secrecy energy efficiency maximization problem. Numerical results assess the performance of the proposed methods.

Naoki Iwamoto, Hideichi Sasaoka, Hisato Iwai

Jia Zhu, Yulong Zou, Senior Member +4 more

Abstract—In this paper, we consider a multiple-input multiple-output (MIMO) system consisting of one source, one destination and one eavesdropper, where each node is equipped with an arbitrary number of antennas. To improve the security of source-destination transmissions, we investigate the antenna selection at the source and propose the optimal antenna selection (OAS) and suboptimal antenna selection (SAS) schemes, depending on whether the source node has the global channel state information (CSI) of both the main link (from source to destination) and wiretap link (from source to eavesdropper). Also, the traditional space-time transmission (STT) is studied as a benchmark. We evaluate the secrecy performance of STT, SAS, and OAS schemes in terms of the probability of zero secrecy capacity. Furthermore, we examine the generalized secrecy diversity of STT, SAS, and OAS schemes through an asymptotic analysis of the probability of zero secrecy capacity, as the ratio between the average gains of the main and wiretap channels tends to infinity. This is different from the conventional secrecy diversity which assumes an infinite signal-to-noise ratio (SNR) received at the destination under the condition that the eavesdropper has a finite received SNR. It is shown that the generalized secrecy diversity orders of STT, SAS, and OAS schemes are the product of the number of antennas at source and destination. Additionally, numerical results show that the proposed OAS scheme strictly outperforms both the STT and SAS schemes in terms of the probability of zero secrecy capacity. Index Terms—MIMO, antenna selection, space-time code, eavesdropping attack, secrecy diversity.

Eduard Axel Jorswieck

Jia Zhu, Yulong Zou, Gongpu Wang +2 more

In this paper, we consider a multiple-input-multiple-output (MIMO) system consisting of one source, one destination, and one eavesdropper, where each node is equipped with an arbitrary number of antennas. To improve the security of source-destination transmissions, we investigate the antenna selection at the source and propose the optimal antenna selection (OAS) and suboptimal antenna selection (SAS) schemes, depending on whether the source node has the global channel state information (CSI) of both the main link (from source to destination) and the wiretap link (from source to eavesdropper). Moreover, the traditional space-time transmission (STT) is studied as a benchmark. We evaluate the secrecy performance of STT, SAS, and OAS schemes in terms of the probability of zero secrecy capacity. Furthermore, we examine the generalized secrecy diversity of the STT, SAS, and OAS schemes through an asymptotic analysis of the probability of zero secrecy capacity as the ratio between the average gains of the main and wiretap channels tends to infinity. This is different from the conventional secrecy diversity that assumes an infinite signal-to-noise ratio (SNR) received at the destination under the condition that the eavesdropper has a finite received SNR. It is shown that the generalized secrecy diversity orders of the STT, SAS, and OAS schemes are the product of the number of antennas at source and destination. Additionally, numerical results show that the proposed OAS scheme strictly outperforms both the STT and the SAS schemes in terms of the probability of zero secrecy capacity.

Ahmed M. Alaa, Yasmine A. H. Fahmy