Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Transactions on Information Theory

On the Secure Degrees of Freedom of Relaying With Half-Duplex Feedback

Tung T. Kim, H. Vincent Poor

Published Dec 29, 2010• 17 citations
Publisher

Abstract

Secure communication protocols over a single-relay system in the presence of a multiple-antenna eavesdropper are investigated. When there is no direct link between the source and the destination, an amplify-and-forward (AF) protocol that allows both the destination and the source to jam the eavesdropper is shown to achieve secrecy rates that grow linearly with the transmit power in dB, even if all the legitimate nodes have strictly fewer antennas than the eavesdropper. The number of achievable secure degrees of freedom is quantified and shown to match an upper bound when the number of antennas at the destination is sufficiently large. However, in the presence of a direct link between source and destination, this scaling rule no longer applies. The bottleneck of the AF scheme in the presence of a direct source-destination link is identified, motivating the use of another AF scheme and a novel compress-and-forward protocol that can achieve a positive number of secure degrees of freedom using an insecure feedback link.

DOI
10.1109/tit.2010.2090250

Related papers

Secure relaying: Can publicly transferred keys increase degrees of freedom?

Tung T. Kim, H. Vincent Poor

Secure communication over a half-duplex relay system in the presence of an external wiretapper is investigated. In such a scenario, conventional relaying protocols generally provide secrecy rates that converge to a finite constant in the high signal-to-noise ratio (SNR) regime. It is shown in this work that strictly superior performance can be achieved by allowing the destination to transfer random keys in the form of known interference to the relay insecurely over the wireless medium. When there is no direct link between the source and the destination, an amplify-and-forward (AF) protocol is shown to achieve a secrecy rate that scales as 1/2 log SNR, if each of the legitimate nodes has a single antenna only. However, in the presence of a direct link between source and destination, this scaling rule no longer applies. The bottleneck of the AF scheme in the presence of a direct source-destination link is identified, motivating the use of multiple antennas at the destination to almost surely guarantee a secure degree of freedom of one half over the channel. The results hold even if the eavesdropper has more antennas than the source and the relay combined.

Allerton Conference on Communication, Control, and Computing•Sep 1, 2009•2 citations

Secure Communications With Insecure Feedback: Breaking the High-SNR Ceiling

Tung T. Kim, H. Vincent Poor

A multiple-antenna Gaussian wiretap channel in which the number of antennas at the source is not greater than that at the eavesdropper is considered. Without feedback, the secrecy capacity over such a channel generally converges to a constant at high signal-to-noise ratio (SNR). A half-duplex secure protocol allowing the destination to actively transfer random keys in the form of known interference is proposed. It is shown that using multiple antennas at the destination is instrumental in achieving a secrecy rate that grows linearly with logSNR. The pre-log factor of the secrecy rate, i.e., the number of secure degrees of freedom, is characterized, revealing an interesting interplay between the numbers of antennas at the three communication nodes. The relationship of the achievable secure degrees of freedom to those obtained in the case without feedback is finally discussed.

IEEE Transactions on Information Theory•Jul 21, 2010•6 citations

Secure amplify-and-forward relaying in linear chains with a single eavesdropper

Tulika Agrawal, Samar Agnihotri

The problem of secure unicast communication over multihop wireless relay networks with directed links in the presence of an eavesdropper is considered. In the existing literature this problem has been considered in one or both of the following two scenarios: (A) relay nodes employ relaying schemes, such as Decode-and-Forward (DF), (B) the source communicates with the destination over a two-hop relay network. We argue that computationally complex relaying schemes such as DF render end-to-end performance characterization intractable, without providing any performance guarantee in general channel and network scenarios. Therefore, we consider one of the simplest relaying scheme: Amplify-and-Forward (AF) that allows us to provide guarantees on the optimal performance over a wide range of channel conditions. A node performing AF-relaying scales and forwards the signal received at its input. Further, with AF-relaying the end-to-end performance characterization problem remains tractable for much larger class of networks than those that can be considered with other relaying schemes. The key contribution of this work is twofold. We first provide the optimal vector of scaling factors that maximizes the achievable AF secrecy rate, no matter which relay the eavesdropper listens to. Further, we prove that in high-SNR regime, the optimal AF secrecy rate thus achieved is within a constant gap from the cutset upper bound on the secrecy capacity.

International Conference on Signal Processing and Communications (SPCOM)•Jun 1, 2016•2 citations

The Gaussian wiretap channel with noisy public feedback: Breaking the high-SNR ceiling

Tung T. Kim, H. Vincent Poor

A multiple-antenna Gaussian wiretap channel in which the number of antennas at the source is not larger than that at the eavesdropper is considered. Without feedback, the secrecy capacity over such a channel generally converges to a constant at high signal-to-noise ratio (SNR). A half-duplex secure protocol allowing the destination to actively broadcast random keys over insecure channels is proposed. It is shown that using multiple antennas at the destination is instrumental in achieving a secrecy rate that grows linearly with log SNR. The pre-log factor of the secrecy rate, i.e. the secure degree of freedom, is characterized, revealing an interesting interplay between the numbers of antennas at the three communication nodes.

Asilomar Conference on Signals, Systems and Computers (ACSSC)•Jan 1, 2009•3 citations

Improving Physical Layer Security of AF Relay Networks via Beam-Forming and Jamming

Abdelhamid Salem, Khairi Ashour Hamdi

In this paper the cooperation of beam-forming and artificial noise (AN) in two-hop amplify-and- forward (AF) relaying system is proposed to enhance the security. we consider a half duplex AF relaying network with a multi-antenna source node and a destination in the presence of a passive eavesdropper.Since channel state information (CSI) of the eavesdropper is unknown, the AN transmitted by the source in the first phase and by the relays in the second phase is in all directions except the legitimate node one. As such two scenarios are considered here,: i) when all the relays amplify and forward the information source signal ii) when only the best relay is selected to amplify and forward the information source signal. The beam-former weights and the power allocation are obtained by solving an optimization problem. Results reveal that the proposed system can provide considerable improvements in terms of secrecy rate. It is also found that increasing the AN power, relative to the information signal power, will further improve the secrecy rate.

IEEE Vehicular Technology Conference•Sep 1, 2016•7 citations

Physical Layer Security With RF Energy Harvesting in AF Multi-Antenna Relaying Networks

Abdelhamid Salem, Khairi Ashour Hamdi, Khaled Maaiuf Rabie

In this paper, we analyze the secrecy capacity of a half-duplex energy harvesting (EH)-based multi-antenna amplify-and-forward relay network in the presence of a passive eavesdropper. During the first phase, while the source is in the transmission mode, the legitimate destination transmits an auxiliary artificial noise (AN) signal which has two distinct purposes: 1) to transfer power to the relay and 2) to improve system security. Since the AN is known at the legitimate destination, it is easily cancelled at the intended destination, which is not the case at the eavesdropper. In this respect, we derive new exact analytical expressions for the ergodic secrecy capacity for various well-known EH relaying protocols, namely, time switching relaying (TSR), power splitting relaying (PSR), and ideal relaying receiver (IRR). Monte Carlo simulations are also provided throughout our investigations to validate the analysis. The impacts of some important system parameters, such as EH time, power splitting ratio, relay location, AN power, EH efficiency, and the number of relay antennas, on the system performance are investigated. The results reveal that the PSR protocol generally outperforms the TSR approach in terms of the secrecy capacity.

IEEE Transactions on Communications•May 27, 2016•131 citations
Secure communication protocols over a single-relay system in the presence of a multiple-antenna eavesdropper are investigated. When there is no direct link between the source and the destination, an amplify-and-forward (AF) protocol that allows both the destination and the source to jam the eavesdropper is shown to achieve secrecy rates that grow linearly with the transmit power in dB, even if all the legitimate nodes have strictly fewer antennas than the eavesdropper. The number of achievable secure degrees of freedom is quantified and shown to match an upper bound when the number of antennas at the destination is sufficiently large. However, in the presence of a direct link between source and destination, this scaling rule no longer applies. The bottleneck of the AF scheme in the presence of a direct source-destination link is identified, motivating the use of another AF scheme and a novel compress-and-forward protocol that can achieve a positive number of secure degrees of freedom using an insecure feedback link.
Secure communication over a half-duplex relay system in the presence of an external wiretapper is investigated. In such a scenario, conventional relaying protocols generally provide secrecy rates that converge to a finite constant in the high signal-to-noise ratio (SNR) regime. It is shown in this work that strictly superior performance can be achieved by allowing the destination to transfer random keys in the form of known interference to the relay insecurely over the wireless medium. When there is no direct link between the source and the destination, an amplify-and-forward (AF) protocol is shown to achieve a secrecy rate that scales as 1/2 log SNR, if each of the legitimate nodes has a single antenna only. However, in the presence of a direct link between source and destination, this scaling rule no longer applies. The bottleneck of the AF scheme in the presence of a direct source-destination link is identified, motivating the use of multiple antennas at the destination to almost surely guarantee a secure degree of freedom of one half over the channel. The results hold even if the eavesdropper has more antennas than the source and the relay combined.
A multiple-antenna Gaussian wiretap channel in which the number of antennas at the source is not greater than that at the eavesdropper is considered. Without feedback, the secrecy capacity over such a channel generally converges to a constant at high signal-to-noise ratio (SNR). A half-duplex secure protocol allowing the destination to actively transfer random keys in the form of known interference is proposed. It is shown that using multiple antennas at the destination is instrumental in achieving a secrecy rate that grows linearly with logSNR. The pre-log factor of the secrecy rate, i.e., the number of secure degrees of freedom, is characterized, revealing an interesting interplay between the numbers of antennas at the three communication nodes. The relationship of the achievable secure degrees of freedom to those obtained in the case without feedback is finally discussed.
The problem of secure unicast communication over multihop wireless relay networks with directed links in the presence of an eavesdropper is considered. In the existing literature this problem has been considered in one or both of the following two scenarios: (A) relay nodes employ relaying schemes, such as Decode-and-Forward (DF), (B) the source communicates with the destination over a two-hop relay network. We argue that computationally complex relaying schemes such as DF render end-to-end performance characterization intractable, without providing any performance guarantee in general channel and network scenarios. Therefore, we consider one of the simplest relaying scheme: Amplify-and-Forward (AF) that allows us to provide guarantees on the optimal performance over a wide range of channel conditions. A node performing AF-relaying scales and forwards the signal received at its input. Further, with AF-relaying the end-to-end performance characterization problem remains tractable for much larger class of networks than those that can be considered with other relaying schemes. The key contribution of this work is twofold. We first provide the optimal vector of scaling factors that maximizes the achievable AF secrecy rate, no matter which relay the eavesdropper listens to. Further, we prove that in high-SNR regime, the optimal AF secrecy rate thus achieved is within a constant gap from the cutset upper bound on the secrecy capacity.
A multiple-antenna Gaussian wiretap channel in which the number of antennas at the source is not larger than that at the eavesdropper is considered. Without feedback, the secrecy capacity over such a channel generally converges to a constant at high signal-to-noise ratio (SNR). A half-duplex secure protocol allowing the destination to actively broadcast random keys over insecure channels is proposed. It is shown that using multiple antennas at the destination is instrumental in achieving a secrecy rate that grows linearly with log SNR. The pre-log factor of the secrecy rate, i.e. the secure degree of freedom, is characterized, revealing an interesting interplay between the numbers of antennas at the three communication nodes.
In this paper the cooperation of beam-forming and artificial noise (AN) in two-hop amplify-and- forward (AF) relaying system is proposed to enhance the security. we consider a half duplex AF relaying network with a multi-antenna source node and a destination in the presence of a passive eavesdropper.Since channel state information (CSI) of the eavesdropper is unknown, the AN transmitted by the source in the first phase and by the relays in the second phase is in all directions except the legitimate node one. As such two scenarios are considered here,: i) when all the relays amplify and forward the information source signal ii) when only the best relay is selected to amplify and forward the information source signal. The beam-former weights and the power allocation are obtained by solving an optimization problem. Results reveal that the proposed system can provide considerable improvements in terms of secrecy rate. It is also found that increasing the AN power, relative to the information signal power, will further improve the secrecy rate.
In this paper, we analyze the secrecy capacity of a half-duplex energy harvesting (EH)-based multi-antenna amplify-and-forward relay network in the presence of a passive eavesdropper. During the first phase, while the source is in the transmission mode, the legitimate destination transmits an auxiliary artificial noise (AN) signal which has two distinct purposes: 1) to transfer power to the relay and 2) to improve system security. Since the AN is known at the legitimate destination, it is easily cancelled at the intended destination, which is not the case at the eavesdropper. In this respect, we derive new exact analytical expressions for the ergodic secrecy capacity for various well-known EH relaying protocols, namely, time switching relaying (TSR), power splitting relaying (PSR), and ideal relaying receiver (IRR). Monte Carlo simulations are also provided throughout our investigations to validate the analysis. The impacts of some important system parameters, such as EH time, power splitting ratio, relay location, AN power, EH efficiency, and the number of relay antennas, on the system performance are investigated. The results reveal that the PSR protocol generally outperforms the TSR approach in terms of the secrecy capacity.