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

Eduard Axel Jorswieck

Published Apr 15, 2010• 28 citations
OpenAlex

Abstract

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.

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Beamforming for fading wiretap channels with partial channel information

Sabrina Gerbracht, Anne Wolf, Eduard Axel Jorswieck

Secrecy on the physical layer receives increased research interest. Especially in the wireless communication scenarios, the interest in confidentiality of messages increases. In this paper, we discuss the effectiveness of the beamforming strategies maximum ratio transmission (MRT), zero forcing (ZF), and an optimized beamforming (BF) strategy for the transmission under secrecy constraints. The applied channel model is the flat-fading MISO (multiple-input single-output) wiretap channel, where the channel to the eavesdropper is only partly known at the transmitter. The scenario with perfect and no channel information to the eavesdropper are included as special cases. We show that under certain conditions the achievable secrecy rates for the transmission with optimized beam-forming can be increased by transmitting artificial noise (AN) in the null space of the channel to the intended receiver, which produces additional interference only at the eavesdropper. We provide a characterization of the optimal beamforming and artificial noise beamforming and analyze the optimal power allocation for asymptotic cases (low and high SNR as well as no and perfect channel information). Numerical simulations illustrate the results.

International ITG Workshop on Smart Antennas•Feb 1, 2010•34 citations
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.
The problem that we consider is the secrecy communication in bilateral transmitting scenario. The model is connected via wireless signal between two points: the transmitter and the receiver. We assume that the transmitter has a single transmit antenna while the receiver has two (one transmit, one receive). In recent papers, it is shown that artificial noise could be used to increase the secrecy capacity. However, for one transmitter antenna case, helper nodes can only be used. In this paper we propose a new 2-Stage artificial noise sending method to substitute helper nodes. So the cost of helper nodes can be saved. The comparison of artificial noise transmitting with Beamforming is given in this paper. It can be proved to increase the secrecy capacity via our approach.
We consider the problem of secure communication in wireless fading channels in the presence of non-colluding passive eavesdroppers. The transmitter has multiple antennas and is able to simultaneously transmit an information bearing signal to the intended receiver and artificial noise to the eavesdroppers. We obtain an analytical closed-form lower bound for secrecy capacity, which is used as the objective function to optimize transmit power allocation between the information signal and the artificial noise. Our analytical and numerical results show that equal power allocation is a simple and generic strategy which achieves near optimal capacity performance. We also find that adaptive power allocation based on each channel realization provides no or insignificant capacity improvement over equal power allocation.
This paper considers secure transmission with the aid of a helper for finite alphabet signals in multiple-input-multiple-output multiple antenna eavesdropper networks, where the helper transmits a jamming signal along with the confidential message sent by the source node to confuse the eavesdropper. For the scenario in which the only statistical channel-state-information (CSI) of the eavesdropper links is available at the transmitter, the ergodic secrecy rate lacks closed-form expression, and the evaluation of the ergodic secrecy rate is computationally prohibitive. To address this problem, an accurate approximation of the ergodic secrecy rate is proposed to reduce the computational complexity. Utilizing this approximation of the ergodic secrecy rate, the joint optimization of precoding design and power allocation between the source and the helper is investigated to improve the ergodic secrecy rate. Furthermore, to achieve a tradeoff between computational complexity and performance, low-complexity schemes without iteration are proposed based on the analysis at extreme signal-to-noise ratio (SNR). In the low SNR regime, we prove that it is optimal to transmit confidential messages with full power, and the beamforming design is the first-order optimal precoder. At high SNR, we transform the problem of precoding design into a semi-definite programming problem, which can be efficiently solved by the interior-point method.
Abstract — The problem of secret communication between two nodes over a wireless link is considered, where a passive eavesdropper may overhear the communication. It is desired that the eavesdropper be unable to decode the message. We show that secrecy can be achieved by adding artificially generated noise to the information bearing signal such that it does not degrade the intended receiver’s channel. We consider two different scenarios; one in which the transmitter has multiple transmit antennas and the other in which the transmitter has a single antenna but ‘helper ’ nodes are available. In the multiple antenna scenario, the degrees of freedom provided by the multiple antennas is used to generate noise intelligently so that it degrades only the eavesdropper’s channel. In the multiple helper scenario, even though the transmitter does not have multiple antennas, the helper nodes simulate the effect of multiple antennas and allow the transmitter to generate artificial noise as in the previous case.
Exploiting the randomness embedded in wireless channels, the physical-layer security techniques can provide additional security robustness against malicious eavesdropping at the physical layer of communication systems. To further this line of study, this thesis focuses on developing advanced multi-antenna transmission strategies for enhancing the secrecy performance of wireless communication systems. Assuming perfect channel feedback from the desired receiver and none from the eavesdropper, we consider beamforming with smartly injected artificial noise, aiming to confuse the eavesdropper whilst leaving the desired receiver unaffected. The system parameters are either chosen to be fixed for all transmissions, or adaptively adjusted based on the channel feedback from the desired receiver. For both cases, we provide novel and explicit design solutions for achieving the maximum throughput subject to a secrecy outage constraint. We then derive accurate approximations for the maximum throughput, and give new insights into the additional power cost for achieving a higher security level and the throughput gain of adaptive transmission over non-adaptive transmission. Having investigated the perfect feedback scenario, we then relax the feedback assumption and consider practical effects imposed by limited feedback constraints on the channel from the desired receiver to the transmitter. To deal with quantization error due to limited feedback whilst also accounting for unknown channel of the eavesdropper, we specify a connection outage constraint to guarantee the reliability of desired communication and a secrecy outage constraint to guard against malicious eavesdropping. Under dual outage constraints, we derive a novel optimized rate-adaptive transmission design to maximize the average secrecy throughput. New insights regarding the optimal power/feedback allocation and the number of feedback bits required for efficient quantization are obtained through our analysis. Our preceding study focused on isolated point-to-point transmission without any interference. However, the performance of contemporary wireless networks is often limited by interference from concurrent transmissions. To characterize the impact of interference on secure communication, we consider an interference-limited large-scale network. To confuse the malicious eavesdroppers, in addition to information-bearing signals, the transmitters are designed to generate artificial noise through either beamforming or antenna sectoring in a distributed manner. For both cases, using tools from stochastic geometry, we provide a statistical characterization of the reliability performance of desired communication and the secrecy performance against eavesdropping. We then investigate the networkwide secrecy throughput performance and optimize the transmit power allocation. Our analysis reveals interesting differences between the beamforming and sectoring approaches in terms of the optimal power allocation and the maximum networkwide secrecy throughput.
Secrecy on the physical layer receives increased research interest. Especially in the wireless communication scenarios, the interest in confidentiality of messages increases. In this paper, we discuss the effectiveness of the beamforming strategies maximum ratio transmission (MRT), zero forcing (ZF), and an optimized beamforming (BF) strategy for the transmission under secrecy constraints. The applied channel model is the flat-fading MISO (multiple-input single-output) wiretap channel, where the channel to the eavesdropper is only partly known at the transmitter. The scenario with perfect and no channel information to the eavesdropper are included as special cases. We show that under certain conditions the achievable secrecy rates for the transmission with optimized beam-forming can be increased by transmitting artificial noise (AN) in the null space of the channel to the intended receiver, which produces additional interference only at the eavesdropper. We provide a characterization of the optimal beamforming and artificial noise beamforming and analyze the optimal power allocation for asymptotic cases (low and high SNR as well as no and perfect channel information). Numerical simulations illustrate the results.