Positive Secrecy Rate Research Articles

On Channel-Aware Secure HARQ-IR

In this paper, we study secure hybrid automatic retransmission request (HARQ) over block-fading channels when the channel from a legitimate transmitter (i.e., Alice) to an eavesdropper (i.e., Eve) is less noisy than that to a legitimate receiver (i.e., Bob). In order to have a positive secrecy rate, we exploit the notion of the channel reciprocity in time division duplex mode, where the shared channel state information between Alice and Bob is used as a secret key. The resulting HARQ scheme is referred to as channel-aware secure HARQ (CAS-HARQ) in this paper. In this scheme, in order to keep Eve ignorant of the confidential message from Alice to Bob, deliberative transmissions of random message blocks are considered when the channel to Bob is weak. We derive closed-form expressions for bounds on the probabilities of connection outage and secrecy outage to see reliability and security, respectively, of CAS-HARQ. Based on our analysis, we can see that it is possible to have a positive secrecy rate with certain outage probabilities even if the channel to Eve is less noisy than that to Bob.

EE‐RS and PA for untrusted relay network at high signal‐to‐noise ratio regime

In this study, the authors investigate the energy-efficient (EE) relay selection (RS) and power allocation (PA) in a cooperative secured system. Their scenario includes a multiple-antenna source, a multiple-antenna destination and multiple amplify-and-forward untrusted relay nodes, where the relay nodes only have the channel-amplitude information. To prevent the untrusted relays from intercepting the source message and to achieve positive secrecy rate, the destination-based cooperative jamming technique is used. By maintaining a minimum required secrecy rate, three optimal joint RS and power minimisation schemes are studied. The first objective is minimising the total transmit power consumption, and therefore obtaining the corresponding EE-RS and PA schemes. Second, they focus on relay power minimisation, and third sum power minimisation of the relay and one mobile node by considering a weighted factor are investigated. Closed-form solutions are presented for three practical optimised networks. Finally, some numerical results are provided to show the merits of the proposed scheme. They also give some insights to system design.

Destination-Aided Cooperative Jamming for Dual-Hop Amplify-and-Forward MIMO Untrusted Relay Systems

In this paper, we consider a dual-hop amplify-and-forward (AF) multiple-input–multiple-output (MIMO) relay network, where the source, relay, and destination are each equipped with multiple antennas. The relay is untrusted if it is willing to forward the signal to the destination and, at the same time, acts as a potential eavesdropper to interpret the message from the source. Since there exists no direct link between the source and the destination, a positive secrecy rate cannot be obtained. Addressing this issue, we propose a joint destination-aided cooperative jamming and precoding at both the source and the relay scheme: joint source, relay, and destination precoding (JP). We target at maximizing the secrecy rate by jointly designing the source, relay, and destination precoding matrices and propose an alternating iterative optimization algorithm to tackle the nonconvex problem. Then, a comprehensive study on the asymptotic performance is conducted in a high signal-to-noise ratio (SNR) regime. In particular, we present simple closed-form expressions for the two key performance parameters in the asymptotic secrecy rate, i.e., the high-SNR slope and the high-SNR power offset. Finally, numerical results are conducted to demonstrate the validity of the proposed secure scheme and its performance analysis.

Physical Layer Security for Space Shift Keying Transmission With Precoding

We investigate the effect of transmitter side channel state information on the achievable secrecy rates of space shift keying. Through derivation of the gradient of the secrecy rate, we formulate an iterative algorithm to maximize the achievable secrecy rates. We also introduce two lower complexity signal design algorithms for different scenarios based on the number of antennas at the eavesdropper. Our results illustrate the effectiveness of the proposed precoding techniques in attaining positive secrecy rates over a wide range of signal to noise ratios.

Joint optimal power allocation and relay selection to establish secure transmission in uplink transmission of untrusted relays network

In this paper, the authors deal with secure transmission in two-hop amplify-and-forward network with untrusted relays. To prevent the untrusted relays from intercepting the source message and to achieve positive secrecy rate, the destination-based cooperative jamming technique is used. The authors propose joint secure best relay selection (BRS) and optimal power allocation (OPA) for uplink transmission of a cellular network when the base station is equipped with very large-scale antenna arrays. Then, the common performance metrics such as ergodic secrecy rate (ESR) and secrecy outage probability are evaluated for the optimised network. Moreover, the diversity order and diversity-multiplexing tradeoff of the system are examined. The authors obtain that the diversity order of joint BRS and OPA scenario is equal to number of relays. Finally, some numerical and simulation results are presented to validate the theoretical analysis and to show the advantages offered by the presented systems. They reveal interesting results that, by increasing number of untrusted relay nodes, the system performance improves. For example, for target ESR 2 bits/s/Hz and ten untrusted relay nodes, the optimised network saves about 5 dB for uplink transmission, in comparison with the system applying the BRS and equal power allocation.

Secure Space-Time Communications Over Rayleigh Flat Fading Channels

In this paper, we consider the wire-tap channel model consisting of three users, namely, a transmitter, a legal receiver, and an eavesdropper, where the eavesdropper has possible unlimited centralized or distributed multiple antennas, while the legal user has just a single antenna. With this model, we study the realization of strict positive secrecy rate through Rayleigh flat fading channels using M-ary phase shift keying (PSK) and orthogonal space-time block code (OSTBC) based on channel reciprocal principle. We demonstrate that the information rate at the eavesdropper can be reduced to zero and a positive communication rate at the legal receiver can be realized if the transmitter employs a proper phase precoder based on the channel reciprocal, and uses OSTBC and M-ary PSK modulations for data transmissions. Application examples of space-time codes for positive secrecy rate are illustrated. As we have given the eavesdropper more capabilities than the legal receiver and thus captured a worst case scenario, any positive secrecy rate that is achieved serves as a lower bound on the secrecy capacity.

Transmitter Precoding-Aided Spatial Modulation for Secrecy Communications

Precoding-aided spatial modulation (PSM), which conveys information partially by the indices of receive antennas, has some advantages over conventional spatial modulation (SM) using the indices of transmit antennas. In PSM, the precoder may be optimized for different purposes. In this paper, the authors study the transmitter design in the PSM systems, which motivates to provide secrecy communications. Specifically, the authors consider a pair of communication terminals overheard by an eavesdropper. The precoder is optimized by jointly minimizing the power received by the eavesdropper and maximizing the power received by the desired terminal. Both the error performance and the ergodic secrecy rate achievable are studied when assuming communications over independent Rayleigh fading channels. The authors studies show that positive secrecy rate and low-complexity detection can be attainable simultaneously for the desired receiver even when the eavesdropper employs more receive antennas than the desired receiver.

Destination‐based cooperative jamming in untrusted amplify‐and‐forward relay networks: resource allocation and performance study

In this study, the authors study the problem of secure transmission in two-hop amplify-and-forward systems with an untrusted relay. To prevent the untrusted relay from intercepting the source message and to achieve positive secrecy rate, the destination-based cooperative jamming technique is used. In this method, the destination sends an intended jamming signal to the relay. This jamming signal helps protecting the source message from being captured reliably at the untrusted relay, while the destination cancels itself intended jamming signal. The optimal power allocation (OPA) strategy is considered for the proposed system. They observe that the objective function is a quasi-concave function at high signal-to-noise-ratio regimes. Based on this OPA strategy, in the first step, the outage probability of the system is investigated. It is investigated for three cases. In the two cases, either of the source or the destination node is equipped with large-scale antennas, and in the third case, both of them are equipped with large-scale antenna arrays. In all the cases, the closed-form expressions are derived. In the second step, they investigate the ergodic secrecy rate and present the closed-form solutions for all the mentioned cases. Finally, simulation results indicate the accuracy of the derived equations.

On the Fast Fading Gaussian Wiretap Channel With Statistical Channel State Information at the Transmitter

In this paper, we investigate the ergodic secrecy capacity of the fast fading Gaussian wiretap channel when only the statistics of the channel state information are known at the transmitter. We derive conditions for the existence of degradedness and a positive ergodic secrecy capacity under the usual stochastic order, the convex order, and the increasing convex order between the legitimate and eavesdropper channels. For more general orders, we prove the secrecy capacity of layered erasure wiretap channels and propose a layered signaling for the achievable scheme, and we derive an upper bound on the capacity for fast fading Gaussian wiretap channels. Finally, the numerical results show that under Nakagami-m fast fading channels, the proposed layered signaling outperforms the Gaussian codebook in several cases. In particular, in certain cases, the Gaussian codebook can achieve only a zero secrecy rate, whereas the proposed scheme achieves positive secrecy rates. Therefore, the connectivity of wireless networks can be significantly improved by the proposed scheme.

Jamming Based on an Ephemeral Key to Obtain Everlasting Security in Wireless Environments

Secure communication over a wiretap channel is considered in the disadvantaged wireless environment, where the eavesdropper channel is (possibly much) better than the main channel. We present a method to exploit inherent vulnerabilities of the eavesdropper's receiver to obtain everlasting secrecy. Based on an ephemeral cryptographic key pre-shared between the transmitter Alice and the intended recipient Bob, a random jamming signal is added to each symbol. Bob can subtract the jamming signal before recording the signal, while the eavesdropper Eve is forced to perform these non-commutative operations in the opposite order. Thus, information-theoretic secrecy can be obtained, hence achieving the goal of converting the vulnerable "cheap" cryptographic secret key bits into "valuable" information-theoretic (i.e. everlasting) secure bits. We evaluate the achievable secrecy rates for different settings, and show that, even when the eavesdropper has perfect access to the output of the transmitter (albeit through an imperfect analog-to-digital converter), the method can still achieve a positive secrecy rate. Next we consider a wideband system, where Alice and Bob perform frequency hopping in addition to adding the random jamming to the signal, and we show the utility of such an approach even in the face of substantial eavesdropper hardware capabilities.

Secrecy Performance Analysis for TAS-MRC System With Imperfect Feedback

In this paper, we investigate the secrecy performance for a multiple-input multiple-output (MIMO) wiretap channel in the presence of a multiantenna eavesdropper. In particular, the legitimate transmitter uses transmit antenna selection (TAS) to transmit on a single antenna with the largest signal-to-noise ratio (SNR) while both the legitimate receiver and the eavesdropper adopt maximal ratio combining (MRC) for reception. We derive exact closed-form expressions for the probabilities of achieving positive secrecy rate and secrecy outage in the case of imperfect feedback due to feedback delay and/or feedback error. Furthermore, we derive the asymptotic secrecy outage probability at high SNR, which accurately reveals the secrecy diversity loss due to imperfect feedback. Simulation results are provided to verify our analytical results and illustrate the impact of imperfect feedback on the secrecy performance of such a wiretap system.

Joint Power Control in Wiretap Interference Channels

Interference in wireless networks degrades the signal quality at the terminals. However, it can potentially enhance the secrecy rate. This paper investigates the secrecy rate in a two-user interference network where one of the users, namely user 1, requires to establish a confidential connection. User 1 wants to prevent an unintended user of the network to decode its transmission. User 1 has to transmit such that its secrecy rate is maximized while the quality of service at the destination of the other user, user 2, is satisfied, and both user's power limits are taken into account. We consider two scenarios: 1) user 2 changes its power in favor of user 1, an altruistic scenario, 2) user 2 is selfish and only aims to maintain the minimum quality of service at its destination, an egoistic scenario. It is shown that there is a threshold for user 2's transmission power that only below or above which, depending on the channel qualities, user 1 can achieve a positive secrecy rate. Closed-form solutions are obtained in order to perform joint optimal power control. Further, a new metric called secrecy energy efficiency is introduced. We show that in general, the secrecy energy efficiency of user 1 in an interference channel scenario is higher than that of an interference-free channel.

Relay selection for secure backscatter wireless communications

The growing demand for anti-eavesdropping security has inspired the study of physical-layer security in wireless communications. Relay-assisted secure backscatter communications are considered. The secrecy rate of the system is studied and the condition for a positive secrecy rate is analysed. The optimal relay selection algorithm and a suboptimal selection algorithm with much lower computational complexity are proposed. Simulation results show that the designed selection algorithms significantly outperform random selection in terms of average secrecy rate. The suboptimal selection approximately achieves the same average secrecy rate as the optimal selection.

On the Secrecy Capacity of Block Fading Channels With a Hybrid Adversary

We consider a block fading wiretap channel, where a transmitter attempts to send messages securely to a receiver in the presence of a hybrid half-duplex adversary, which arbitrarily decides to either jam or eavesdrop the transmitter-to-receiver channel. We provide bounds to the secrecy capacity for various possibilities on receiver feedback and show special cases where the bounds are tight. We show that, without any feedback from the receiver, the secrecy capacity is zero if the transmitter-to-adversary channel stochastically dominates the effective transmitter-to-receiver channel. However, the secrecy capacity is nonzero even when the receiver is allowed to feed back only one bit at the end of each block. Our novel achievable strategy improves the rates proposed in the literature for the nonhybrid adversarial model. We also analyze the effect of multiple adversaries and delay constraints on the secrecy capacity. We show that our novel time sharing approach leads to positive secrecy rates even under strict delay constraints.

MIMO Wiretap Channels With Unknown and Varying Eavesdropper Channel States

In this paper, a class of information theoretic secrecy problems is addressed where the eavesdropper channel state is completely unknown to the legitimate parties. In particular, a Gaussian MIMO wiretap channel is considered, where the eavesdropper channel state can vary from one channel use to the next, and the overall channel state sequence is known only to the eavesdropper. When the eavesdropper has fewer antennas than the transmitter and its intended receiver, a positive secrecy rate in the sense of strong secrecy is proved to be achievable and shown to match with the converse in secure degrees of freedom. This yields the conclusion that secure communication is possible regardless of the location or channel states of the eavesdropper. Additionally, it is observed that, the present setting renders the secrecy capacity problems for some multiterminal wiretap-type channels more tractable as compared to the case with full or partial knowledge of eavesdropper channel states. To demonstrate this observation, secure degrees of freedom regions are derived for the Gaussian MIMO multiple access (MAC) wiretap channel and the two-user Gaussian MIMO broadcast (BC) wiretap channel, where the transmitter(s) and intended receiver(s) have the same number of antennas.

Ergodic Secret Message Capacity of the Wiretap Channel with Finite-Rate Feedback

We study the secret message capacity of an ergodic block fading wiretap channel with partial channel state information at the transmitter and perfect channel state information at the receivers, under both a short term power constraint (STPC) and a long term power constraint (LTPC). We consider that in addition to the statistics of the main and the eavesdropper channel state information (CSI), the sender is provided by the legitimate receiver with a q-bit feedback, at the beginning of each coherence block, through an error-free public channel, with capacity q bits. We establish upper and lower bounds on the secrecy capacity. We show that the lower and the upper bounds coincide asymptotically as q → ∞. When applied to Rayleigh fading channels, we show that, a 4-bit feedback achieves about 90% of the secrecy capacity when perfect main CSI is available at the transmitter. Finally, asymptotic analysis at high and low Signal-to-Noise Ratio (SNR) is presented. It is found that the capacity is bounded at high-SNR, whereas at asymptotically low-SNR, the lower bounds and the upper bound scale linearly with SNR under STPC. Furthermore, subject to LTPC, the capacity at low-SNR is equal to the capacity of the main channel without secrecy constraint and with perfect CSI at both the transmitter and the receiver, under a mild condition on the fading statistics. We also show that a positive secrecy rate is achievable even when the feedback is at the end of each coherence block and q=1.

Secret Wireless Communication with Public Feedback by Common Randomness

In this letter, we propose a feedback scheme to improve the secrecy rate of a wireless communication system which can help us to get a higher achievable secrecy rate than the traditional one-way communication scheme for Gaussian wiretap channel. It is shown that if the power of sending signal is large enough, positive secrecy rate can be achieved even when the eavesdropper's channel quality is better than the main channel. Closed-form solution of the achievable secrecy rate is derived.

Secure Communications with Untrusted Secondary Nodes in Cognitive Radio Networks

We consider a cooperation scenario between primary users and untrusted secondary users in cognitive radio networks. The secondary users are willing to help the primary users to relay the primary users' messages in reward for being allowed to share the primary users' spectrum bands. However, the primary users might be reluctant to accept this help, since the secondary users are untrustworthy and may try unauthorized decoding of the primary users' messages. This paper will answer the question: when is this cooperation mutually beneficial for primary and secondary users? Taking an approach of information-theoretic secrecy, such as coding techniques for wiretap channels, the primary users can allow the secondary users to sense and relay the message, while ensuring that the secondary users are ignorant of the primary users' messages. We characterize an achievable secrecy rate of primary users with a rate of the secondary users' communication. From the derived rate pairs, an optimization problem is formulated such that the secondary transmitter distributes its transmit power to maximize its data rate while providing a higher secrecy rate to the primary users. We demonstrate that this cooperation can provide a positive secrecy rate, even when a non-cooperative scheme achieves a zero secrecy rate.

On the secrecy rate of limited feedback beamforming over multiple-input single-output wiretap channels

The secrecy rate of limited feedback beamforming is studied for a Multiple-Input Single-Output (MISO) wiretap channel with a multi-antenna eavesdropper. We first obtain the secrecy rate of limited feedback beamforming achieved at the legitimate receiver. We then derive a lower bound for the asymptotic secrecy rate in the large system limit. From this bound, we observe a threshold for the ratio of eavesdrop antennas to transmit antennas to obtain a positive secrecy rate. We further show that the secrecy rate loss due to limited feedback decays with the number of feedback bits per transmit antenna.

Amplify‐and‐forward‐based cooperative jamming strategy with power allocation for secure communication

SummaryThis paper deals with the use of jamming transmission for secure amplify‐and‐forward‐based relay networks with total power constraints. An approach that the source and the relay use some of their available power to transmit jamming signals in order to create interference at the eavesdropper is investigated. Assume that the relay and destination have an a priori knowledge of the jamming signals. A power allocation policy that defines how the available power is distributed between the message signal and that of the jamming signal is presented. The results show that the proposed approach can increase the secrecy level and that a positive secrecy rate can be achieved even when the eavesdropper may be near the source. Copyright © 2014 John Wiley & Sons, Ltd.