Positive Secrecy Rate Research Articles

Integrated Sensing and Secure Communication with XL-MIMO.

This paper studies extremely large-scale multiple-input multiple-output (XL-MIMO)-empowered integrated sensing and secure communication systems, where both the radar targets and the communication user are located within the near-field region of the transmitter. The radar targets, being untrusted entities, have the potential to intercept the confidential messages intended for the communication user. In this context, we investigate the near-field beam-focusing design, aiming to maximize the achievable secrecy rate for the communication user while satisfying the transmit beampattern gain requirements for the radar targets. We address the corresponding globally optimal non-convex optimization problem by employing a semidefinite relaxation-based two-stage procedure. Additionally, we provide a sub-optimal solution to reduce complexity. Numerical results demonstrate that beam focusing enables the attainment of a positive secrecy rate, even when the radar targets and communication user align along the same angle direction.

Secure Transmission in NOMA-Enabled Industrial IoT With Resource-Constrained Untrusted Devices

The security of confidential information associated with devices in the industrial Internet of Things (IIoT) network is a serious concern. This article focuses on achieving a non-orthogonal multiple access (NOMA)-enabled secure IIoT network in the presence of untrusted devices by jointly optimizing the resources, such as decoding order and power allocated to devices. Assuming that the devices are resource-constrained for performing perfect successive interference cancellation (SIC), we characterize the residual interference at receivers with the linear model. Firstly, considering all possible decoding orders in an untrusted scenario, we obtain secure decoding orders that are feasible to obtain a positive secrecy rate for each device. Then, under the secrecy fairness criterion, we formulate a joint optimization problem of maximizing the minimum secrecy rate among devices. Since the formulated problem is non-convex and combinatorial, we first obtain the optimal secure decoding order and then solve it for power allocation by analyzing Karush-Kuhn-Tucker points. Thus, we provide the closed-form global-optimal solution of the formulated optimization problem. Numerical results validate the analytical claims and demonstrate an interesting observation that the conventional decoding order and assigning more power allocation to the weak device, as presumed in many works on NOMA, is not an optimal strategy from the secrecy fairness viewpoint. Also, the average percentage gain of about <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$22.75\%$</tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$50.58\%$</tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$94.59\%$</tex-math></inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$98.16\%$</tex-math></inline-formula> , respectively, is achieved by jointly optimized solution over benchmarks ODEP (optimal decoding order, equal power allocation), ODFP (optimal decoding order, fixed power allocation), FDEP (fixed decoding order, equal power allocation), and FDFP (fixed decoding order, fixed power allocation).

Secure Transmission for THz-Empowered RIS-Assisted Non-Terrestrial Networks

The non-terrestrial networks (NTNs) are recognized as a key component to provide cost-effective and high-capacity ubiquitous connectivity in the future wireless communications. In this paper, we investigate the secure transmission in a terahertz (THz)-empowered reconfigurable intelligent surface (RIS)-assisted NTN (T-RANTN), which is composed of a low-Earth orbit satellite transmitter, an RIS-installed high-altitude platform (HAP) and two unmanned aerial vehicle (UAV) receivers, only one of which is trustworthy. An approximate ergodic secrecy rate (ESR) expression is derived when the atmosphere turbulence and pointing error due to the characteristics of THz as well as the phase errors resulting from finite precision of RIS and imperfect channel estimation are taken into account simultaneously. Furthermore, according to the statistical and perfect channel state information of the untrustworthy receiver, we optimize the phase shifts of RIS to maximize the lower bound of secrecy rate (SR) and instantaneous SR, respectively, by using semidefinite relaxation method. Simulation results show that both the approximate expression for the ESR and the optimization algorithms are serviceable, and even when the jitter standard variance of the trustworthy receiver is greater than that of the untrustworthy one, a positive SR can still be guaranteed.

Short Blocklength Wiretap Channel Codes via Deep Learning: Design and Performance Evaluation

We design short blocklength codes for the Gaussian wiretap channel under information-theoretic security guarantees. Our approach consists in decoupling the reliability and secrecy constraints in our code design. Specifically, we handle the reliability constraint via an autoencoder, and handle the secrecy constraint with hash functions. For blocklengths smaller than or equal to 128, we evaluate through simulations the probability of error at the legitimate receiver and the leakage at the eavesdropper for our code construction. This leakage is defined as the mutual information between the confidential message and the eavesdropper’s channel observations, and is empirically measured via a neural network-based mutual information estimator. Our simulation results provide examples of codes with positive secrecy rates that outperform the best known achievable secrecy rates obtained non-constructively for the Gaussian wiretap channel. Additionally, we show that our code design is suitable for the compound and arbitrarily varying Gaussian wiretap channels, for which the channel statistics are not perfectly known but only known to belong to a pre-specified uncertainty set. These models not only capture uncertainty related to channel statistics estimation, but also scenarios where the eavesdropper jams the legitimate transmission or influences its own channel statistics by changing its location.

Secure Transmission Over Multiple Access Wiretap Channel by Cross-Time Interference Injection

Due to the openness of wireless communication, information transmitted in the multiple access channel is vulnerable to eavesdropping by illegitimate users. Classic artificial noise-assisted schemes can improve security but are not suitable for power-constrained users. To address this problem, we propose a cross-time interference injection scheme in this paper, which improves security by introducing cross-time self-interference and inter-user interference, and does not require artificial noise. The proposed scheme exploits the properties of the Hadamard matrix and the wireless channels, so that the eavesdropping channel suffers from stronger interference than the legitimate channel. We analyze the security performance when both the legitimate receiver and the eavesdropper exploit the successive interference cancellation (SIC) scheme, including the secrecy sum rate, the secrecy capacity, and the secrecy outage probability. We further investigate the effect of the number of eavesdropper’s antennas, the number of legitimate users, and the number of time slots used by the scheme on the security performance, and obtain the corresponding relationship between these parameters when achieving a positive secrecy rate. Finally, simulation results corroborate our theoretical analysis.

Security-Reliability Tradeoff Analysis of Untrusted Full-Duplex Relay Networks

In this work, we investigate the physical layer security problem of wireless cooperative network, where the communication from a source to a destination is assisted by an untrusted full-duplex amplify-and-forward (AF) relay. In order to realize a positive secrecy rate, cooperative jamming is exploited at the destination. The secrecy outage probability (SOP), connection outage probability (COP), and effective secrecy throughput (EST) are, respectively, derived in closed-form expressions for the fixed gain relaying (FGR) scheme and the variable gain relaying (VGR) scheme. Subsequently, we conduct an asymptotic analysis for both the relaying schemes in the high signal-to-noise ratio (SNR) region to offer valuable insights into practical design. Theory and simulation results demonstrate that the self-interference caused by full-duplex transmission is harmful for the reliability performance, while it is beneficial to the security performance. Moreover, the EST of the considered system increases as the self-interference level decreases, which implies that the self-interference deteriorates an overall performance in terms of the security-reliability tradeoff.

Secure Transmission Design for Cooperative NOMA in the Presence of Internal Eavesdropping

The application of successive interference cancellation (SIC) introduces critical security risks to cooperative non-orthogonal multiple access (NOMA) systems in the presence of untrustworthy network nodes, referred to as internal eavesdroppers. To address this potential security and reliability flaw, by assuming all users are untrusted, this letter investigates the effective secrecy throughput (EST) for a cooperative NOMA system, where a near user serves as an amplify-and-forward relay to help forward the information of a far user. Considering the inverse power allocation and SIC decoding order, a novel jamming strategy is proposed to enhance the security performance of the far user. Gauss-Chebyshev approximations of ESTs over Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> channels are derived. Asymptotic EST expressions are proposed to provide further insights. Numerical results demonstrate that the proposed jamming strategy and the inverse power allocation and SIC decoding order are both essential for achieving positive secrecy rates for both users.

Secrecy Capacity of a Gaussian Wiretap Channel With ADCs is Always Positive

We consider a complex Gaussian wiretap channel with finite-resolution analog-to-digital converters (ADCs) at both the legitimate receiver and the eavesdropper. For this channel, we show that a positive secrecy rate is always achievable as long as the channel gains at the legitimate receiver and at the eavesdropper are different, regardless of the quantization levels of the ADCs. For the achievability, we first consider the case of the one-bit ADCs at the legitimate receiver and apply a binary input distribution where the two input points have the same phase when the channel gain at the legitimate receiver is less than that at the eavesdropper, and otherwise the opposite phase. Then the result is generalized for the case of arbitrary finite-resolution ADCs at the legitimate receiver by translating the input distribution appropriately. We also provide numerical lower bounds on the achievable secrecy rates, and analyze the tendency of the secrecy rates according to the channel difference, the power constraint, and the quantization levels for some cases. For the special case of the real Gaussian wiretap channel with one-bit ADCs at both the legitimate receiver and the eavesdropper, we show that our choice of phase does not lose any optimality for the Wyner code.

Rate-compatible multi-edge type low-density parity-check code ensembles for continuous-variable quantum key distribution systems

In this paper, we propose a design rule of rate-compatible punctured multi-edge type low-density parity-check (MET-LDPC) code ensembles with degree-one variable nodes for the information reconciliation (IR) of continuous-variable quantum key distribution (CV-QKD) systems. In addition to the rate compatibility, the design rule effectively resolves the high error-floor issue which has been known as a technical challenge of MET-LDPC codes at low rates. Thus, the proposed design rule allows one to implement rate-compatible MET-LDPC codes with good performances both in the threshold and low-error-rate regions. The rate compatibility and the improved error-rate performances significantly enhance the efficiency of IR for CV-QKD systems. The performance improvements are confirmed by comparing complexities and secret key rates of IR schemes with MET-LDPC codes whose ensembles are optimized with the proposed and existing design rules. In particular, the SNR range of positive secrecy rate increases by 1.44 times, and the maximum secret key rate improves by 2.10 times as compared to the existing design rules. The comparisons clearly show that an IR scheme can achieve drastic performance improvements in terms of both the complexity and secret key rate by employing rate-compatible MET-LDPC codes constructed with code ensembles optimized with the proposed design rule.

Copula based analysis of impact of wireless channels correlation on the physical layer security performances in a wireless wiretap channel with artificial noise

AbstractIn this article, a wireless wiretap channel with artificial noise assisted transmission and active eavesdropper is considered, where, wireless channel coefficients are correlated. Aiming at analyzing wireless channels correlation effects on the physical layer security, we exploit copula theory and obtain closed form expressions for the probability of positive secrecy rate, average secrecy rate, and generalized secrecy outage probability. Then, the obtained analytical results are evaluated numerically under positive dependence, independence and negative dependence correlation structures and it is shown that in different scenarios, the effect of correlated fading on the security performance can be beneficial or harmful.

On the Zero-Outage Secrecy-Capacity of Dependent Fading Wiretap Channels

It is known that for a slow fading Gaussian wiretap channel without channel state information at the transmitter and with statistically independent fading channels, the outage probability of any given target secrecy rate is non-zero, in general. This implies that the so-called zero-outage secrecy capacity (ZOSC) is zero and we cannot transmit at any positive data rate reliably and confidentially. When the fading legitimate and eavesdropper channels are statistically dependent, this conclusion changes significantly. Our work shows that there exist dependency structures for which positive zero-outage secrecy rates (ZOSR) are achievable. In this paper, we are interested in the characterization of these dependency structures and we study the system parameters in terms of the number of observations at legitimate receiver and eavesdropper as well as average channel gains for which positive ZOSR are achieved. First, we consider the setting that there are two paths from the transmitter to the legitimate receiver and one path to the eavesdropper. We show that by introducing a proper dependence structure among the fading gains of the three paths, we can achieve a zero secrecy outage probability (SOP) for some positive secrecy rate. In this way, we can achieve a non-zero ZOSR. We conjecture that the proposed dependency structure achieves maximum ZOSR. To better understand the underlying dependence structure, we further consider the case where the channel gains are from finite alphabets and systematically and globally solve the ZOSC. In addition, we apply the rearrangement algorithm to solve the ZOSR for continuous channel gains. The results indicate that the legitimate link must have an advantage in terms of the number of antennas and average channel gains to obtain positive ZOSR. The results motivate further studies into the optimal dependency structures.

Secure Cognitive Radio Communication via Intelligent Reflecting Surface

In this paper, an intelligent reflecting surface (IRS) assisted spectrum sharing underlay cognitive radio (CR) wiretap channel (WTC) is studied, and we aim at enhancing the secrecy rate of secondary user in this channel subject to total power constraint at secondary transmitter (ST), interference power constraint (IPC) at primary receiver (PR) as well as unit modulus constraint at IRS. Due to extra IPC and eavesdropper (Eve) are considered, all the existing solutions for enhancing secrecy rate of IRS-assisted non-CR WTC as well as enhancing transmission rate in IRS-assisted CR channel without eavesdropper fail in this work. Therefore, we propose new numerical solutions to optimize the secrecy rate of this channel under full primary, secondary users’ channel state information (CSI) and three different cases of Eve’s CSI: full CSI, imperfect CSI with bounded estimation error, and no CSI. To solve the difficult non-convex optimization problem, an efficient alternating optimization (AO) algorithm is proposed to jointly optimize the beamformer at ST and phase shift coefficients at IRS. In particular, when optimizing the phase shift coefficients during each iteration of AO, a Dinkelbach based solution in combination with successive approximation and penalty based solution is proposed under full CSI and a penalty convex-concave procedure solution is proposed under imperfect Eve’s CSI. For no Eve’s CSI case, artificial noise (AN) aided approach is adopted to help enhancing the secrecy rate. Simulation results show that our proposed solutions for the IRS-assisted design greatly enhance the secrecy performance compared with the existing numerical solutions with and without IRS under full and imperfect Eve’s CSI. And positive secrecy rate can be achieved by our proposed AN aided approach given most channel realizations under no Eve’s CSI case so that secure communication also can be guaranteed. All of the proposed AO algorithms are guaranteed to monotonic convergence.

Guaranteeing Positive Secrecy Rate for NOMA System Against Internal Eavesdropping

Non-orthogonal multiple access systems will face serious physical layer security (PLS) problems in the present of internal eavesdropper. However, in the existing schemes, it's difficult to always guarantee the positive secrecy rate of the system. To this end, we consider the PLS against internal eavesdropping in two-users scenario and the beamforming design and optimal power allocation problems are given. The developed analytical results demonstrate that the proposed scheme can absolutely achieve positive secrecy rate if provided sufficient power. Simulation results show that the performance of proposed scheme is better than the existing solutions.

Decoding Orders for Securing Untrusted NOMA

This letter focuses on exploring a new decoding order to resolve the secrecy issue among untrusted nonorthogonal multiple access users. In this context, firstly, we identify the total number of possible decoding orders analytically. Then, we propose a decoding order strategy ensuring positive secrecy rate for all users, and obtain the number of feasible secure decoding orders based on this proposed strategy numerically. Thereafter, we present a suboptimal policy to avoid the computational complexity involved in finding the best secure decoding order. Numerical results illustrate that the suboptimal solution provides a performance gain of about 137% over therelevant benchmark.

Robust Secure Design for RIS-Aided NOMA Network Against Internal Near-End Eavesdropping

The reconfigurable intelligent surface (RIS) aided non-orthogonal multiple access (NOMA) network is applied to improve spectral efficiency and energy efficiency of wireless systems. Due to the incorporation of NOMA, RIS-aided NOMA system suffers from physical layer security (PLS) problem when an internal near user (NU) is the eavesdropper. In this case, it is difficult to always guarantee positive secrecy rate. Therefore, a scheme of artificial noise (AN) cooperative jamming and beamforming design is proposed against internal eavesdropper for RIS-aided NOMA in this paper. It is proved theoretically that the positive secrecy rate can be guaranteed if providing sufficient power. In addition, the power allocation of base station is further studied to minimize the total power consumption under the constraints of data rate and secrecy rate, and the closed-form solutions are achieved. Simulation results show that the performance of the proposed scheme is superior to the existing solutions.

Secure Resource Allocation for Cooperative OFDMA System With Untrusted AF Relaying

In this paper, we consider a cooperative orthogonal frequency division multiple access (OFDMA) system, where a source communicates with multiple users with the help of an untrusted relay. Since we assume no direct links between source and users because of the shadowing effect, the positive secrecy rate of the system cannot be obtained directly. Addressing this issue, we employ the user-aided cooperative jamming method to improve the secrecy performance. With the aim of maximizing the weighted sum secrecy rate, we formulate a joint resource allocation problem of power allocation, subcarrier assignment and subcarrier pairing. By using the alternative optimization and the Lagrange dual method, we solve this non-convex problem efficiently. Furthermore, to reduce the calculation complexity, we propose two suboptimal algorithms. Numerical results are presented to demonstrate the advantage of the proposed algorithms compared with the benchmarks on the secrecy performance. Moreover, we show that our proposed algorithms are more sensitive to user priority weights than benchmarks.

Enhanced physical layer security for cognitive radio systems through joint spectrum access and power allocation

Physical layer (PHY) security is an important issue in wireless communication systems. In this study, the authors investigate the interactions between the PHY security performance and the spectrum access technique in a cooperative cognitive radio (CR) network. In the classical spectrum access, if the measured energy on a given subchannel is less than a threshold, the subband is dedicated for CR transmission. Here, they consider a probabilistic spectrum access (PSA), which assigns to each primary subchannel a probability which is determined according to the measured energy on that subchannel. In addition, both spectrum access and CR power allocation are performed simultaneously. They formulate the general outage probability and some important PHY security performance metrics, such as average secrecy rate, secrecy outage probability, and probability of positive secrecy rate in terms of the spectrum access and optimal power allocation functions. The authors' numerical analysis indicates that the PSA method achieves a superior PHY security and outage performance compared to the classical threshold-based spectrum sensing and power allocation method.

Physical Layer Security Designs for 5G NOMA Systems With a Stronger Near-End Internal Eavesdropper

Serial interference cancellation (SIC) technology is the key to ensure a higher system capacity for NOMA. However, SIC may also introduce some critical security risks, since it requires near-end users (NU) demodulate far-end users’ (FU) signals and make the cancellations. It is hard to obtain positive secrecy rate in the presence of a stronger NU eavesdropper. To this end, this paper studies the security designs for a 5G NOMA system with a stronger NU internal eavesdropper. We first consider the two-user case and then extend our results to a multi-user case. After adjusting the order of SIC and employing a cooperative jammer, an optimal power allocation problem is built subject to users’ data rate and total power constraints. The global closed-form optimal solution is achieved for the two-user case, while a closed-form sub-optimal solution is obtained for the multi-user case. For better insight, the jamming gain is introduced to approximately measure the performance gain achieved. Simulation results show that positive secrecy rate is obtained while the users’ data rate are guaranteed.

Achieving Positive Secrecy Rate in Wireless Multiple Access Wiretap Channels

In this paper, we study the secure transmission in multiple access wiretap channels when the instantaneous channel state information (CSI) of the wiretap channels is unknown by the legitimate users. We propose a two-phase jamming-assisted secure transmission scheme based on the randomness and independence of wireless channels. In this scheme, we appropriately design artificial noise in two transmission phases and make sure that the eavesdropper's channel is degraded by the artificial noise but the legitimate user's channel is free of the artificial noise. We analyze the capacity of the legitimate channel after using successive interference cancellation (SIC), and demonstrate that the eavesdropping capacity has an upper bound. Furthermore, we prove that a positive secrecy rate can be achieved and the achievable secrecy rate can be maximized by allocating appropriate power to the private information and the artificial noise.

Securing Multi-User Broadcast Wiretap Channels With Finite CSI Feedback

In this work, we investigate the problem of secure broadcasting over block-fading wiretap channels with limited channel knowledge at the transmitter. More particularly, we analyze the effect of having a finite rate feedback on the throughput of multi-user broadcast wiretap channels. We consider that the transmitter is only provided by a $b$-bits feedback of the main channel state information (CSI) sent by each legitimate receiver, at the beginning of each fading block, over error-free public links with limited capacity. Also, we assume that the transmitter is aware of the statistics of the eavesdropper's CSI but not of its channel's realizations. Under these assumptions of CSI uncertainty, we characterize the ergodic secrecy capacity of the system when a common message is broadcasted to all legitimate receivers, the ergodic secrecy sum-capacity when multiple independent messages are transmitted, and the ergodic secrecy capacity region for the broadcast channel with confidential messages (BCCM). In all three scenarios, we show that as long as the transmitter has some knowledge of the main CSI, obtained even through a 1-bit CSI feedback, a non-zero secrecy rate can still be achieved. The impact of having the feedback sent over a binary erasure channel (BEC) is also investigated for the BCCM case. Here again, and even with the possibility of having the feedback bits erased, a positive secrecy rate can still be achieved as long as the erasure event is not a probability-one event. An asymptotic analysis of the obtained results is provided for the high SNR regime, and the scaling law of the system, when the number of legitimate receivers is large, is also presented.