This paper presents a quantified assessment of the physical layer security capabilities of reconfigurable intelligent surface (RIS)-aided wireless systems under eavesdropping. Specifically, we derive a closed-form expression for the ergodic secrecy capacity (ESC) that is adaptable to different types of fading and RIS size. The channels between the transmitter (TX) and RIS, the RIS and legitimate receiver as well as the TX and eavesdropper are assumed to follow independent mixture Gamma (MG) distributions. Note that MG is capable of modeling a large variety of well-known distributions, including Gaussian, Rayleigh, Nakagami-m, Rice, and others. The results reveal that as the RIS size increases, although the legitimate links diversity order increases, the ESC gain decreases.
A simple approximation for the secrecy outage probability (SOP) over generalized-K fading channels is developed. This approximation becomes tighter as the average signal-to-noise ratio (SNR) of the wiretap channel decreases. Based on this simple expression, we also analyze the asymptotic SOP in the high SNR region of the main channel. Besides simplifying the SOP expression significantly, this asymptotic SOP expression reveals the secrecy diversity order in a general case. Numerical results demonstrate the high accuracy of our proposed approximation results.
The secrecy outage performance of wireless communication systems operating over spatially correlated composite fading channels is analyzed in this paper. We adopt a multiplicative composite channel model for both the legitimate communication link and the link between the eavesdropper and the legitimate transmitter, consisting of Nakagami-$m$ distributed small-scale fading and shadowing (large-scale fading) modeled by the Gamma distribution. We consider the realistic case where small-scale fading between the links is independent, but shadowing is arbitrarily correlated, and present novel analyt…
An alternative or supplementary approach named as physical layer security has been proposed to afford an extra security layer on top of the conventional cryptography technique. In this paper, an overview of secrecy performance investigations over the classic Alice-Bob-Eve wiretap fading channels is conducted. On the basis of the classic wiretap channel model, we have comprehensively listed and thereafter compared the existing works on physical layer secrecy analysis considering the small-scale, large-scale, composite, and cascaded fading channel models. Exact secrecy metrics expressions, inclu…
In this paper, the physical layer security aspects of a wireless framework over α-\k{appa}-μ shadowed (AKMS) fading channel are examined by acquiring closed-form novel expressions of average secrecy capacity, secure outage probability (SOP), and strictly positive secrecy capacity. The lower bound of SOP is derived along with the asymptotic expression of SOP at the high signal-to-noise ratio regime in order to achieve secrecy diversity gain. Capitalizing on these expressions, the consequences due to the simultaneous occurrence of fading and shadowing are quantified. Finally, Monte-Carlo simulat…
This paper presents a polar coding scheme to achieve secrecy in block fading binary symmetric wiretap channels without the knowledge of instantaneous channel state information (CSI) at the transmitter. For this model, a coding scheme that hierarchically utilizes polar codes is presented. In particular, on polarization of different binary symmetric channels over different fading blocks, each channel use is modeled as an appropriate binary erasure channel over fading blocks. Polar codes are constructed for both coding over channel uses for each fading block and coding over fading blocks for cert…
The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The secrecy capacity region is first established for the parallel Gaussian BCC, and the optimal source power allocations that achieve the boundary of the secrecy capacity region are derived…
This paper deals with the secrecy capacity of the radio channel in interference-limited regime. We assume that interferers are uniformly scattered over the network area according to a Point Poisson Process and the channel model consists of path-loss, log-normal shadowing and Nakagami-m fading. Both the probability of non-zero secrecy capacity and the secrecy outage probability are then derived in closed-form expressions using tools of stochastic geometry and higher-order statistics. Our numerical results show how the secrecy metrics are affected by the disposition of the desired receiver, the …
Theoretical studies on physical layer security often adopt the secrecy outage probability as the performance metric for wireless communications over quasi-static fading channels. The secrecy outage probability has two limitations from a practical point of view: a) it does not give any insight into the eavesdropper's decodability of confidential messages; b) it cannot characterize the amount of information leakage to the eavesdropper when an outage occurs. Motivated by the limitations of the secrecy outage probability, we propose three new secrecy metrics for secure transmissions over quasi-sta…
The secrecy performance of realistic wireless multicast scenarios can be significantly deteriorated by the simultaneous occurrence of multipath and shadowing. To resolve this security threat, in this work an opportunistic relaying-based dual-hop wireless multicast framework is proposed in which the source dispatches confidential information to a bunch of receivers via intermediate relays under the wiretapping attempts of multiple eavesdroppers. Two scenarios, i.e. non-line of sight (NLOS) and line of sight (LOS) communications along with the multiplicative and LOS shadowing are considered wher…
We investigate the secure communications over correlated wiretap Rayleigh fading channels assuming the full channel state information (CSI) available. Based on the information theoretic formulation, we derive closed-form expressions for the average secrecy capacity and the outage probability. Simulation results confirm our analytical expressions.
In this paper, the secrecy analysis of physical layer when both the main and wiretap channels undergo $κ-μ$ shadowed fading channel is investigated. In particular, the average secrecy capacity (ASC), secure outage probability (SOP), the lower bound of SOP (SOP$^L$), and the probability of strictly positive secrecy capacity (SPSC) are derived by using the classic Wyner's wiretap model. Two different scenarios for the fading parameters, i.e., $μ$ and $m$ which represents the shadowing impact have been studied. These parameters are chosen first as arbitrary numbers, thus the performance metrics a…
We consider a two user fading Multiple Access Channel with a wire-tapper (MAC-WT) where the transmitter has the channel state information (CSI) to the intended receiver but not to the eavesdropper (eve). We provide an achievable secrecy sum-rate with optimal power control. We next provide a secrecy sum-rate with optimal power control and cooperative jamming (CJ). We then study an achievable secrecy sum rate by employing an ON/OFF power control scheme which is more easily computable. We also employ CJ over this power control scheme. Results show that CJ boosts the secrecy sum-rate significantly…
In this paper, we investigate the secrecy performance of stochastic MIMO wireless networks over small-scale $α$-$μ$ fading channels, where both the legitimate receivers and eavesdroppers are distributed with two independent homogeneous Poisson point processes (HPPPs). Specifically, accounting for the presence of non-colluding eavesdroppers, secrecy performance metrics, including the connection outage probability (COP), the probability of non-zero secrecy capacity (PNZ) and ergodic secrecy capacity, are derived regarding the $k$-th nearest/best user cases. The index for the $k$-th nearest user …
We investigate the secrecy capacity of an ergodic fading wiretap channel in which the main channel is correlated with the eavesdropper channel. In this study, the full Channel State Information (CSI) is assumed, and thus the transmitter knows the channel gains of the legitimate receiver and the eavesdropper. By analyzing the resulting secrecy capacity we quantify the loss of the secrecy capacity due to the correlation. In addition, we study the asymptotic behavior of the secrecy capacity as Signal-to-Noise Ratio (SNR) tends to infinity. The capacity of an ordinary fading channel logarithmicall…
We consider the secure transmission of information over an ergodic fading channel in the presence of an eavesdropper. Our eavesdropper can be viewed as the wireless counterpart of Wyner's wiretapper. The secrecy capacity of such a system is characterized under the assumption of asymptotically long coherence intervals. We first consider the full Channel State Information (CSI) case, where the transmitter has access to the channel gains of the legitimate receiver and the eavesdropper. The secrecy capacity under this full CSI assumption serves as an upper bound for the secrecy capacity when only …
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, t…
Secrecy outage probability (SOP) and secrecy rate (SR) of the reconfigurable intelligent surface (RIS) assisted wireless networks under Rician fading are investigated in this paper. More precisely, we enhance the secrecy performance of the considered networks by suppressing the wiretap channel instead of maximizing the main channel. We propose a simple heuristic algorithm to find out the optimal phase-shift of each RIS's element. Simulation results based on the Monte-Carlo method are given to verify the superiority of the proposed optimal phase-shifts compared to the random phase-shifts design…
The amount of sensitive data, which is transmitted wirelessly will increase with future technologies. This raises many questions about secure data transmission. Besides cryptography, information-theoretic security gained increasing attention over the recent years. Among others, it deals with the problem of secure data transmission on the physical layer to a legitimate receiver (Bob) in the presence of an eavesdropper (Eve). In this work, we investigate upper and lower bounds on the secrecy outage probability for slowly-fading wiretap channels with an arbitrary dependency structure between the …
In this paper, we consider the transmission of confidential messages over slow fading wireless channels in the presence of an eavesdropper. We propose a transmission scheme that employs a single reconfigurable antenna at each of the legitimate partners, whereas the eavesdropper uses a single conventional antenna. A reconfigurable antenna can switch its propagation characteristics over time and thus it perceives different fading channels. It is shown that without channel side information (CSI) at the legitimate partners, the main channel can be transformed into an ergodic regime offering a \tex…
This article investigates physical layer security (PLS) in reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) channels. Existing researches ignore the problem that secrecy rate can not be calculated if the eavesdropper's instantaneous channel state information (CSI) is unknown. Furthermore, without the secrecy rate expression, beamforming and phase shifter optimization with the purpose of PLS enhancement is not available. To address these problems, we first give the expression of secrecy outage probability for any beamforming…
This paper studies physical-layer secure transmissions from a transmitter to a legitimate receiver against an eavesdropper over slow fading channels, taking into account the impact of finite blocklength secrecy coding. A comprehensive analysis and optimization framework is established to investigate secrecy throughput for both single- and multi-antenna transmitter scenarios. Both adaptive and non-adaptive design schemes are devised, in which the secrecy throughput is maximized by exploiting the instantaneous and statistical channel state information of the legitimate receiver, respectively. Sp…
We consider the multi-antenna wiretap channel in which the transmitter wishes to send a confidential message to its receiver while keeping it secret to the eavesdropper. It has been known that the secrecy capacity of such a channel does not increase with signal-to-noise ratio when the transmitter has no channel state information (CSI) under mild conditions. Motivated by Jafar's robust interference alignment technique, we study the so-called staggered multi-antenna block-fading wiretap channel where the legitimate receiver and the eavesdropper have different temporal correlation structures. Ass…
The optimal power allocation that maximizes the secrecy capacity of block fading Gaussian (BF-Gaussian) networks with causal channel state information (CSI), M-block delay tolerance and a frame based power constraint is examined. In particular, we formulate the secrecy capacity maximization as a dynamic program. We propose suitable linear approximations of the secrecy capacity density in the low SNR, the high SNR and the intermediate SNR regimes, according to the overall available power budget. Our findings indicate that when the available power resources are very low (low SNR case) the optima…
A realistic performance assessment of any wireless technology requires the use of a channel model that reflects its main characteristics. The independent and identically distributed Rayleigh fading channel model has been (and still is) the basis of most theoretical research on multiple antenna technologies in scattering environments. This letter shows that such a model is not physically appearing when using a reconfigurable intelligent surface (RIS) with rectangular geometry and provides an alternative physically feasible Rayleigh fading model that can be used as a baseline when evaluating RIS…
In this paper we consider the secure transmission over the fast fading multiple antenna Gaussian broadcast channels with confidential messages (FMGBC-CM), where a multiple-antenna transmitter sends independent confidential messages to two users with information theoretic secrecy and only the statistics of the receivers' channel state information are known at the transmitter. We first use the same marginal property of the FMGBC-CM to classify the non-trivial cases, i.e., those not degraded to the common wiretap channels. We then derive the achievable rate region for the FMGBC-CM by solving the …
On the Secrecy Performance of Continuous-Aperture Arrays Over Fading Channels
School of Cyber Science and Engineering, Southeast University（东南大学网络空间安全学院）；School of Electronic Engineering and Computer Science, Queen Mary University of London（伦敦大学玛丽女王学院电子工程与计算机科学学院）；Department of Electrical and Electronic Engineering, The University of Hong Kong（香港大学电气电子工程学系）
In the spectrum-sharing technology, a secondary user may utilize the primary user's licensed band as long as its interference to the primary user is below a tolerable value. In this paper, we consider a scenario in which a secondary user is operating in the presence of both a primary user and an eavesdropper. Hence, the secondary user has both interference limitations and security considerations. In such a scenario, we study the secrecy capacity limits of opportunistic spectrum-sharing channels in fading environments and investigate the optimal power allocation for the secondary user under ave…
In this paper, we investigate the physical layer security over the Alternate Rician Shadowed fading channel, which is a novel channel model for body-centric wireless links and land mobile satellite. We derive exact closed-form expressions for the average secrecy capacity (ASC), secrecy outage probability (SOP), and probability of non-zero secrecy capacity (PNZ) for two cases: (i) m is a positive real number and (ii) m is a positive integer number, where m describes the level of fluctuation of the line-of-sight component. In the first case, SOP is derived in terms of the Meijer's G-function, wh…
In this paper, we consider the transmission of confidential information over a $κ$-$μ$ fading channel in the presence of an eavesdropper, who also observes $κ$-$μ$ fading. In particular, we obtain novel analytical solutions for the probability of strictly positive secrecy capacity (SPSC) and the lower bound of secure outage probability (SOP$^L$) for channel coefficients that are positive, real, independent and non-identically distributed ($i.n.i.d.$). We also provide a closed-form expression for the probability of SPSC when the $μ$ parameter is assumed to only take positive integer values. We …
Through ordinary transmissions over wireless multicast networks are greatly hampered due to the simultaneous presence of fading and shadowing of wireless channels, secure transmissions can be enhanced by properly exploiting random attributes of the propagation medium. This study focuses on the utilization of those attributes to enhance the physical layer security (PLS) performance of a dual-hop wireless multicast network over kappa-mu shadow-fading channel under the wiretapping attempts of multiple eavesdroppers. In order to improve the secrecy level, the best relay selection strategy among mu…
This paper considers secure communication over free-space optical (FSO) links suffering from turbulence-induced fading. In particular, we study the average secrecy capacity of applying physical layer security to achieve security in an FSO communication system with binary-level on-off keying intensity modulation and threshold detection, a widely used system in FSO communication. We first define the instantaneous secrecy capacity for our system and then provide a lower bound of it, which is achieved based on a simple design principle for practical applications and yields a simpler equation. We n…
The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The broadcast channel from the source node to receivers 1 and 2 is corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The parallel BCC with i…
Node selection is a simple technique to achieve diversity and thereby enhance the physical layer security in future wireless communication systems which require low complexity. High-speed data transmission often encounters frequency selective fading. In this context, we evaluate the exact closed-form expression for the ergodic secrecy rate (ESR) of the optimal source-destination pair selection scheme with single-carrier cyclic-prefix modulation, where the destination and eavesdropper channels both exhibit independent frequency selective fading with an arbitrary number of multipath components. …
Ensuring the physical layer security (PHY-security) of millimeter wave (mmWave) communications is one of the key factors for the success of 5G. Recent field measurements show that conventional fading models cannot accurately model the random fluctuations of mmWave signals. To tackle this challenge, the fluctuating two-ray (FTR) fading model has been proposed. In this correspondence, we comprehensively analyze the PHY-security in mmWave communications over FTR fading channels. More specifically, we derive analytical expressions for significant PHY-security metrics, such as average secrecy capac…
This paper presents a detailed secrecy outage performance analysis of correlated multi-antenna wiretap channels with three popular diversity combining schemes, namely maximal ratio combining, selection combining, and equal gain combining at the legitimate receiver. For single input multiple output wiretap channels, both exact and asymptotic expressions are derived for the secrecy outage probability (SOP) of these systems. The findings suggest that, compared with the scenario where all the channels are independent, correlation of the main channels alone increases the SOP by a factor of 1/ det(U…
With the completion of standardization of fifth-generation (5G) networks, the researchers have begun visioning sixth-generation (6G) networks that are predicted to be human-centric. Hence, similar to 5G networks, besides high data rate, providing secrecy and privacy will be the center of attention by the wireless research community. To support the visions beyond 5G (B5G) and 6G, in this paper we propose a secure radio frequency (RF)-free-space optical (FSO) mixed framework under the attempt of wiretapping by an eavesdropper at the RF hop. We assume the RF links undergo alpha-eta-mu fading wher…
This paper considers point to point secure communication over flat fading channels under an outage constraint. More specifically, we extend the definition of outage capacity to account for the secrecy constraint and obtain sharp characterizations of the corresponding fundamental limits under two different assumptions on the transmitter CSI (Channel state information). First, we find the outage secrecy capacity assuming that the transmitter has perfect knowledge of the legitimate and eavesdropper channel gains. In this scenario, the capacity achieving scheme relies on opportunistically exchangi…
The existing investigations on artificial noise (AN) security systems assumed that only null spaces is used to send AN signals, and all eigen-subchannels should be used to transmit messages. Our previous work proposed an AN scheme that allocates some of eigen-subchannels to transmit AN signals for improving secrecy rates. Nevertheless, our previous work considered only uncorrelated MIMO Rayleigh fading channels. In fact, the correlations among antennas exist in realistic scattering channel environments. In this paper, we extend our previous AN scheme to spatially correlated Rayleigh fading cha…
The focus of this paper is an information-theoretic study of retransmission protocols for reliable packet communication under a secrecy constraint. The hybrid automatic retransmission request (HARQ) protocol is revisited for a block-fading wire-tap channel, in which two legitimate users communicate over a block-fading channel in the presence of a passive eavesdropper who intercepts the transmissions through an independent block-fading channel. In this model, the transmitter obtains a 1-bit ACK/NACK feedback from the legitimate receiver via an error-free public channel. Both reliability and con…
In this paper, the delay limited secrecy capacity of the flat fading channel is investigated under two different assumptions on the available transmitter channel state information (CSI). The first scenario assumes perfect prior knowledge of both the main and eavesdropper channel gains. Here, upper and lower bounds on the secure delay limited capacity are derived and shown to be tight in the high signal-to-noise ratio (SNR) regime (for a wide class of channel distributions). In the second scenario, only the main channel CSI is assumed to be available at the transmitter. Remarkably, under this a…
The fading wire-tap channel is investigated, where the source-to-destination channel and the source-to-wire-tapper channel are corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information is assumed to be known at both the transmitter and the receiver. The parallel wire-tap channel with independent subchannels is first studied, which serves as an information-theoretic model for the fading wire-tap channel. The secrecy capacity of the parallel wire-tap channel is established. This result is then specialized to give the secrecy …
In this paper we study the problem of half-duplex active eavesdropping in fast fading channels. The active eavesdropper is a more powerful adversary than the classical eavesdropper. It can choose between two functional modes: eavesdropping the transmission between the legitimate parties (Ex mode), and jamming it (Jx mode) -- the active eavesdropper cannot function in full duplex mode. We consider a conservative scenario, when the active eavesdropper can choose its strategy based on the legitimate transmitter-receiver pair's strategy -- and thus the transmitter and legitimate receiver have to p…
In this paper, we investigate the physical layer security in the reconfigurable intelligent surface (RIS)-aided cell-free networks. A maximum weighted sum secrecy rate problem is formulated by jointly optimizing the active beamforming (BF) at the base stations and passive BF at the RISs. To handle this non-trivial problem, we adopt the alternating optimization to decouple the original problem into two sub-ones, which are solved using the semidefinite relaxation and continuous convex approximation theory. To decrease the complexity for obtaining overall channel state information (CSI), we exten…
Leveraging on the reconfigurable intelligent surface (RIS) paradigm for enabling the next Internet of Things (IoT) and 6G era, this paper develops a comprehensive theoretical framework characterizing the performance of RIS-assisted communications in a plethora of propagation environments. We derive unified mathematical models for the outage probability and ergodic capacity of single and multiple-element RIS over Fox's H fading channel, which includes as special cases nearly all linear and non linear multi-path and shadowing fading models adopted in the open literature. For gleaning further ins…
Simultaneous wireless information and power transfer (SWIPT) has recently drawn significant interests for its dual use of radio signals to provide wireless data and energy access at the same time. However, a challenging secrecy communication issue arises as the messages sent to the information receivers (IRs) may be eavesdropped by the energy receivers (ERs), which are presumed to harvest energy only from the received signals. To tackle this problem, we propose in this paper an artificial noise (AN) aided transmission scheme to facilitate the secrecy information transmission to IRs and yet mee…
This paper investigates the secrecy performance of sub-optimal transmitter selection (SS) and optimal selection (OS) schemes in a system comprising multiple transmitters, multiple eavesdroppers, and a single destination in frequency-selective fading channels with single carrier cyclic prefix modulation. Considering unreliable backhaul links between the access point and the transmitters, we analyze secrecy performance in two scenarios: when backhaul activity knowledge is available (KA) and when backhaul activity knowledge is unavailable (KU). Closed-form expressions for the secrecy outage proba…
In this era of 5G technology, the ever-increasing demands for high data rates lead researchers to develop hybrid satellite-terrestrial (HST) networks as a substitution to the conventional cellular terrestrial systems. Since an HST network suffers from a masking effect which can be mitigated by adopting the terrestrial relaying strategy, in this work, we focus on wireless multicasting through an HST relaying net-work (HSTRN) in which a satellite sends messages to multiple terrestrial nodes via multiple relays under the wiretapping efforts of multiple eavesdroppers. Our concern is to protect the…
This paper investigates the impact of realistic propagation conditions on the achievable secrecy performance of multiple-input multiple-output systems in the presence of an eavesdropper. Specifically, we concentrate on the $κ$-$μ$ shadowed fading model because its physical underpinnings capture a wide range of propagation conditions, while, at the same time, it allows for much better tractability than other state-of-the-art fading models. By considering transmit antenna selection and maximal ratio combining reception at the legitimate and eavesdropper's receiver sides, we study two relevant sc…
In this paper, we consider secure transmissions in ergodic Rayleigh fast-faded multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) wiretap channels with only statistical channel state information at the transmitter (CSIT). When the legitimate receiver has more (or equal) antennas than the eavesdropper, we prove the first MIMOME secrecy capacity with partial CSIT by establishing a new secrecy capacity upper-bound. The key step is to form an MIMOME degraded channel by dividing the legitimate receiver's channel matrix into two submatrices, and setting one of the submatrices to b…
We consider a fading wiretap channel model where the transmitter has only statistical channel state information, and the legitimate receiver and eavesdropper have perfect channel state information. We propose a sequence of non-random lattice codes which achieve strong secrecy and semantic security over ergodic fading channels. The construction is almost universal in the sense that it achieves the same constant gap to secrecy capacity over Gaussian and ergodic fading models.
Reconfigurable intelligent surface (RIS)-aided wireless communications have drawn significant attention recently. We study the physical layer security of the downlink RIS-aided transmission framework for randomly located users in the presence of a multi-antenna eavesdropper. To show the advantages of RIS-aided networks, we consider two practical scenarios: Communication with and without RIS. In both cases, we apply the stochastic geometry theory to derive exact probability density function (PDF) and cumulative distribution function (CDF) of the received signal-to-interference-plus-noise ratio.…
We analyze a secure dual-hop mixed radio frequency-free space optical (RF-FSO) downlink simultaneous wireless information and power transfer (SWIPT) systems. The FSO link and all RF links experience Gamma-Gamma, independent and identical Nakagami-$m$ fading, respectively. We analyze the effects of atmospheric turbulence, pointing error, detection technology, path loss, and energy harvesting on secrecy performance. Signal-to-noise ratios at both legitimate and illegitimate receivers are not independent since they are both simultaneously influenced by the FSO link. We derive the closed-form expr…
