Double Rayleigh Fading Channels Research Articles

Secrecy and Throughput Performance of Cooperative Cognitive Decode-and-Forward Relaying Vehicular Networks with Direct Links and Poisson Distributed Eavesdroppers

Cooperative communication and cognitive radio can effectively improve spectrum utilization, coverage range, and system throughput of vehicular networks, whereas they also incur several security issues and wiretapping attacks. Thus, security and threat detection are vitally important for such networks. This paper investigates the secrecy and throughput performance of an underlay cooperative cognitive vehicular network, where a pair of secondary vehicles communicate through a direct link and the assistance of a decode-and-forward (DF) secondary relay in the presence of Poisson-distributed colluding eavesdroppers and under an interference constraint set by the primary receiver. Considering mixed Rayleigh and double-Rayleigh fading channels, we design a realistic relaying transmission scheme and derive the closed-form expressions of secrecy and throughput performance, such as the secrecy outage probability (SOP), the connection outage probability (COP), the secrecy and connection outage probability (SCOP), and the overall secrecy throughput, for traditional and proposed schemes, respectively. An asymptotic analysis is further presented in the high signal-to-noise ratio (SNR) regime. Numerical results illustrate the impacts of network parameters on secrecy and throughput and reveal that the advantages of the proposed scheme are closely related to the channel gain of the relay link compared to the direct link.

Performance analysis of ambient backscatter communication empowered IoV networks

This paper investigates the performance of Internet-of-Vehicles networks supporting vehicular communication applications empowered by ambient backscatter communication technology. Specifically, we consider that the tag and reader are mounted on the vehicles while the ambient radio frequency source is a fixed infrastructure, allowing for both vehicle-to-vehicle and vehicle-to-infrastructure modes of communication in the network under consideration. We evaluate the exact outage probability expression for the AmBC-enabled Internet-of-Vehicles systems by characterizing the fading associated with vehicle-to-infrastructure and vehicle-to-vehicle transmissions as Rayleigh distributed and cascaded (double) Rayleigh distributed, respectively. Also, asymptotic outage probability expression is derived under high signal-to-noise ratio regime, from which a meaningful discussion on the system’s diversity order is carried out. Moreover, we deduce the tight ergodic capacity expression over mixed Rayleigh and double-Rayleigh fading channels. Finally, the simulation studies verify the proposed theoretical framework and show the impact of various channel and system parameters on the outage probability and ergodic capacity performance.

Physical layer security performance of NOMA-assisted vehicular communication systems over double-Rayleigh fading channels

In this paper, we investigate the secrecy performance of a downlink non-orthogonal multiple access enabled V2V communication system wherein a source vehicle communicates with two authenticated user vehicles, i.e., far user and near user, in the presence of a passive eavesdropper vehicle. Moreover, we formulate two scenarios based on the eavesdropper’s decoding capabilities; (1) Scenario I: when the eavesdropper vehicle has comparable decoding capabilities as with the authorized user vehicles, and (2) Scenario II: when the eavesdropper is entirely capable of perfectly decoding the signals from both authorized user vehicles. For such a system configuration with Scenarios I &II, we deduce the analytical expressions for the secrecy outage probability (SOP) and ergodic secrecy capacity over independent but not necessarily identically distributed double-Rayleigh fading channels. Further, to obtain insights into the secrecy diversity order for the legitimate user vehicles under Scenarios I &II, we present the asymptotic SOP analysis by taking three cases into account; (1) Case 1: when the average transmit signal-to-noise ratio approaches infinity, (2) Case 2: when the average channel gains of the user vehicles tend to infinity with fixed average channel gains corresponding to the eavesdropper, and (3) Case 3: when the average channel gains pertaining to the user vehicles and the eavesdropper tend to infinity. From which, we can infer that the secrecy diversity order of the far user vehicle is zero for Cases 1, 2, & 3, whereas the secrecy diversity order of the near user vehicle is zero for Cases 1 & 3 and one for Case 2, under Scenarios I &II. The numerical and simulation results corroborate our theoretical investigations. Our results demonstrate the impact of transmit power, power allocation factor, channel conditions of legitimate users and eavesdropper on the system’s secrecy performance.

Performance analysis and optimization of energy harvesting cognitive multi-hop relay network over mixed Rayleigh and double-Rayleigh fading channels

In this paper, we investigate the outage performance of an energy harvesting underlay cognitive multi-hop relay network. In the network, energy-constrained secondary network (SN) nodes harvest energy from radio frequency signal of a power beacon (PB) node. The source node transmits information to destination node via multiple intermediate relay nodes by using a time division broadcast protocol, and the hardware impairments of SN nodes’ transceiver are modeled. The outage performance of SN is analyzed and evaluated by accurately approximate and asymptotic closed-form expressions of outage probability (OP) over quasi-static mixed Rayleigh and double-Rayleigh fading channels. Additionally, due to the complexity of OP expression, a chaotic dragonfly algorithm (CDA) is proposed to jointly optimize energy harvesting ratio and PB node’s abscissa, which can achieve OP minimization of SN. Extensive simulations demonstrate the correctness of theoretical analysis and the effectiveness of the proposed CDA.

Improved S-AF and S-DF Relaying Schemes Using Machine Learning Based Power Allocation Over Cascaded Rayleigh Fading Channels

We investigate the performance of a dual-hop intervehicular communications (IVC) system with relay selection strategy. We assume a generalized fading channel model, known as cascaded Rayleigh (also called n*Rayleigh), which involves the product of n independent Rayleigh random variables. This channel model provides a realistic description of IVC, in contrast to the conventional Rayleigh fading assumption, which is more suitable for cellular networks. Unlike existing works, which mainly consider double-Rayleigh fading channels (i.e, n = 2); our system model considers the general cascading order n, for which we derive an approximate analytic solution for the outage probability under the considered scenario. Also, in this study we propose a machine learning-based power allocation scheme to improve the link reliability in IVC. The analytical and simulation results show that both selective decode-and-forward (S-DF) and amplify-and-forward (S-AF) relaying schemes have the same diversity order in the high signal-to-noise ratio regime. In addition, our results indicate that machine learning algorithms can play a central role in selecting the best relay and allocation of transmission power.

Evaluating the Performance of Full-Duplex Energy Harvesting Vehicle-to-Vehicle Communication System over Double Rayleigh Fading Channels

In this paper, we analyze the performance of vehicle-to-vehicle (V2V) communication system, which employs full-duplex (FD) and energy harvesting (EH) techniques at source and relay nodes from power beacon (PB) through radio frequency. Unlike previous systemswhere all nodes located at fixed locations, we investigate the case that three nodes (source, relay,and destination) are moving vehicles. Therefore, the channels between them follow double (cascade) Rayleigh fading distributions. Furthermore, the source and relay nodes can harvest the energy from PB for data transmission when they move on the road. We derive the exact expressions of the outage probability (OP) and symbol error probability (SEP) of the proposed system and then intensively study the impacts of various parameters such as the number transmission antennas of PB, the time duration for EH, the distances between nodes, and the residual self-interference (RSI) at the FD relay node on the system performance. Monte-Carlo simulations validate all theory analysis. Numerical results show that system performance is strongly impacted by the number of transmission antennas of the power beacon, the EH duration, the RSI, and the distances between nodes. Moreover, for a given transmission of power beacon and the SIC capability of the FD relay node, there exist optimal EH duration and optimal distance from the source to relay, which provide the best system performance.

Toward Physical-Layer Security for Internet of Vehicles: Interference-Aware Modeling

The physical-layer security (PLS) of wireless networks has witnessed significant attention in next-generation communication systems due to its potential toward enabling protection at the signal level in dense network environments. The growing trends toward smart mobility via sensor-enabled vehicles are transforming today's traffic environment into Internet of Vehicles (IoVs). Enabling PLS for IoVs would be a significant development considering the dense vehicular network environment in the near future. In this context, this article presents a PLS framework for a vehicular network consisting a legitimate receiver and an eavesdropper, both under the effect of interfering vehicles. The double-Rayleigh fading channel is used to capture the effect of mobility within the communication channel. The performance is analyzed in terms of the average secrecy capacity (ASC) and secrecy outage probability (SOP). We present the standard expressions for the ASC and SOP in alternative forms, to facilitate analysis in terms of the respective moment generating function (MGF) and characteristic function of the joint fading and interferer statistics. Closed-form expressions for the MGFs and characteristic functions were obtained and Monte Carlo simulations were provided to validate the results. Approximate expressions for the ASC and SOP were also provided, for easier analysis and insight into the effect of the network parameters. The results attest that the performance of the considered system was affected by the number of interfering vehicles as well as their distances. It was also demonstrated that the system performance closely correlates with the uncertainty in the eavesdropper's vehicle location.

Large Intelligent Surfaces With Discrete Set of Phase-Shifts Communicating Through Double-Rayleigh Fading Channels

Despite many studies already published on large intelligent surfaces (LIS), there are still some gaps in mathematical models in the face of possible scenarios. In this work, we evaluate the performance of a single-input single-output (SISO) system in which an LIS acts as a controllable scatterer. We consider that the direct link between the transmitting and receiving devices is non-existent due to a blockage. Quantization phase errors at the LIS are considered since a high precision configuration of the reflection phases is not always feasible. We derive exact closed-form expressions for the spectral efficiencies, outage probabilities, and average symbol error rate (SER) of different modulations schemes. We assume a more comprehensive scenario in which b bits are dedicated to the phase adjustment of the LIS' elements. Based on Monte Carlo simulations, we prove the excellent accuracy of our approach and investigate the behavior of the power scaling law and the power required to reach a specific capacity, depending on the number of reflecting elements. We show that an LIS with approximately fifty elements and four dedicated bits for phase quantization outperforms the conventional system without LIS.

Performance of downlink NOMA‐enabled vehicular communications over double Rayleigh fading channels

Non-orthogonal multiple access (NOMA) is an attractive candidate for future wireless networks. Recently, vehicular communications with NOMA have received substantial research attention owing to their appealing advantages. In this study, the authors investigate the performance of downlink power-domain NOMA-enabled vehicular communications, in which a base station communicates with two users UE1 (far user) and UE2 (near user). Since all the nodes are moving vehicles, the channels for vehicular links experience independent and non-identically distributed double-Rayleigh fading. Specifically, the authors derive the outage probabilities of individual users and overall system under two scenarios of interest, viz. (i) when the rate of NOMA system falls below the fixed target rate and (ii) when NOMA system achieves lower rate than orthogonal multiple access (OMA) rate. The authors also derive the average bit error rate (ABER) and ergodic capacity expressions for the considered system. The numerical and simulation results validate the proposed analytical findings, and demonstrate the impacts of various parameters on the system performance. The authors further show that NOMA scheme is superior than OMA in terms of outage probability and ergodic capacity, whereas OMA outperforms NOMA in terms of ABER because OMA users do not have inter-user interferences.

Secrecy Performance of Cooperative Cognitive AF Relaying Networks With Direct Links Over Mixed Rayleigh and Double-Rayleigh Fading Channels

This paper investigates the secrecy performance of an underlay cooperative cognitive relaying network, wherein a secondary source vehicle communicates with a fixed secondary destination terminal via a direct link and with the assistance of a secondary amplify-and-forward relay vehicle in the presence of a passive secondary eavesdropper vehicle, taking into consideration of interference at the primary user. We assume that the eavesdropper vehicle takes the advantages of both the relay link and direct link. We consider that vehicle-to-vehicle links are modeled as double-Rayleigh fading, while vehicle-to-fixed infrastructure links are modeled as Rayleigh fading. Such a scenario finds it relevancy in vehicle-to-vehicle communication and/or vehicle-to-infrastructure communication under spectrum sharing heterogeneous cooperative vehicular networks. For such a realistic scenario, in particular, we derive a tight lower bound expression of the secrecy outage probability under mixed Rayleigh and double-Rayleigh fading channels. We also present an effective secrecy diversity order analysis and show that the considered system can achieve a secrecy diversity order of 2 for infinitely large average channel gain values of the main links. Finally, we demonstrate the accuracy of our analytical findings via numerical and simulation results and show the impact of channel conditions, primary interference constraints, and direct links on the secrecy performance of the considered system.

Secrecy Analysis of Cooperative Vehicular Relaying Networks over Double-Rayleigh Fading Channels

In this paper, we investigate physical-layer security performance of the cooperative vehicular relaying networks, wherein the communication from a source vehicle to the destination vehicle is assisted by an amplify-and-forward (AF) relay vehicle in the presence of a passive eavesdropper vehicle. We assume that the communication links between the vehicles experience double-Rayleigh fading. We also consider two AF relaying protocols: (1) fixed gain relaying which requires partial channel state information (CSI), and (2) variable gain relaying which requires full CSI. Specifically, we derive the novel intercept probability and ergodic secrecy capacity expressions for both fixed and variable gain relaying in the presence of double-Rayleigh fading channels. The numerical and simulation results verify our theoretical and analytical findings, and show the impacts of channel conditions and relay and eavesdropper locations on the system secrecy performance.

Outage probability and ergodic capacity analysis in power splitting based full-duplex relaying networks of double rayleigh fading channel for vehicular communications

<p><span>In this </span><span lang="EN-GB">research</span><span>, we present and investigate the system performance analysis in terms of the outage probability (OP) and ergodic capacity (EC) of the Full-duplex (FD) relaying networks via double Rayleigh fading channel. In this system model, we propose the power splitting (PS) protocol for the vehicular communications network. Firstly, we analyze and derive the integral form of the system OP and EC. Then, the correctness of the OP and EC expressions are verified by the Monte Carlo simulation. Finally, we can see that the analytical and the simulation results are matched with each other in the connection with the main system parameter.</span></p>

Performance analysis of vehicle-to-vehicle communication with full-duplex amplify-and-forward relay over double-Rayleigh fading channels

In this paper, we investigate a vehicle-to-vehicle (V2V) communication system where a full-duplex (FD) relay uses amplify-and-forward (AF) protocol. We consider two cases of the AF protocol at the FD relay, i.e. fixed and variable gain relaying. Furthermore, the channels between the nodes are characterized as the double (cascaded) Rayleigh fading distributions. We derive the exact closed-form expressions of the outage probabilities (OPs) and symbol error rates (SERs) in these two cases. Numerical results show the impacts of the double Rayleigh fading channels on the system performance in comparison with those of Rayleigh fading channels. Moreover, the effects of the distance, path loss exponent, and residual self-interference (RSI) on the system performance are also studied. We find that for a given node transmission power, there exist optimal distances between vehicles for the fixed and variable gain relaying which provide the best system performance. All analysis results in this paper are validated by Monte-Carlo simulation results to confirm the correctness of the derived mathematical expressions.

Performance Analysis of Full-Duplex Vehicle-to-Vehicle Relay System over Double-Rayleigh Fading Channels

In this paper, we study the performance of a full-duplex (FD) relay system in vehicle-to-vehicle (V2V) communication. In this relay communication system, the communication link from the source node to the relay node can be modeled by Rayleigh fading or double (cascaded) Rayleigh fading distributions while the link from the relay node to the destination node is modeled by double Rayleigh fading distribution. Through the numerical calculation, we obtain the exact analytical expressions for the outage probabilities (OPs) and symbol error rates (SERs) in two cases, i.e. case A (the first hop is the Rayleigh fading channel and the second hop is double Rayleigh fading channel) and case B (two hops are the double Rayleigh fading channels). From these obtained mathematical expressions, the impacts of the distances between the communication nodes and the residual self-interference caused by the imperfect self-interference cancellation at the FD relay are studied. In addition, the effects of path loss exponent and the transmission power at the FD relay are also investigated. Numerical results show that the system performance in terms of OP and SER in the case of double Rayleigh fading channels is significant lower than the case of Rayleigh fading channels. Monte-Carlo simulations are conducted to validate the correctness of these numerical results.

On Physical Layer Security of Double Rayleigh Fading Channels for Vehicular Communications

In this letter, we study the physical layer secrecy performance of the classic Wyner’s wiretap model over double Rayleigh fading channels for vehicular communications links. We derive novel and closed-form expressions for the average secrecy capacity (ASC) taking into account the effects of fading, path loss, and eavesdropper location uncertainty. The asymptotic analysis for ASC is also conducted. The derived expressions can be used for secrecy capacity analysis of a number of scenarios including vehicular-to-vehicular (V2V) communications. The obtained results reveal the importance of taking the eavesdropper location uncertainty into consideration while designing V2V communication systems.

Physical Layer Security in Cooperative AF Relaying Networks With Direct Links Over Mixed Rayleigh and Double-Rayleigh Fading Channels

In this paper, we investigate the secrecy performance of a dual-hop cooperative relaying network, where a source node communicates with a destination node via an amplify-and-forward relay node and via direct link in the presence of a passive eavesdropper. In this network, the eavesdropper exploits the advantages of both direct and relay links. We assume that the source, relay, and eavesdropper nodes are mobile, and the destination node is stationary. Moreover, we consider that the source-relay, relay-destination, and source-destination links experience Rayleigh fading, whereas source-eavesdropper and relay-eavesdropper links undergo double-Rayleigh fading. Examples of such scenario are encountered in vehicle-to-vehicle communication and/or vehicle-to-infrastructure communication under cooperative vehicular networks. In particular, we derive new tight closed-form expressions for the secrecy outage probability and ergodic secrecy capacity of the considered system under mixed fading environments. In addition, we present an effective secrecy diversity order within the main-to-eavesdropper ratio ranges of practical interest, and demonstrate that the secrecy diversity order of 2 can be achieved. Finally, the numerical and simulation results corroborate our analytical findings, and show the occurrence conditions for secrecy outage probability and ergodic secrecy capacity floors, and impacts of channel conditions and relay and eavesdropper positions on the system secrecy performance.

STTC design for vehicular communication systems employing fixed‐gain AF PLNC over cascaded fading channels

In this study, the authors combine physical layer network coding (PLNC) and space-time trellis coding (STTC) techniques to improve the error performance of vehicle-to-vehicle (V2V) communication systems where all fading channels are assumed to undergo double Rayleigh fading (DRF) which is worse than Rayleigh fading used in cellular communications. In the authors' analysis, they show that the DRF channels can be modelled by using the mixture gamma distribution. After that, pairwise error probability (PEP) analysis is performed for a fixed-gain amplify-and-forward PLNC V2V system employing STTC over the DRF channels, and an upper bound for the PEP is obtained. By examining the behaviour of the upper bound expression in the high SNR region, they derive a new design criterion for STTCs. Finally, using this criterion they propose novel STTCs with 4 and 8 states for V2V systems employing PLNC over the DRF channels.

Throughput and Delay Analysis of HARQ With Code Combining Over Double Rayleigh Fading Channels

This paper proposes the use of hybrid automatic repeat request (HARQ) with code combining (HARQ-CC) to offer reliable communications over double Rayleigh channels. The double Rayleigh fading channel is of particular interest to vehicle-to-vehicle communication systems as well as amplify-and-forward relaying and keyhole channels. This paper studies the performance of HARQ-CC over double Rayleigh channels from an information theoretic perspective. Analytical approximations are derived for the $\epsilon$ -outage capacity, the average number of transmissions, and the throughput of HARQ-CC. Moreover, we evaluate the delay experienced by Poisson-arriving packets for HARQ-CC. We provide analytical expressions for the average waiting time, the packets sojourn time, the average consumed power, and the energy efficiency. In our investigation, we take into account the impact of imperfect feedback on different performance metrics. Additionally, we explore the tradeoff between energy efficiency and the throughput. The proposed scheme is shown to maintain the outage probability below a specified threshold $\epsilon$ , which ensures the link reliability. Meanwhile, HARQ-CC adapts implicitly the transmission rate to the channel conditions such that the throughput is maximized. Our results demonstrate that HARQ-CC allows improving the achievable communication rate compared to fixed time diversity schemes. To maximize the throughput of HARQ-CC, the rate per HARQ round should be less than the rate required to meet the outage constraint. Our investigation of the performance of HARQ-CC over Rayleigh and double Rayleigh channels shows that double Rayleigh channels have a higher severity of fading and result in a larger degradation of the throughput. Our analysis reveals that HARQ with incremental redundancy achieves a larger throughput compared to HARQ-CC, whereas HARQ-CC is simpler to implement, has a lower decoding complexity, and requires less memory resources.

Full Duplex AF and DF Relaying Under Channel Estimation Errors for V2V Communications

In this paper, we investigate the outage performance of full-duplex (FD) and half-duplex (HD) vehicle to vehicle (V2V) networks. We consider two vehicular communication scenarios with the assistance of roadside unit (RSU), i.e., RSU-to-vehicle-to-vehicle (RVV) and vehicle-to-RSU-to- vehicle (VRV) scenarios. In particular, we analyze the outage performance of vehicular networks with the amplify-and-forward (AF) and decode-and-forward (DF) protocols under the effect of residual loop-back-interference (LBI) and channel estimation errors. For RVV scenario, the upper bounds for the outage probability of the AF based FD and HD relaying over double Rayleigh fading channels are derived. Moreover, we derive the approximate closed form expressions for the outage probability of the DF based FD and HD relaying protocol over Rayleigh fading channels; For VRV scenario, the exact closed-form expressions for the outage probability of the AF and DF relaying protocols are presented in case of FD and HD modes. Furthermore, we derive the approximate closed-form expressions for the outage probability of hybrid FD/HD mode on AF and DF relaying protocols. The numerical and simulation results corroborate our theoretical ones and quantify the impact of the data rates, channel estimation errors and the residual LBI on the system performance.

Modeling of Non-WSSUS Double-Rayleigh Fading Channels for Vehicular Communications

This paper deals with the modeling of nonstationary time-frequency (TF) dispersive multipath fading channels for vehicle-to-vehicle (V2V) communication systems. As a main contribution, the paper presents a novel geometry-based statistical channel model that facilitates the analysis of the nonstationarities of V2V fading channels arising at a small-scale level due to the time-varying nature of the propagation delays. This new geometrical channel model has been formulated following the principles of plane wave propagation (PWP) and assuming that the transmitted signal reaches the receiver antenna through double interactions with multiple interfering objects (IOs) randomly located in the propagation area. As a consequence of such interactions, the first-order statistics of the channel model’s envelope are shown to follow a worse-than-Rayleigh distribution; specifically, they follow a double-Rayleigh distribution. General expressions are derived for the envelope and phase distributions, four-dimensional (4D) TF correlation function (TF-CF), and TF-dependent delay and Doppler profiles of the proposed channel model. Such expressions are valid regardless of the underlying geometry of the propagation area. Furthermore, a closed-form solution of the 4D TF-CF is presented for the particular case of the geometrical two-ring scattering model. The obtained results provide new theoretical insights into the correlation and spectral properties of small-scale nonstationary V2V double-Rayleigh fading channels.