Expression For Probability Research Articles

Quantization rule for transition suppression in dynamic two-level system

The transmission probability in a generic two-quasi-state system is addressed. An approximate expression for the transmission probability between the two quasi-states is derived for the case where the energy gap between the two states varies. Unlike the Landau-Zener formula, the temporal change can have a generic form and can vanish several times. In particular, when the energy gap vanishes twice, an analytical quantization rule for the suppression of transmission between two quasi-states is derived.

STAR-RIS-NOMA empowered vehicle-to-vehicle communications: Outage and ergodic capacity analysis

This paper delves into the performance evaluation of a non-orthogonal multiple access (NOMA) enabled vehicle-to-vehicle (V2V) communication system empowered by simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS). Herein, we consider that a moving access point (AP) transmits superimposed signals to nearby and distant NOMA vehicles simultaneously via reflection and transmission through a STAR-RIS equipped vehicle with 2N reconfigurable elements, respectively. Specifically, by characterizing all V2V channels as double-Rayleigh fading distributed, we derive the outage probability (OP) and ergodic capacity (EC) expressions for each NOMA vehicle, by employing both perfect and imperfect successive interference cancellation (SIC) at nearby vehicle user. Furthermore, we present the asymptotic OP behavior at high signal-to-noise ratio (SNR) regime to gain deeper insights into the diversity order of NOMA vehicles. The findings reveal that the nearby vehicle under perfect SIC and far vehicle experience a diversity order of Nπ4256−π2, which is the function of number of reconfigurable elements (N) in the STAR-RIS. Whereas, a zero diversity order is obtained for nearby user under imperfect SIC case. Moreover, we analytically discuss the high SNR slopes of EC for both user vehicles. Furthermore, Monte-Carlo simulations are conducted to validate our analytical results under various channel and system parameter configurations. We also provide a comparison between the proposed scheme and STAR-RIS based orthogonal multiple access and cooperative relaying systems.

Secrecy performance intelligent prediction for CRNs: An Self-CondenseNet approach

This paper studies the physical layer security (PLS) of cognitive radio networks (CRNs) with Fisher–Snedecor F distribution. To resolve the security issues within CRNs, we derived exact expressions of the security outage probability (SOP) and the probability of strict positive secrecy capacity (SPSC) for the first time, where the SOP and SPSC are uniformly given by Meijer’s G-function. The correctness of the theoretical derivations is proved by Monte Carlo simulations. The results indicate that reducing m and increasing the ratio of (ms,μE) will reduce SOP and increase SPSC. Moreover, we proposed the Self-CondenseNet model to predict the security performance of the system. By comparing with three deep learning algorithms of Transformer, MLP-Mixer and CondenseNet, the results show that the proposed Self-CondenseNet has the best prediction performance. Compared with the CondenseNet, the proposed Self-CondenseNet has a 78.26% higher accuracy and a 12.86% lower time complexity. Compared with the MLP-Mixer, the proposed Self-CondenseNet has a 85.29% higher accuracy. The comparison results show that the proposed algorithm has high prediction accuracy and low time complexity, and can be widely used in complex and changeable scenarios such as 5G, Internet of Vehicles (IoV), and mobile vehicle networking .etc.

Coverage Probability Analysis of a Double IRS Assisted SISO Communication System

Intelligent reflecting surface (IRS) improves wireless communication efficiency and coverage probability. Existing studies focus on IRS deployment but overlook optimal fading channels. This research aims to identify and analyze the most effective channel fading estimation for the double IRS system model. The coverage probability using two-IRS is derived under different fading channels like Rayleigh and Rician to find the optimal solution in a Single-Input-Single-Output (SISO) system. Additionally, a closed-form expression for the coverage probability using statistical channel state information is derived while assuming no direct path between the transmitter and receiver. The analytical results are validated through simulations. It offers valuable insights into the modeling and analysis of double IRS-assisted wireless communication systems.

Weighted joint LRTs for cooperative spectrum sensing using K-means clustering

In this paper, a blind centralized cooperative spectrum sensing (CSS) with soft decision fusion is considered. The fusion center (FC) constructs the energy vector from the collaborating secondary nodes. The energy feature is assumed to be an efficient measure, as it is widely used and directly correlates with the strength of the received signal. The K-means clustering algorithm is employed to extract descriptive statistical features about the distributions of the absence and presence of the primary user (PU) signal, such as the mean and non-centrality parameter. In the framework of this statistical analysis, the signal-to-noise ratio (SNR) at each node is easily estimated and examined. Equal, selective, and weighted combining techniques are applied to develop three joint likelihood ratio test (JLRT)-based algorithms. These algorithms are implemented in the context of simple hypothesis testing, where the distribution of the data is fully specified. Furthermore, they are justified by the Neyman-Pearson theorem, which constructs the most powerful test for a given significance level. The proposed selective and weighted JLRT approaches are based on the estimated SNRs at each sensor, reflecting their reliability. Several comparison scenarios between the proposed algorithms, K-means, fuzzy c-means (FCM), and OR-rule are simulated over Rayleigh fading channel with low average SNR and few samples. The simulation results reveal that the proposed tests outperform other CSS techniques. Additionally, asymptotic theoretical expressions for probability of detection and the probability of false alarm are derived, which show high agreement with the simulated results.

Improving the security of NOMA cognitive networks

Aiming at the scenario where the eavesdropper try to eavesdrop on the confidential messages of secondary trusted users, two physical-layer network coding (PNC) strategies, namely dual power superposition (PS-PS) encoding strategy and bit-level exclusive-or power superposition (XOR-PS) encoding strategy, are proposed to improve the security performance of cognitive non-orthogonal multiple access (NOMA) networks with the help of the data transmitted by the primary user. Considering the overlay spectrum sharing mechanism and the imperfect successive interference cancellation (SIC) technology, we first derive the closed-form accurate expressions of the outage probability and intercept probability of the secondary network with these two schemes over Rayleigh fading, and also give the asymptotic outage probability in the high signal-to-noise ratio (SNR) regime. Then, the correctness of the theoretical results is verified by simulation. For comparison, we also use the scheme without the assistance of the primary user as the benchmark scheme, which is represented by NPS. Finally, the simulation results show that the security of the proposed PS-PS and XOR-PS schemes is much better than that of the NPS scheme in the case of without reducing the outage performance.

Reliability and Security Performances Analysis of Rate Splitting Based VLC System With HARQ

This work first attempts to investigate the reliability and physical layer security (PLS) performances of a rate splitting (RS) based visible light communication (VLC) system with one trusted user and one untrusted user. Specifically, the hybrid automatic repeat request (HARQ) protocol is adopted at the trusted user and the movement of users is assumed to be subject to the random way point (RWP) model with four decoding strategies considered at receiver side. The exact closed-form expressions of outage probability (OP) for both users are then obtained, and the analytical expressions of secrecy outage probability (SOP), reliable and secure transmission probability (RSP), and effective secrecy throughput (EST) of trusted user are also mathematically derived. Through simulations, it is found that to guarantee the reliability and PLS performances, the trusted user should first decode the untrusted user’s private stream and the untrusted user should first decode the trusted user’s private stream. Besides, the reliability and PLS performances of RS-VLC system could be enhanced with the appropriate increase in the maximum transmission round of HARQ with the best decoding strategy. Moreover, they could be further enhanced by the proper common stream power allocation coefficient. This work will benefit the research and development of indoor VLC system.

Secure and covert communication strategy of UAV based on hybrid RF/FSO system

The hybrid radio frequency (RF)/free-space optical (FSO) system can improve communication security by using complimentary characteristics and mitigating the risks of RF links being susceptible to co-channel interference (CCI) and malicious eavesdropping. We investigate the secure and covert communication performance of unmanned aerial vehicles (UAVs) equipped with a hybrid RF/FSO system. In terms of secure communication, UAVs employ the strategy of transmitting private data concurrently through RF and FSO links, considering two modes based on active eavesdropping by a malicious user. Closed-form expressions for the secrecy outage probability (SOP) and effective secrecy throughput (EST) are derived. With respect to covert communication, the communication strategy is to utilize the RF link to generate interfering signals, thus aiding the FSO signals in accomplishing covert communication. We formulate an optimization problem that maximizes the EST while considering transmit power and user-acceptable detection error probability. A two-stage gradient-based iterative solution algorithm is proposed. The numerical results demonstrate the effectiveness of the proposed secure and covert communication strategy based on the hybrid RF/FSO system, which is expected to enhance the communication security of UAVs in the RF-challenged environment.

Capacity and delay performance analysis for large-scale UAV-enabled wireless networks

In this paper, we analyze the capacity and delay performance of a large-scale Unmanned Aerial Vehicle (UAV)-enabled wireless network, in which untethered and tethered UAVs deployed with content files move along with mobile Ground Users (GUs) to satisfy their coverage and content delivery requests. We consider the case where the untethered UAVs are of limited storage, while the tethered UAVs serve as the cloud when the GUs cannot obtain the required files from the untethered UAVs. We adopt the Ornstein-Uhlenbeck (OU) process to capture the mobility pattern of the UAVs moving along the GUs and derive the compact expressions of the coverage probability and capacity of our considered network. Using tools from martingale theory, we model the traffic at UAVs as a two-tier queueing system. Based on this modeling, we further derive the analytical expressions of the network backlog and delay bounds. Through numerical results, we verify the correctness of our analysis and demonstrate how the capacity and delay performance can be significantly improved by optimizing the percentage of the untethered UAVs with cached contents.

Performance Analysis of Antenna-relay Selection in CNOMA Systems under Practical Impairments

Selection strategies prove to be a valuable approach in mitigating complexity associated with antenna selection (AS) and relay selection (RS), optimizing signal transmission through a streamlined number of antennas/relays, and enhancing overall system performance. This paper offers a comprehensive analysis, deriving closed-form expressions for the outage probability (OP) and throughput in proposed scenarios that leverage the best relay selection (BRS) and transmit antenna selection (TAS) protocol for cooperative non-orthogonal multiple access (CNOMA), along with partial relay selection (PRS) and TAS protocol for CNOMA. The study extends to Rayleigh fading channels, considering practical impairments such as successful interference cancellation (SIC) error, channel estimation error (CEE), and feedback delay error. In comparing the proposed system to conventional CNOMA, our findings highlight the substantial impact of SIC, CEE, and feedback delay imperfections on the performance of both proposed scenarios. Notably, the application of BRS-based TAS protocol outperforms PRS-based TAS in terms of OP and throughput. The close alignment between analytical, asymptotic, and simulation results attests to the credibility of conducted analysis.

UAV aided NOMA relaying with energy harvesting architecture: Performance analysis

In this work, we consider a dual hop Non Orthogonal Miltiple Access (NOMA) based communication network between Source S and two destination users UA , UB which is aided by an Unmanned Aerial Vehicle (UAV) relay R. The energy constrained UAV relay harvests energy from signal transmitted by the source through Power Splitting (PS) and further transmits the signal using Amplify and Forward (AF) protocol to the destination users through NOMA. For the proposed network, we derive analytical expressions for outage probability and ergodic capacity. The impact of parameters like PS ratio and UAV altitude is studied on the overall system performance. Further, the performance of the proposed system is also compared with Orthogonal Multiple Access (OMA) scheme. The results obtained show that the energy harvesting capacity of UAV is significantly affected under Linear and Non Linear EH models. The numerical analysis done is verified through Monte Carlo Simulations.

A Novel Hybrid FSO-mm Wave System for Enhanced Mobile Network Capacity and Reliability

The ever-growing demand for high-bandwidth communication in mobile networks necessitates innovative solutions that provide exceptional capacity and reliability. This paper introduces a novel dual hop hybrid system model that leverages the complementary strengths of free space optics (FSO) and millimeter-wave (mm W) communication, while incorporating a direct mm W link for added robustness. This paper analyzes the comprehensive performance of the proposed hybrid system using a single threshold selection combining. We consider a scenario where the channel state for the FSO link adheres to a Log-Normal distribution under conditions of weak turbulence. For the millimeter wave link, we assume it follows a Nakagami-m distribution, which encompasses a broad range of commonly encountered radio frequency (RF) fading distributions. The proposed system's performance is analyzed by deriving analytical expressions for average bit error rate (ABER) and outage probability (OP). The theoretical results of the proposed system, which are verified using Monte-Carlo simulations, unveil that under turbulence and adverse weather conditions, the performance of the proposed system over a standalone FSO system is improved significantly due to mm W backup link.

Communicating uncertainty in intelligence forecasts using verbal expressions of probability and confidence

ABSTRACT The National Intelligence Council provides guidelines for how to interpret expressions of uncertainty in analytic reports, including verbal expressions of both probability (e.g. ‘likely’ or ‘unlikely’) and confidence (i.e. ‘low’, ‘moderate’, and ‘high’). This study examined how people interpret intelligence forecasts made with these expressions. 1315 participants provided quantitative and qualitative interpretations of forecasts in two studies.. The results indicated that participants used expressions of confidence to interpret the likelihood of events and that the inclusion of expressions of confidence did not improve interpretations of forecasts. Recommendations were made for research exploring alternative methods to convey uncertainty.

Local detouredness: A new phenomenon for modelling route choice and traffic assignment

This study introduces the novel concept of local detouredness, i.e. detours on subsections of a route, as a new phenomenon for understanding and modelling route choice. Traditionally, Stochastic User Equilibrium (SUE) traffic assignment models have been concerned with judging the attractiveness of a route by its total route cost. However, through empirical analysis we show that considering solely the global properties of a route is insufficient. We find that it is important to consider local detouredness both when determining realistic and tractable route choice sets and when determining route choice probabilities. For example, analysis of observed route choice data shows that route usage tends to decay with local detouredness, and that there is an apparent limit on the amount of local detouredness seen as acceptable. No existing models can account for this systematically and consistently, which is the motivation for the new route choice model proposed in this paper: the Bounded Choice Model with Local Detour Threshold (BCM-LDT). The BCM-LDT model incorporates the effect of local detouredness on route choice probability, and has an in-built mechanism that assigns zero probabilities to routes violating a bound on total route costs and/or a threshold on local detouredness. Thereby, the model consistently predicts which routes are used and unused. Moreover, the probability expression is closed-form and continuous. SUE conditions for the BCM-LDT are given, and solution existence is proven. Exploiting the special structure of the problem, a novel solution algorithm is proposed where flow averaging is integrated with a modified branch-and-bound method that iteratively column-generates all routes satisfying local and global bounds. Numerical experiments are conducted on small-scale and large-scale networks, establishing that equilibrated solutions can be found and demonstrating the influence of the BCM-LDT parameters on choice set size and flow allocation.

Analyzing error probability in aerial full-duplex relay systems: Exact formulations and optimization techniques

In this study, we investigate the performance of aerial full-duplex relay (AFDR) systems. In particular, we examine two practical scenarios: one where there is no direct link between the transmitter and user, and another where such a link exists. For both scenarios, we develop mathematical models to calculate the closed-form expressions of symbol error probabilities (SEPs) for AFDR systems, using a realistic channel aligned with the fifth generation (5G) and beyond yardsticks. To take care of residual self-interference (RSI) in AFDR, we propose an optimal power allocation strategy. Our numerical findings indicate that the performance in the case with a direct link is considerably higher than that in the case without this link. Additionally, we analyze thoroughly the effects of key parameters such as transmit power, RSI levels, carrier frequencies, and AFDR positions. The effect of RSI is significantly strong, and our proposed optimal power allocation method substantially improves system performance, especially in high transmit power scenarios where error floors may occur. Importantly, the optimal power level is dramatically lower than the conventional value where the optimal power cannot be found. Thus, besides reducing the SEPs, optimal power also helps to prolong the time of operation of AFDR. Monte-Carlo simulations are performed to confirm the accuracy of our derived expressions and demonstrate the efficacy of the proposed approaches in practical scenarios.

Incoherent Detection Performance Analysis of the Distributed Multiple-Input Multiple-Output Radar for Rice Fluctuating Targets

Utilizing spatial diversity, the distributed multiple-input multiple-output (MIMO) radar has the potential advantage of improving system detection performance. In this paper, the incoherent detection performance of distributed multiple-input multiple-output (MIMO) radars is investigated for Rice fluctuating targets. To calculate the incoherent detection probability, the moment generating function (MGF) of the Rice variable is expanded as the infinite series form. By inverting the product of MGFs of multiple independent Rice variables, new closed-form expressions for the probability density function (PDF) of the sum of independent and weighted squares of Rice variables are proposed. The proposed PDF expression for the sum of independent, non-identically distributed (i.n.i.d.) Rice variables involves an infinite series in terms of the confluent Lauricella function. Specially, the PDF for the sum of independent identically distributed (i.i.d.) Rice is expressed as the confluent hypergeometric function-based infinite series. In addition, the uniform convergence of the proposed PDF expression is also validated. Using this proposed expression, the closed-form and approximate expressions of the incoherent detection probability of MIMO radar are derived, respectively. Numerically evaluated results are illustrated and compared with Monte Carlo (MC) simulations to validate the accuracy of the derivations.

Axion-photon mixing in 3D: classical equations and geometric optics

Light particle-photon mixing in magnetised plasmas plays a vital role in constraining the existence of new physics, especially axions, dark photons, and ultra-high-frequency gravitational waves. Recently, we derived an expression for the resonant conversion of axions to photons in inhomogeneous media using kinetic theory to derive photon transport equations. In this work, we show how the same expression for the conversion probability can be obtained from the classical wave equations of axion-electrodynamics by deriving an equivalent transport equation along the photon worldline. This result provides further corroboration of this expression for the resonant production of photons from light particles, which has also recently been supported by independent numerical simulations of full axion-electrodynamics. In addition, this new approach provides a more general expression that accounts for mixing away from resonance, which is integrated along the whole worldline of the photon in a way that naturally incorporates a curved photon trajectory relevant to refractive media where the photon and light-particle worldlines differ.

Quantum multi-anomaly detection

A source assumed to prepare a specified reference state sometimes prepares an anomalous one. We address the task of identifying these anomalous states in a series of n preparations with k anomalies. We analyze the minimum-error protocol and the zero-error (unambiguous) protocol and obtain closed expressions for the success probability when both reference and anomalous states are known to the observer and anomalies can appear equally likely in any position of the preparation series. We find the solution using results from association schemes theory, thus establishing a connection between graph theory and quantum hypothesis testing. In particular, we use the Johnson association scheme which arises naturally from the Gram matrix of this problem. We also study the regime of large n and obtain the expression of the success probability that is non-vanishing. Finally, we address the case in which the observer is blind to the reference and the anomalous states. This scenario requires a universal protocol for which we prove that in the asymptotic limit, the success probability corresponds to the average of the known state scenario.

Rosen–Zener transition in a nonlinear nonreciprocal two-level system

The dynamics of the Rosen–Zener transition (RZT) in interacting two-level systems within nonreciprocal systems is examined, where nonreciprocity stems from asymmetric couplings between energy levels. For the linear case, an analytical expression for the RZT probability is derived. In the nonlinear scenario, numerical experiments are utilized to investigate the impact of various initial states and scanning periods on transition probabilities under adiabatic conditions. Additionally, an equivalent classical Hamiltonian is formulated to elucidate the origin of transition asymmetry under different initial state conditions. The influence of energy level detuning on the RZT is explored, leading to the suggestion of new applications for studying parameters of two-level systems related to nonlinearity and nonreciprocity. This opens avenues for potential Rosen–Zener–Stückelberg interferometry implementations.

Performance analysis of CSI independent cache-aided NOMA ordering

This paper introduces a Non-Orthogonal Multiple Access (NOMA) ordering technique, called the region-based ordering method, which operates independently of channel state information (CSI) for vehicular-to-infrastructure (V2I) networks. Caching has been Integrated with NOMA to significantly enhance outage probability, ergodic sum rate, and latency performance compared to traditional NOMA systems. The performance of the proposed method is evaluated under various cache content availability scenarios and compared to dynamic ordered NOMA, which relies on instantaneous CSI for user ordering. A closed-form analytical expression for outage probability is derived for a Rayleigh fading channel and validated through Monte Carlo simulations. The analysis demonstrates that the proposed method is as effective as the dynamic ordering method. Additionally, cache-aided NOMA significantly improves outage performance and reduces delivery delay compared to conventional NOMA.