On Asymptotics of Optimal Stopping Times

We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward. In this analysis, we obtained asymptotic expressions for the expectation and variance of the optimal stopping time as the number of drawn variables became large. In the case of distributions with infinite upper bound, the asymptotic behaviour of these statistics depends solely on the algebraic power of the probability distribution decay rate in the upper limit. In the case of densities with finite upper bound, the asymptotic behaviour of these statistics depends on the algebraic form of the distribution near the finite upper bound. Explicit calculations are provided for several common probability density functions.

Performance Evaluation of UAV-Based NOMA Networks with Hardware Impairment

In this paper, we evaluate the outage performance of a non-orthogonal multiple access (NOMA)-enabled unmanned aerial vehicle (UAV) where two users on the ground are simultaneously served by a UAV for a spectral efficiency purpose. In practice, hardware impairments at the transceiver cause distortion noise, which results in the performance loss of wireless systems. As a consequence, hardware impairment is an unavoidable factor in the system design process. Hence, we take into account the effects of hardware impairment (HI) on the performance of the proposed system. In this setting, to evaluate the system performance, the closed-form expressions of the outage probability of two NOMA users and the ergodic capacity are derived as well as their asymptotic expressions for a high signal-to-noise ratio (SNR). Finally, based on Monte-Carlo simulations, we verify the analytical expressions and investigate the effects on the main system parameters, i.e., the transmit SNR and level of HI, on the system performance metrics. The results show that the performance for the near NOMA user is better than of that for the far NOMA user in the case of perfect hardware; however, in the case of hardware impairment, an inversion happens at a high transmit power of the UAV in terms of the ergodic capacity.

Effective Capacity Analysis of NOMA Networks with Short Packets

Low latency and a massive connection have become the requirements of energy internet wireless communication. Effective capacity analysis of non-orthogonal multiple access (NOMA) networks with short packets is of vital importance in energy internet communication planning and design. Low-latency communications are one of the main application scenarios in next-generation wireless networks. This paper focuses on the effective capacity of NOMA networks, where the finite blocklength, delay exponent, and transmission error probability are taken into account. New exact and asymptotic expressions of effective capacities are derived for arbitrarily ordered users with a finite blocklength. Based on the analytical results, the high Signal-to-Noise Ratio slopes of effective capacity in NOMA networks are carefully attained. The numerical results validate that (a) non-orthogonal users are capable of obtaining a larger effective capacity when the blocklength decreases, and that (b), as the value of the error probability and delay exponent increases, the effective capacity of non-orthogonal users worsens.

Partial Relay Selection for Secure Cooperative NOMA Networks

In this paper, we investigate physical layer security of multi-relay non-orthogonal multiple access (NOMA) networks with partial relay selection considering decode-and-forward (DF) and amplify-and-forward (AF) protocols. We propose a partial relay scheme aiming to select the best relay based on the highest signal-to-noise-ratio (SNR) of the first link. We derive new exact and asymptotic expressions for strictly positive secrecy capacity (SPSC) and secrecy outage probability (SOP) considering Rayleigh fading channels. Numerical results demonstrate that AF and DF provide almost a similar secrecy performance. Moreover, they prove that partial relay selection improves SPSC and reduces SOP when the relay-cluster is closer to the legitimate receiver.

Brown-York charges with mixed boundary conditions

We compute the Hamiltonian surface charges of gravity for a family of conservative boundary conditions, that include Dirichlet, Neumann, and York’s mixed boundary conditions defined by holding fixed the conformal induced metric and the trace of the extrinsic curvature. We show that for all boundary conditions considered, canonical methods give the same answer as covariant phase space methods improved by a boundary Lagrangian, a prescription recently developed in the literature and thus supported by our results. The procedure also suggests a new integrable charge for the Einstein-Hilbert Lagrangian, different from the Komar charge for non-Killing and non-tangential diffeomorphisms. We study how the energy depends on the choice of boundary conditions, showing that both the quasi-local and the asymptotic expressions are affected. Finally, we generalize the analysis to non-orthogonal corners, confirm the matching between covariant and canonical results without any change in the prescription, and discuss the subtleties associated with this case.

Relay Selection-and-Jamming Scheme with Nonlinear Energy Harvesting

When direct source-destination communications are in outage, relay selection is a preferable solution to improve reliability for this communications. However, such a relay selection makes the eavesdropper better overhear source data through both source-relay and relay-destination communication hops, losing data security. To improve both reliability and security, this paper proposes a relay selection-and-jamming (RaJ) scheme to select one intermediate node as a conventional relay and another node as a jammer. To enhance energy efficiency, all intermediate nodes harvest radio frequency energy in source signals for their operations with nonlinear energy harvesting (NL-EH). The security and reliability of the RaJ scheme are assessed through suggested rigorous/asymptotic expressions and are significantly better than two benchmark schemes without neither jamming nor both relay selection and jamming. Additionally, they can be optimized with reasonable selection of specifications. Moreover, the NL property of the energy harvesters dramatically affects the reliability but negligibly degrades the security for the RaJ scheme. Furthermore, the linear EH (L-EH) is more reliable but less secure than the NL-EH.

Riesz basis property and exponential stability for one-dimensional thermoelastic system with variable coefficients

In this paper, we study Riesz basis property and stability for a nonuniform thermoelastic system with Dirichlet-Dirichlet boundary condition, where the heat subsystem is considered as a control to the whole coupled system. By means of the matrix operator pencil method, we obtain the asymptotic expressions of the eigenpairs, which are exactly coincident to the constant coefficients case} We then show that there exists a sequence of generalized eigenfunctions of the system, which forms a Riesz basis for the state space and the spectrum determined growth condition is therefore proved. As a result, the exponential stability of the system is concluded.

Magnetic nonsingular black holes in lovelock gravity coupled to exponential electrodynamics

The model of exponential electromagnetic field is coupled to Lovelock gravitational field in [Formula: see text]-dimensional spacetime geometry. In this context, new class of magnetically charged nonsingular or regular Lovelock black holes has been introduced. The asymptotic behavior of resulting metric function in the vicinity of [Formula: see text] is studied. The obtained asymptotic expressions in both even and odd critical dimensions show the finiteness and regularity of the solution at [Formula: see text]. The thermodynamic quantities such as Hawking temperature and specific heat capacity at constant magnetic charge corresponding to the nonsingular black hole are computed. The tunneling probability associated with Hawking radiations from these black holes is calculated as well.

Cascaded Double κ-μ Shadowed Fading Channels

In this study, the cascaded double shadowed fading model is mathematically introduced. A novel expression is obtained for the cumulative distribution function (CDF) of the cascaded double shadowed fading channels by using Meijer’s G function and Laplace transform. Based on the obtained CDF expression, the exact and asymptotic expressions are derived for the outage probability (OP), the bit error rate (BER) for various modulations of the considered channel model. The OP and the average BER curves with exact simulations obtained by the proposed expressions are presented for different parameters and modulation schemes of the considered channel model. Finally, the accuracy of the derived OP and the average BER expressions is confirmed.

Cascaded κ-μ Fading Channels with Colluding and Non-Colluding Eavesdroppers: Physical-Layer Security Analysis

In this paper, the physical-layer security for a three-node wiretap system model is studied. Under the threat of multiple eavesdroppers, it is presumed that a transmitter is communicating with a legitimate receiver. The channels are assumed to be following cascaded κ-μ fading distributions. In addition, two scenarios for eavesdroppers’ interception and information-processing capabilities are investigated: colluding and non-colluding eavesdroppers. The positions of these eavesdroppers are assumed to be random in the non-colluding eavesdropping scenario, based on a homogeneous Poisson point process (HPPP). The security is examined in terms of the secrecy outage probability, the probability of non-zero secrecy capacity, and the intercept probability. The exact and asymptotic expressions for the secrecy outage probability and the probability of non-zero secrecy capacity are derived. The results demonstrate the effect of the cascade level on security. Additionally, the results indicate that as the number of eavesdroppers rises, the privacy of signals exchanged between legitimate ends deteriorates. Furthermore, in this paper, regarding the capabilities of tapping and processing the information, we provide a comparison between colluding and non-colluding eavesdropping.