The analysis of coverage probability,ASE and EE in heterogeneous ultra-dense networks with power control

The ultra-dense network is a promising technology to increase the network capacity in the forthcoming fifthgeneration(5G)mobile communication networks by deploying lots of low power Small Base Stations(SBSs)which overlap with Macro Base Stations(MBSs).The interference and energy consumption increase rapidly with the number of SBSs although each SBS transmits with small power.In this paper,we model a downlink heterogeneous ultra-dense network where a lot of SBSs are randomly deployed with MBSs based on the Poisson point process.We derive the coverage probability and its variance,and analyze the area spectral efficiency and energy efficiency of the network considering three Fractional Power Control(FPC)strategies.The numerical results and Monte Carlo simulation results show that power control can mitigate the interference and balance the performances of inner-user and edge-user equipments.Especially,a great improvement of energy efficiency is archived with a little loss of area spectral efficiency when FPC is adopted.Finally,we analyze the effect of base stations’(BSs’)sleeping on the performance of the network when it is partially loaded.

A Statistical Index for Evaluating the CTV Coverage Loss of Brain Stereotactic Radiosurgery When the PTV Margin Is Zero

Purpose: To develop a new statistical index “percent CTV (clinical target vo-lume) coverage probability” (%CCP), defined as the probability that a specific percent (e.g., 95%) of the CTV can be reliably covered by the prescription dose, for evaluating the coverage loss of brain (fractionated) stereotactic radiosurgery (SRS/fSRS) when the PTV (planning target volume) margin is zero. Methods: The random variable Q for CTV percent coverage was derived using a previously developed model for CTV random motion that follows a three-dimensional (3D) independent normal distribution with a zero mean and a standard deviation of 𝜎𝑆(for translation) or 𝜎𝛿(for rotation). Assuming both CTV and PTV are spherical with the same diameter dCTV, the cumulative distribution function of Q could be obtained analytically using the relation of sphere-sphere intersection. The %CCP was then derived as the reliability function of Q and was used to quantify the coverage loss for selected dCTV. Results: The 95%-95% clinical goal (95% of the times, at least 95% of the CTV is covered) is not achievable with dCTV mm. For common CTVs (dCTV mm) encountered in SRS/fSRS, only 60%-90% of the CTV could be reliably covered by the prescription dose 95% of the time. For 𝜎𝑆=0.5mm and 𝜎𝛿 =0.4˚, the 95% CCP was the highest when the distance between the CTV and the isocenter 𝑑𝐼⇔𝑇=0 and gradually decreased with the increasing 𝑑𝐼⇔𝑇. Conclusions: The %CCP was successfully derived for evaluating the CTV coverage loss for brain SRS/fSRS. When the PTV margin is zero, the 95%-95% clinical goal cannot be achieved for most targets (dCTV mm).

Energy Efficiency Optimization for Heterogeneous Cellular Networks Modeled by Matérn Hard-Core Point Process

The Poisson point process(PPP) has been widely used in wireless network modeling and performance analysis due to the independence between its nodes. Therefore, it may not be a suitable model for many of the exclusive networks between the nodes. This paper analyzes the energy efficiency(EE) and optimizes the two-tier heterogeneous cellular networks(Het Nets). Considering the mutual exclusion between macro base stations(MBSs) distribution, the deployment of MBSs is modeled by the Matérn hard-core point process(MHCPP), and the deployment of pico base stations(PBSs) is modeled by the PPP. We adopt a simple approximation method to study the signal to interference ratio(SIR) distribution in two-tier MHCPP-PPP networks and then derive the coverage probabilities, the average data rates and the energy efficiency of Het Nets. Finally, an optimization algorithm is proposed to improve the EE of Het Nets by controlling the transmit power of PBSs. The simulation results show that the EE of a system can be effectively improved by selecting the appropriate transmit power for the PBSs. In addition, two-tier MHCPP-PPP Het Nets have higher energy efficiency than two-tier PPP-PPP Het Nets.

Physical Layer Security of Multi-hop Aided Downlink MIMO heterogeneous Cellular Networks

This study investigates physical layer security in downlink multipleinput multiple-output(MIMO) multi-hop heterogeneous cellular networks(MHCNs),in which communication between mobile users and base stations(BSs) is established by a single or multiple hops,to address the problem of insufficient security performance of MIMO heterogeneous cellular networks.First,two-dimensional homogeneous Poisson point processes(HPPPs) are utilized to model the locations of K-tier BSs in MIMO MHCNs and receivers,including those of legitimate users and eavesdroppers.Second,based on the channel gain distribution and the statistics property of HPPP,the achievable ergodic rates of the main and eavesdropper channels in direct and ad hoc links are derived,respectively.Third,the secrecy coverage probability and the achievable ergodic secrecy throughput of downlink MIMO MHCNs are explored,and their expressions are derived.Lastly,the correctness of the theoretical derivation is verified through Monte Carlo simulations.

Interval Estimation in a Two Parameter Weibull Distribution Based on Type-2 Censored Data

In this paper, we consider the construction of the approximate profile- likelihood confidence intervals for parameters of the 2-parameter Weibull distribution based on small type-2 censored samples. In previous research works, the traditional Wald method has been used to construct approximate confidence intervals for the 2-parameter Weibull distribution under type-2 censoring scheme. However, the Wald technique is based on normality assumption and thus may not produce accurate interval estimates for small samples. The profile-likelihood and Wald confidence intervals are constructed for the shape and scale parameters of the 2-parameter Weibull distribution based on simulated and real type-2 censored data, and are hence compared using confidence length and coverage probability.

Open Access Strategy in Cloud Computing-Based Heterogenous Networks Constrained by Wireless Fronthaul

Cloud computing.based heterogeneous networks(C.Het Nets) have been considered as promising network architecture of future wireless communication systems. However, its performance is constrained by the capability of fronthaul. To study the performance limit of C.Het Nets, the coverage performance of the open access strategy in C.Het Nets is analyzed in this paper. In particular, the non.ideal condition of fronthaul in C.Het Nets is characterized by establishing a stochastic geometry.based model, and a tight lower bound on coverage probability is derived for downlink transmissions. Based on the derived results, the constraint of the fronthaul is given to ensure that open access strategy can achieve the best coverage performance. Finally, the simulation results are provided to verify the theoretical results and show the impact of fronthaul constrains.

Confidence Interval Estimation of the Correlation in the Presence of Non-Detects

This article deals with correlating two variables that have values that fall below the known limit of detection (LOD) of the measuring device;these values are known as non-detects (NDs). We use simulation to compare several methods for estimating the association between two such variables. The most commonly used method, simple substitution, consists of replacing each ND with some representative value such as LOD/2. Spearman’s correlation, in which all NDs are assumed to be tied at some value just smaller than the LOD, is also used. We evaluate each method under several scenarios, including small to moderate sample size, moderate to large censoring proportions, extreme imbalance in censoring proportions, and non-bivariate normal (BVN) data. In this article, we focus on the coverage probability of 95% confidence intervals obtained using each method. Confidence intervals using a maximum likelihood approach based on the assumption of BVN data have acceptable performance under most scenarios, even with non-BVN data. Intervals based on Spearman’s coefficient also perform well under many conditions. The methods are illustrated using real data taken from the biomarker literature.

Confidence Intervals for the Binomial Proportion: A Comparison of Four Methods

This paper presents four methods of constructing the confidence interval for the proportion p of the binomial distribution. Evidence in the literature indicates the standard Wald confidence interval for the binomial proportion is inaccurate, especially for extreme values of p. Even for moderately large sample sizes, the coverage probabilities of the Wald confidence interval prove to be erratic for extreme values of p. Three alternative confidence intervals, namely, Wilson confidence interval, Clopper-Pearson interval, and likelihood interval, are compared to the Wald confidence interval on the basis of coverage probability and expected length by means of simulation.

Coverage in Cooperative LEO Satellite Networks

Low-earth orbit(LEO)satellite networks ignite global wireless connectivity.However,signal outages and co-channel interference limit the coverage in traditional LEO satellite networks where a user is served by a single satellite.This paper explores the possibility of satellite cooperation in the downlink transmissions.Using tools from stochastic geometry,we model and analyze the downlink coverage of a typical user with satellite cooperation under Nakagami fading channels.Moreover,we derive the joint distance distribution of cooperative LEO satellites to the typical user.Our model incorporates fading channels,cooperation among several satellites,satellites'density and altitude,and co-channel interference.Extensive Monte Carlo simulations are performed to validate analytical results.Simulation and numerical results suggest that coverage with LEO satellites cooperation considerably exceeds coverage without cooperation.Moreover,there are optimal satellite density and satellite altitude that maximize the coverage probability,which gives valuable network design insights.

Planning failure-censored constant-stress partially accelerated life test

This article deals with the case of the failure-censored constant-stress partially accelerated life test （CSPALT） for highly reliable materials or products assuming the Pareto distribution of the second kind. The maximum likelihood （ML） method is used to estimate the parameters of the CSPALT model. The performance of ML estimators is investigated via their mean square error. Also, the average confidence interval length （IL） and the associated co- verage probability （CP） are obtained. Moreover, optimum CSPALT plans that determine the optimal proportion of the test units al- located to each stress are developed. Such optimum test plans minimize the generalized asymptotic variance （GAV） of the ML estimators of the model parameters. For illustration, Monte Carlo simulation studies are given and a real life example is provided.

Through Foreign Eyes Global media descends on Beijing

THE 19th National Congress of the Communist Party of China（CPC）attracted global attention with1,818 journalists from abroad to cover the event in Beijing on October 18-24,more coverage than for the18th CPC National Congress.Most of them have been based in China or visited China on several occasions.They have witnessed the changes of Chinese people＇s life in the past five years.

Coverage analysis of cache-enabled small cell networks with stochastic geometry methods

Caching popular content in the storage of small cells is deemed as an efficient way to decrease latency, offload backhaul and satisfy user＇s demands. In order to investigate the performance of cache-enabled small cell networks, coverage probability is studied in both single-point transmission and cooperative multipoint（Co MP） transmission scenarios. Meanwhile, the caching distribution modeled as Zipf and uniform distribution are both considered. Assuming that small base stations（SBSs） are distributed as a homogeneous Poisson point process（HPPP）, the closed-form expressions of coverage probability are derived in different transmission cases. Simulation results show that Co MP transmission achieves a higher coverage probability than that of single-point transmission. Furthermore, Zipf distribution-based caching is more preferable than uniform distribution-based caching in terms of coverage probability.

Coverage and rate analysis of user beam selection in mm-wave heterogeneous networks

Millimeter wave(mm-wave)communication is widely considered to be a promising technique for 5G(Fifth Generation)cellular systems.Owing to the high path loss of mm-wave channels,5G networks could employ a heterogeneous structure that consists of an MBS(Macro Base Station)and numerous SBSs(Small Base Stations).In this paper,we analyze the coverage and rate performance of an mm-wave heterogeneous network.Using user beam selection,we derive analytical expressions for the coverage probabilities of the SBSs and MBS.Furthermore,the average achievable rate for a typical user is also investigated.It is shown that the analytical results closely follow those of the simulations with marginal differences.

Empirical Likelihood for Partially Linear Errors-in-variables Models with Longitudinal Data

Empirical likelihood inference for partially linear errors-in-variables models with longitudinal data is investigated.Under regularity conditions,it is shown that the empirical log-likelihood ratio at the true parameters converges to the standard Chi-squared distribution.Furthermore,we consider some estimates of the unknown parameter and the resulting estimators are shown to be asymptotically normal.Some simulations and a real data analysis are given to illustrate the performance of the proposed method.

Downlink and Uplink Decoupling in Heterogeneous Networks for 5G and Beyond

To meet the explosively increased data traffic demand from 5G and beyond,one of the most promising technologies is densified heterogeneous networks(HetNets).In HetNets,base stations(BSs)are brought closer and closer to users by densifying small BSs,which results in considerable high spectral efficiency and energy efficiency for cellular systems.However,HetNet topology challenges the traditional cellular systems.One of the most important challenges is user association.Aiming to avoid the drawback brought by coupled access(CA)in user association of HetNets,a decoupled access(DA)approach has emerged recently.By allowing access points in uplink(UL)and downlink(DL)association to be different,DA significantly improves UL performance of HetNets.This article focuses on recent works in DA.First,typical scenarios of HetNets for DA are described,which is followed by presenting two major decoupled association policies under typical scenarios.Then,DA shows its superiority over CA under different scenarios and decoupled association policies via various performance metrics.Finally,future work on DA in HetNets is discussed.

Empirical Likelihood Inference for a Partially Linear Errors-in-variables Model with Covariate Data Missing at Random

The authors study the empirical likelihood method for partially linear errors-in-variables model with covariate data missing at random. Empirical likelihood ratios for the regression coeffidents and the baseline function are investigated, and the corresponding empirical log-likelihood ratios are proved to be asymptotically standard chi-squared, which can be used to construct confidence regions. The finite sample behavior of the proposed methods is evaluated by a simulation study which indicates that the proposed methods are comparable in terms of coverage probabilities and average length of confidence intervals. Finally, the Earthquake Magnitude dataset is used to illustrate our proposed method.