On the distribution function of the spread-spectrum code acquisition time

81 8-354-2674 Abstract - Simple models for the patterns as well as their cumulative gain probability and probability density functions of the JPUNASA Deep Space Network (DSN) antennas are developed. These a~ needed for the study and evaluation of interference from unwanted sources such as the emerging terrestrial system, High Density Fixed Service (HDFS), with the Ka-band receiving antenna systems in Goldstone Station of the JPLNASA Deep Space Network. Several different models for the high gain ground antennas of the JPUNASA Deep Space Network @SN) are considered. The model definitions are then used to evaluate cumulative probability functions and probability density functions for the gain values at a receiving antenna randomly located anywhere in the far field of the model antenna. Both two-dimensional models which simulate the pattern in a plane cut through the boresight of the antenna and the range of the angle from boresight to *180 degrees and three- dimensional ones in which the pattem is given anywhere in the half-space above the ground, with the range of angle from zero at boresight to 90 degrees are considered. In both cases, regular as well as smooth interpolated models have been developed. The gain value as seen by a receiver at a random location and exposed to the radiation from a transmitting antenna with a given gain profile, can be thought of as a uniformly distributed random variable. Formulas are derived and various plots are presented for the gain models and their associated cumulative probability functions and probability density functions.

As wind turbines more widely used with newer manufactured types and larger electrical power scales, a brief mathematical modelling for these wind turbines operating power curves is needed for optimal site matching selections. In this paper, 24 commercial wind turbines with different ratings and different manufactures are modelled using single cumulative probability density functions modelling equations. A new mean of a composite cumulative probability density function is used for better modelling accuracy. Invasive weed optimization algorithm is used to estimate different models designing parameters. The best cumulative density function model for each wind turbine is reached through comparing the RMSE of each model. Results showed that Weibull-Gamma composite is the best modelling technique for 37.5% of the reached results.

In this paper, we have derived and studied new probability distributions by extending the 2‐dimensional Rayleigh distribution (RD). First, we extend the RD to 3 dimensions and then generalize it to k dimensions for any positive integer k ≥ 3. The distributions are named the 3‐dimensional Rayleigh distribution (3‐DRD) and k‐dimensional Rayleigh distribution (k‐DRD), respectively. For both 3‐DRD and k‐DRD, detailed mathematical and statistical properties including derivations of the corresponding cumulative distribution, probability density, survival, and hazard functions, moments, moment generating functions, mode, skewness, kurtosis, and differential entropy are obtained in closed forms. Parameter estimation is done for both models using the maximum likelihood estimation method and some statistical properties of the estimator are discussed for each case. Interestingly, the commonly known Normal, Rayleigh, Maxwell–Boltzmann, chi‐square, gamma, and Erlang distributions are related to the newly developed extended RDs as special cases. For the 3‐DRD, plots of cumulative distribution, probability density, survival, and hazard functions are exhibited, a simulation study is carried out, and random samples are generated using the standard accept–reject (AR) algorithm to check the efficiency of the maximum likelihood estimates of the parameter. Moreover, the new 3‐DRD model is fitted to one simulated and three real datasets, revealing good performance compared to four existing Rayleigh‐based distributions. This study will contribute new knowledge to the field of applied statistics and probability, and the findings will be used as a basis for future research in the field.

ABSTRACTThe left-sided truncated normal distribution is especially important in quality engineering where we remove the left side of the distribution, for example, due to estimation of the life of used products. Although the theoretical background of truncated normal distribution is already established, there is very little work on mathematical approximation of the probability density and the cumulative probability density functions. In this article, a high accuracy mathematical approximation of the left-sided truncated normal distribution is proposed. A full analysis of errors and recommendations for implementation using Microsoft Excel are provided at the end of this article.

Influence of second-order wave force and focusing position on dynamic responses of tension leg platform under a freak wave

In this paper, the probabilistic behavior of plain concrete beams subjected to flexure is studied using a continuous mesoscale model. The model is two-dimensional where aggregate and mortar are treated as separate constituents having their own characteristic properties. The aggregate is represented as ellipses and generated under prescribed grading curves. Ellipses are randomly placed so it requires probabilistic analysis for model using the Monte Carlo simulation with 20 realizations to represent geometry uncertainty. The nonlinear behavior is simulated with an isotropic damage model for the mortar, while the aggregate is assumed to be elastic. The isotropic damage model softening behavior is defined in terms of fracture mechanics parameters. This damage model is compared with the fixed crack model in macroscale study before using it in the mesoscale model. Then, it is used in the mesoscale model to simulate flexure test and compared to experimental data and shows a good agreement. The probabilistic behavior of the model response is presented through the standard deviation, moment parameters and cumulative probability density functions in different loading stages. It shows variation of the probabilistic characteristics between pre-peak and post-peak behaviour of load-CMOD curves.

This paper presents the measured results of a switching DC excitation control system on a self-excited wind induction generator (WIG) under sudden connection of a static load. An intelligent power-system recorder/monitor is employed to measure three-phase voltages and currents at the terminals of the WIG and the load for 5 minutes. A laboratory 300 W wound-rotor induction machine driven by a blushless DC motor is utilized to simulate the studied WIG system. Since the generated harmonic currents are randomly varied, total harmonic distortion of current (THD <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</inf> ) using cumulative probability density function is employed to determine the penetration of harmonic distortion due to the addition of witching DC excitation system. The results show that the harmonic currents generated by the studied WIG may be severely amplified to a higher level by the excitation capacitors connected at its stator terminals.

River response to rapid Holocene environmental change: evidence and explanation in British catchments

The majority of color histogram equalization methods do not yield uniform histogram in gray scale. After converting a color histogram equalized image into gray scale, the contrast of the converted image is worse than that of an 1-D gray scale histogram equalized image. We propose a novel 3-D color histogram equalization method that produces uniform distribution in gray scale histogram by defining a new cumulative probability density function in 3-D color space. Test results with natural and synthetic images are presented to compare and analyze various color histogram equalization algorithms based upon 3-D color histograms. We also present theoretical analysis for nonideal performance of existing methods.

This study addresses the development of probability distributions of travel times for one‐dimensional (vertical) solute transport in soils. The field‐scale soils are considered heterogeneous, with stationary fluctuations of soil hydraulic properties in the horizontal direction but nonstationary fluctuations of these properties in the vertical direction due to layering of the soil, which induces nonstationary heterogeneity. Approximate ensemble probability distribution functions of conservative solute travel time for vertical convective solute transport were derived directly from the convective transport stochastic partial differential equation, under both deterministic and stochastic soil surface water flux (infiltration rate) and under unsteady and nonuniform soil water flows. General depth‐varying initial and time‐varying boundary conditions were used in these derivations. The magnitude of the approximation in the theoretical probability distribution functions of travel time is quantified mathematically. Utilizing the soil water content data from a University of California, Davis, field site, it is shown that the mathematical condition for this approximation is satisfied for this field. The spatial heterogeneity is represented through a nonstationary soil water content random field which covaries both in time and in space. Dispersion emerges naturally in the derived ensemble probability distribution functions of solute travel time, owing to the stochasticity of soil water content at field scale. Then the theoretical expression for mean solute concentration over a field is derived, by means of the theoretical solute travel time distribution, as a function of time and soil depth, under vertical transport with rectangular pulse solute loading for the upper boundary condition. Comparisons of theoretical probability density functions of solute travel time against their empirical counterparts, obtained from field experimental observations under steady but nonuniform soil water flow, show good agreement. Comparisons of theoretical mean solute concentrations, as they evolve with time and soil depth, against field experimental observations also show good agreement. However, further field experiments under unsteady flow conditions are required for the comprehensive validation of the developed theory.

In this paper, the performance of a mixed Terahertz/free-space optical (THz/FSO) wireless transmission system is studied, where the joint effects of channel fading and pointing errors are considered for both THz and FSO links. Employing the semi-blind amplify-and-forward protocol, we derive the cumulative distribution function and probability density function of the end-to-end signal-to-noise ratio. By applying the derived statistics, exact expressions for the outage probability (OP), average bit error rate (BER), and average channel capacity are obtained. In order to attain useful physical insights, asymptotic OP and average BER expressions are also presented. Based on them, the diversity gain is determined, which is shown to depend on channel fading and pointing errors of both links. In addition, by taking into account the hardware impairments, the OP of the non-ideal hardware system is derived. Moreover, the analysis is extended to multi-antenna scenarios and the asymptotic OP is obtained. Finally, illustrative numerical results are plotted and it can be observed that the path loss, channel fading, pointing errors and hardware impairments lead to a considerable degradation in system performance.

In this paper, we study the performance of point-to-point communication in spectrum sharing systems under the peak interference power constraint of multiple primary users. In particular, we assume that the channels undergo independent but not necessarily identically distributed Nakagami-m fading with integer values of fading severity parameter m. The cumulative distribution function and probability density function for the signal-to-noise ratio are derived. Based on these formulas, we obtain analytical expressions for the outage probability, the ergodic capacity, and the symbol error probability. Numerical results are also provided to investigate the impact of the peak interference power-to-noise ratio, the number of primary users, and fading parameters on the performance of the secondary network.

SER performance investigation of a MPPM relay-aided FSO system with three decision thresholds over EW fading channel considering pointing errors

We consider a point process (PP) generated by superimposing an independent Poisson point process (PPP) on each line of a 2D Poisson line process (PLP). Termed PLP-PPP, this PP is suitable for modeling networks formed on an irregular collection of lines, such as vehicles on a network of roads and sensors deployed along trails in a forest. Inspired by vehicular networks in which vehicles connect with their nearest wireless base stations (BSs), we consider a random bipartite associator graph in which each point of the PLP-PPP is associated with the nearest point of an independent PPP through an edge. This graph is equivalent to the partitioning of PLP-PPP by a Poisson Voronoi tessellation (PVT) formed by an independent PPP. We first characterize the exact distribution of the number of points of PLP-PPP falling inside the ball centered at an arbitrary location in as well as the typical point of PLP-PPP. Using these distributions, we derive cumulative distribution functions (CDFs) and probability density functions (PDFs) of kth contact distance (CD) and the nearest neighbor distance (NND) of PLP-PPP. As intermediate results, we present the empirical distribution of the perimeter and approximate distribution of the length of the typical chord of the zero-cell of this PVT. Using these results, we present two close approximations of the distribution of node degree of the random bipartite associator graph. In a vehicular network setting, this result characterizes the number of vehicles connected to each BS, which models its load. Since each BS has to distribute its limited resources across all the vehicles connected to it, a good statistical understanding of load is important for an efficient system design. Several applications of these new results to different wireless network settings are also discussed.

In this paper, the error performance analysis is performed for the decode-and-forward (DF) based dual hop mixed radio frequency-free space optical (RF-FSO) communication system with a direct RF link. The direct link between the source-destination (S-D) and the link between source-relay (S-R) are Nakagami-m distributed asymmetric radio frequency (RF) links and the R-D link is a free space optical (FSO) link characterized by the path loss, Gamma-Gamma distributed turbulence, and pointing errors. Selection combining diversity scheme is used to evaluate the performance of this dual branch cooperative system. For the considered system, novel closed-form mathematical expressions of cumulative distribution function and probability density function of instantaneous signal-to-noise ratio are derived. Using these, new mathematical expressions are obtained for the outage probability and the average bit error rate (BER) for various modulation techniques. The effects of fading, turbulence, and pointing errors are observed on the outage probability and the BER of the considered system. These performance metrics are also compared with those of a DF based dual hop mixed RF-FSO system without direct link. The improvement in the performance is observed due to the diversity introduced by addition of RF link.