Optimal simple step-stress plan for cumulative exposure model using log-normal distribution

Optimal times of changing stress level for simple step-stress plans under a cumulative exposure model using the log-normal distribution are determined for a wide range of values of the parameters in the model. A table of optimal times of changing stress level for various model parameters values is obtained. A formula for optimal time of changing stress level is also estimated from the table. This paper provides an optimal life testing plan which will enable us to accurately estimate the 50th percentile of the life time of a product being tested without having to wait long time for the product to fail.     

地海面复合场景的杂波建模方法

地海杂波对采用前视以及下视成像的机载、弹载雷达具有十分重要的影响,对港口成像,会同时受到地杂波和海杂波的影响。文章提出复合场景杂波的后向散射系数模型,推导了复合场景杂波的幅度分布公式,并对由对数正态杂波与韦伯杂波组成的复合杂波分布进行了仿真。仿真中,地海杂波功率比选取了0.001到50之间的一系列典型值,并将不同情况下复合杂波的幅度分布与单一对数正态分布模型和Weibull分布模型得到的杂波分布进行了比较,结果表明二者的复合杂波分布依赖于二者的功率比。     

Probability distributions for the number of radio transceivers which can communicate with one another

This paper considers points which can communicate with one another and which are uniformly and randomly distributed on the plane, assuming an inverse power law for attenuation and log-normal shadowing. First, a probability distribution is obtained for the distance between a pair of such points. Communication is assumed to be possible if the attenuation of a signal transmitted from one point, say a mobile phone, does not exceed some specified value by the time it reaches the other, say a base station. The probability distribution of the number of base stations which can hear such a signal from a given mobile is found. An example shows how the probability that a mobile is in a handover region between two or more base stations can be evaluated. The analysis is extended to the case where the power law changes at a specified distance from the mobile, and also to consider the effect of an area within the plane containing a greater density of mobiles and/or base stations (a hot spot). A final result gives the conditional distribution for the number of base stations within some specified area of the plane, given the number within some larger area containing that specified area. The results also apply to the number of mobiles within range of a base station and, in an ad hoc network, to the number of nodes within range of a given node.     

A new empirical distribution for the uncertainty analysis of the top event of a fault tree

A new empirical statistical distribution is reported, which describes the probability distribution of the unavailability Q_TOP for the top event of a fault tree. The distribution can be fitted using linear regression analysis. Investigations into the fit of the new distribution are reported, and as specific examples, two fault trees described in Reactor Safety Study are studied. The proposed distribution fits very well in both the cases, as shown by the χ² test. For comparison, Johnson's S_L and S_B distributions, the log-normal distribution and the hybrid log-normal distribution are fitted to the same fault trees using the exact regression analysis method. Johnson's S_B distribution cannot be fitted in the case of one of the fault trees as the necessary iterative process does not converge. For the other fault tree, the S_B distribution fits very well. Johnson's S_L distribution, the log-normal distribution and the hybrid log-normal distribution do not fit as well as the distribution proposed here and the χ² test failed. Also, Johnson's distributions require the use of either an approximate method, involving a number of trials and errors, or non-linear regression analysis for fitting. The proposed distribution can, on the other hand, be fitted exactly using linear regression analysis and is, therefore, no more difficult to fit than the log-normal distribution. It is therefore concluded that the proposed distribution is most suited to describe the probability distribution of the unavailability for the top event of fault tree. Its suitability as a substitute for Johnson's distributions is also investigated. As specific examples, two statistical distributions in a text-book, for which fitting of Johnson's distributions has been suggested, are studied. The proposed distribution fits very well, as shown by the χ² test. The proposed distribution is thus a good substitute for Johnson's S_B distribution.     

Comparison of asymptotic backscattering models (SSA, WCA, and LCA) from one-dimensional Gaussian ocean-like surfaces

In this paper, recent asymptotic backscattering models are compared for one-dimensional multiscale dielectric sea surfaces with Gaussian statistics and by considering the Elfouhaily et al. height spectrum. We focus on the calculations of the normalized radar cross sections (NRCS) obtained from the weighted and local curvature approximations (WCA and LCA), recently published by Elfouhaily, and of the first- and second-order small slope approximation (SSA(1) plus SSA(2) denoted as SSA), developed by Voronovich. Voronovich et al. (2002 Waves Random Media 11 247-269) presented simulations of the SSA by making an assumption over the SSA(2) contribution (the model is referred to as SSAM). The NRCS computation is then similar to SSA(1), where the sea spectrum is substituted by a modified spectrum defined as the product of the sea spectrum by the second-order polarization term. The second-order statistical moment of WCA is calculated rigorously for any two-dimensional height correlation of the surface with Gaussian statistics. The NRCS of the WCA, WCAQ (obtained from a quadratic approximation of WCA), LCA, SSA, and SSAM backscattering models are compared for moderate wind speeds, for microwave frequencies and for backscattering angles ranging from 0 (nadir) to 70/spl deg/.     

Dual diversity over correlated log-normal fading channels

A great deal of attention has been devoted in the literature to studying the bit error rate (BER) performance of diversity combining systems in the presence of Rayleigh, Rice, and Nagakami-m fading. By comparison, the literature is relatively sparse in comparable analyses over log-normal channels which typically characterize shadowing from indoor obstacles and moving human bodies. One reason for this disparity stems from the difficulty in evaluating the exact average BER when log-normal variates are involved, using, for example, the moment-generating function (MGF) approach, due to the inability of expressing the MGF itself in a simple closed form. Since it is possible to evaluate the marginal and joint statistical moments as well as the cumulative distribution function (CDF) associated with a log-normal distribution in closed form, we rather focus here on other performance measures, namely, average combined output signal-to-noise ratio, amount of fading, and outage probability. The first two performance measures depend only on the moments, whereas the outage probability depends solely on the cdf. Closed-form expressions (in terms of known functions), single-integral representations, or upper and lower bounds are obtained for these measures corresponding to maximal-ratio combining, selection combining, and switch-and-stay combining schemes, allowing for the possibility of correlation between the two branches. Numerical evaluations of these expressions illustrating the performances of each individual diversity type as well as comparisons among them are also presented.     

Minimization of backscattering of a cylinder by double loading

A theory is presented on the minimization of the backscattering of a cylinder by loading a cylinder at two points with lumped impedances. The induced current on a doubly loaded cylinder when illuminated by a plane electromagnetic wave at an arbitrary angle is obtained. The optimum loading to eliminate the broadside backscattering which is caused by the symmetrical component of the induced current is established. A suitable loading to reduce the off-broadside backscattering, due to the antisymmetrical component of the induced current, is also determined. A proper choice of the impedance and the position of double loading can lead to the reduction of the backscattering over a wide aspect range. The useful formulas for optimum loading and some graphical illustrations are included. The advantages of double loading over central loading are discussed.     

Branching model for vegetation

A branching model is proposed for the remote sensing of vegetation. The frequency and angular responses of a two-scale cylinder cluster are calculated to demonstrate the significance of vegetation architecture. The results indicate that the architecture of vegetation plays an important role in determining the observed coherent effects. A two-scale branching model is implemented for soybean with its internal structure and the resulting clustering effects considered. At the scale of soybean fields, the relative location of soybean plants is described by a pair distribution function. The polarimetric backscattering coefficients are obtained in terms of the scattering properties of soybean plants and the pair distribution function. Theoretical backscattering coefficients evaluated using the hole-correction pair distribution are in good agreement with extensive data from soybean fields. The hole-correction approximation, which prevents two soybean plants from overlapping each other, is more realistic and improves the agreement between the model calculation and experimental data near normal incidence     

Variability of sector averaged signals for UHF propagation incities

The theoretical model proposed by D.O. Reudink (1974) for the range dependence of UHF propagation over cities so as to predict the statistical properties of the sector-averaged signal is extended. It is shown that the observed distribution of sector averages can be explained by two features of the urban environment, the first of which is the presence of variations of building height. The second feature consists of differences in building construction and design, and the presence of foliage. These sources of variation are independent and act in cascade, so that the received signal is a product of the corresponding coefficients. The cascading of these two randomly distributed coefficients leads to a distribution of signal levels that is close to log-normal and that has a 5 to 95% variability near to measured values     

Multiple scattering and depolarization by a randomly rough Kirchhoff surface

A matrix approach has been developed to compute bistatic scattering coefficients which include shadowing and multiple scattering effects for a randomly rough Kirchhoff surface. The method permits the computation of these coefficients in terms of the existing single-scatter bistatic scattering coefficients. Thus the effects of multiple scattering are readily recognized from the expressions obtained. The bistatic scattering coefficients are shown to satisfy energy conservation to at least two significant figures. It is observed that while polarized backscattering is dominated by the single-scattering process, the depolarized backscattering is due to multiple scattering. Unlike depolarization by slightly rough surfaces or volume scattering, the angular behavior of the depolarized backscattering is similar to that of the polarized backscattering. The transitional behavior of the relative dominance between single and multiple scattering for the polarized and depolarized scattering coefficient as a function of the azimuth angle is illustrated.     

Backscattering enhancement of electromagnetic waves fromtwo-dimensional perfectly conducting random rough surfaces: a comparisonof Monte Carlo simulations with experimental data

Predictions of an exact numerical model for scattering from a surface randomly rough in two directions are compared with experimental data. The numerical model is based on Monte Carlo simulation using an iterative version of the method of moments known as the sparse-matrix flat-surface iterative approach (SMFSIA). Experimental data is obtained from millimeter wave laboratory experiments in which the bistatic scattering patterns of fabricated surfaces with known statistical parameters were measured. The surfaces studied have both a Gaussian height distribution and correlation function, so that their statistics are characterized by an RMS height and correlation length. An RMS height of 1 wavelength and correlation lengths ranging from 1.41-3 wavelengths are investigated, and the phenomenon of backscattering enhancement is observed both in the numerical predictions and experimental data. A comparison of the absolute value of the bistatic scattering coefficient as normalized by the incident power shows the theory and experiment to be in good agreement     

Analysis of a Narrow Capacitive Strip in Waveguide

A theoretical determination is made for the susceptance of a narrow conducting strip inserted vertically into a waveguide. The theory is based upon a variational form for the susceptance. A suitable current distribution along the strip is obtained for the variational equation, and is found to be similar to that determined from analysis of backscattering by a cylindrical obstacle irradiated from an incident plane wave. Accurate theoretical results may be obtained using a sinusoidal current distribution having a phase constant of /spl pi//2d, where d is the strip depth. Experimental results agree closely with the theory in the dominant-mode range and also at frequencies below cutoff.     

Effects of electron-density distribution on the back scattering from an anisotropic plasma cylinder

The backscattering cross-section of a radially inhomogeneous plasma cylinder with an impressed axial static magnetic field is obtained for an incident H wave. The electron-density distribution is assumed to have a parabolic profile. Significant variation of the backscattering cross-section as a function of the density profile is found.     

Probability distribution of CW induced currents on randomly oriented subresonant loops and wires

The deterministic prediction of both transient and CW field coupling to large complex electrical systems poses such a formidable problem that other approaches to predicting the coupling may be useful The continuous wave coupling to a complicated electrical system is analyzed in terms of random small dipole interactions in the low-frequency limit (wavelengthsggsystem components' sizes). Both random coupling to the incident wave and random interactions among the dipoles are considered. The variables being randomized are the incident direction and polarization, the sizes and orientations of the dipoles, the mutual coupling strengths, and the lumped load impedances. The resulting normalized current distributions are shown to be insensitive to the details of the model except at the extremely low and high percentiles. The magnetic dipole case is investigated in detail. Its resulting induced current distribution roughly resembles, but is not, a log-normal distribution with a standard deviation in the vicinity ofsim6dB. This result provides insight into some recent measurements obtained for EMP transient field coupling to large systems. An important implication of the results is that for a variety of complicated systems, essentially consisting of many small elements that the coupling is dominated by low-frequency magnetic fields, the central parts of the induced current probability distributions are similar and nearly log-normal. However, conclusions based on the extrapolation of log-normality from measured values near the median to the extreme percentiles may be susceptible to sizeable errors. The electric dipole ease is presented very briefly here, only to the extent of its basic formulations. We refer interested readers to our original report for some basic results for this case and also for the effects caused by an elliptically polarized incident wave versus a linearly polarized one.     

An asymptotic solution for currents in the penumbra region with discontinuity in curvature

An analytical asymptotic result is obtained for evaluating the current distribution on a perfectly conducting surface composed of a flat plate smoothly joined to a parabolic cylinder with the join in the penumbra region. The result presents some improvements over a previous solution of the current distribution obtained by other investigators. The analytical result can be conveniently applied to estimating the backscattering cross section of a cone-sphere.     

Estimation of surface roughness parameters from dual-frequencymeasurements of radar backscattering coefficients

A simple model was developed for estimating the surface roughness parameters of a bare soil field. The model uses a set of dual-frequency measurements of the field's radar backscattering coefficients, which can be matched to calculated results obtained with assumed values for the surface roughness parameters, as represented by the surface height standard deviation σ and its correlation lengths. Scatter plots of measured and calculated radar backscattering coefficients at the C -band (4.25-GHz) frequency versus those at L-band (1.5 GHz) show that it is feasible to estimate the surface roughness parameters using this technique. The estimated values for σ are in excellent agreement with those of measurements. However, there are discrepancies between the estimated and measured values for the correlation length L. For a very rough field, the geometrical optics model could be more appropriate for modeling the C-band data     

Empirical Statistical Model for LTE Downlink Channel Occupancy

This paper develops an empirical statistical channel occupancy model for downlink long-term evolution (LTE) cellular systems. The model is based on statistical distributions mixtures for the holding times of the channels. Moreover, statistical distribution of the time when the channels are free is also considered. The data is obtained through an extensive measurement campaign performed in Stockholm, Sweden. Two types of mixtures are considered, namely, exponential and log-normal distributions to fit the measurement findings. The log-likelihood of both mixtures is used as a quantitative measure of the goodness of fit. Moreover, finding the optimal number of linearly combined distributions using the Akaike information criterion is investigated. The results show that good fitting can be obtained by using either exponential or log-normal distributions mixture. Even though, the fitting is done for a representative case with a tempo-spatial consideration, the model is yet applicable in general for LTE and other cellular systems in a wider sense.

     

Backscattering from a randomly rough dielectric surface

A backscattering model for scattering from a randomly rough dielectric surface is developed. Both like- and cross-polarized scattering coefficients are obtained. The like-polarized scattering coefficients contain single scattering terms and multiple scattering terms. The single scattering terms are shown to reduce to the first-order solutions derived from the small perturbation method when the roughness parameters satisfy the slightly rough conditions. When surface roughnesses are large but the surface slope is small, only a single scattering term corresponding to the standard Kirchhoff model is significant. If the surface slope is large, the multiple scattering term will also be significant. The cross-polarized backscattering coefficients satisfy reciprocity and contain only multiple scattering terms. The difference between vertical and horizontal scattering coefficients increases with the dielectric constant and is generally smaller than that predicted by the first-order small perturbation model. Good agreements are obtained between this model and measurements from statistically known surfaces     

Antenna Effective Aperture Measurement With Backscattering Modulation

A scattering measurement method for antenna characterization is described. The antenna backscattering is modulated by an oscillator circuit. The modulation begins, when a known RF power is transferred to the oscillator circuit from the antenna. This enables the measurement of the effective aperture of the antenna, from which the antenna bandwidth and radiation pattern are obtained. A theory for antenna aperture measurement is developed using a simple circuit model for the antenna-oscillator system. A dipole and a PIFA with a reactive input impedance at the application frequency were measured. The antenna aperture was measured to an accuracy of 9%, and the measurements complied with simulated and measured references. The method provides simple and accurate bandwidth and radiation pattern measurements with the reactive load the antenna is designed to work with.     

NUMERICAL SIMULATIONS OF POLARIZED SCATTERING FROM RANDOM CLUSTERS OF SPATIALLY-ORENTED, NON-SPHERICAL SCATTERS

Employing multiple scattering formulation of T-matrix method, numerical simulations are developed and applied to polarized scattering from random clusters of spatially-oriented, non-spherical particles. Polarized scattering is numerically presented for the functional dependence on particle shape, size, spatial distribution and orientation, and other physical parameters. Numerical calculations of backscattering from randomly clustered particles are well compared with that from independent particles and clusters. It can be seen that spatial distribution and orientation of non-spherical particles can have significant effect on scattering.