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Polarimetric SAR Speckle Statistics
Published in Jong-Sen Lee, Eric Pottier, Polarimetric Radar Imaging, 2017
The Rayleigh speckle model agrees reasonably well for measurements over homogeneous regions in SAR images with a coarse spatial resolution, but often fails over heterogeneous backscattering media by SAR with a finer resolution. For the latter case, many other statistical distributions, such as, the K-distribution, the log-normal, and Weibull distributions have been found to be useful in modeling the amplitude statistics. The K-distribution has its particular attractiveness, because it is derived based on a physical scattering process [5], and because the K-distribution reduces to the Rayleigh distribution in the case of homogeneous media. For 1-look SAR data, the K-distribution can be derived either by assuming that the number of scatterers in a resolution cell has a negative Binomial distribution or by using a product model of a Rayleigh distributed amplitude and a gamma distributed variable as a texture descriptor [6]. We use the product model because of its simplicity in deriving the K-distribution for both intensity and amplitude SAR images. The multilook K-distributions will be derived first, and then the single-look K-distributions are obtained as special cases.
Radiowave Propagation
Published in Indrakshi Dey, Propagation Modeling for Wireless Communications, 2022
where ν and w are positive parameters accounting for the effective number of scatterers. As ν→∞, K-distribution reduces (57) to Rayleigh distribution and (58) to gamma distribution. K-distribution is useful for modeling diverse scattering phenomena in wireless environments.
Single-Channel Receiver Over Fading Channels in the Presence of CCI
Published in Stefan R. Panić, Mihajlo Stefanović, Jelena Anastasov, Petar Spalević, Fading and Interference Mitigation in Wireless Communications, 2013
Stefan R. Panić, Mihajlo Stefanović, Jelena Anastasov, Petar Spalević
Composite propagation environments of multipath fading, superimposed by lognormal or gamma shadowing, result in lognormal or gamma-based fading models, such as Rayleigh-, Rician-, or Nakagami-lognormal and Nakagami-gamma fading channels. However, as based fading models are analytically very difficult to handle and, therefore, rather complicated, mathematical expressions have been derived for the performance of digital communication systems operating in such environments. However, the generalized K distribution [15] is a generic and versatile distribution for the accurate modeling of a great variety of short-term fading in conjunction with long-term fading (shadowing) channel conditions. This composite distribution is convenient for modeling multipath/ shadowing correlated fading environments when the correlations between the instantaneous signal powers and the ones between their average powers are different. The case when transmission over generalized K fading channels has been exposed to the influence of CCI will be observed here. The desired signal envelope and interfering one are both generalized K random variables with the PDFs, respectively [16, Eq. (1)]: () fR(R)=4Γ(md)Γ(kd)(mdΩd)(md+kd)/2Rmd+kd−1Kkd−md(2RmdΩd);
Distributions for two-point statistics of scattered signals with variable scattering strength
Published in Waves in Random and Complex Media, 2023
James G. Ronan, D. Keith Wilson, Vladimir E. Ostashev
One of the main motivations for favoring the as the modulating distribution is that it is the Bayesian conjugate prior of the gamma. Thus the integration, Equation (1), yields a relatively simple functional form. While models can be formulated with other modulating distributions besides the , the results are not as simple. For example, Jakeman and Pusey [11], and Andrews and Phillips [2], used a second gamma pdf for the modulation, resulting in the K-distribution (or ‘gamma-gamma’ distribution in Andrews and Phillips's terminology), which involves a modified Bessel function of the second kind. The K- and distributions behave quite similarly [17]. Wilson et al. [12] showed that the agrees extremely well with outdoor sound propagation simulations incorporating realistic turbulent scattering, refraction, ground reflections, and random variations in wind velocity and surface heat flux.
Application and comparative analysis of radiative heat transfer models for coal-fired furnace
Published in Numerical Heat Transfer, Part A: Applications, 2022
Shesh N. Dhurandhar, Ankit Bansal, Sivaram Pramod Boppudi, Medha Dakshina Murty Kadiyala
The k-distribution in Eq. (23) is a function of local surface temperature Tsi through the blackbody function and of the reference gas state through the absorption coefficient, It is clear from the above analysis that we have transformed the spectral dependence of the problem from λ-space to κ-space (the probability density function space). However, it is even more convenient to transform the k-distribution (PDF) into a much smoother g-space (cumulative probability density function). Now, dividing the Eq. (23) by i.e., k-distribution at reference absorption coefficient spectrum and at reference Planck function temperature, we get where is the weight function, quite similar to weights (but much more accurate) of the WSGG model. The point to note here is that in comparison to weights in the WSGG model, the k-distribution model weights are much more accurate. The cumulative k-distribution is given by where the value of g varies from 0 to 1. since the cumulative k-distribution has a very smooth distribution, a very efficient Gaussian quadrature scheme can be used for integration in the g-space. Eq. (24) can be written as with and
Research on uplink performance of MIMO terrestrial-satellite laser communication based on OSM-MBM joint modulation
Published in Journal of Modern Optics, 2022
Haibo Wang, Qianqian Wang, Yi Wang
In the terrestrial-satellite laser communication uplink, the M distribution can characterize most of the current atmospheric models, such as K distribution, Gamma-Gamma distribution, etc., and the M distribution covers all channel conditions of weak, medium, and strong turbulence. Considering the combined effects of light intensity scintillation, beam wander and angle of arrival fluctuation, the probability density function of the M distribution channel can be expressed as [19]: where is a positive parameter related to the effective number of large-scale units in the scattering process, and is a natural number related to the diffraction effect produced by small-scale eddy currents, representing the value of the fading parameter. The contribution of the coherent average power is given by . In equation, is the average power of the line-of-sight(LOS) term, and and represent the definite phase of the LOS term, and the definite phase coupled to the LOS scattering term. The classical scattering component is expressed as , represents the average power of , and is the ratio of the scattered power coupled with the LOS and the power of all scattered components. The average power of the total scattering is represented by . The Gamma function is represented by .