On the Utility of Laguerre Series for the Envelope PDF in Multipath Fading Channels

Abstract

-It is well known that multipath fading significantly affects the performance of communication systems. In order to incorporate the impact of this random phenomenon on system analysis and design, in many cases we need to calculate the probability density function (PDF) of the received signal envelope in multipath fading channels. In this paper, we consider a general multipath fading channel with arbitrary number of paths, where the amplitudes of multipath components are arbitrary correlated positive random variables, independent of phases, whereas the phases are independent and identically distributed random variables with uniform distributions. Since the integral form of the envelope PDF for such a general channel model is too complicated to be used for analytic calculations, we propose two infinite expansions for the PDF, a Laguerre series and a power series. Based on the tight uniform upper bounds on the truncation error of these two infinite series, we show that the Laguerre series is superior to the power series due to the fact that for a fixed number of terms, it yields a smaller truncation error.This Laguerre series with a finite number of terms, which expresses the envelope PDF just in terms of simple polynomial-exponential kernels, is particularly useful for mathematical performance prediction of communication systems in those indoor and outdoor multipath propagation environments, where the number of strong multipath components is small.

Generic stochastic modeling of vehicle-to-vehicle wireless channels

“…A simple, yet physical, way to model the amplitude term is to group the terms exp( ) ll aj  in equation (9) Thus, grouping the multipath components into specular and diffuse results in the following representation of equation (9) [49, Ch. (4)], [53], [54] , (9) and (10) are modeled as uniformly distributed random variables in [ , ]   .…”

“…In the most general case treated in [54], amplitudes and also independent of each other and uniformly distributed in [ , ]   . The specular part will not obey the central limit theorem (CLT) and will be a complex nonGaussian random variable.…”

“…The model in [54] generates several other PDFs encountered in the literature as special cases [49, Ch. (5)], [53], [55].…”

Multipath Comparison for GPS Observation MASS Station Data and RTK Station

“…Satu isyarat adalah langsung dari satelit, manakala isyarat yang lainnya merupakan isyarat-isyarat tidak langsung yang dipantulkan oleh objekobjek di sekitar antena sebelum tiba di antena penerima (El-Rabbany 2002). Disebabkan multipath menjadi punca ralat yang besar, banyak kajian telah dilakukan bagi melihat kesan multipath ini (Abdi 2009;Satirapod & Rizos 2003;Soloviev & Graas 2009;Wanninger & May 2000). Multipath memberikan kesan yang berbeza terhadap pengukuran julat pseudo (15-150 m) dan fasa pembawa (£ 5 cm untuk L 1 ) kerana frekuensi isyaratnya yang berlainan di mana multipath adalah bergantung kepada frekuensi (Seeber 2003).…”

Bit error rate in multipath wireless channels with several specular paths

“…Problem formulation: The received signal in a multipath fading channel with N specular components and a diffuse component can be represented by R exp( jQ) = N i=1 a i exp( jF i ) + A 0 exp( jF 0 ) [2,4], where R and Q are the received amplitude and phase, j 2 = −1, a i and F i are the amplitude and phase of the ith specular component, and A 0 and F 0 are the amplitude and phase of the diffuse component. The phases F i , i = 0, 1, 2, .…”