Comments on "A new theoretical model for the prediction of rapid fading variations in an indoor environment"

In this paper, a new distribution, named POCA, is introduced for modeling envelope fluctuations due to fast fading in indoor environments. The main motivation has been the small number of scatterers in those environments, which makes the central limit theorem invalid for in-phase and quadrature components. Hence they are no longer Gaussian and envelope is not Rayleigh-distributed. POCA, the new envelope distribution, is obtained by assuming t distribution for in-phase and quadrature components. In this comment, first a short summary of three possible approaches for deriving the envelope distribution for indoor channels, where the number of scatterers is usually small, has been provided. Thereafter, based on various detailed theoretical considerations and also measurement results, the deficiency of POCA for prediction of rapid envelope variations in indoor channels has been demonstrated. Having the number of scatterers large is the main assumption in modeling the envelope probability density function (PDF) for fast fading (or local fading, if spatial variations are concerned instead of temporal fluctuations). Whenever other conditions of central limit theorem (CLT), like independence of multipath components received from scatterers, etc. are met, the inphase (I) and quadrature (Q) components of the received signal become Gaussian variables. In Comments on “A New Theoretical Model for the Prediction of Rapid Fading Variations in an Indoor Environment” Ali Abdi 2/9 general, they are dependent Gaussian variables with different non-zero means and unequal variances. The envelope PDF for this general case is presented in [1, eq. (4.6-28)]. The classical Rayleigh and Rice PDFs and the less-known Hoyt PDF are special cases of [1, eq. (4.6-28)]. However, as is pointed out, for indoor propagation channel the number of scatterers is usually small. So CLT does not hold and it does not make sense to consider [1, eq. (4.6-28)] or its special cases like Rayleigh, Rice, ..., as the envelope PDF for indoor environments. In order to find a suitable indoor envelope PDF, we may consider any of the following three approaches which have mainly been used for modeling the envelope PDF in other propagation environments. Each of them has its own advantages and disadvantages, not discussed here due to space limitations: Model-free approach: In this approach no assumption is made about the physical mechanism that generates envelope fluctuations. Usually a known and flexible PDF with two or three parameters is picked up and then its appropriateness is verified by doing statistical goodness-offit tests on real data. Weibull and lognormal PDFs are two examples of this kind, used for indoor channels [2]. Stacy PDF [3] is also promising for indoor environments. More suitable candidates may be found in [4] [5]. A more general method is to consider an infinite orthogonal expansion for the envelope PDF and then obtain the first few coefficients from data, as is done in [6] for statistical modeling of radar cross section using Legendre orthogonal polynomials. Since envelope is a positive-valued random process, Laguerre polynomials constitute the natural set of orthogonal basis for expanding the envelope PDF [7]. Random-vector-model approach: Here each multipath component is considered as a random vector with random length and angel. Then the superposition of multipath components at the receiver corresponds to the addition of random vectors. In this way, finding the envelope PDF reduces to calculating the PDF of the resulting vector. There are a couple of numerical and analytic methods for calculating the PDF of the resulting vector (see [7] and references therein). Expansion in terms of Laguerre polynomials is discussed in [7], along with a numerical