7 research outputs found
Approximation to Distribution of Product of Random Variables Using Orthogonal Polynomials for Lognormal Density
We derive a closed-form expression for the orthogonal polynomials associated
with the general lognormal density. The result can be utilized to construct
easily computable approximations for probability density function of a product
of random variables, when the considered variates are either independent or
correlated. As an example, we have calculated the approximative distribution
for the product of Nakagami-m variables. Simulations indicate that accuracy of
the proposed approximation is good with small cross-correlations under light
fading condition.Comment: submitted to IEEE Communications Lette
On stochastic comparisons of largest order statistics in the scale model
Let be
independent nonnegative random variables with , , where , and is an
absolutely continuous distribution. It is shown that, under some conditions,
one largest order statistic is smaller than another one
according to likelihood ratio ordering. Furthermore, we
apply these results when is a generalized gamma distribution which includes
Weibull, gamma and exponential random variables as special cases
Statistics of α - μ random variables and their applications in wireless multihop relaying and multiple scattering channels
Exact results for the probability density function (PDF) and cumulative distribution function (CDF) of the sum of ratios of products (SRP) and the sum of products (SP) of independent α-μ random variables (RVs) are derived. They are in the form of 1-D integral based on the existing works on the products and ratios of α-μ RVs. In the derivation, generalized Gamma (GG) ratio approximation (GGRA) is proposed to approximate SRP. Gamma ratio approximation (GRA) is proposed to approximate SRP and the ratio of sums of products (RSP). GG approximation (GGA) and Gamma approximation (GA) are used to approximate SP. The proposed results of the SRP can be used to calculate the outage probability (OP) for wireless multihop relaying systems or multiple scattering channels with interference. The proposed results of the SP can be used to calculate the OP for these systems without interference. In addition, the proposed approximate result of the RSP can be used to calculate the OP of the signal-to-interference ratio (SIR) in a multiple scattering system with interference
Outage Probability of Dual-Hop Selective AF With Randomly Distributed and Fixed Interferers
The outage probability performance of a dual-hop amplify-and-forward
selective relaying system with global relay selection is analyzed for
Nakagami- fading channels in the presence of multiple interferers at both
the relays and the destination. Two different cases are considered. In the
first case, the interferers are assumed to have random number and locations.
Outage probability using the generalized Gamma approximation (GGA) in the form
of one-dimensional integral is derived. In the second case, the interferers are
assumed to have fixed number and locations. Exact outage probability in the
form of one-dimensional integral is derived. For both cases, closed-form
expressions of lower bounds and asymptotic expressions for high
signal-to-interference-plus-noise ratio are also provided. Simplified
closed-form expressions of outage probability for special cases (e.g., dominant
interferences, i.i.d. interferers, Rayleigh distributed signals) are studied.
Numerical results are presented to show the accuracy of our analysis by
examining the effects of the number and locations of interferers on the outage
performances of both AF systems with random and fixed interferers.Comment: 35 pages, 11 figures, accepted with minor revisions for publication
as a regular paper in the IEEE Transactions on Vehicular Technology on
21/09/201
Novel approximations to the statistics of products of independent random variables and their applications in wireless communications
A novel analytical framework for evaluating the statistics of the product of independent random variables is proposed. Compared with other methods, which use either infinite series or special functions, the new method provides simple and efficient closed-form approximations, in terms of elementary functions, such as powers and exponentials. Numerical results, which are used to check the accuracy of the new approximations, show that it is quite accurate in most regions of interest. As an application, the proposed analytical results can be efficiently used in wireless communications theory to evaluate in closed form the outage probability of cascaded fading channels, as well as the rate offset of the hybrid automatic repeat request (H-ARQ) transmission. Numerical examples show that the derived expressions provide significant insights on the behaviors of important system parameters as the outage probability and the rate offset