On the Computation of the Higher Order Statistics of the Channel Capacity over Generalized Fading Channels

The higher-order statistics (HOS) of the channel capacity $\mu_n=\mathbb{E}[\log^n(1+\gamma_{end})]$, where $n\in\mathbb{N}$ denotes the order of the statistics, has received relatively little attention in the literature, due in part to the intractability of its analysis. In this letter, we propose a novel and unified analysis, which is based on the moment generating function (MGF) technique, to exactly compute the HOS of the channel capacity. More precisely, our mathematical formalism can be readily applied to maximal-ratio-combining (MRC) receivers operating in generalized fading environments (i.e., the sum of the correlated noncentral chi-squared distributions / the correlated generalized Rician distributions). The mathematical formalism is illustrated by some numerical examples focussing on the correlated generalized fading environments.Comment: Submitted to IEEE Wireless Communications Letter, February 18, 201

Impact of Pointing Errors on the Performance of Mixed RF/FSO Dual-Hop Transmission Systems

In this work, the performance analysis of a dual-hop relay transmission system composed of asymmetric radio-frequency (RF)/free-space optical (FSO) links with pointing errors is presented. More specifically, we build on the system model presented in [1] to derive new exact closed-form expressions for the cumulative distribution function, probability density function, moment generating function, and moments of the end-to-end signal-to-noise ratio in terms of the Meijer's G function. We then capitalize on these results to offer new exact closed-form expressions for the higher-order amount of fading, average error rate for binary and M-ary modulation schemes, and the ergodic capacity, all in terms of Meijer's G functions. Our new analytical results were also verified via computer-based Monte-Carlo simulation results.Comment: 6 pages, 3 figure

Some Fractional Calculus results associated with the II-Function

The effect of Marichev-Saigo-Maeda (MSM) fractional operators involving third Appell function on the $I$ function is studied. It is shown that the order of the $I$-function increases on application of these operators to the power multiple of the $I$-function. The Caputo-type MSM fractional derivatives are introduced and studied for the $I$-function. As special cases, the corresponding assertions for Saigo and Erd\'elyi-Kober fractional operators are also presented. The results obtained in this paper generalize several known results obtained recently in the literature.Comment: arXiv admin note: text overlap with arXiv:1408.476

On the Sum of Order Statistics and Applications to Wireless Communication Systems Performances

We consider the problem of evaluating the cumulative distribution function (CDF) of the sum of order statistics, which serves to compute outage probability (OP) values at the output of generalized selection combining receivers. Generally, closed-form expressions of the CDF of the sum of order statistics are unavailable for many practical distributions. Moreover, the naive Monte Carlo (MC) method requires a substantial computational effort when the probability of interest is sufficiently small. In the region of small OP values, we propose instead two effective variance reduction techniques that yield a reliable estimate of the CDF with small computing cost. The first estimator, which can be viewed as an importance sampling estimator, has bounded relative error under a certain assumption that is shown to hold for most of the challenging distributions. An improvement of this estimator is then proposed for the Pareto and the Weibull cases. The second is a conditional MC estimator that achieves the bounded relative error property for the Generalized Gamma case and the logarithmic efficiency in the Log-normal case. Finally, the efficiency of these estimators is compared via various numerical experiments

On the Sum of Gamma Random Variates with Application to the Performance of Maximal Ratio Combining over Nakagami-m Fading Channels

The probability distribution function (PDF) and cumulative density function of the sum of L independent but not necessarily identically distributed gamma variates, applicable to maximal ratio combining receiver outputs or in other words applicable to the performance analysis of diversity combining receivers operating over Nakagami-m fading channels, is presented in closed form in terms of Meijer G-function and Fox H̅-function for integer valued fading parameters and non-integer valued fading parameters, respectively. Further analysis, particularly on bit error rate via PDF-based approach, too is represented in closed form in terms of Meijer G-function and Fox H̅-function for integer-order fading parameters, and extended Fox H̅--function (Ĥ) for non-integer-order fading parameters. The proposed results complement previous results that are either evolved in closed-form, or expressed in terms of infinite sums or higher order derivatives of the fading parameter m