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 Multivariate Gamma-Gamma (ΓΓ\Gamma \Gamma) Distribution with Arbitrary Correlation and Applications in Wireless Communications

The statistical properties of the multivariate Gamma-Gamma ($\Gamma \Gamma$) distribution with arbitrary correlation have remained unknown. In this paper, we provide analytical expressions for the joint probability density function (PDF), cumulative distribution function (CDF) and moment generation function of the multivariate $\Gamma \Gamma$ distribution with arbitrary correlation. Furthermore, we present novel approximating expressions for the PDF and CDF of the sum of $\Gamma \Gamma$ random variables with arbitrary correlation. Based on this statistical analysis, we investigate the performance of radio frequency and optical wireless communication systems. It is noteworthy that the presented expressions include several previous results in the literature as special cases.Comment: 7 pages, 6 figures, accepted by IEEE Transactions on Vehicular Technolog

BER of MRC for M-QAM with imperfect channel estimation over correlated Nakagami-m fading

In this contribution, we provide an exact BER analysis for M-QAM transmission over arbitrarily correlated Nakagami-m fading channels with maximal-ratio combining (MRC) and imperfect channel estimation at the receiver. Assuming an arbitrary joint fading distribution and a generic pilot-based channel estimation method, we derive an exact BER expression that involves an expectation over (at most) 4 variables, irrespective of the number of receive antennas. The resulting BER expression includes well-known PDFs and the PDF of only the norm of the channel vector. In order to obtain the latter PDF for arbitrarily correlated Nakagami-m fading, several approaches from the literature are discussed. For identically distributed and arbitrarily correlated Nakagami-m channels with integer m, we present several BER performance results, which are obtained from numerical evaluation and confirmed by straightforward computer simulations. The numerical evaluation of the exact BER expression turns out to be much less time-consuming than the computer simulations

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