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

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

Experimental and Analytical Investigations of an Optically Pre-Amplified FSO-MIMO System With Repetition Coding Over Non-Identically Distributed Correlated Channels

This paper presents theoretical and experimental bit error rate (BER) results for a freespace optical (FSO) multiple-input-multiple-output system over an arbitrarily correlated turbulence channel. We employ an erbium-doped fiber amplifier at the receiver (Rx), which results in an improved Rx’s sensitivity at the cost of an additional non-Gaussian amplified spontaneous emission noise. Repetition coding is used to combat turbulence and to improve the BER performance of the FSO links. A mathematical framework is provided for the considered FSO system over a correlated non-identically distributed Gamma-Gamma channel; and analytical BER results are derived with and without the pre-amplifier for a comparative study. Moreover, novel closed-form expressions for the asymptotic BER are derived; a comprehensive discussion about the diversity order and coding gain is presented by performing asymptotic analysis at high signal-tonoise ratio (SNR). To verify the analytical results, an experimental set-up of a 2 × 1 FSO-multiple-inputsingle-output (MISO) system with pre-amplifier at the Rx is developed. It is shown analytically that, both correlation and pre-amplification do not affect the diversity order of the system, however, both factors have contrasting behaviour with respect to coding gain. Further, to achieve the target forward error correction BER limit of 3.8 × 10−3 , a 2 × 1 FSO-MISO system with a pre-amplifier requires 6.5 dB lower SNR compared with the system with no pre-amplifier. Moreover, an SNR penalty of 2.5 dB is incurred at a higher correlation level for the developed 2×1 experimental FSO set-up, which is in agreement with the analytical findings

Experimental characterization and mitigation of turbulence induced signal fades within an ad hoc FSO network

Optical beams propagating through the turbulent atmospheric channel suffer from both the attenuation and phase distortion. Since future wireless networks are envisaged to be deployed in the ad hoc mesh topology, this paper presents the experimental laboratory characterization of mitigation of turbulence induced signal fades for two ad hoc scenarios. Results from measurements of the thermal structure constant along the propagation channels, changes of the coherence lengths for different turbulence regimes and the eye diagrams for partially correlated turbulences in free space optical channels are discussed. Based on these results future deployment of optical ad hoc networks can be more straightforwardly planned