Approximate BER performance of generalized selection combining in Nakagami-m fading

The error performance of generalized selection combining (GSC), which optimally combines the K highest signal-to-noise ratio (SNR) signals out of L total diversity signals, in Nakagami-m fading was recently evaluated using moment generating function (MGF) of the GSC output SNR. However, no single closed-form expression for the MGF exists for arbitrary K and L. In fact, closed-form expression for the MGF is possible only for individual combination of K and L. In this letter, a single closed-form expression for approximating the MGF is, therefore, derived and employed in evaluating the approximate error performance. Although the approximation is only applicable for GSC with K being a factor of L, it nonetheless achieves a high degree of accuracy.published_or_final_versio

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 Fisher-Snedecor F Variates and its Application to Maximal-Ratio Combining

Capitalizing on the recently proposed Fisher-Snedecor F composite fading model, in this letter, we investigate the sum of independent but not identically distributed (i.n.i.d.) Fisher-Snedecor F variates. First, a novel closed-form expression is derived for the moment generating function of the instantaneous signal-to-noise ratio. Based on this, the corresponding probability density function and cumulative distribution function of the sum of i.n.i.d. Fisher- Snedecor F variates are derived, which are subsequently employed in the analysis of multiple branch maximal-ratio combining (MRC). Specifically, we investigate the impact of multipath and shadowed fading on the outage probability and outage capacity of MRC based receivers. In addition, we derive exact closed-form expressions for the average bit error rate of coherent binary modulation schemes followed by an asymptotic analysis which provides further insights into the effect of the system parameters on the overall performance. Importantly, it is shown that the effect of multipath fading on the system performance is more pronounced than that of shadowing.Comment: 5 pages, 3 figure

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

Performance Analysis of Multihop Wireless Links over Generalized-K Fading Channels

The performance of multihop links is studied in this contribution by both analysis and simulations, when communicating over Generalized-$K$ ($K_G$) fading channels. The performance metrics considered include symbol error rate (SER), outage probability, level crossing rate (LCR) and average outage duration (AOD). First, the expressions for both the SER and outage probability are derived by approximating the probability density function (PDF) of the end-to-end signal-to-noise ratio (SNR) using an equivalent end-to-end PDF. We show that this equivalent end-to-end PDF is accurate for analyzing the outage probability. Then, the second-order statistics of LCR and AOD of multihop links are analyzed. Finally, the performance of multihop links is investigated either by simulations or by evaluation of the expressions derived. Our performance results show that the analytical expressions obtained can be well justified by the simulation results. The studies show that the $K_G$ channel model as well as the expressions derived in this paper are highly efficient for predicting the performance metrics and statistics for design of multihop communication links