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

A Framework for Uplink Intercell Interference Modeling with Channel-Based Scheduling

This paper presents a novel framework for modeling the uplink intercell interference (ICI) in a multiuser cellular network. The proposed framework assists in quantifying the impact of various fading channel models and state-of-the-art scheduling schemes on the uplink ICI. Firstly, we derive a semianalytical expression for the distribution of the location of the scheduled user in a given cell considering a wide range of scheduling schemes. Based on this, we derive the distribution and moment generating function (MGF) of the uplink ICI considering a single interfering cell. Consequently, we determine the MGF of the cumulative ICI observed from all interfering cells and derive explicit MGF expressions for three typical fading models. Finally, we utilize the obtained expressions to evaluate important network performance metrics such as the outage probability, ergodic capacity, and average fairness numerically. Monte-Carlo simulation results are provided to demonstrate the efficacy of the derived analytical expressions.Comment: IEEE Transactions on Wireless Communications, 2013. arXiv admin note: substantial text overlap with arXiv:1206.229