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

Adaptive Power Control for Single and Multiuser Opportunistic Systems

In this dissertation, adaptive power control for single and multiuser opportunistic systems is investigated. First, a new adaptive power-controlled diversity combining scheme for single user systems is proposed, upon which is extended to the multiusers case. In the multiuser case, we first propose two new threshold based parallel multiuser scheduling schemes without power control. The first scheme is named on-off based scheduling (OOBS) scheme and the second scheme is named switched based scheduling (SBS) scheme. We then propose and study the performance of thresholdbased power allocation algorithms for the SBS scheme. Finally, we introduce a unified analytical framework to determine the joint statistics of partial sums of ordered RVs with i.i.d. and then the impact of interference on the performance of parallel multiuser scheduling is investigated based on our unified analytical framework

An Accurate Sample Rejection Estimator of the Outage Probability With Equal Gain Combining

We evaluate the outage probability (OP) for L-branch equal gain combining (EGC) receivers operating over fading channels, i.e., equivalently the cumulative distribution function (CDF) of the sum of the L channel envelopes. In general, closed form expressions of OP values are out of reach. The use of Monte Carlo (MC) simulations is not a good alternative as it requires a large number of samples for small values of OP. In this paper, we use the concept of importance sampling (IS), being known to yield accurate estimates using fewer simulation runs. Our proposed IS scheme is based on sample rejection where the IS density is the truncation of the underlying density over the L dimensional sphere. It assumes the knowledge of the CDF of the sum of the L channel gains in closed-form. Such an assumption is not restrictive since it holds for various challenging fading models. We apply our approach to the case of independent Rayleigh, correlated Rayleigh, and independent and identically distributed Rice fading models. Next, we extend our approach to the interesting scenario of generalised selection combining receivers combined with EGC under the independent Rayleigh environment. For each case, we prove the desired bounded relative error property. Finally, we validate these theoretical results through some selected experiments

Design and performance evaluation of RAKE finger management schemes in the soft handover region

We propose and analyze new finger assignment/management techniques that are applicable for RAKE receivers when they operate in the soft handover region. Two main criteria are considered: minimum use of additional network resources and minimum call drops. For the schemes minimizing the use of network resources, basic principles are to use the network resources only if necessary while minimum call drop schemes rely on balancing or distributing the signal strength/paths among as many base stations as possible. The analyses of these schemes require us to consider joint microscopic/macroscopic diversity techniques which have seldom been considered before and as such, we tackle the statistics of several correlated generalized selection combining output signal-to-noise ratios in order to obtain closed-form expressions for the statistics of interest. To provide a general comprehensive framework for the assessment of the proposed schemes, we investigate not only the complexity in terms of the average number of required path estimations/comparisons, the average number of combined paths, and the soft handover overhead but also the error performance of the proposed schemes over independent and identically distributed fading channels. We also examine via computer simulations the effect of path unbalance/correlation as well as outdated/imperfect channel estimations. We show through numerical exam ples that the proposed schemes which are designed for the minimum use of network resources can save a certain amount of complexity load and soft handover overhead with a very slight performance loss compared to the conventional generalized selection combining-based diversity systems. For the minimum call drop schemes, by accurately quantifying the average error rate, we show that in comparison to the conventional schemes, the proposed distributed schemes offer the better error performance when there is a considerable chance of loosing the signals from one of the active base stations