Order statistics find applications in various areas of communications and signal processing. In this paper, we introduce an unified analytical framework to determine the joint statistics of partial sums of ordered random variables (RVs). With the proposed approach, we can systematically derive the joint statistics of any partial sums of ordered statistics, in terms of the moment generating function (MGF) and the probability density function (PDF). Our MGF-based approach applies not only when all the K ordered RVs are involved but also when only the K s (K s < K) best RVs are considered. In addition, we present the closed-form expressions for the exponential RV special case. These results apply to the ⋆ This work was supported in part by Qatar Telecom (Qtel). This is an extended version of a paper which was presented in performance analysis of various wireless communication systems over fading channels.

In this paper, we propose a multi-human detection algorithm based on impulse radio ultrawideband radar system. With our proposed algorithm, the multi-human detection can be performed by repeatedly performing clustering and detecting processes. More specifically, the system detects an effective peak of the first single cluster which is composed of peaks adjacent to each other and then repeat this process until effective peaks of clusters caused by multiple people are successfully detected sequentially. As our performance metrics, we take into account the performance analysis in terms of the error probability based on the results of the statistical analysis. More specifically, we first cross-verify that the empirical result theoretically follows the Log-normal distribution by comparing the theoretical and empirical results obtained through laboratory experiments. Then, we statistically analyze the received signals under the Lognormal distribution assumption. After that, this statistical result is adopted to the performance analysis of the error probability in terms of the total error probability. Note that the performance of our proposed algorithm is affected by the threshold value. Based on it, the optimal threshold is analyzed and we provide the sample guidelines for optimally adjusting the threshold value under given various environment factors. Finally, some selected experimental results are presented to show the validity of our proposed algorithm by comparing the performance between the proposed algorithm and the conventional algorithm.

The joint statistics of partial sums of ordered random variables (RVs) are often needed for the accurate performance characterization of a wide variety of wireless communication systems. A unified analytical framework to determine the joint statistics of partial sums of ordered independent and identically distributed (i.i.d.) random variables was recently presented. However, the identical distribution assumption may not be valid in several real-world applications. With this motivation in mind, we consider ⋆ This is an extended version of a paper which was presented in IEEE International Symposium on Information Theory analysis of the capture probability of generalized selection combining (GSC)-based RAKE receivers operating over frequency-selective fading channels with a non-uniform power delay profile. We also discussed a couple of other sample applications of the generic results presented in this work.

In this paper, we investigate both the bit error rate (BER) and outage performance of free-space optical (FSO) links over strong turbulence combined with various pointing error conditions. Considering atmospheric turbulence and pointing errors as main factors that deteriorate the quality of an optical link, we obtain a unified finite series approximation of the composite probability density function, which embraces generalized pointing error models. This approximations leads to new unified formulas for the BER and outage capacity of an FSO link, which account for the two possible detection mechanisms of intensity modulation/direct detection and heterodyne detection. Selected simulation results confirm that the newly derived approximations can give precise predictions of both the average BER and the outage capacity of FSO communication that are generally applicable to all environments.