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Register a new userTechnical Report: An MGF-based Unified Framework to Determine the Joint Statistics of Partial Sums of Ordered i.n.d. Random Variables
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Sung Sik Nam
Publication date
2013
fields
Informatics Engineering
and research's language is
English
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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 in this paper the more general case in which the random variables are independent but not necessarily identically distributed (i.n.d.). More specifically, we extend the previous analysis and introduce a new more general unified analytical framework to determine the joint statistics of partial sums of ordered i.n.d. RVs. Our mathematical formalism is illustrated with an application on the exact performance 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.
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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 Ks (Ks < K) best RVs are considered. In addition, we present the closed-form expressions for the exponential RV special case. These results apply to the performance analysis of various wireless communication systems over fading channels.
A new finger replacement technique which is applicable for RAKE receivers in the soft handover (SHO) region has been proposed and studied in [1], [2] under the ideal assumption that the fading is both independent and identically distributed from path to path. To supplement our previous work, we present a general comprehensive framework for the performance assessment of the proposed finger replacement schemes operating over independent and non-identically distributed (i.n.d.) faded paths. To accomplish this object, we derive new closed-form expressions for the target key statistics which are composed of i.n.d. exponential random variables. With these new expressions, the performance analysis of various wireless communication systems over more practical environments can be possible.
This paper investigates the physical-layer security for a random indoor visible light communication (VLC) network with imperfect channel state information (CSI) and a protected zone. The VLC network consists of three nodes, i.e., a transmitter (Alice), a legitimate receiver (Bob), and an eavesdropper (Eve). Alice is fixed in the center of the ceiling, and the emitted signal at Alice satisfies the non-negativity and the dimmable average optical intensity constraint. Bob and Eve are randomly deployed on the receiver plane. By employing the protected zone and considering the imperfect CSI, the stochastic characteristics of the channel gains for both the main and the eavesdropping channels is first analyzed. After that, the closed-form expressions of the average secrecy capacity and the lower bound of secrecy outage probability are derived, respectively. Finally, Monte-Carlo simulations are provided to verify the accuracy of the derived theoretical expressions. Moreover, the impacts of the nominal optical intensity, the dimming target, the protected zone and the imperfect CSI on secrecy performance are discussed, respectively.
In this paper, we investigate the physical-layer security for a spatial modulation (SM) based indoor visible light communication (VLC) system, which includes multiple transmitters, a legitimate receiver, and a passive eavesdropper (Eve). At the transmitters, the SM scheme is employed, i.e., only one transmitter is active at each time instant. To choose the active transmitter, a uniform selection (US) scheme is utilized. Two scenarios are considered: one is with non-negativity and average optical intensity constraints, the other is with non-negativity, average optical intensity and peak optical intensity constraints. Then, lower and upper bounds on the secrecy rate are derived for these two scenarios. Besides, the asymptotic behaviors for the derived secrecy rate bounds at high signal-to-noise ratio (SNR) are analyzed. To further improve the secrecy performance, a channel adaptive selection (CAS) scheme and a greedy selection (GS) scheme are proposed to select the active transmitter. Numerical results show that the lower and upper bounds of the secrecy rate are tight. At high SNR, small asymptotic performance gaps exist between the derived lower and upper bounds. Moreover, the proposed GS scheme has the best performance, followed by the CAS scheme and the US scheme.
In this paper, we investigate the performance of a mixed radio-frequency-underwater wireless optical communication (RF-UWOC) system where an unmanned aerial vehicle (UAV), as a low-altitude mobile aerial base station, transmits information to an autonomous underwater vehicle (AUV) through a fixed-gain amplify-and-forward (AF) or decode-and-forward (DF) relay. Our analysis accounts for the main factors that affect the system performance, such as the UAV height, air bubbles, temperature gradient, water salinity variations, and detection techniques. Employing fixed-gain AF relaying and DF relaying, we derive closed-form expressions for some key performance metrics, e.g., outage probability (OP), average bit error rate (ABER), and average channel capacity (ACC). In addition, in order to get further insights, asymptotic analyses for the OP and ABER are also carried out. Furthermore, assuming DF relaying, we derive analytical expressions for the optimal UAV altitude that minimizes the OP. Simulation results show that the UAV altitude influences the system performance and there is an optimal altitude which ensures a minimum OP. Moreover, based on the asymptotic results, it is demonstrated that the diversity order of fixed-gain AF relaying and DF relaying are respectively determined by the RF link and by the detection techniques of the UWOC link.
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