scholarly journals LEVEL CROSSING RATE OF PRODUCT OF TWO NAKAGAMI-m RANDOM VARIABLES AND RAYLEIGH RANDOM VARIABLE

2018 ◽  
Vol 8 (2) ◽  
Author(s):  
Srđan Maričić ◽  
Nenad Milošević
Keyword(s):  
Performance Analysis ◽  
Communication System ◽  
Rayleigh Fading ◽  
Random Variables ◽  
Random Variable ◽  
Random Processes ◽  
Level Crossing ◽  
The Third ◽  
Level Crossing Rate ◽  
Wireless Relay

In this paper, the level crossing rate of product of two Nakagami random variables and Rayleigh random variable will be calculated. This result can be used in the performance analysis of wireless relay communication system with three sections: Nakagami-m fading is present in the first and second section and Rayleigh fading is present in the third section. Also, the obtained result can be used for calculation of the level crossing rate of the product of three Rayleigh random processes, and the level crossing rate of the product of two Rayleigh random processes and Nakagami-m random process. The influence of the parameter m on the level crossing rate is analysed and considered. Key words: Level crossing rate, Nakagami-m random variable, Rayleigh random variable

scholarly journals Product of Three Random Variables and its Application in Relay Telecommunication Systems in the Presence of Multipath Fading

2019 ◽  
Vol 1 ◽  
pp. 83-92 ◽  
Author(s):  
Dragana Krstic ◽  
Petar Nikolic ◽  
Danijela Aleksic ◽  
Sinisa Minic ◽  
Dragan Vuckovic ◽  
...  
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Multipath Fading ◽  
Independent Random Variables ◽  
Radio System ◽  
Multipath Fading Channel ◽  
Level Crossing Rate ◽  
Telecommunication Systems ◽  
Wireless Relay ◽  
The Impact

In this paper, the product of three random variables (RVs) will be considered. Distribution of the product of independent random variables is very important in many applied problems, including wireless relay telecommunication systems. A few of such products of three random variables are observed in this work: the level crossing rate (LCR) of the product of a Nakagami-m random variable, a Rician random variable and a Rayleigh random variable, and of the products of two Rician RVs and one Nakagami-m RV is calculated in closed forms and presented graphically. The LCR formula may be later used for derivation of average fade duration (AFD) of a wireless relay communication radio system with three sections, working in the multipath fading channel. The impact of fading parameters and multipath fading power on the LCR is analyzed based on the graphs presented.

scholarly journals APPLICATION OF LAPLACE APPROXIMATION FORMULA IN PERFORMANCE ANALYSIS OF WIRELESS RELAY COMMUNICATION SYSTEM IN MULTIPATH FADING ENVIRONMENT

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
ČASLAV STEFANOVIĆ
Keyword(s):  
Performance Analysis ◽  
Communication System ◽  
Multipath Fading ◽  
Laplace Approximation ◽  
Average Level ◽  
Approximation Formula ◽  
Level Crossing ◽  
Relay Communications ◽  
Level Crossing Rate ◽  
Wireless Mobile Communication

In this paper, Laplace approximation formula is efficiently used to calculate infinite-series expression for average level crossing rate (LCR) of the product of Nakagami-m and kappa-mu random processes. The results can be used in performance analysis of dual-hop relay wireless mobile communication system in specific multipath fading environment when the first section is under the influence of NLOS multipath environment while the second section is under the influence of LOS multipath fading environment. The influences of multipath fading parameters on the LCR of the proposed model are examined, graphically presented and discussed. Moreover, analytical approach of applying Laplace approximation formula in multi-hop systems is further considered by obtaining closed form expressions for the LCR of the product of three and four Nakagami-m processes, respectively. Key words: average level crossing rate, kappa-mu multipath fading, Laplace approximation formula, Nakagami-m distribution, relay communications system.

Real-valued Random Processes

2015 ◽  
Author(s):  
Arno Berger ◽  
Theodore P. Hill
Keyword(s):  
Brownian Motion ◽  
Random Variables ◽  
Random Variable ◽  
Random Processes ◽  
Geometric Brownian Motion ◽  
Independent Random Variables ◽  
Benford’S Law ◽  
Random Maps ◽  
Random Samples ◽  
Benford's Law

Benford's law arises naturally in a variety of stochastic settings, including products of independent random variables, mixtures of random samples from different distributions, and iterations of random maps. This chapter provides the concepts and tools to analyze significant digits and significands for these basic random processes. Benford's law also arises in many other important fields of stochastics, such as geometric Brownian motion, random matrices, and Bayesian models, and the chapter may serve as a preparation for specialized literature on these advanced topics. By Theorem 4.2 a random variable X is Benford if and only if log ¦X¦ is uniformly distributed modulo one.

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