scholarly journals Efficient Numerical Methods for Analysis of Square Ratio of κ-μ and η-μ Random Processes with Their Applications in Telecommunications

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Gradimir V. Milovanović ◽  
Suad Suljović ◽  
Stefan R. Panić ◽  
Ismet Kalčo ◽  
Mihajlo Č. Stefanović
Keyword(s):  
Multipath Fading ◽  
Computational Procedure ◽  
Random Processes ◽  
Cumulative Distribution ◽  
Performance Criteria ◽  
Selection Combining ◽  
Weight Functions ◽  
Quadrature Formulas ◽  
Transmission Parameters ◽  
Probability Density Function Pdf

We will provide statistical analysis of the square ratio of κ-μ and η-μ random processes and its application in the signal-to-interference ratio (SIR) based performance analysis of wireless transmission subjected to the influence of multipath fading, modelled by κ-μ fading model, and undesired occurrence of co-channel interference (CCI), distributed as η-μ random process. First contribution of the paper is deriving exact closed expressions for the probability density function (PDF) and cumulative distribution function (CDF) of square ratio of κ-μ and η-μ random processes. Further, a verification of accuracy of these PDF and CDF expressions was given by comparison with the corresponding approximations obtained by the high-precision quadrature formulas of Gaussian type with respect to the weight functions on (0,+∞). The computational procedure of such quadrature rules is provided by using the constructive theory of orthogonal polynomials and the MATHEMATICA package OrthogonalPolynomials created by Cvetković and Milovanović (2004). Capitalizing on obtained expression, important wireless performance criteria, namely, outage probability (OP), have been obtained, as functions of transmission parameters. Also, possible performance improvement is observed through a glance at SC (selection combining) reception employment based on obtained expressions.

scholarly journals Performance of macro diversity wireless communication system operating in Weibull multipath fading environment

2017 ◽  
Vol 30 (4) ◽  
pp. 599-609
Author(s):  
Suad Suljovic ◽  
Dejan Milic ◽  
Zorica Nikolic ◽  
Stefan Panic ◽  
Mihajlo Stefanovic ◽  
...  
Keyword(s):  
Communication System ◽  
Output Signal ◽  
System Performance ◽  
Multipath Fading ◽  
Cumulative Distribution ◽  
Selection Combining ◽  
Small Scale ◽  
Weibull Fading ◽  
Fading Parameter ◽  
Severity Parameter

In this paper, we consider wireless mobile radio communication system with macro diversity reception. Signal is subject to Weibull small scale fading and Gamma large scale fading resulting in system performance degradation. Receiver uses macro diversity selection combining (SC) technique in order to reduce the impact of long term fading effects, and two micro diversity SC branches are used to mitigate Weibull short term fading effects on system performance. Probability density function (PDF), and cumulative distribution function (CDF), as well as level crossing rate (LCR) and average fade duration (AFD) of the SC receiver output signal envelope are evaluated. The obtained expressions converge rapidly for all considered values of Weibull fading parameter and Gamma shadowing severity parameter. Mathematical results are studied in order to analyze the influence of Weibull fading parameter and Gamma shadowing severity parameter on statistical properties of the SC receiver output signal.

scholarly journals Performance Analysis of 5G Transmission over Fading Channels with Random IG Distributed LOS Components

2017 ◽  
Vol 2017 ◽  
pp. 1-4
Author(s):  
Dejan Jaksic ◽  
Risto Bojovic ◽  
Petar Spalevic ◽  
Dusan Stefanovic ◽  
Slavisa Trajkovic
Keyword(s):  
Closed Form ◽  
Fading Channels ◽  
Cumulative Distribution ◽  
Component Ratio ◽  
Transmission Parameters ◽  
Inverse Gamma ◽  
Level Crossing Rate ◽  
Distributed Process ◽  
Random Nature ◽  
Probability Density Function Pdf

Mathematical modelling of the behavior of the radio propagation at mmWave bands is crucial to the development of transmission and reception algorithms of new 5G systems. In this study we will model 5G propagation in nondeterministic line-of-sight (LOS) conditions, when the random nature of LOS component ratio will be observed as Inverse Gamma (IG) distributed process. Closed-form expressions will be presented for the probability density function (PDF) and cumulative distribution function (CDF) of such random process. Further, closed-form expressions will be provided for important performance measures such as level crossing rate (LCR) and average fade duration (AFD). Capitalizing on proposed expressions, LCR and AFD will be discussed in the function of transmission parameters.

scholarly journals LCR of SC receiver output signal over α-κ-μ multipath fading channels

2016 ◽  
Vol 29 (2) ◽  
pp. 261-268 ◽  
Author(s):  
Suad Suljovic ◽  
Dejan Milic ◽  
Stefan Panic
Keyword(s):  
Fading Channels ◽  
Output Signal ◽  
Multipath Fading ◽  
Selection Combining ◽  
Multipath Fading Channels ◽  
Signal Envelope ◽  
Transmission Parameters ◽  
Dominant Component ◽  
Level Crossing Rate ◽  
Wireless Mobile Communication

Wireless mobile communication system with selection combining (SC) diversity receiver is investigated in this paper. Received signal envelope experiences ?-?-? short term fading resulting in system performance degradation. Level crossing rate (LCR) and average fade duration (AFD) of SC receiver output signal envelope are obtained as rapidly converging infinite series expressions. Numerically evaluated results are presented graphically, in order to discuss the effects of transmission parameters: multipath fading severity, dominant component power and nonlinearity propagation parameter on observed LCR performance of dual SC.

scholarly journals Performance analysis of system with triple selection combining over correlated Weibull fading channel in the presence of cochannel interference

2010 ◽  
Vol 23 (1) ◽  
pp. 87-96 ◽  
Author(s):  
Petar Spalevic ◽  
Nikola Sekulovic ◽  
Georgios Zachos
Keyword(s):  
Fading Channels ◽  
Cochannel Interference ◽  
Cumulative Distribution ◽  
Performance Criteria ◽  
Selection Combining ◽  
Wireless System ◽  
Average Output ◽  
Weibull Fading ◽  
Average Bit Error Probability ◽  
Correlated Weibull Fading

In this paper, closed-form expressions for probability density function (PDF) and cumulative distribution function (CDF) of the signal-to-interference ratio (SIR) at the output of the triple selection combining (SC) receiver over correlated Weibull fading channels in the presence of correlated cochannel interference (CCI) are derived. These expressions are used to study wireless system performance criteria, such as outage probability, average bit error probability and average output SIR. .

scholarly journals On the Performance Analysis of Switched Diversity Combining Receivers over Fisher–Snedecor ℱ Composite Fading Channels

Sensors ◽  
2021 ◽  
Vol 21 (9) ◽  
pp. 3014
Author(s):  
Weijun Cheng ◽  
Xiaoting Wang ◽  
Tengfei Ma ◽  
Gang Wang
Keyword(s):  
Fading Channels ◽  
Error Probability ◽  
Signal To Noise Ratio ◽  
Multipath Fading ◽  
Performance Criteria ◽  
Statistical Characteristics ◽  
Diversity Combining ◽  
Systematic Analysis ◽  
Average Bit Error Probability ◽  
Switched Diversity Combining

In some emerging wireless applications, such as wearable communication and low-power sensor network applications, wireless devices or nodes not only require simple physical implementation approaches but also require certain reliable receiver techniques to overcome the effects of multipath or shadowed fading. Switched diversity combining (SDC) systems could be a simple and promising solution to the above requirements. Recently, a Fisher–Snedecor ℱ composited fading model has gained much interest because of its modeling accuracy and calculation tractability. However, the performance of SDC systems over ℱ fading channels has not yet been analyzed in the open literature. To this end, this paper presents a systematic analysis of SDC systems over ℱ fading channels, including dual-branch switch-and-stay combining (SSC), multibranch switch-and examine combining (SEC), and SEC with post-examining selection (SECps) systems. We first investigate the statistical characteristics of univariate and bivariate ℱ distributions. Then, these statistical expressions are introduced into the above SDC systems and the statistical metrics of the output signal-to-noise ratio (SNR) for these systems are deduced in different ℱ fading scenarios. Thirdly, certain exact and novel expressions of performance criteria, such as the outage probability, the average bit error probability and average symbol error probability, as well as the average channel capacity for SSC, SEC, and SECps are derived. To find the optimum performance, optimal analysis is performed for the independent and identically distributed cases. Finally, numerical evaluation and simulations are carried out to demonstrate the validity of the theoretical analysis under various ℱ fading scenarios. According to the obtained results, the multipath fading parameter has more influence on the performance of SDC systems than the shadowing parameter, the correlation coefficient, or the average SNR. Importantly, the SDC systems can provide switched diversity gains only when the switching threshold is not too large or too small compared to the average SNR.

scholarly journals Multichannel spectrum sensing over correlated fading channels with diversity reception

2021 ◽  
Author(s):  
Salam Al-Juboori ◽  
Xavier Fernando
Keyword(s):  
Closed Form ◽  
Fading Channels ◽  
Spectrum Sensing ◽  
Detection Probability ◽  
Multipath Fading ◽  
Primary User ◽  
Secondary User ◽  
Selection Combining ◽  
Standard Normal Distribution ◽  
Correlated Fading

Accurate detection of white spaces is crucial to protect primary user against interference with secondary user. Multipath fading and correlation among diversity branches represent essential challenges in Cognitive Radio Network Spectrum Sensing (CRNSS). This dissertation investigates the problem of correlation among multiple diversity receivers in wireless communications in the presence of multipath fading. The work of this dissertation falls into two folds, analysis and solution. In the analysis fold, this dissertation implements a unified approach of performance analysis for cognitive spectrum sensing. It considers a more realistic sensing scenario where non-independent multipath fading channels with diversity combining technique are assumed. Maximum Ratio Combining (MRC), Equal Gain Combining (EGC), Selection Combining (SC) and Selection and Stay Combining (SSC) techniques are employed. Arbitrarily, constant and exponentially dual, triple and L number of Nakagami-m correlated fading branches are investigated. We derive novel closed-form expressions for the average detection probability for each sensing scenario with simpler and more general alternative expressions. Our numerical analysis reveals the deterioration in detection probability due to correlation especially in deep fading. Consequently, an increase in the interference rate between the primary user and secondary user is observed by three times its rate when independent fading branches is assumed. However, results also show that this effect could be compensated for, through employing the appropriate diversity technique and by increasing the diversity branches. Therefore, we say that the correlation cannot be overlooked in deep fading, however in low fading can be ignored so as to reduce complexity and computation. Furthermore, at low fading, low false alarm probability and highly correlated environments, EGC which is simpler scheme performs as good as MRC which is a more complex scheme. Similar result are observed for SC and SSC. For the solution fold and towards combatting the correlation impact on the wireless systems, a decorrelator implementation at the receiver will be very beneficial. We propose such decorrelator scheme which would significantly alleviate the correlation effect. We derive closed-form expressions for the decorrelator receiver detection statistics including the Probability Density Function (PDF) from fundamental principles, considering dual antenna SC receiver in Nakagami-m fading channels. Numerical results show that the PDF of the bivariate difference could be perfectly represented by a semi-standard normal distribution with zero mean and constant variance depending on the bivariate's parameters. This observation would significantly help simplifying the design of decorrelator receiver. The derived statistics can be used in the problem of self-interference for multicarrier systems. Results also show the outage probability has been improved by double, due to the decorrelator.

scholarly journals The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey’shTransformation as a Special Case

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Georg M. Goerg
Keyword(s):  
Heavy Tails ◽  
Random Variable ◽  
R Package ◽  
Heavy Tail ◽  
Cumulative Distribution ◽  
Lambert W Function ◽  
Inverse Transformation ◽  
Heavy Tailed ◽  
Probability Density Function Pdf ◽  
Special Case

I present a parametric, bijective transformation to generate heavy tail versions of arbitrary random variables. The tail behavior of thisheavy tail Lambert  W × FXrandom variable depends on a tail parameterδ≥0: forδ=0,Y≡X, forδ>0 Yhas heavier tails thanX. ForXbeing Gaussian it reduces to Tukey’shdistribution. The Lambert W function provides an explicit inverse transformation, which can thus remove heavy tails from observed data. It also provides closed-form expressions for the cumulative distribution (cdf) and probability density function (pdf). As a special case, these yield analytic expression for Tukey’shpdf and cdf. Parameters can be estimated by maximum likelihood and applications to S&P 500 log-returns demonstrate the usefulness of the presented methodology. The R packageLambertWimplements most of the introduced methodology and is publicly available onCRAN.

scholarly journals Quadrature formulas associated with rational modifications of the Chebyshev weight functions

2006 ◽  
Vol 51 (3-4) ◽  
pp. 419-430 ◽  
Author(s):  
L. Darius ◽  
P. González-Vera ◽  
M. Jiménez Paiz
Keyword(s):  
Weight Functions ◽  
Quadrature Formulas
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