Simple closed-form asymptotic symbol error rate of selection combining and its power loss compared to the maximal ratio combining over Nakagami m fading channels

2010 ◽  
Vol 58 (4) ◽  
pp. 1142-1150 ◽  
Author(s):  
Ning Kong ◽  
Laurence Milstein
Keyword(s):  
Closed Form ◽  
Fading Channels ◽  
Error Rate ◽  
Power Loss ◽  
Symbol Error Rate ◽  
Maximal Ratio Combining ◽  
Selection Combining

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 A Closed-Form Approximation to the Distribution for the Sum of Independent Non-identically Generalized Gamma Variates and Applications

2021 ◽  
Vol 8 (1) ◽  
pp. 33-44
Author(s):  
Toufik Chaayra ◽  
Hussain Ben-azza ◽  
Faissal El Bouanani
Keyword(s):  
Closed Form ◽  
Fading Channels ◽  
Performance Metrics ◽  
Approximate Expression ◽  
Maximal Ratio Combining ◽  
Generalized Gamma ◽  
The Moment ◽  
Probability Density Function Pdf ◽  
Closed Form Approximation ◽  
Fox’S H Function

Evaluating the sum of independent and not necessarily identically distributed (i.n.i.d) random variables (RVs) is essential to study different variables linked to various scientific fields, particularly, in wireless communication channels. However, it is difficult to evaluate the distribution of this sum when the number of RVs increases. Consequently, the complex contour integral will be difficult to determine. Considering this issue, a more accurate approximation of the distribution function is required. By assuming the probability density function (PDF) of a generalized gamma (GG) RV evaluated in terms of a proper subset H1,0 1,1 class of Fox’s H-function (FHF) and the moment-based approximation to estimate the FHF parameters, a closed-form tight approximate expression for the distribution of the sum of i.n.i.d GG RVs and a sufficient condition for the convergence are investigated. The proposed approximate may be an analytical useful tool for analyzing the performance of certain numbers branch maximal-ratio combining receivers subject to GG fading channels. Hence, various closed-form performance metrics are derived and examined in terms of FHF. Numerical simulations are carried out to illustrate the theoretical results.

Sign in / Sign up

Export Citation Format

Share Document