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.

Effect of CSI Imperfection on Cognitive Underlay Transmission over Nakagami-m Fading Channel

2015 ◽  
Vol 1 ◽  
pp. 59
Author(s):  
Nguyen Hong Giang ◽  
Vo Nguyen Quoc Bao ◽  
Hung Nguyen-Le
Keyword(s):  
Fading Channels ◽  
System Performance ◽  
Performance Metrics ◽  
Maximal Ratio Combining ◽  
Relay Nodes ◽  
Channel State ◽  
Primary Network ◽  
Secondary Network ◽  
System Designs ◽  
Approximate Expressions

This paper analyzes the performance of a cognitive underlay system over Nakagami-m fading channels, where maximal ratio combining (MRC) is employed at secondary destination and relay nodes. Under the condition of imperfect channel state information (CSI) of interfering channels, system performance metrics for the primary network and for the secondary network are formulated into exact and approximate expressions, which can be served as theoretical guidelines for system designs. To verify the performance analysis, several analytical and simulated results of the system performance are provided under various system and channel settings.

scholarly journals Performance Analysis of AF Relays with Maximal Ratio Combining in Nakagami-m Fading Environments

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Dong Qin ◽  
Yuhao Wang ◽  
Tianqing Zhou
Keyword(s):  
Performance Metrics ◽  
Signal To Noise Ratio ◽  
Ergodic Capacity ◽  
Moment Generating Function ◽  
Maximal Ratio Combining ◽  
Modulation Scheme ◽  
Amplify And Forward ◽  
Generalized Gaussian Noise ◽  
The Moment ◽  
Fading Environments

This paper investigates the maximal ratio combining (MRC) performance of an amplify and forward (AF) relay system in Nakagami-m fading environments. The study considers a general scenario with distinct m fading parameters for the following three links, source to relay link, and source to destination link and relay to destination link. We derive new closed form expressions for the statistics of important performance metrics, including the moment generating function, outage probability, higher order moments of equivalent signal to noise ratio (SNR), ergodic capacity, and average symbol error probability (SEP) of common modulation types. In particular, we focus on analytical SEP expressions in the context of an additive white generalized Gaussian noise (AWGGN). As an active area of research, generalized noise receives much attention for its flexible model. However, analytical performance of modulation scheme in generalized noise type has not been found in open literature for AF relaying with MRC despite its practical usefulness. Without the help of analytical solutions, the SEP in generalized noise can only be obtained by a large number of repeated simulation experiments. Therefore, we present the general SEP expression by using special Fox’s H function. Simulation results verify the accuracy of our theoretical analysis and show that the diversity order of MRC criterion linearly depends upon Nakagami parameters of three links.

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 Reconfigurable Intelligent Surface assisted Two–Way Communications: Performance Analysis and Optimization

2020 ◽  
Author(s):  
Saman Atapattu ◽  
Rongfei Fan ◽  
Prathapasinghe Dharmawansa ◽  
Gongpu Wang ◽  
JAMIE EVANS ◽  
...  
Keyword(s):  
Closed Form ◽  
Fading Channels ◽  
Spectral Efficiency ◽  
Rayleigh Fading ◽  
Performance Metrics ◽  
Optimal Solution ◽  
Single Element ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Semidefinite Programming Problem

In this paper, we investigate the two-way communication between two users assisted by a re-configurable intelligent surface (RIS). The scheme that two users communicate simultaneously in the same time slot over Rayleigh fading channels is considered. The channels between the two users and RIS can either be reciprocal or non-reciprocal. For reciprocal channels, we determine the optimal phases at the RIS to maximize the signal-to-interference-plus-noise ratio (SINR). We then derive exact closed-form expressions for the outage probability and spectral efficiency for single-element RIS. By capitalizing the insights obtained from the single-element analysis, we introduce a gamma approximation to model the product of Rayleigh random variables which is useful for the evaluation of the performance metrics in multiple-element RIS. Asymptotic analysis shows that the outage decreases at $\left(\log(\rho)/\rho\right)^L$ rate where $L$ is the number of elements, whereas the spectral efficiency increases at $\log(\rho)$ rate at large average SINR $\rho$. For non-reciprocal channels, the minimum user SINR is targeted to be maximized. For single-element RIS, closed-form solutions are derived whereas for multiple-element RIS the problem turns out to be non-convex. The latter is relaxed to be a semidefinite programming problem, whose optimal solution is achievable and serves as a sub-optimal solution.

scholarly journals Reconfigurable Intelligent Surface assisted Two–Way Communications: Performance Analysis and Optimization

2020 ◽  
Author(s):  
Saman Atapattu ◽  
Rongfei Fan ◽  
Prathapasinghe Dharmawansa ◽  
Gongpu Wang ◽  
JAMIE EVANS ◽  
...  
Keyword(s):  
Closed Form ◽  
Fading Channels ◽  
Spectral Efficiency ◽  
Rayleigh Fading ◽  
Performance Metrics ◽  
Optimal Solution ◽  
Single Element ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Semidefinite Programming Problem

In this paper, we investigate the two-way communication between two users assisted by a re-configurable intelligent surface (RIS). The scheme that two users communicate simultaneously in the same time slot over Rayleigh fading channels is considered. The channels between the two users and RIS can either be reciprocal or non-reciprocal. For reciprocal channels, we determine the optimal phases at the RIS to maximize the signal-to-interference-plus-noise ratio (SINR). We then derive exact closed-form expressions for the outage probability and spectral efficiency for single-element RIS. By capitalizing the insights obtained from the single-element analysis, we introduce a gamma approximation to model the product of Rayleigh random variables which is useful for the evaluation of the performance metrics in multiple-element RIS. Asymptotic analysis shows that the outage decreases at $\left(\log(\rho)/\rho\right)^L$ rate where $L$ is the number of elements, whereas the spectral efficiency increases at $\log(\rho)$ rate at large average SINR $\rho$. For non-reciprocal channels, the minimum user SINR is targeted to be maximized. For single-element RIS, closed-form solutions are derived whereas for multiple-element RIS the problem turns out to be non-convex. The latter is relaxed to be a semidefinite programming problem, whose optimal solution is achievable and serves as a sub-optimal solution.

Energy Detection with Diversity Reception

2017 ◽  
Vol 3 (1) ◽  
pp. 20
Author(s):  
Sanjeewa P. Herath ◽  
Nandana Rajatheva ◽  
Tho Le-Ngoc ◽  
Chintha Tellambura
Keyword(s):  
Fading Channels ◽  
Energy Detection ◽  
Moment Generating Function ◽  
Rician Fading ◽  
Diversity Combining ◽  
Diversity Reception ◽  
The Moment ◽  
Performance Gains ◽  
Probability Density Function Pdf ◽  
Rician Fading Channels

We characterize the performance of energy detector (ED) over square-law, square-law selection, and switch-and-stay diversity combining schemes. The exact average probabilities of a miss (Pm), and a false alarm (Pf) are derived in closed-form. To derive Pm for versatile Nakagami-m and Rician fading channels, a twofold approach, using the probability density function (PDF) and the moment generating function (MGF), is applied. Using the PDF method, the achievable diversity order over the Nakagami-m channel is derived. However, this method becomes intractable when analyzing Pm of the aforementioned combiners in Rician channels, but the MGF method can handle this case. Our analysis helps to quantify the performance gains of ED due to diversity reception. Theoretical derivations are verified through numerical Monte-Carlo simulation results.

scholarly journals A Closed-Form Approximation for the Error Probability of BPSK Fading Channels

2007 ◽  
Vol 6 (6) ◽  
pp. 2051-2054 ◽  
Author(s):  
Alfonso Martinez ◽  
Albert Guillen i Fabregas ◽  
Giuseppe Caire
Keyword(s):  
Closed Form ◽  
Fading Channels ◽  
Error Probability ◽  
Closed Form Approximation
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