In studying the performance of coded communications over memoryless channels (with or without fading), the results are given as upper bounds on the average bit error probability (BEP). In principle, there are three different approaches to arriving at these bounds, all of which employ obtaining the so-called pairwise error probability , or the probability of choosing one symbol sequence over another for a given pair of possible transmitted symbol sequences, followed by a weighted summation over all pairwise events. In this chapter, we will focus on the results obtained from the third approach since these provide the tightest upper bounds on the true performance. The first emphasis will be placed on evaluating the pairwise error probability with and without CSI, following which we shall discuss how the results of these evaluations can be used via the transfer bound approach to evaluate average BEP of coded modulation transmitted over the fading channel.

Coded Communication over Fading Channels

In this paper, we present novel closed-form expressions for the probability density function (PDF) and cumulative distribution function (CDF) of ratio of random variable and product of two random variables for the cases where random variables are Rayleigh, Weibull, Nakagami-m and α-μ distributed. An application of obtained results in performance analysis of multi-hop wireless communication systems in different transmission environments is detailed described. The proposed theoretical analysis is also complemented by various graphically presented numerical results. Streszczenie. W artykule zaprezentowano wyrazenia na funkcje gestości prawdopodobienstwa PDF i kumulacyjną funkcje dystrybucji stosunku zmiennej przypadkowej i iloczynu dwoch zmiennych gdy zmienne przypadkowe są dystrybucją Rayleigh, Weibull, Nakagami-m i α-μ. Analiza ma zastosowanie do bezprzewodowych sieci komunikacyjnych w roznych warunkach transmisji. (Rozklad stosunku zmiennych przypadkowych i iloczynu tych zmiennych oraz wykorzystanie tych parametrow do analizy systemow komunikacji bezprzewodowej)

The distribution of ratio of random variable and product of two random variables and its application in performance analysis of multi-hop relaying communications over fading channels

We consider in this paper distributed beamforming for two-way cognitive radio networks in an effort to improve the spectrum efficiency and enhance the performance of the cognitive (secondary) system. In particular, we consider a spectrum sharing system where a set of amplify-and-forward (AF) relays are employed to help a pair of secondary transceivers in the presence of multiple licensed (primary) users. The set of relays participate in the beamforming process, where the optimal beamformer weights are obtained via a linear optimization method. For this system, we investigate the transmission protocols over two and three time-slots. To study and compare the performance tradeoffs between the two transmission protocols, for both of them, we derive closed-form expressions for the cumulative distribution function (CDF) and the moment generating function (MGF) of the equivalent end-to-end signal-to-noise ratio (SNR) at the secondary receiver. We analyze the performance of the proposed methods where closed-form expressions for the user outage probability and the average error probability are derived for independent and identically distributed Rayleigh fading channels. Numerical results demonstrate the efficacy of beamforming in enhancing the secondary system performance in addition to mitigating the interference to the primary users. In addition, our results show that the three time-slot protocol outperforms the two time-slot protocol in certain scenarios where it offers a good compromise between bandwidth efficiency and system performance.

Distributed Beamforming for Spectrum-Sharing Systems With AF Cooperative Two-Way Relaying

The Fisher-Snedecor $\mathcal {F}$ distribution has been recently proposed as a more accurate and mathematically tractable composite fading model than traditional established models in some practical cases. In this paper, we firstly derive exact closed-form expressions for the main statistical characterizations of the ratio of products of $\mathcal {F}$ -distributed random variables, including the probability density function, the cumulative distribution function and the moment generating function. Secondly, simple and tight approximations to the distribution of products and ratio of products of $\mathcal {F}$ -distributed random variables are presented. These analytical results can be readily employed to evaluate the performance of several emerging system configurations, including full-duplex relaying systems operating in the presence of co-channel interference and wireless communication systems enhanced with physical-layer security. The proposed mathematical analysis is substantiated by numerically evaluated results, accompanied by equivalent ones obtained using Monte Carlo simulations.

On the Distribution of the Ratio of Products of Fisher-Snedecor $\mathcal {F}$ Random Variables and Its Applications

Improper handling of on-ramp merging may cause severe decrease of traffic efficiency and contribute to lower fuel economy, even increasing the collision risk. Cooperative control for connected and automated vehicles (CAVs) has the potential to significantly reduce the negative impact and improve safety and traffic efficiency. Implementation of cooperative on-ramp merging requires the assistance of the vehicle to vehicle (V2V) and vehicle to infrastructure (V2I) communication, wherein the communication delay may cause negative impact on CAV cooperative control. In this paper, scenario of on-ramp merging for CAVs considering the V2I communication delay are studied. Statistical characteristics of the V2I communication delay are explored from both literature and real field test, and a communication delay estimation model based on statistical techniques are proposed. Specifically, we firstly model the CAV on-ramp merging scenario using optimal control in ideal situation. Then, several statistical characteristics of the V2I communication are investigated especially the probability density function of the V2I communication delay in several application scenarios. Further, we proposed a communication delay estimation model and used the modified vehicle state to compute the corresponding control law. Real field test of V2I communication delay indicated that distribution of V2I communication delay could correlate with the application scenario and normal distribution can be generally adopted to approximate the probability density function (PDF) when the number of samples is large enough. Numerical simulation of the CAV on-ramp merging scenario considering the V2I communication delay revealed that dynamic performance of the control process would be deteriorated impacted by the V2I communication delay and it might further impact the final control effect and lead to potential lateral collision in the merging area. 

On-Ramp Merging Strategies of Connected and Automated Vehicles Considering Communication Delay

In this paper, the performance of wireless system employing microdiversity to mitigate the effects of short-term fading and macrodiversity to reduce long-term fading (shadowing) effects is studied. The system model assumes implementation of maximal-ratio combining (MRC) at the microlevel and selection combining (SC) at the macrolevel. The received signal envelope follows a Rician distribution and it also suffers gamma shadowing. Novel expressions for the probability density function (PDF), cumulative distribution function (CDF), and moment-generating function (MGF) of the output signal-to-noise ratio (SNR) are obtained. Several useful performance criteria, such as the moments of the output SNR and outage probability are analytically derived. Moreover, the average bit error probability (ABEP) for noncoherent binary differential phase-shift keying (BDPSK) is calculated using the MGF based approach while the ABEP for coherent binary phase-shift keying (BPSK) is studied by averaging the conditional bit error probability over the PDF. Numerical results are graphically presented to show the effects of various system parameters to the system performance, as well as the enhancement due to use of the combination of micro- and macrodiversity. Some of numerical results are complemented by equivalent computer simulated results which validate the accuracy of the proposed analysis. The agreement between the Rician-gamma and Rician-lognormal fading model is also established.

Performance Analysis of System with Micro- and Macrodiversity Reception in Correlated Gamma Shadowed Rician Fading Channels

In this paper, the performance of L-branch selection combining receiver over correlated Weibull fading channels in the presence of correlated Weibull-distributed cochannel interference is analyzed. Closed-form expressions for probability density function and cumulative distribution function of the signal-to-interference ratio at the output of the selection combining receiver present main contribution of this paper. Numerical results are also presented to show the effects of various parameters as the fading severity, correlation and number of branches on outage probability. Copyright © 2009 John Wiley & Sons, Ltd.

This paper analyzes the outage performance of L-branch SC receiver over correlated Weibull fading channels in the presence of correlated Weibull-distributed co-channel interference. In order to carry out this analysis, closed-form expression for the outage probability of considered system is derived. Presented numerical results show the effects of various parameters as the fading severity, correlation and number of branch on the outage probability. Copyright © 2009 John Wiley & Sons, Ltd.

http://www.doiserbia.nb.rs/ft.aspx?id=0353-36701001087S

Performance analysis of system with L-branch selection combining over correlated Weibull fading channels in the presence of cochannel interference

In this letter, we analyze the error performance of a mobile communication system with microdiversity and macrodiversity reception in gamma-shadowed Rician fading channels for a binary differential phase-shift keying modulation scheme. Analytical expressions for the probability density function (PDF) and moment-generating function (MGF) are derived. The average bit error probability can be calculated by averaging the conditional bit error probability over the PDF or using the MGF-based approach. Numerical results are graphically presented to show the effects of macrodiversity, correlation, number of diversity branches, and severity of both fading and shadowing.

https://onlinelibrary.wiley.com/doi/pdf/10.4218/etrij.10.0209.0448

Effect of Microdiversity and Macrodiversity on Average Bit Error Probability in Gamma-Shadowed Rician Fading Channels

We present an infinite-series representation for the average level crossing rate (LCR) of dual selection combining (SC) receivers, operating over correlated Rician fading channels, in the presence of Rayleigh cochannel interference (CCI). Numerical results are presented to illustrate the proposed mathematical analysis and to point out the effect of the branch correlation and fading severity on the average LCR.

Nikola M. Sekulovic

Papers

Performance Analysis of System with Micro- and Macrodiversity Reception in Correlated Gamma Shadowed Rician Fading Channels

Performance analysis of system with L-branch selection combining over correlated Weibull fading channels in the presence of cochannel interference

Effect of Microdiversity and Macrodiversity on Average Bit Error Probability in Gamma-Shadowed Rician Fading Channels

Average Level Crossing Rate of Dual Selection Diversity in Correlated Rician Fading with Rayleigh Cochannel Interference

The distribution of ratio of random variable and product of two random variables and its application in performance analysis of multi-hop relaying communications over fading channels