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

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 Cooperative Diversity Wireless Networks over Nakagami-m Fading Channel

This letter analyzes the performance of cooperative diversity wireless networks using amplify-and-forward relaying over independent, non-identical, Nakagami-m fading channels. The error rate and the outage probability are determined using the moment generating function (MGF) of the total signal-to-noise-ratio (SNR) at the destination. Since it is hard to find a closed form for the probability density function (PDF) of the total SNR, we use an approximate value instead. We first derive the PDF and the MGF of the approximate value of the total SNR. Then, the MGF is used to determine the error rate and the outage probability. We also use simulation to verify the analytical results. Results show that the derived error rate and outage probability are tight lower bounds particularly at medium and high SNR     

Performance evaluation of generalized selection diversity systems over Nakagami‐m fading channels

The generalized selection combining (GSC) scheme that adaptively combines a subset of M strongest paths out of L available diversity paths finds applications in several wideband receivers and broadband wireless communications. In this paper, exact closed‐form expressions for the moment generating function (MGF), the probability density function (PDF) and the cumulative density function (CDF) of the GSC(M, L) output signal‐to‐noise ratio (SNR) in independent and identically distributed (i.i.d) Nakagami‐m fading channels are derived while the fading index is a positive integer. These expressions hold for any M and L and provide a comprehensive framework for performance analysis including the derivation of closed‐form formulas for the average symbol error probability (ASEP) of a broad class of binary and M‐ary modulations, mean combined SNR and the outage probability of GSC(M, L) receiver structures. When the Nakagami‐m fading index is not an integer, the MGF of GSC(M, L) output SNR is derived as an (M − 1)‐fold infinite series. With this MGF, analytical expressions for both the outage probability and error rates can be readily obtained. An easily programmable recursive solution of the MGF of GSC(M, L) output SNR is also outlined for both the positive integer and noninteger fading severity index cases. Copyright © 2002 John Wiley & Sons, Ltd.     

Series solutions for π/4-DQPSK BER with MRC

Simple series expressions for bit error rate (BER) of π/4 shifted differential quaternary phase-shift keying (π/4-DQPSK) over some common fading environments (Rayleigh, Rician and Nakagami-m) are derived. Both single- and multi-channel reception scenarios are considered. In case of multi-antenna reception, it is assumed that the fading is independent and identically distributed (IID), and the receiver follows optimum maximal ratio combining (MRC). The derived expressions, computed through probability density function (PDF)-based approach, give an exact match with moment-generating function (MGF)-based solutions but get rid of numerical integrations involved in MGF approach. Further, the analytical results presented in this article consist of finite or rapidly converging infinite series and thus a trade-off between precision and complexity can be easily realised by choosing a specific number of terms. Bounds on the error resulting from truncation of the infinite series are also derived. Moreover, it was shown that the series solutions, when reasonably truncated, still provide better approximations than the previous attempts.     

Nakagami-m衰落信道下固定增益中继系统性能分析

 在Nakagami-m衰落信道下,分析了两跳固定增益放大转发中继通信系统的性能.首先采用基于概率密度函数(PDF)的性能分析法推导了无协作分集时系统的中断概率和平均误符号率(ASER)的闭合表达式,然后采用基于矩生成函数(MGF)的方法推导了有协作分集时系统的中断概率和ASER表达式以及接收信噪比的n阶矩的闭合表达式.仿真结果显示,所推导的闭合表达式与数值仿真结果吻合良好,协作分集和较大的m值可提升系统性能,中继前后两跳的信道质量对系统性能的影响并不相同.     

SER Performance of Amplify-and-Forward Cooperative Diversity Over Asymmetric Fading Channels

In this paper, the performance of amplify-and-forward (AF) cooperative diversity is analyzed over asymmetric fading channels. The source–relay and the relay–destination links experience Rayleigh fading while the source–destination link is subject to generalized Gamma fading. First, the probability density function (PDF) and the moment generating function (MGF) of the source–relay–destination link and the MGF of the source–destination link are derived. Then, the symbol error rate (SER) is determined based on the MGF of the total end-to-end signal-to-noise ratio (SNR). Moreover, the SER performance of N-relay assisted AF cooperative diversity is illustrated for M-ary phase shift keying (M-PSK) and M-ary quadrature amplitude modulation (M-QAM). Based on the derived MGF expressions, the numerical results are obtained by varying the modulation types and channel parameters for different scenarios.     

On the Performance Analysis of Digital Modulations in Generalized-K Fading Channels

In this paper we present novel expressions for several performance metrics of communication systems operating over a composite fading environment modelled by the generalized-K distribution. Initially, for a generalized-K fading channel with arbitrary values for the small and large-scale fading parameters we derive a closed-form expression for the moment generating function (MGF) of the received signal-to-noise ratio (SNR) and utilize it to obtain the exact average symbol error probability for a variety of digital modulations using the MGF based approach. Then, for integer values of the small-scale fading parameter, we derive a novel closed-form expression for the cumulative distribution function of the received SNR, which is then used to obtain closed-form expressions for the outage probability, the average bit error probability of various digital modulations, and the ergodic capacity of the generalized-K fading channel.     

Effects of pointing errors and channel fading on the performance of free‐space optically‐preamplified PPM systems

In this paper, we study the impact of pointing errors and channel fading on the performance of free‐space, optically preamplified, M ‐ary PPM systems. We consider two types of free‐space optical links: (i) inter‐satellite links and (ii) inter‐building links. For inter‐satellite links, only pointing error is considered. Starting with a Rayleigh model for the pointing error angle, we derive analytically the PDF for the pointing error parameter and for the signal‐to‐noise ratio (SNR) per bit. For inter‐building links, we derive the density function for the SNR per bit that includes the combined effects of pointing errors and channel fading, assuming Rayleigh‐distributed pointing errors. The channel fading models considered in this study for inter‐buildings links are the log‐normal and gamma–gamma models. We provide the error probability as a function of the average SNR per bit for both types of links. To cover systems with and without forward error correction, we compute the average SNR per bit required to achieve a bit error rate of 10^?4 and 10^?9. The corresponding power penalties are computed for different symbol sizes, scintillation indexes, and pointing jitters. Copyright © 2016 John Wiley & Sons, Ltd.     

On the performance analysis of wireless receiver using generalized-gamma fading model

In this paper, we provide a unified analysis for wireless system over generalized fading channels that is modeled by the two parameter generalized gamma model. This model is versatile enough to represent short-term fading such as Weibull, Nakagami-m, or Rayleigh as well as shadowing. The performance measures such as the amount of fading, average bit error rate, and signal outage are considered for analysis. With the aid of moment generating function (MGF) approach and Padé approximation (PA) technique, outage probability and average bit error rate have been evaluated for a variety of modulation formats. We first use the PA technique to find a simple way to evaluate compact rational expressions for the MGF of output signal-to-noise ratio, unlike previously derived intricate expressions in terms of Fox’s H and MeijerG functions. Using these rational expressions, we evaluate the performance of wireless receivers under a range of representative channel fading conditions. Our results are validated through computer simulations, which shows perfect match.     

More Accurate ASER Bound for Opportunistic Amplify-and-Forward Relay Systems

In this letter, we have derived more accurate average symbol error rate (ASER) for opportunistic amplify-and-forward (OAF) relay systems with for M-phase shift keying (M-PSK) over rayleigh fading channels. At first, the exact ASER is expressed without any approximation. In addition, we have derived the modified moment generating function (MGF) by extension of the probability density function (PDF) of the order statistic to the given relay’s selection probability for OAF relay system. Then, the ASER bound to be more accurate and another ASER form of previous researches are respectively derived by utilizing the modified MGF. Furthermore, the accuracy of derived ASER bound is analytically confirmed by comparison with each other. Simulation results are finally presented to validate the analysis.     

A general method for calculating error probabilities over fading channels

Signal fading is a ubiquitous problem in mobile and wireless communications. In digital systems, fading results in bit errors, and evaluating the average error rate under fairly general fading models and multichannel reception is often required. Predominantly to date, most researchers perform the averaging using the probability density function method or the moment generating function (MGF) method. This paper presents a third method, called the characteristic function (CHF) method, for calculating the average error rates and outage performance of a broad class of coherent, differentially coherent, and noncoherent communication systems, with or without diversity reception, in a myriad of fading environments. Unlike the MGF technique, the proposed CHF method (based on Parseval's theorem) enables us to unify the average error-rate analysis of different modulation formats and all commonly used predetection diversity techniques (i.e., maximal-ratio combining, equal-gain combining, selection diversity, and switched diversity) within a single common framework. The CHF method also lends itself to the averaging of the conditional error probability involving the complementary incomplete Gamma function and the confluent hypergeometric function over fading amplitudes, which heretofore resisted to a simple form. As an aside, we show some previous results as special cases of our unified framework.     

Unified analysis of switched diversity systems in independent andcorrelated fading channels

The moment generating function (MGF) of the signal power at the output of dual-branch switch-and-stay selection diversity (SSD) combiners is derived. The first-order derivative of the MGF with respect to the switching threshold is also derived. These expressions are obtained for the general case of correlated fading and nonidentical diversity branches, and hold for any common fading distributions (e.g., Rayleigh, Nakagami-m, Rician, Nakagami-q). The MGF yields the performance (bit or symbol error probability) of a broad class of coherent, differentially coherent and noncoherent digital modulation formats with SSD reception. The optimum switching threshold (in a minimum error rate sense) is obtained by solving a nonlinear equation which is formed by using the first-order derivative of the MGF. This nonlinear equation can be simplified for several special cases. For independent and identically distributed diversity branches, the optimal switching threshold in closed form is derived for three generic forms of the conditional error probability. For correlated Rayleigh or Nakagami-m fading with identical branches, the optimal switching threshold in closed form is derived for the noncoherent binary modulation formats. We show previously published results as special cases of our unified expression. Selected numerical examples are presented and discussed     

Distribution of outage intervals in macrodiversity cellular systems

A general model for the analysis of outage intervals in mobile radio systems with macrodiversity is proposed. In a log-normal shadowing environment, reception diversity from two base stations is considered in the general case of different fading margins. Through a level-crossing analysis, the probability density function (PDF) of the outage interval is derived. It is seen that exact expressions can be obtained for the average outage occurrence rate and the average outage duration. The exact expressions are used to also improve the accuracy of the PDF at small values of the fading margins, by forcing the PDF to meet the exact average through a proper choice of its parameters. As a particular case, explicit solutions are derived for minimum duration outages     

Probability of bit error for MPSK modulation with diversityreception in Rayleigh fading and log-normal shadowing channel

In an additive white Gaussian noise channel subject to Rayleigh fading and log-normal shadowing, consideration is given to diversity reception with K-port macroscopic selection and L-branch microscopic maximal-ratio combining, and analytical expressions are derived for upper and lower bounds on the bit error probabilities for BPSK, QPSK, 8-PSK, and 16-PSK modulations. The derived expressions can be evaluated at any location in the serving cell. Error-probability can be calculated by averaging over all possible locations within the serving cell. By evaluating these bounds, numerical results for the following cases are presented: without diversity reception, microdiversity combining, macrodiversity selection, and simultaneous use of macrodiversity selection and microdiversity combining. For symmetrical arrangement of macrodiversity ports against the lognormal shadowing, error probability at the equidistant point gives upper bounds on the error probabilities for most of the area in the serving cell. Error probability at the equidistant point is a good estimate of the error probability obtained by averaging over all possible locations in the cell     

Exact Error Rate Analysis of Output-Threshold Generalized Selection Combining (OT-GSC)

Generalized selection combining (GSC) is one of the most widely investigated low-complexity diversity techniques. Recently, output-threshold GSC (OT-GSC) was proposed as a power-saving variant of traditional GSC scheme. In this paper, we present an exact performance analysis of OT-GSC over Rayleigh fading channels. In particular, we derive the cumulative distribution function (CDF), probability density function (PDF) and moment generation function (MGF) of the combined SNR with OT-GSC. Then, we apply these results to study the outage probability and average error rate performance of OT-GSC. This analysis allows for a thorough and accurate comparison of OT-GSC with other variants of GSC, such as minimum selection GSC.     

Performance of cooperative diversity using Equal Gain Combining (EGC) over Nakagami-m fading channels

Cooperative diversity is a promising technology for future wireless networks. In this paper, we derive exact closed-form expressions for the average bit error rate (BER) and outage probability (Pout) for differential equal gain combining (EGC) in cooperative diversity networks. The considered network uses amplify-and-forward relaying over independent non-identical Nakagami-m fading channels. The performance metrics (BER and Pout) are derived using the moment generating function (MGF) method. Furthermore, we found (in terms of MGF) the SNR moments, the average signal-to-noise ratio (SNR) and amount of fading. Numerical results show that the differential EGC can bene?t from the path-loss reduction and outperform the traditional multiple-input single output (MISO) system. Also, numerical results show that the performance of the differential EGC is comparable to the maximum ratio combining (MRC) performance.     

Moment Generating Function Based Performance Analysis of Maximal-Ratio Combining Diversity Receivers in the Generalized-K Fading Channels

In this paper, we have analyzed the performance of maximal ratio combing (MRC) diversity receiver of the wireless communication systems over the composite fading environment, which is modelled by using the generalized-K distribution. However, this distribution has been considered as a versatile distribution for the precise modelling of a great variety of the short-term fading in conjunction with the long-term fading (shadow fading) channel conditions. In this proposed analysis, we have derived the mathematical expression for the moment generating function (MGF) of the generalized-K fading channel model that is used to evaluate a novel closed-form expression of the average bit error rate for (BER) the binary phase-shift keying /binary frequency-shift keying and average symbol error rate (SER) for the rectangular quadrature amplitude modulation scheme. We have also derived the mathematical expressions for the outage probability as well as the channel capacity for the generalized-K fading channel model.     

Unified analysis of EGC diversity over Weibull fading channels

In this paper, the performance analysis based on PDF approach of an L ‐branch equal gain combiner (EGC) over independent and not necessarily identical Weibull fading channels is presented. Several closed‐form approximate expressions are derived in terms of only one Fox H‐function as PDF, cumulative distribution function, and moments of the EGC output Signal‐to‐noise ratio (SNR), outage probability, amount of fading, channel capacity, and the average symbol error rate for various digital modulation schemes. All results are illustrated and verified by simulations using computer algebra systems.     

Performance of generalized selection combining receivers in K fading channels

In this letter, we present a moment generating function (MGF) based performance analysis of generalized selection combining (GSC) receivers operating over independent and identically distributed (i.i.d.) K fading channels. Analytical expressions for the marginal MGF of the signal-to-noise ratio of a single diversity branch for integer plus one-half values of the fading parameter are obtained and used to efficiently evaluate the average error probability of GSC receivers.     

Efficient performance evaluation for generalized selection combining on generalized fading channels

The authors propose an efficient moment generating function (MGF)-based method to evaluate the performance of generalized selection combining (GSC) over different fading channels. Employing a recently proposed method which is, however, only applicable to GSC diversity with independent and identically distributed branches, they derive a general MGF expression for the GSC output signal-to-noise ratio (SNR) for generalized fading channels, where the channel statistics in different diversity branches may be nonidentical or even distributed according to different distribution families. The resulting MGF expression is applicable to the analysis of the error probability, the outage probability, and the SNR statistics for GSC in a number of wireless communications scenarios with generalized fading. Numerical examples are presented to illustrate the application of the new analysis.