On efficacy of Rayleigh‐inverse Gaussian distribution over K‐distribution for wireless fading channels

For studying performance characteristics of radio channels, the knowledge about the probability density function (pdf) of fading–shadowing effects is essential. K‐distribution corresponding to Rayleigh–gamma distribution (RGD) is widely used to approximate a more realistic Rayleigh–lognormal distribution (RLD) which does not have a closed form expression. A new composite Rayleigh‐inverse Gaussian distribution (RIGD), an alternative to K‐distribution, is analyzed with regards to its suitability and effectiveness in radio channels. Detailed investigations are made to study the performance characteristics of RIGD and K‐distribution (RGD) in terms of Kullback–Leibler (KL) measure of divergence. Based on these investigations, it is found that RIGD is better suited for capturing fading–shadowing aspects of radio channels instead of K‐distribution. Copyright © 2006 John Wiley & Sons, Ltd.     

Performance of generalized selection combining over Weibull fading channels

The literature is relatively sparse in performance analysis of diversity combining schemes over Weibull fading channels, despite the fact that the Weibull distribution is often found to be suitably fit for empirical fading channel measurements. In this paper, we capitalize on some interesting results due to Lieblein on the order statistics of Weibull random variables to derive exact closed‐form expressions for the combined average signal‐to‐noise ratio (SNR) as well as amount of fading (AF) at a generalized selection combining (GSC) output over Weibull fading channels. We also use some simple AF‐based mappings between the fading parameters of the Weibull distribution and those of the Nakagami, Rice, and Hoyt distributions to obtain the approximate but accurate average SNR and AF of GSC over these types of channels. The mathematical equations are validated and illustrated by some numerical examples for scenarios of practical interest. Copyright © 2006 John Wiley & Sons, Ltd.     

Closed‐form expressions for the average channel capacity of the α– μ fading model under different adaptive transmission protocols

In this paper,we consider a small‐scale multipath fading channel following the α– μ generalized fading model distribution.We first derive an expression for the amount of fading () for this channel model to show the generalization attribute of this fading model recently reported in the literature. Then, we derive closed‐form expressions for the average channel capacity considering this channel distribution under different adaptive transmission protocols, namely the simultaneous power and rate adaptation protocol, the optimal rate adaptation with fixed power protocol, and the channel inversion with fixed‐rate protocol. All the obtained expressions are in closed‐form and general expressions that can reduce to other channel capacity expressions that are well‐known and to some others that are not known for Rayleigh, Nakagami‐m, and Weibull, as special cases. The derived expressions in this paper are new and have not been previously reported in the literature. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

考虑混合SC/MRC分集的层叠分布式天线系统SER性能分析

针对Nakagami/lognormal复合衰落信道,研究了层叠分布式天线系统(Cascade Distributed Antenna System-CDAS)在CDMA网络中的平均误符号率性能.推导出了采用混合SC/MRC分集接收机的层叠分布式天线系统平均误符号率性能公式.利用推导出的平均误符号率表达式,分析了多径密度函数(Multipath Intensity Profile-MIP)衰减因子、空时分集维数、活动用户数以及阴影衰落因子对平均误符号率性能的影响.仿真表明层叠分布式天线系统可以有效对抗衰落,提高系统容量以及削弱对数正态阴影衰落的影响.     

Error Rates in Generalized Shadowed Fading Channels

Most of the existing models to describe the shadowed fading channels use either the Suzuki or Nakagami-lognormal probability density function (pdf), both based on lognormal shadowing. However, these two density functions do not lead to closed form solutions for the received signal power, making the computations of error rates and outages very cumbersome. A generalized or compound fading model which takes into account both fading and shadowing in wireless systems, is presented here. Starting with the Nakagami model for fading, shadowing is incorporated using a gamma distribution for the average power in the Nakagami fading model. This compound pdf developed here based on a gamma-gamma distribution is analytically simpler than the two pdfs based on lognormal shadowing and is general enough to incorporate most of the fading and shadowing observed in wireless channels. The performance of coherent BPSK is evaluated using this compound fading model.     

Statistical Models for Fading and Shadowed Fading Channels in Wireless Systems: A Pedagogical Perspective

A unified analysis of statistical models for describing fading, shadowing, and shadowed fading channels is presented from a pedagogical viewpoint. The different probability density functions such the Rayleigh, Nakagami, gamma, generalized gamma, Weibull, lognormal, Nakagami-lognormal, K distribution, generalized K distribution, and Nakagami inverse Gaussian distribution are presented and the relationships among them are detailed. These density functions are compared in terms of two quantitative measures, namely the amount of fading and outage probability. A general approach to fading and shadowed fading channels using a cluster based approach is also presented to link several of the distributions. It is expected that this overview will be very helpful to students and educators who are engaged in the study of wireless systems and the adverse impact of fading and shadowing in wireless data transmission.     

增强合作中继系统在多径阴影联合衰落信道下的性能分析

针对数字通信系统在多径阴影联合衰落信道下不易获得性能闭式解的问题,运用MG（mixture Gamma）模型近似了NL（Nakagami-lognormal）衰落信道模型,在各跳具有独立不同衰落分布下研究和推导了增强合作中继系统的误码率和中断性能,数值和仿真分析验证了理论分析的正确性。结果表明运用MG近似NL模型有助于合作中继系统在多径阴影联合衰落信道下的性能研究。     

一种无线信道复合衰落模型的分析与仿真

移动通信过程中由于移动设备所处的环境不同,存在不同的信道衰落,从各种衰落模型的相互关系出发,提出了一种移动无线衰落信道混合应用模型。通过实现瑞利衰落分布和对数正态分布,经线性和非线性变换可以得到Nakagami和Suzuki等分布。对提出的复合衰落模型进行仿真,仿真结果符合理论值。该混合衰落模型设计和仿真方法可以用于指导信道模拟器设计和通信系统仿真。     

Combined orthogonal physical‐layer network coding over fading two‐way relay channels

This paper proposes a new physical‐layer network coding (PNC) scheme, named combined orthogonal PNC (COPNC), for fading two‐way relay channels. The scheme is based on orthogonal PNC (OPNC). In the scheme, the two source nodes employ orthogonal carriers, and the relay node makes an orthogonal combining of the two information bits rather than exclusive or (XOR), which is employed in most PNC schemes. The paper also analyzes the bit error rate (BER) performance of PNC, OPNC, and COPNC for Rayleigh fading model. Simulation results for Rayleigh and Nakagami‐m fading channels show that COPNC can provide outstanding BER performance compared with PNC and OPNC, especially when the uplink channel conditions are asymmetric. The results in Nakagami‐m channels also imply that COPNC will provide higher BER gain with more severe fading depth. Potential works about COPNC are also presented in this paper. Copyright © 2013 John Wiley & Sons, Ltd.     

Outage analysis in wireless channels with multiple interferers subject to shadowing and fading using a compound pdf model

Wireless communication systems are subject to short- and long-term fading of the channel. Instead of the commonly used Nakagami–lognormal model to account for the conditions existing in these shadowed fading channels, a compound probability density function (pdf) model is used to evaluate the performance of wireless systems. While the Nakagami–lognormal lacks a closed-form solution to the pdf of the received power in shadowed fading channels, the compound pdf has an analytical expression for the pdf of the received signal power. The synergy between these two models for the analysis of wireless systems is explored by calculating the bit error rate in a DPSK modem as well as the outage probability in a wireless system in a shadowed fading channel. This is followed by the computation of the outage probability in the general case where both the desired and cochannels are subject to shadowing and fading. The analyses were carried out for both fixed number of cochannels and random number of cochannels. Results demonstrate the usefulness of the compound pdf model for the performance analyses of wireless systems in shadowed fading channels.     

分布式天线系统混合SC/MRC分集中断概率性能

在频率选择性复合Nakagami/lognormal衰落信道条件下,研究了层叠分布式天线系统(Cascade Distributed Antenna System--CDAS)采用混合SC/MRC分集的中断概率性能.针对中断概率性能,分析了多径密度函数(Multipath Intensity Profile MIP)衰减因子、空时分集维数、活动用户数、每比特平均接收信噪比以及衰落因子对系统性能的影响.仿真表明CDAS系统可以有效对抗衰落,提高系统容量,削弱对数正态阴影衰落影响.     

A class of generalized models for shadowed fading channels

The commonly used models for shadowed fading channels arise by compounding the Nakagami distribution with others such as the log-normal and gamma distributions. A distribution that is more flexible than the Nakagami distribution is the well known Weibull distribution. In this paper, we derive a collection of generalized models for shadowed fading channels by compounding the Weibull distribution with other distributions belong to some fifteen flexible families. We also illustrate the superior performance of these models over the standard Nakagami models.     

Performance Analysis of Land Mobile Satellite Communication Systems with Equal-Gain Combining over Shadowed-Rice Fading Channels

An accurate model for performance analysis of land mobile satellite (LMS) channels is the Shadowed-Rice (SR) fading model. Recently, an approximate SR model has been proposed by the author for LMS channels. Compared with the existing models, the proposed model is analytically tractable and makes it possible to approximate very accurately the probability density function (PDF) of the SR random variable (RV) by a finite weighted sum of Rice PDFs. In this paper and based on the proposed model, the statistics of the sum of independent SR RVs is studied. While this problem is well understood for common fading models such as the Rayleigh, Rice, and Nakagami, a minor attention has been devoted to the SR case. In this paper and by using the well-known Beaulieu series approach, the PDF and the Cumulative distribution function (CDF) of the sum of independent SR RVs are derived in the form of infinite convergent series. In this regard, analytical, closed-form expressions are derived for the coefficients of the Beaulieu series. To give an application of the presented results, the performance of LMS communication system employing equal-gain combining (EGC) diversity techniques over SR fading channel is investigated and novel closed-form expression is derived for the outage probability of the system.     

Downlink System Capacity Analysis in Distributed Antenna Systems

This paper focuses on the downlink system capacity in distributed antenna systems (DAS). Due to the complexity of actual wireless environments, a composite channel model is established which takes into account three factors, i.e., path loss, lognormal shadowing and Rayleigh fading. Based on the channel model, the probability density function (PDF) of the output signal-to-noise ratio (SNR) is derived. To facilitate the analysis, the distribution of the output SNR is approximated by a lognormal distribution. After that, by making use of selective diversity (SD) scheme for distributed antennas, an approximate analytical expression of the capacity for a mobile station (MS) over a given position is derived. Furthermore, considering the distribution of MSs in the system, a closed-form expression of the system capacity is obtained. Numerical results show that the closed-form expression can evaluate the system capacity performance of DAS very accurately.     

General Order Selection Combining for Nakagami and Weibull Fading Channels

In this paper, some analytical results for general order selection (GOS) over independent but not necessarily identically distributed (i.n.d.) Weibull and Nakagami fading channels are presented. The Weibull fading parameters are assumed to be equal whereas the Nakagami fading parameters are assumed to be integer-valued. It is shown that the pdf of the q-th order statistic can be expressed as a linear combination of Weibull and Nakagami pdf's respectively. Closed-form expressions for the moment generating functions and general moments are derived. In addition, exact closed-form expressions for the symbol error rate are obtained for a number of modulation schemes. Numerical results show that for the same average channel gains, the performance on i.n.d. channels may be better or worse than on i.i.d. channels.     

Average probability of packet error with diversity reception over arbitrarily correlated fading channels

Closed form expressions for the average probability of packet error (PPE) are presented for no diversity, maximum ratio combining (MRC), selection combining (SC) and switch and stay combining (SSC) diversity schemes. The average PPE for the no diversity case is obtained in two alternative expressions assuming arbitrarily correlated Nakagami and Rician fading channels. For the MRC case, L diversity branches are considered and the channel samples are assumed to follow Nakagami distribution and to be arbitrarily correlated in both time and space. For the SC diversity scheme with L diversity branches, two bounds on the average PPE are derived for both slow and fast fading channels. The average PPE in this case is obtained in an infinite integral form for Nakagami channels while it is reduced to a closed form expression for the Rayleigh case. The average PPE is also derived in the case of SSC diversity with dual branches for both slow and fast Rayleigh fading channels. The new formulas are applicable for all modulation schemes where the conditional probability of error has an exponential dependence on the signal‐to‐noise ratio. The average PPE is then used to obtain a modified expression for the throughput for network protocols. In general, the diversity gain exhibits a little diminishing effect as the number of diversity branches increases. In addition, the system is found to be more sensitive to the space correlation than to the time correlation. The effects of different system parameters and diversity schemes are studied and discussed. Specific figures about the system performance are also provided. Copyright © 2004 John Wiley & Sons, Ltd.     

Unified Analysis for SIR-Based Power and Rate Control in Multipath Fading Channels

In this paper, we present a unified analysis on various signal-to-interference power ratio (SIR)-based power and rate control schemes in independent and nonidentical multipath fading channels. We study wireless direct sequence code division multiple access (DS-CDMA) systems with RAKE reception and derive new expressions for a mobile user's average SIR, average transmission power, and average data rate in terms of the probability distribution of the SIR. The performance of SIR-based combined power/rate control, power control, rate control, truncated power control, and truncated rate control schemes in independent and nonidentical Rayleigh fading channels is presented and compared. By substituting appropriate SIR distributions, this general mathematical framework can be applied to other fading channels such as the Nakagami, Rician, and lognormal channels     

Mobile fading—Rayleigh and lognormal superimposed

A closed solution is presented showing the composite probability distribution of power levels derived from short term Rayleigh fading with superimposed long term lognormal variations of mean value. An example shows how the results can be applied to the prediction of bit error rates in a mobile radio data transmission channel, and how the error rate will vary with standard deviation of the lognormal distribution.     

Performance analysis of selective combining decode‐and‐forward relay networks over Nakagami‐n and Nakagami‐q fading channels

In this paper, we present the performance of selective combining decode‐and‐forward relay networks in independent and non‐identically distributed Nakagami‐n and Nakagami‐q fading channels by using the best–worse and the decoding‐set approaches. The outage probability, moment generation function, symbol error probability and average channel capacity are derived in closed‐form using the signal to noise ratio (SNR) statistical characteristics. After that, we analyze the outage probability at high SNRs, and then, we optimize it. Beside the optimum method, we have proposed a sub‐optimum adaptive method. Also, we derive the outage probability for the selection‐combining case with the direct link between the source and the destination. Finally, for comparison with analytical formulas, we perform some Monte‐Carlo simulations. Copyright © 2012 John Wiley & Sons, Ltd.