New analytical expressions for the performance metrics of wireless communication system over Weibull/Lognormal composite fading

A realistic propagation scenario is more frequently characterized by a composite multipath/shadowed fading. In this work, a class of Weibull/Lognormal (W-LN) composite fading channel has been analysed and investigated. New analytical approximations to various important performance metrics of wireless communication systems such as the average symbol error probability (SEP), the outage probability, the amount of fading (AF), and the channel capacity are derived. Further, an asymptotic analysis of the composite fading channel is carried out and closed form expressions of the average SEP with and without maximal ratio combining (MRC) diversity along with the coding and diversity gain are presented. The solutions are presented in terms of Fox H-function and are valid for both the integer and non-integer values of the multipath and shadowing parameters. The results are validated via Monte-Carlo simulations and exact numerical results.     

Maximal Ratio Combining (MRC) in Shadowed Fading Channels in Presence of Shadowed Fading Cochannel Interference (CCI)

Simultaneous existence of multipath fading and shadowing leads to worsening conditions in wireless channels. This is further compounded by the interference from other base stations operating at the same frequency. The effect of this cochannel interference (CCI) and shadowed fading in error rates is studied when maximal ratio combining is used to mitigate short term fading. The CCI channels were also treated as undergoing shadowed fading. The generalized K distribution was used to model the signal-to-noise ratio of composite shadowed fading channel. The probability density functions of the signal-to-noise ratio taking into account the presence of multipath fading, shadowing and CCI were derived and used for the estimation of error rates. Results demonstrated the existence of degradation in the channel manifested as increased error rates and higher error floors. The improvements in the channel obtained through diversity were also demonstrated. The approach presented here can be easily adapted to the analysis of other diversity schemes in shadowed fading channels.     

Performance analysis of lognormally shadowed generalized Gamma fading channels

A new composite channel model is proposed for the performance analysis of shadowed fading channels. This model is represented as a mixture of generalized Gamma (GG) multipath fading and lognormal shadowing. GG distribution includes the Rayleigh, Nakagami, and Weibull as special cases; hence the presented model, which is referred to as GG‐L, is a generic model that covers many well‐known composite fading models, including the Rayleigh–lognormal (R‐L), Nakagami–lognormal (N‐L), and Weibull–lognormal (W‐L). The main drawback of the lognormal‐based composite models is that the composite probability density function (PDF) is not in closed form, thereby making the performance evaluation of communication links in these channels cumbersome. To bypass this problem, an approximation method is developed which makes it possible to derive a closed‐form, analytical expression for GG‐L composite distribution. The proposed method only needs the mean and the variance of the underlying lognormal distribution, and hence, bypasses the required complicated integration needed to calculate the PDF of the received signal envelope in GG‐L channel. Based on this method, the most statistical characteristics, such as cumulative density function (CDF) and moments of the GG‐L composite distribution, are derived and used for the performance analysis of a single receiver operating over GG‐L fading channel. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Approximate Outage Analysis of Land Mobile Satellite Systems in Lognormally Shadowed Rician Channels

Among the proposed models for land mobile satellite (LMS) channels, the shadowed Rice model proposed originally by Loo, has found wide applications in different frequency bands. In Loo’s model, it is assumed that the received signal is affected by nonselective Rice fading with lognormal shadowing on the direct component only, while the diffuse scattered component has constant average power level. The resulting composite probability density function (PDF) includes an infinite-range integral and is not available in closed-form, thereby making the performance evaluation of LMS communication links in these channels cumbersome. To bypass this problem, in this paper an approximation method is developed which makes it possible to describe the envelope PDF as a sum of weighted Rice’s PDFs. Therefore, in contrast with Loo’s PDF, the proposed method leads to an easy-to-use, closed-form approximate expression for the PDF and also for the most statistical characteristics, such as cumulative distribution function and moments of the signal envelop in shadowed Rice channels. Based on the derived expressions, the performance analysis of a single receiver operating over lognormally shadowed Rice channel is investigated in terms of the outage probability. Numerically evaluated results show the good accuracy of the proposed approximation method.     

CDF and MGF based analysis over Rayleigh TWDP shadowed fading channel for indoor communication

Recently, the two-wave with diffuse power (TWDP) distribution has been extensively used to model the shadowing in multipath-faded/shadowed indoor environment. In this article, novel expressions for joint moments, mean, second moment, variance and cumulative distribution function for Rayleigh TWDP shadowed fading model are derived. By using the derived expression of mean and variance, the expression for amount of fading is obtained. Also, the outage probability, moment generating function and average bit error rate (ABER) for various modulation schemes namely binary phase shift keying (BPSK), binary frequency shift keying (BFSK), minimum shift keying (MSK), differentially coherent phase shift keying (DCPSK) and non-coherent frequency shift keying (NCFSK) are calculated. The derived expressions for cumulative distribution function, outage probability and ABER are presented in analytical format and have been numerically evaluated. Moreover, the numerical results of ABER using MSK and DPSK modulation schemes is compare with results of Rayleigh Gamma composite fading model. The study shows that better outage probability (0.01) is observed at 40dB average signal to noise ratio (SNR) with 5dB lowest threshold SNR, however, at higher threshold SNR (>5dB) with fixed average SNR (40dB), poor outage probability performance are obtained. Further, at higher shadowing (10dB), for fixed average SNR (15dB), minimum error probability (10^?4) is observe, while at lower shadowing (less than 10dB), higher error probability (greater than 10^?4) is observed that represents poor BER performance.     

Performance of an energy detector over η-μ/lognormal composite channel with cooperative sensing

The η-μ/lognormal composite distribution corresponds to a physical realistic scenario where the multipath effect is characterised by well-known η-μ generalised model and shadowing effect is captured by the lognormal (LN) distribution. In this work, an approximate closed-form of η-μ/LN distribution is derived using Gauss-Hermite (GH) integration. Further, the derived probability density function is utilised to develop the closed-form expression as well as infinite series representation of the average probability of energy detection (PD) and average area under the receiver operating characteristics curve (AUC) along with their respective upper bound of the truncation error. Maximal ratio combining (MRC) microdiversity technique is applied over η-μ/LN composite fading model and then its average PD is derived. In order to reduce the total probability of error, the optimisation of the detection threshold parameter is done. The result clearly shows the significant improvement in the detection probability when the optimised threshold parameter is used. Further, an extensive analysis of the optimisation of the cooperative spectrum sensing (CSS) over η-μ/LN distribution with ‘v-out-of-U’ rule at fusion center assuming erroneous feedback channels is also carried out. The closed-form expressions are validated by comparing them with exact results and Monte Carlo simulation.     

Modelling and Performance Analysis of Energy Detector Over Weibull–Shadowed Fading Channel with Application to Cooperative Sensing

In this work, we investigate and analyse the performance of the energy detector over Weibull–Shadowed composite fading channel. To this end, we have derived the novel expressions for the probability of detection (PD) and the average area under the receiver operating characteristic curve (AUC). Furthermore, the asymptotic analysis of such performance metrics has been carried out and the simpler and closed-form expressions of the PD and the average AUC have been proposed with maximal ratio combining, equal gain combining, and selection combining diversity schemes. Finally, the derived results have been applied to cooperative system considering erroneous channel between secondary users and a fusion center. The derived expressions are valid for both integer and non-integer values of the multipath and shadowing parameters. The derived analytical results are corroborated by both exact numerical results and Monte-Carlo simulations, and it is shown that the performance of cooperative system not only depends on the parameters of composite fading distribution but also on the erroneous feed-back channel.     

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.     

阴影Nakagami-m衰落信道条件下分布式天线系统中断分析

This paper presents an outage analysis of distributed antennas system (DAS) suffering from shadowed Nakagami-m fading environment where the desired signal also suffers from cochannel interference. The desired signal and interfering signal are subjected to path loss, multipath and shadowing fading. Based on Wilkinson's method, the signal to interference ratio (SIR) probability density function ( PDF) of fixed DAS is obtained. Some numerical results of outage probability with different parameters are analyzed. The analysis results can provide sufficient precision for evaluating the outage performance of DAS     

The bivariate generalized-Κ (ΚG) distribution and its application to diversity receivers

The correlated bivariate generalized-K (K_G) distribution, with not necessarily identical shaping and scaling parameters, is introduced and studied. This composite distribution is convenient for modeling multipath/shadowing correlated fading environments when the correlations between the signal envelopes and their powers are different. Generic infinite series expressions are derived for the probability density function (PDF), the cumulative distribution function (CDF) and the joint moments. Assuming identical shaping parameters, simpler expressions for the PDF, CDF and the characteristic function (CF) are provided, while the joint moments are derived in closed form. Furthermore, the PDFs of the product and ratio of two correlated K_G random variables are obtained. Capitalizing on these theoretical expressions for the statistical characteristics of the correlated K_G distribution, the performance analysis of various diversity reception techniques, such as maximal ratio combining (MRC), equal gain combining (EGC) and selection diversity (SD), over bivariate K_G fading channels is presented. For the SD, the outage probability is studied, while for the MRC and EGC the average bit error probability is obtained. The proposed analysis is accompanied by numerical results, clearly demonstrating the usefulness of the theoretical approach as well as the appropriateness of the K_G distribution to model multipath/shadowing fading channels.     

Closed‐Form Expressions for Selection Combining System Statistics over Correlated Generalized‐K Fading Channels in the Presence of Interference

This paper considers the effects of simultaneous correlated multipath fading and shadowing on the performances of a signal‐to‐interference ratio (SIR)‐based dual‐branch selection combining (SC) diversity receiver. This analysis includes the presence of cochannel interference. A generalized fading/shadowing channel model in an interference‐limited correlated fading environment is modeled by generalized‐K distribution. Closed‐form expressions are obtained for probability density function and cumulative distribution function of the SC output SIR, as well as for the outage probability. Based on this, the influence of various fading and shadowing parameter values and the correlation level on the outage probability is examined.     

Performance analysis of κ-μ/gamma shadowed fading model over indoor off body communication channel

The κ-µ/gamma distribution has an importance role to model the small scale fading and shadowing over human off body indoor communication channel. This composite fading model has various special cases like κ-µ, Rician, Nakagami-m, Rayleigh, Rayleigh/gamma, Nakagami/gamma and Rice/logormal. In this paper, the expression for bit error rate (BER) using various modulation schemes, average channel capacity (ACC) and outage probability (OP) over κ-µ/gamma shadowed fading channel are derived. All the derived expressions are novel and presented in analytical form. The expression for BER and channel capacity are in form of well-known Meijer G function, whereas the outage probability expression is obtained from cumulative distribution function (CDF) proposed in previous literature. The derived expressions of BER (BPSK), average channel capacity and outage probability reduces to special cases for validation purpose. The study shows that binary phase shift keying (BPSK) modulation technique has better BER performance as compare to other modulation techniques. Moreover, on increasing α and β while κ and µ kept constant and vice versa, the ACC get increases but below the Additive white Gaussian Noise (AWGN) channel capacity as expected. Also, better outage probability performance is obtained at lowest threshold signal to noise ratio (5 dB).     

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.     

Detection performance of cooperative spectrum sensing with hard decision fusion in fading channels

In this paper, we investigate the detection performance of cooperative spectrum sensing (CSS) using energy detector in several fading scenarios. The fading environments comprise relatively less-studied Hoyt and Weibull channels in addition to the conventional Rayleigh, Rician, Nakagami-m and log-normal shadowing channels. We have presented an analytical framework for evaluating different probabilities related to spectrum sensing, i.e. missed detection, false alarm and total error due to both of them, for all the fading/shadowing models mentioned. The major theoretical contribution is, however, the derivation of closed-form expressions for probability of detection. Based on our developed framework, we present performance results of CSS under various hard decision fusion strategies such as OR rule, AND rule and Majority rule. Effects of sensing channel signal-to-noise ratio, detection threshold, fusion rules, number of cooperating cognitive radios (CRs) and fading/shadowing parameters on the sensing performance have been illustrated. The performance improvement achieved with CSS over a single CR-based sensing is depicted in terms of total error probability. Further, an optimal threshold that minimises total error probability has been indicated for all the fading/shadowing channels.     

Measurements and models of a land mobile satellite channel and their applications to MSK signals

The fading and shadowing effects observed on land mobile satellite signals are characterized in statistical terms. Models are developed in terms of probability distribution of the signal's envelope and phase as well as its rate of change with time. The multipath fading and shadowing effects modelled are typical of those encountered in a mobile-satellite link in rural and suburban areas. A comparison of the models with experimental data at 870 MHz and 1542 MHz is given. Applications of the models to predict performance of a minimum shift keying (MSK) signal at 2400 bits/s show that large margins are required to compensate for the effects of fading and shadowing. In addition, the results show that conventional coherent demodulation of a MSK signal may not be feasible due to phase variation caused by fading and shadowing. On the other hand, the results show that random FM has negligible effect on the probability of error of the MSK signal at 2400 bits/s when frequency demodulation is used.     

Performance analysis of hexagonal cellular networks in fading channels

This paper analyzes the location‐dependent performance metrics of coverage probability and spectral efficiency in hexagonal cellular networks under Rayleigh fading with a general distribution for shadowing and also including two special cases of no shadowing and lognormal shadowing. The effects of system parameters such as frequency reuse factor, transmission probability of base stations, and signal‐to‐interference‐plus‐noise ratio gap from Shannon capacity are accurately characterized. The proposed approach is applied to fractional frequency reuse (FFR) scheme where the impact of FFR on spectral efficiency is evaluated. Numerical results show that (i) in a lognormal‐shadowed Rayleigh fading channel with the shadowing standard deviation of 12 dB, the cell area wide spectral efficiency is degraded by approximately 40% compared with when there is Rayleigh fading without shadowing; (ii) the improvement in spectral efficiency achieved by FFR over the universal frequency reuse increases as the transmission probability increases and the shadowing becomes less severe; and (iii) in Rayleigh fading without shadowing environment where all the base stations are actively transmitting, FFR achieves approximately 20% improvement in spectral efficiency in the cell edge area. Interestingly, this improvement increases to about 30% if a 3‐dB signal‐to‐interference‐plus‐noise ratio gap from Shannon capacity is further accounted. Copyright © 2015 JohnWiley & Sons     

Weibull-gamma composite distribution: alternative multipath/shadowing fading model

The Weibull-gamma (WG) distribution, which is appropriate for modelling fading environments when multipath is superimposed on shadowing, is introduced and studied. For this composite distribution the probability density, cumulative distribution, characteristic functions and the moments are derived in closed form. Furthermore, the average bit error and outage probabilities of a receiver operating over WG fading channels are assessed and compared with the corresponding performances obtained using other composite distributions.     

分布式天线系统中的系统下行中断概率分析

本文针对分布式天线系统的系统下行中断概率问题展开研究.文章首先建立了包含路径损耗、阴影衰落和瑞利衰落的复合信道模型.接着,在接收端采用最大比合并的方式接收信号,并运用矩生成函数推导出输出信噪比的概率密度函数.然后,对分布式天线采用选择传输策略,并分析出给定移动台位置时的中断概率的表达式.最后,考虑小区内移动台任意分布特...     

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。