Unified performance analysis over Mckay–Meijer G shadowed fading channel

ABSTRACT

Composite fading models have been considered as the suitable fading models for scenarios such as indoor communication and free space optical. Most of the composite fading models are based on Nakagami-m fading distribution in which amount of fading parameter ranges from 0.5 (most severe fading) to infinity (no fading). However, using the McKay–Meijer G function, one of the recent article presents McKay shadowed fading distribution which shows that the fading severity may have values more than that of the most severe case of Nakagami-m fading. In this paper, using the conditional unified expression for conditional bit error rate (BER), a unified expression of the average bit error rate (ABER) over McKay–Meijer G shadowed fading model has been proposed. The proposed unified expression includes the ABER of almost all the modulation schemes. In addition, expression for ABER of binary phase shift keying modulation over McKay fading channel under generalised Gaussian distribution has been derived. Finally, analytical expressions of adaptive capacity under different adaptive schemes namely, COPRA, CORA, CCIFR and truncated CIFR have been presented. Through numerical analysis, different results have been compared with similar results available in the literature.     

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.     

Performance analysis of cooperative network over Nakagami and Rician fading channels

This paper presents an analysis on the performance of single‐relay and multiple fixed‐relay cooperative network. The relay nodes operate in amplify‐and‐forward (AF) mode and transmit the signal through orthogonal channels. We consider maximal‐ratio combining at the destination to get the spatial diversity by adding the received signals coherently. The closed‐form moment‐generating function (MGF) for the total equivalent signal‐to‐noise ratio (SNR) is derived. The exact expressions of symbol‐error rate, outage capacity, and outage probability are obtained using the closed‐form MGF for single‐relay and multiple‐relay cooperative network with M‐ary phase shift keying (M‐PSK) and M‐ary quadrature amplitude modulation (M‐QAM) over independent and non‐identical Nakagami‐m channels and Rician fading channels. The approximated closed‐form expression of ergodic capacity is derived for both Nakagami‐m and Rician fading channels. The performance of the system is analyzed at various relay locations. The theoretical results are then compared with the simulation results obtained for binary PSK, quadrature PSK, and 16‐QAM modulation schemes to verify the analysis. Here, the expressions derived can be easily and more efficiently used to compute the performance parameters than doing Monte Carlo simulations. It is shown that cooperation is significant only for low K values for Rician by plotting cooperation gain versus K. The results show that the cooperative network performs best when the relay is located in the middle of source to destination link, at lower SNR values, and the performance of the system is worst if the relay is located closer to the source than to the destination. Copyright © 2013 John Wiley & Sons, Ltd.     

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     

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.     

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.     

Closed‐form solutions to SEP integrals over generalized fading distributions η−μ and κ−μ using approximate computing

The fading channels often involve complex expressions, when it comes to computing the integrals required for performance evaluation of various digital modulation schemes. In this paper, usefulness of exponential‐based approximations to the Gaussian‐Q function in computing these integrals is discussed. We present generic symbol error probability (SEP) expressions over η?μ and κ?μ fading distributions, which can be tailored for any digital modulation technique using different approximations. The resulting expressions thus obtained comprise only elementary mathematical functions thereby avoiding complex evaluations of hypergeometric functions. We explore all the exponential‐based approximations proposed till date and conclude that apart from being mathematically simple, they also lead to accurate expressions for performance analysis of various digital modulation schemes.     

Outage probability of cellular mobile radio systems with selective co‐channel interference cancellation receiver in overloaded array environments

This article outlines a general numerical procedure for computing the probability of outage of a cellular mobile radio system that is equipped with a smart antenna to suppress a few strongest co‐channel interferers (CCI) out of a total of N_I active interferers by adaptive null‐steering. Aside from the interference‐limited case, refined outage criterion that either treat receiver noise as CCI or consider a minimum detectable receiver signal threshold are studied. Exact closed‐form expressions for both the basic and refined outage criterion are also derived by assuming that all the CCI signals are subject to Nakagami‐m fading with a positive integer fading severity index. Selected numerical examples are provided to illustrate the application of the theory which includes the investigation into the effects of fade distribution of the CCI signals and traffic loading on the outage probability, and also the study of spectrum utilization efficiency improvement using a selective co‐channel interference nulling (cancellation) technique. Copyright © 2002 John Wiley & Sons, Ltd.     

Performance analysis of a variable‐gain amplify‐and‐forward relayed mixed RF‐FSO system

In this work, an amplify‐and‐forward variable‐gain relayed mixed RF‐FSO system is studied. The considered dual‐hop system consists of a radio frequency (RF) link followed by a free space optical (FSO) channel. The RF link is affected by short‐term multipath fading and long‐term shadowing effects and is assumed to follow the generalized‐K fading distribution that approximates accurately several important distributions often used to model communication channels. The FSO channel experiences fading caused by atmospheric turbulence that is modeled by the gamma‐gamma distribution characterizing moderate and strong turbulence conditions. The FSO channel also suffers path loss and pointing error induced misalignment fading. The performance of the considered system is analyzed under the collective influence of distribution shaping parameters, pointing errors that result in misalignment fading, atmospheric turbulence, and path loss. The moment‐generating function of the Signal power to noise power ratio measured end‐to‐end for this system is derived. The cumulative distribution function for the Signal power to noise power ratio present between the source and destination receiver is also evaluated. Further, we investigate the error and outage performance and the average channel capacity for this system. The analytical expressions in closed form for the outage probability, symbol and bit error rate considering different modulation schemes and channel capacity are also derived. The mathematical expressions obtained are also demonstrated by numerical plots.     

Performance evaluation of L-maximal ratio combining diversity with estimation error for Shadowed Beaulieu-Xie fading channels

To provide the increasing demand for wireless technologies, high capacity with lower latency is vital. New emerging technologies like 5G, millimeter wave, THz, and so forth are able to characterize such complex fading and shadowed environments. Spatial diversity is one of the techniques to minimize fading in the wireless communication channel. The performance of the wireless communication system can be further optimized by using estimators at the receivers. The influence of imperfect channel estimation on the performance over shadowed Beaulieu-Xie (SBX) fading channels with L-maximal ratio combining (MRC) diversity is studied. The probability density function (PDF) of the received output signal-to-noise ratio (SNR) with L-MRC over SBX fading channels is derived. Further PDF of the received output SNR, outage probability, and average bit error rate (ABER) using the derived PDF is evaluated for L-MRC diversity with channel estimation error over SBX fading channels. ABER expression for Gray-coded rectangular quadrature amplitude modulation over the SBX channel is also evaluated. The study also includes how the system performs under the effect of different shadowing and fading parameters.     

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.     

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).     

A New Approach to Bivariate Hoyt Distribution and its Application in Performance Analysis of Dual-Diversity Receivers

Novel infinite series based expressions for the bivariate Hoyt distribution are derived. More specifically, expressions for the joint probability density function (JPDF) and the joint cumulative distribution function (JCDF) of two Hoyt fading envelopes are derived, and proposed for use in performance analyses of dual-branch diversity receivers operating over correlated Hoyt fading channels. Using these reasonably simple and mathematically tractable expressions, we evaluate the performance of a dual-branch selection combining (SC) diversity receiver in terms of the outage probability (P _out ) and the average bit error probability (ABEP) criteria. The ABEP performance is evaluated for binary differential phase-shift-keying (BDPSK) and binary non-coherent frequency-shift keying (BNFSK) modulation schemes.     

CDMA-SFBC Downlink Performance

In this paper a generic code division multiple access (CDMA)-space frequency block coded (SFBC) system for downlink transmission is proposed. Closed form expressions for the bit error rate (BER) performance of the proposed CDMA-SFBC downlink system are derived and numerically evaluated considering different scenarios. The closed form BER expressions are derived for both the M-ary phase shift keying (MPSK) and the M-ary quadrature amplitude modulation (MQAM) techniques considering different CDMA-SFBC configurations. The BER expressions are evaluated for a wide range of system parameters assuming Rayleigh fading. These parameters include M-ary size and channel estimation error variance. Such evaluations are crucial not only for system performance prediction, but also for network management, monitoring and future cross-layer design.     

Performance evaluation of cellular mobile radio systems with interference ing of dominant interferers

This paper develops an analytical framework for characterizing the average symbol error rate and outage performance of a smart antenna system in cellular mobile radio environments. Specifically, the carrier-to-interference ratio statistics with N remaining (uncancelled) "weakest" cochannel interference (CCI) signals from a total of N/sub I/ signals are derived, given that both the desired user signal and the CCI signal amplitudes are subjected to Rayleigh, Rice, Nakagami-m, or Nakagami-q fading. General expressions for the outage probability and the average symbol-error rate performance of different digital modulation schemes in the presence of CCI signals are derived. Selected numerical results are presented to demonstrate the utility of the analysis in assessing the selective interference ing performance in different fading environments.     

Performance comparison of dual‐hop hybrid decode‐or‐amplify‐forward relay schemes for M‐ary quadrature amplitude modulation burst transmission over Rayleigh fading channels

This paper shows the analytical performance expressions of M‐ary quadrature amplitude modulation burst symbol transmission for hybrid decode‐or‐amplify‐forward (HDAF) relay schemes over quasi‐static Rayleigh‐fading channels. First, we derive the probability density function of the received instantaneous signal‐to‐noise ratio as the simplified form, which is related to all the possible occurrence probabilities of error‐events for M‐ary quadrature amplitude modulation burst transmission. On the basis of the derived probability density function, we express average bit error probability, average symbol error probability, and average burst error rate as closed forms, which can be also applied to both amplify‐and‐forward and adaptive decode‐and‐forward (ADF) schemes. The analysis and simulation results show that HDAF scheme for burst transmission can achieve the performance of ADF scheme with symbol‐by‐symbol transmission, which is the achievable lower bound. Furthermore, the outage probability, the normalized channel capacity, and the goodput performance are also derived as closed forms. The analysis shows the superiority of HDAF scheme to ADF scheme. Comparison with simulations confirms that the derived analytical expressions are accurate over all signal‐to‐noise ratio regions and for different numbers of relays and modulation orders.     

多蜂窝上行链路通信系统性能分析

考虑存在来自其他蜂窝的不同功率同信道干扰的多用户上行链路,分析了多天线基站采用多用户调度和最大比合并接收时的系统性能。在期望信号和干扰信号分别经历Nakgami-m和Rayleigh衰落时,运用基于概率密度函数的性能分析法推导了系统中断概率的闭合表达式。仿真结论显示,系统中断概率的解析曲线与数值仿真结果一致,系统性能随着天线数和用户数的增大而提升,多天线和多用户分集增益明显,干扰功率有较大差异时系统中断概率性能有所下降。     

Performance of DSWC diversity system using suboptimum adaptive switching threshold in independent and correlated nakagami‐m fading channels

The use of dual switched combining (DSWC) diversity reception scheme, for combating the detrimental effects of fading on digital transmissions, is popular due to its simpler implementation. The performance of switched diversity strategy is dependent on the selection of the switching threshold. But, for the analysis and design of the DSWC diversity system, the closed form analytical solution for optimum adaptive switching threshold is not possible for most of the modulation schemes in correlated fading environment. This letter presents an approximate, but simple and closed form, generic expression for adaptive switching threshold, called in this case as suboptimum adaptive switching threshold, in independent and correlated Nakagami‐m fading channels for a wide range of binary and M‐ary modulation schemes. It is shown that the average symbol error rate (ASER) performance obtained using this suboptimum adaptive switching threshold is almost same as obtained using optimum adaptive switching threshold. Copyright © 2005 John Wiley & Sons, Ltd.     

Performance analysis of equal-gain diversity receivers over generalized Gamma fading channels

Generalized Gamma (GG) distribution is a generic model that covers many well-known fading distributions as special cases. This paper deals with the performance analysis of L-branch equal gain combining (EGC) receivers operating over GG fading channels. For these receivers and by using convergent infinite series approach, the probability of error (P_e) can be formulated in the form of an infinite series. The coefficients of P_e series can be derived by calculating complicated integrations over the fading envelope distribution. In this paper, it is shown that the required integrations for the case of GG distribution have a complex closed-form in terms of Meijer's G function, and then, a new approximation method is developed for computation of them. The proposed method only needs mean and variance of the fading envelope; hence it has low complexity and eliminates the need for calculation of complex functions. The presented numerical examples show that the developed method can approximate the required parameters and also the individual coefficients accurately and this accuracy increases with the increase of L. The proposed method is applied to analyze the probability of error performance of the L-branch EGC receiver with both coherent phase shift keying (CPSK) and frequency shift keying (CFSK) modulation schemes under different GG channel conditions. Also the effect of gain unbalance between diversity branches on the probability of error is investigated.     

最大比合并接收系统在n-Rayleigh信道下的性能分析

在n-Rayleigh信道下,研究了MRC(Maximal Ratio Combining)合并接收系统的平均码字错误率(ASEP)性能。基于矩生成函数(MGF)的方法,推导了MRC接收系统在n-Rayleigh衰落信道上采用M进制相移键控(MPSK),M进制正交幅度调制(MQAM)和M进制脉冲幅度调制(MPAM)等几种M进制数字调制方式的ASEP的计算式。然后在不同条件下,仿真了系统的ASEP性能,仿真值与理论值相一致,理论分析的正确性得到了证明。分析结果表明:分集支路数和衰弱因子对系统的ASEP性能有重要影响。