Compound statistical models for shadowed fading channels

The commonly used distribution for shadowed fading channels, the Nakagami-lognormal distribution, arises by compounding the Nakagami and log-normal distributions. This distribution, however, does not have a closed form and recently this led Shankar [Outage probabilities in shadowed fading channels using a compound statistical model. IEE Proc Commun 2005; 152:828–32; Error rates in generalized shadowed fading channels. Wireless Personal Commun 2004; 28:233–8; A compound scattering pdf for the ultrasonic echo envelope and its relationship to K and Nakagami distributions. IEEE Trans Ultrason Ferroelectr Frequency Control 2003; 50:339–43.] to propose an alternative form obtained by compounding the Nakagami and gamma distributions. In this note, we derive a comprehensive collection of models for shadowed fading channels obtained by compounding the Nakagami distribution with 16 flexible families. The calculations involve use of several special functions and their properties. We feel that this work could serve as a useful reference for statistical modeling of shadowed fading channels.     

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.     

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 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.     

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.     

Performance analysis of multi‐input multi‐output systems with maximum likelihood detection over shadowed fading channels

Multiple‐input multiple‐output (MIMO) transmission techniques constitute an important technology in modern wireless communication. Hence, performance analysis methods for such systems are of considerable interest. This paper considers first the average pairwise error probability for uncoded MIMO systems employing maximum likelihood detection over a composite Rayleigh‐Lognormal fading channel with spatial correlation. It provides general results, applicable also to a wider class of shadowing models, concerning asymptotical diversity gains and shows that they are not changed by such shadowing. Then, analytical evaluation techniques for bit‐error‐rate (BER) over composite Rayleigh‐Lognormal fading channels, based on the truncated union bound and the transfer function, are considered. Furthermore, these techniques are modified for applications over spatially correlated channels. This paper shows that such performance evaluation techniques provide good approximations to BER of spatially uncorrelated MIMO systems and also in the presence of moderate spatial correlation, over Rayleigh‐Lognormal fading channels. Copyright © 2013 John Wiley & Sons, Ltd.     

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。     

Macrodiversity analysis of anM-ary noncoherent orthogonal DS/CDMA system on shadowed Rayleigh channels

DS/CDMA noncoherentM-ary orthogonal signaling is presented in a hexagonal cell with three and six corner-based antennas. Multipath Rayleigh channel with lognormal shadowing and perfect power control are assumed. The asynchronous case (uplink) is studied. Bit error rate analysis is carried out to investigate the benefits of combining theM-ary orthogonal signaling and macrodiversity techniques either with uncorrelated or correlated base stations. Comparative analysis between the one central antenna arrangement and the proposed one is presented. The results show that the combination ofM-ary signaling with multiple corner-based antennas improves system performance especially in terms of accommodating more users and supporting new services. The results also show that shadowing does not degrade system performance significantly.     

Performance analysis of single carrier and multicarrier DS‐CDMA systems over generalized fading channels

Using a recently developed moment generating function‐based approach for the performance evaluation of digital communications over fading channels, we present a unified approach for the exact performance analysis of binary direct‐sequence code division multiple access (DS‐CDMA) systems operating over generalized frequency‐selective fading channels. The results are applicable to single carrier systems employing RAKE reception as well as to multicarrier DS‐CDMA systems with frequency diversity. Aside from simplifying previous results both analytically and computationally, the proposed approach also gives a solution for many situations which heretofore defied a simple form. Copyright © 2001 John Wiley & Sons, Ltd.     

分布式编码中广义伽马分布相关噪声模型研究

针对现有相关噪声模型—Laplacian模型不能精确描述相关噪声,导致分布式视频编码(DVC, distributed video coding)系统的率失真性能不高的问题,提出像素域DVC中广义伽马分布相关噪声模型。首先分析了相关噪声的统计特性,发现Laplacian分布的峰值比实际相关噪声分布的低,然后采用广义伽马分布对相关噪声进行拟合,并给出在线估计广义伽马分布参数的方法。实验结果表明,提出的模型能较精确地描述相关噪声,且有效地改善了系统的率失真性能,并减少了解码端计算复杂度。     

Performance analysis of secure communications over correlated slow‐fading additive white Gaussian noise channels

The broadcast nature of communications in wireless communication networks makes it vulnerable to some attacks, particularly eavesdrop attack. Hence, information security can have a key role to protect privacy and avoid identity theft in these networks, especially in distributed networks. In the wireless systems, the signal propagation is affected by path loss, slow fading (shadowing), and fast fading (multi‐path fading). As we know, there is a correlation between communication channels in the real radio environments. This correlation is defined by the correlation between their shadowing and/or multipath fading factors. So when there are several channels in the wireless systems, there is certainly a correlation between the channels. In this paper, we assume that the transmitter knows the full channel state information (CSI), it means the transmitter knows both the channel gains of the illegitimate (ie, eavesdropper) and the legitimate receivers and study the performance of secure communications of single‐input single‐output (SISO) systems consisting of single antenna devices, in the presence of a single antenna passive eavesdropper over correlated slow fading channels, where the main (transmitter to legitimate receiver) and eavesdropper (transmitter to illegitimate receiver) channels are correlated. Finally, we present numerical results and verify the accuracy of our analysis by Monte‐Carlo simulations.     

Performance analysis of TCM with generalized selection combining on Rayleigh fading channels

We derive the computational cutoff rate, R/sub 0/, for coherent trellis-coded modulation (TCM) schemes on independent identically distributed (i.i.d.) Rayleigh fading channels with (K, L) generalized selection combining (GSC) diversity, which combines the K paths with the largest instantaneous signal-to-noise ratios (SNR) among the L available diversity paths. The cutoff rate is shown to be a simple function of the moment generating function (MGF) of the SNR at the output of the (K, L) GSC receiver. We also derive the union bound on the bit error probability of TCM schemes with (K, L) GSC in the form of a simple, finite integral. The effectiveness of this bound is verified through simulations.     

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.     

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.     

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.     

Performance analysis of wireless communication system over nonidentical cascaded generalised gamma fading channels

Multiplicative fading statistics usually encountered in different radio propagation environments. In this context, we evaluate and analyse the performance of a wireless communication system over the nonidentical cascaded generalised Gamma Fading Channels, also known as generalised Bessel‐K fading channel. To this end, the closed‐form expressions for the amount of fading (AOF), the outage probability (OP), the average symbol error probability (SEP), and the channel capacity are derived. In addition approximate expressions for the average SEP with maximal ratio combining (MRC) diversity are also provided. The low‐ and high‐power solutions for the channel capacity are also provided. Furthermore, simplified asymptotic average SEP expressions for MRC and selection combining (SC) are presented to gain the system performance with diversity. The proposed methodologies provide more flexibility to accommodate different radio propagation scenarios. To examine the accuracy of the proposed solutions, numerical and simulation results are compared and shown to fit for variety of fading parameters.     

Performance analysis of shadowed-Rice fading channel with cooperative spectrum sensing

In this paper, the performance analysis of wireless communication system over shadowed-Rice (SR) composite fading channel has been investigated and analysed. The unified analytical expressions of the average symbol error probability (ASEP) for several coherent and non-coherent modulation schemes separately with different constellation sizes are derived for composite fading channel under two different fade mitigation methods, with maximal ratio combining (MRC) microdiversity (Method 1) and MRC applied over the composite fading channel (Method 2). Furthermore, an asymptotic analysis is carried out and a closed-form expression of the ASEP with Method 2 is presented. Analytical expressions of the corresponding average probability of energy detection (PD) are formulated for both the methods. Finally, the derived PD expression is utilised to analyse the performance of cooperative system assuming erroneous feedback channel. Analysis of optimisation of detection threshold as well as number of cognitive users to minimise the total error rate is also carried out. The closed-form expressions are validated by comparing them with exact numerical results and Monte Carlo simulation.     

Analysis of microdiversity and dual channel macrodiversity in shadowed fading channels using a compound fading model

Wireless channels are affected by short-term fading and long-term fading (shadowing). A compound fading model was proposed for the modeling of shadowed fading channels which resulted in a closed form solution for the probability density function (pdf) of the signal-to-noise ratio (SNR). This model is applied to a case where both micro- and macro-diversity schemes are implemented to mitigate short-term fading and shadowing, respectively. Using the compound fading model, it is shown that the pdf of the signal-to-noise ratio after the implementation of maximal ratio combining (MRC) at the micro level and selection combining (SC) at the macro level can be expressed in analytical form. Even when branch correlation exists, the pdf still can be expressed in analytical form. Thus, the compound pdf model offers significant improvement over approaches which use lognormal pdf for shadowing. The performance of a coherent binary phase shift keying (BPSK) modem is evaluated using this approach. The results demonstrate the simplicity and usefulness of the compound pdf in the performance analyses of shadowed fading channels even when branch correlation exists at the base station or correlation exists between base stations.     

Symbol error probability evaluation for PSK modulation schemes in generalized non‐Gaussian noise channels

The average symbol error probability (ASEP) performance over the faded radio frequency (RF) link when the noise is additive in nature and has generalized Laplacian distribution is evaluated in this paper. The additive white generalized Laplacian noise (AWGLN) distribution can model different impulsive and non‐Gaussian noise environments often encountered in practice and provides a robust alternative to Gaussian distribution. A new expression for evaluating the exact symbol error probability over a multilevel M‐ary PSK‐modulated AWGLN channel is derived. Based on the obtained expression, the ASEP for the single‐hop RF link that models the shadowing and fading conditions over the RF channel by a generalized –K (GK) distribution is derived. Further, the error performance of a decode‐and‐forward relayed and GK‐distributed two‐hop RF link is discussed, and the results are validated through numerical plots.     

Performance analysis of combined transmit selection diversity and receive generalized selection combining in Rayleigh fading channels

We analyze the average symbol error rate (SER) of M-PSK and M-QAM modulations with transmit antenna selection diversity (SD) and receive generalized selection combining (GSC) in Rayleigh fading channels. SER formulas are derived in closed form, and numerical results show that transmit SD and receive GSC are flexible to tradeoff performance for complexity.