Level Crossing Rate and Average Fade Duration of Dual Selection Combining With Cochannel Interference and Nakagami Fading

This letter provides closed-form expressions for the outage probability, the average level crossing rate (LCR) and the average fade duration (AFD) of a dual diversity selection combining (SC) system exposed to the combined influence of the cochannel interference (CCI) and the thermal noise (AWGN) in Nakagami fading channel. The branch selection is based on the desired signal power SC algorithm with all input signals assumed to be independent, while the powers of the desired signals in all diversity branches are mutually equal but distinct from the power of the interference signals. The analytical results reduce to known solutions in the cases of an interference-limited system in Rayleigh fading and an AWGN-limited system in Nakagami fading. The average LCR is determined by an original approach that does not require explicit knowledge of the joint PDF of the envelope and its time derivative, which also paves the way for similar analysis of other diversity systems.     

Second‐order statistics of multiuser relay cooperation systems over Nakagami‐m fading channels

To attain overall recognition of the effect of Nakagami‐m channel parameters on the second‐order statistics and to present a guide to the design and configuration of systems, we investigate the average level crossing rate (LCR) and average fading duration (AFD) of multiuser single relay cooperation wireless communications, in which the multiple mobile users communicate with base station under the help of single relay. On the basis of the statistical channel state information (CSI) between mobile users and relay, a single user is selected to communicate with base station. For the multiuser relay cooperation communications, we first present the integral expressions to the LCR and AFD of equivalent end‐to‐end envelope by using strict mathematical proof. Then with appropriate approximation, we obtain the closed‐form solutions to the upper and lower bounds of average LCR and AFD as well as the ones of Laplace approximation. Finally, on the basis of the derivations, we validate the approximations to LCR and AFD, and investigate the effect of the system parameters on LCR and AFD. The comparison results show that the derivations match well the simulations, and the exact values can be bounded by the obtained upper and lower bounds. Copyright © 2013 John Wiley & Sons, Ltd.     

On the second order statistics of non-isotropic Nakagami Hoyt mobile to mobile fading channel

This paper presents second order statistical properties of the mobile to mobile Nakagami Hoyt channel model under non-isotropic condition. The spatial-time correlation function, the power spectral density (PSD), level crossing rate (LCR) and the average duration of fade (ADF) of the Nakagami Hoyt channel have been derived under the assumption that both the transmitter and receiver are non-stationary having non-omnidirectional antennas. Design of simulator using the Inverse Fast Fourier Transform (IFFT) based computation method has been applied for this model. The simulator and analytical results have been corroborated.     

移动通信不规则传播环境多普勒频谱仿真与分析

对移动通信不同数目散射体分布下的接收信号多普勒频谱进行了仿真与分析,并从多普勒频谱得到了相应信号包络及其性能参数电平通过率、平均衰落时延（LCR、AFD）,并在此基础上指出散射体数目在一定程度上影响移动通信信号的多普勒频谱,从而影响信号性能。     

Level Crossing Rate and Average Fade Duration of EGC Systems With Cochannel Interference in Rayleigh Fading

Both the first-order signal statistics (e.g., the outage probability) and the second-order signal statistics [e.g., the average level crossing rate (LCR) and the average fade duration (AFD)] are important design criteria and performance measures for wireless communication systems, including the equal gain combining (EGC) systems in the presence of the cochannel interference (CCI). Although the analytical expressions for the outage probability of the coherent EGC systems are exposed to CCI and various fading channels are already known, the respective expressions for the average LCR and the AFD are not available in the literature. This paper presents such analytical expressions for the Rayleigh fading channel, which are obtained by utilizing a novel analytical approach that does not require the explicit expression for the joint probability density function (pdf) of the instantaneous output signal-to-interference ratio and its time derivative. Applying the characteristic function method and the Beaulieu series, we determined the average LCR and the AFD at the output of an interference-limited EGC system with an arbitrary diversity order and an arbitrary number of cochannel interferers in the form of an infinite integral and infinite series. For the dual diversity case, the respective expressions are derived in closed forms in terms of the gamma and beta functions.     

多用户单中继协作无线上行链路平均电平通过率和衰落持续时间

We investigate the average Level Crossing Rate (LCR) and Average Fading Duration (AFD) of multiuser single relay cooperation wireless uplinks over independent and non-identically distributed (i.ni.d) Rayleigh fading channels. We first present the statistical analyses of the first-hop equivalent envelope. Then, we investigate the LCR and AFD of an equivalent end-to-end envelope, and present the closed-form solutions to LCR and AFD, which are given with integral forms. Finally, we derive the Laplace approximations of LCR and AFD as well as the upper and lower bounds. The numerical results of LCR show that the upper bound is tight. For multiuser systems with different number of mobile users, the analyses indicate that the LCRs are approximately the same at the low level of the envelope. However, at the high level of the envelope there are reasonable differences among the curves of LCRs. Due to that fact that AFD is the inverse function of LCR, the results for AFD are the opposite.     

Second-order statistics for diversity-combining of non-identical correlated hoyt signals

In this paper, exact expressions for the level crossing rate (LCR) and average fade duration (AFD) for two-branch selection, equal-gain and maximal-ratio combining systems in a Hoyt fading environment are presented. The expressions apply to unbalanced, non-identical, correlated diversity channels and have been validated by specializing the general results to some particular cases whose solutions are known. In passing, the joint bidimensional envelope-phase Hoyt distribution with arbitrary fading parameters is obtained.     

Second‐order statistics of system with N‐branch microdiversity and L‐branch macrodiversity operating over gamma shadowed Nakagami‐m fading channels

The problem concerning short‐term fading and long‐term fading (shadowing) and their deleterious effects on wireless systems performance has been in focus for a long time. In this paper, motivated by the results of propagation measurements in land‐mobile and indoor‐mobile systems, and by the fact that gamma distribution can describe shadowing reliably, Nakagami‐m distribution is used to model the signal envelope and gamma distribution is used to model the average signal power. Receive diversity with maximal‐ratio combining and selection combining is implemented at the microlevel and macrolevel, respectively. The general case is explored, which assumes that microdiversity and macrodiversity are provided through arbitrary number of channels. Because shadowing has larger correlation distance than short‐term fading, correlated macrodiversity channels are studied. This paper investigates the dynamics of the received signal. A novel rapidly converging infinite‐series expression for average level crossing rate and average fade duration are obtained. Numerical results are graphically presented to examine the impact of fading severity, shadowing severity, number of diversity branches at the microlevel, number of base stations and correlation between base stations to the system's performance. Computer simulations are also performed to verify the validity and the accuracy of proposed theoretical analysis. Copyright © 2012 John Wiley & Sons, Ltd.     

Level crossing rate and average fade duration of the double nakagami-m random process and application in MIMO keyhole fading channels

We present novel exact expressions and accurate closed-form approximations for the level crossing rate (LCR) and the average fade duration (AFD) of the double Nakagami-m random process. These results are used to study the second order statistics of multiple input multiple output (MIMO) keyhole fading channels with space-time block coding. Numerical and computer simulation examples validate the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations.     

The Impact of Shadowing and the Severity of Fading on the First and Second Order Statistics of the Capacity of OSTBC MIMO Nakagami-Lognormal Channels

This article presents a thorough statistical analysis of the capacity of orthogonal space-time block coded (OSTBC) multiple-input multiple-output (MIMO) Nakagami- lognormal (NLN) channels. The NLN channel model allows to study the joint effects of fast fading and shadowing on the statistical properties of the channel capacity. We have derived exact analytical expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the capacity of MIMO NLN channels. It is observed that an increase in the MIMO dimension or a decrease in the severity of fading results in an increase in the mean channel capacity, while the variance of the channel capacity decreases. On the other hand, an increase in the shadowing standard deviation increases the spread of the channel capacity, however the shadowing effect has no influence on the mean channel capacity. We have also presented approximation results for the statistical properties of the channel capacity, obtained using the Gauss-Hermite integration method. It is observed that approximation results not only reduce the complexity, but also have a very good fitting with the exact results. The presented results are very useful and general because they provide the flexibility to study the impact of shadowing on the channel capacity under different fading conditions. Moreover, the effects of severity of fading on the channel capacity can also be studied. The correctness of theoretical results is confirmed by simulations.     

Statistical Analysis of a Mobile-to-Mobile Rician Fading Channel Model

Mobile-to-mobile communication is an important application for intelligent transport systems and mobile ad hoc networks. In these systems, both the transmitter and receiver are in motion, subjecting the signals to Rician fading and different scattering effects. In this paper, we present a double-ring with a line-of-sight (LOS) component scattering model and a sum-of-sinusoids simulation method to characterize the mobile-to-mobile Rician fading channel. The developed model can facilitate the physical-layer simulation for mobile ad hoc communication systems. We also derive the autocorrelation function, level crossing rate (LCR), and average fade duration (AFD) of the mobile-to-mobile Rician fading channel and verify the accuracy by simulations.     

Second-Order Statistics of η-μ Fading Channels: Theory and Applications

In this work, a number of new closed-form expressions for the eta-mu fading channels involving the joint statistics of the envelope, phase, and their time derivatives are obtained. Level crossing rate (LCR), average fade duration (AFD), and phase crossing rate (PCR) are also derived. The expressions are thoroughly validated by reducing them to some particular known cases and, more generally, by means of Monte Carlo simulation. We then provide alternative (i) singlefold integral exact formulations and (ii) highly-accurate approximations to the level-crossing statistics of multibranch maximal-ratio combining (MRC) and equal-gain combining (EGC) systems, respectively, operating over independent Hoyt fading channels, for which the exact solutions appear in the literature in multifold integral forms.     

Level Crossing Rates in Transmit Beamforming Systems

In this paper, the second-order statistics of the signal to noise ratio (SNR) at the output of a multiple-input-multiple-output (MIMO) system employing maximal ratio combining (MRC) are analyzed. Exact expressions for the level crossing rate (LCR) and the average fade duration (AFD) are derived for the Rayleigh propagation and arbitrary channel matrix dimensions. The analytical results are validated by simulation     

Characterization of Time Variation on 1.9 GHz Fixed Wireless Channels in Suburban Macrocell Environments

We observed temporal fading on 1.9 GHz fixed wireless channels during short-term measurements at 107 different locations in a suburban macrocell environment characterized by flat terrain and heavy foliage in order to determine how the rate of fading varies with average wind speed and distance. For each location, we estimated: (1) the Ricean K-factor using a momentbased estimator and (2) an equivalent Doppler frequency which is related to the maximum Doppler frequency by a factor that depends upon the shape of the Doppler spectrum. We did so by fitting the measured level crossing rate (LCR) and average fade duration (AFD) distributions to expressions normally justified for mobile wireless links using a method recently proposed by Feick, Valenzuela and Ahumada (2007). As has been observed at other sites, the Ricean K-factor decreased with both average wind speed and distance. However, we found that the equivalent Doppler frequency was effectively uncorrelated with wind speed and noticeably increased with distance. Similar measurements at other sites will be required to determine the extent to which these trends are affected by foliage density and tower height.     

A Study of the Influence of Shadowing on the Statistical Properties of the Capacity of Mobile Radio Channels

This paper studies the influence of shadowing on the statistical properties of the channel capacity. The problem is addressed by using a Suzuki process as an appropriate statistical channel model for land mobile terrestrial channels. Using this model, exact solutions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the channel capacity are derived. The results are studied for different levels of shadowing, corresponding to different terrestrial environments. It is observed that the shadowing effect has a significant influence on the variance and the maximum value of the PDF and LCR of the channel capacity, but it has almost no impact on the mean capacity of the channel. The correctness of the theoretical results is confirmed by simulation using a stochastic channel simulator based on the sum-of-sinusoids principle.     

复合衰落信道的衰落统计分析

该文基于条件概率密度方法分析复合衰落信道下接收信号包络及其导数的联合概率密度函数,由此得到了复合衰落信道的平均电平交叉率和平均衰落持续时间的统一表达式,最后结合高斯-厄米特积分给出Rayleigh-Lognormal, Ricean-Lognormal, Nakagami-Lognormal 3种典型复合衰落下接收包络的概率密度函数、累积分布函数、平均电平交叉率、平均衰落持续时间的近似解析式。仿真结果验证了理论分析的正确性。     

On the average outage rate and average outage duration of wireless communication systems with multiple cochannel interferers

This paper studies the average outage rate [or average level crossing rate (LCR)] and average outage duration (AOD) of wireless communication systems subject to cochannel interference. In particular, it presents closed-form expressions for the LCR and AOD when a minimum desired signal power requirement is specified for satisfactory reception. The results are quite general and account for systems operating over independent identically distributed Rician and/or Nakagami fading environments. When applicable, these new expressions are compared to those previously reported in the literature dealing with the LCR and AOD of 1) interference-limited systems when both the desired and interfering signals are subject to Rayleigh type of fading and 2) power-limited systems operating over Rician or Nakagami fading channels. Corresponding numerical examples that illustrate applications of the results are also provided and discussed. These results show that specifying a certain minimum desired signal power requirement induces a floor on the AOD. They also show that the AOD is essentially affected by the the maximum Doppler frequencies (or equivalently the speed) of the desired users.     

Outage probabilities of cellular mobile radio systems with multipleNakagami interferers

Closed-form expressions for outage probabilities of mobile radio channels experiencing multiple, cochannel, independent Nakagami interferers are derived. This is done for the case of Nakagami fading alone with an arbitrary number of interferers. Analytical results for the case of Nakagami fading combined with log-normal shadowing are obtained for a single interferer. The case of multiple shadowed interferers is examined by simulation. The fading severity parameter in the Nakagami distribution may be varied to model different fading conditions. Interferers with similar and different Nakagami statistics are analyzed. The probability of cochannel interference is related to the reuse distance, which is one of the key parameters in the design of cellular mobile radio systems. In addition, the effects of specifying a minimum signal power requirement for satisfactory reception are investigated. A number of system examples that illustrate applications of the results are included     

Performance analysis of mobile radio systems over composite fading/shadowing channels with co-located interference

This paper presents an analytical framework for performance evaluation of mobile radio systems operating in composite fading/shadowing channels in the presence of colocated co-channel interference. The desired user and the interferers are subject to Nakagami fading superimposed on gamma shadowing. The paper starts by presenting generic closed-form expressions for the signal-to-interference ratio (SIR) probability density function (pdf). From this pdf, closed-form expressions for the outage probability, the average bit error rate and the channel capacity are obtained in both cases of statistically identical interferers and multiple interferers with different parameters. The newly derived closed-form expressions of the aforementioned metrics allow us to easily assess the effects of the different channel and interference parameters. It turns out that the system performance metrics are predominantly affected by the fading parameters of the desired user, rather than by the fading parameters of the interferers.     

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.