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.     

Level-crossing rate and average duration of fades of deterministicsimulation models for Rice fading channels

The concept of Rice's sum of sinusoids is often applied to the design of deterministic simulation models for Rice fading channels. This paper investigates in detail the level-crossing rate (LCR), average duration of fades (ADF), and cumulative distribution function (CDF) of such classes of simulation models. Exact and simple approximative formulas are deduced for these statistical quantities. Several numerical results for the derived expressions are presented by using different procedures for the design of the parameters of the deterministic simulation model. Moreover, comparisons with the corresponding simulation results-obtained by evaluating the deterministic simulation models output data-are also given     

等待接收再入遥测信道的近地衰落模型

基于靶场的地形特征、地面接收站的布置特点、等待接收天线以及发射天线的配置情况,提出了等待接收遥测信道的近地衰落模型,它是一个赖斯过程和一指数过程的乘积过程.然后,对信道的统计特性进行了分析,得到了信道的幅度概率密度函数、电平通过率和平均衰落间隔的闲式表达式,并通过仿真曲线分析了信道参数对信道特性的影响.最后,基于真实信道测量数据,给出了一种信道参数的估计方法.     

A three-dimensional two-hemisphere model for unmanned aerial vehicle multiple-input multiple-output channels

The application of unmanned aerial vehicles (UAVs) has recently attracted considerable interest in various areas. A three-dimensional multiple-input multiple-output concentric two-hemisphere model is proposed to characterize the scattering environment around a vehicle in an urban UAV-to-vehicle communication scenario. Multipath components of the model consisted of line-of-sight and single-bounced components. This study focused on the key parameters that determine the scatterer distribution. A time-variant process was used to analyze the nonstationarity of the proposed model. Vital statistical properties, such as the space–time–frequency correlation function, Doppler power spectral density, level-crossing rate, average fade duration, and channel capacity, were derived and analyzed. The results indicated that with an increase in the maximum scatter radius, the time correlation and level-crossing rate decreased, the frequency correlation function had a faster downward trend, and average fade duration increased. In addition, with the increase of concentration parameter, the time correlation, space correlation, and level-crossing rate increased, average fade duration decreased, and Doppler power spectral density became flatter. The proposed model was compared with current geometry-based stochastic models (GBSMs) and showed good consistency. In addition, we verified the nonstationarity in the temporal and spatial domains of the proposed model. These conclusions can be used as references in the design of more reasonable communication systems.     

Statistical Modeling and Analysis of Mobile-to-Mobile Fading Channels in Cooperative Networks Under Line-of-Sight Conditions

Recently, mobile-to-mobile (M2M) cooperative network technology has gained considerable attention for its promise of enhanced system performance with increased mobility support. As this is a new research field, little is known about the statistical properties of M2M fading channels in cooperative networks. So far, M2M fading channels have mainly been modeled under the assumption of non-line-of-sight (NLOS) conditions. In this paper, we propose a new model for M2M fading channels in amplify-and-forward relay links, where it is assumed that a line-of-sight (LOS) component exists in the direct link between the source mobile station and the destination mobile station. Analytical expressions will be derived for the main statistical quantities of the channel envelope, such as the mean value, variance, probability density function (PDF), level-crossing rate (LCR), and average duration of fades (ADF) as well as the channel phase. Our results show that the statistical properties of the proposed M2M channel are quite different from those of double Rayleigh and double Rice channels. In addition, a high-performance channel simulator will be presented for the new M2M channel model. The developed channel simulator is used to confirm the correctness of all obtained theoretical results by simulations.     

On the probability density functions of outage and inter-outage durations of the capacity of Rayleigh fading channels

Approximations for the probability density functions (PDFs) of the capacity outage and inter-outage durations over Rayleigh fading channels are studied. Exact closed form expressions for the Rice probability functions of the level-crossing intervals of the capacity process are derived, assuming a symmetrical Doppler power spectral density (PSD). These probability functions, which are obtained by applying the classical level-crossing theory, are known to describe the PDFs of outage and inter-outage durations only over their initial behavior. Additionally, the derived quantities are used to calculate approximate solutions for the considered PDFs based on the assumption of statistical independence between the level-crossing intervals. Numerical examples, considering Rayleigh mobile-tomobile fading channels, are presented together with simulation results to illustrate the analysis and examine the validity of the derived expressions. Particularly, it is shown that the theoretical results obtained provide accurate approximations for the PDFs of outage and inter-outage durations at low and high outage levels, respectively.     

Mobile-to-mobile fading channels in amplify-and-forward relay systems under line-of-sight conditions: statistical modeling and analysis

This paper deals with the modeling and analysis of narrowband mobile-to-mobile (M2M) fading channels for amplify-and-forward relay links under line-of-sight (LOS) conditions. It is assumed that a LOS component exists in the direct link between the source mobile station (SMS) and the destination mobile station (DMS), as well as in the links via the mobile relay (MR). The proposed channel model is referred to as the multiple-LOS second-order scattering (MLSS) channel model. The MLSS channel model is derived from a second-order scattering process, where the received signal is modeled in the complex baseband as the sum of a single and a double scattered component. Analytical expressions are derived for the mean value, variance, probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the received envelope of MLSS channels. The PDF of the channel phase is also investigated. It is observed that the LOS components and the relay gain have a significant influence on the statistics of MLSS channels. It is also shown that MLSS channels include various other channel models as special cases, e.g., double Rayleigh channels, double Rice channels, single-LOS double-scattering (SLDS) channels, non-line-of-sight (NLOS) second-order scattering (NLSS) channels, and single-LOS second-order scattering (SLSS) channels. The correctness of all analytical results is confirmed by simulations using a high performance channel simulator. Our novel MLSS channel model is of significant importance for the system level performance evaluation of M2M communication systems in different M2M propagation scenarios. Furthermore, our studies pertaining to the fading behavior of MLSS channels are useful for the design and development of relay-based cooperative wireless networks.     

Analysis of M-ary phase-shift keying with diversity reception forland-mobile satellite channels

An analytical technique well suited to numerical analysis is presented for computing the average bit-error rate (BER) and outage probability of M-ary phase-shift keying (PSK) in the land-mobile satellite channel (LMSC) with microdiversity reception. Closed-form expressions are found for L-branch microdiversity using both selection diversity combining (SDC) and maximal ratio combining (MRC). These expressions are extended to include both M-ary coherent PSK (M-PSK) and differential PSK [M-differential PSK (DPSK)]. Following previous empirical studies, the LMSC is modeled as a weighted sum of Rice and Suzuki distributions. Numerical results are provided illustrating the achievable performance of both M-PSK and M-DPSK with diversity reception. Using measured channel parameters, the performance in various mobile environments for various satellite elevation angles is also found     

BER and outage probability for land mobile satellite channel withmaximal ratio combining

An exact analytical technique is presented for computing the average bit error rate (BER) and outage probability of differentially detected PSK in the land mobile satellite channel (LMSC) when L branch maximal ratio combining (MRC) is employed. Following a previous empirical study, the LMSC is modelled as a weighted sum of Rice and Suzuki distributions. Numerical results are provided     

Poisson models and mean-squared error for correlator estimator oftime delay

A method for modeling large errors in correlation-based time-delay estimation is developed in terms of level-crossing probabilities. The level-crossing interpretation for peak ambiguity leads directly to an exact expression for the probability of large error involving the hazard function associated with the level-crossing process. Two models for the distribution of the error over the level-crossing time yield approximations to the mean-square error (MSE) that involve the low-order (<4) finite-dimensional distributions of the associated level-crossing process. Application of an inhomogeneous Poisson model for the level crossings reduces the form of the approximations to a weighted sum of the Cramer-Rao lower bound and the second moment of a function of the level-crossing intensity over time. Explicit expressions for the large error probability and the MSE approximations are obtained under a Gaussian model for the correlator statistics. Results of computer simulation are presented that indicate the accuracy of the approximations     

A note on first passage time problems for Gaussian processes and varying boundaries (Corresp.)

First and second-order approximations to the first passage time conditional probability density function of a stationary Gaussian process, with differentiable sample paths crossing a time-dependent boundary, are explicitly provided. In the limit of infinitely large time, our results coincide with the well-known results of Kac and Rice for the constant level-crossing problem.     

Experimental results on the level-crossing intervals of Gaussian processes (Corresp.)

The statistical properties of the level-crossing intervals of Gausslan random process are experimentally studied. The probability density functions and variances of the level-crossing intervals and the correlation coefficients between successive level-crossing intervals are measured for Gaussian processes having a seventh-order Butterworth power spectral density.     

A study on the multi-peak properties of the level-crossing intervals of a random process

One of the authors found that the distribution density of the level-crossing intervals of a random process had a plural number of the peaks, that is, the multi-peaks. This peculiar property is interpreted by adopting the random excursion model. According to this model, the distribution density at an arbitrary level can be synthesized by superposing the densities at a reference level, so that the resultant density shows the multi-peak property, even though those at the reference level don't. If the level-crossing intervals are mutually independent, it is shown that the renewal function at an arbitrary level is proportional to the function at a reference level and to the probability that the original process stays above the level. Also, the decay constant of the distribution density of the level-crossing intervals is derived.     

The α-μ Distribution: A Physical Fading Model for the Stacy Distribution

This paper introduces a fading model, which explores the nonlinearity of the propagation medium. It derives the corresponding fading distribution-the alpha-mu distribution-which is in fact a rewritten form of the Stacy (generalized Gamma) distribution. This distribution includes several others such as Gamma (and its discrete versions Erlang and central Chi-squared), Nakagami-m (and its discrete version Chi), exponential, Weibull, one-sided Gaussian, and Rayleigh. Based on the fading model proposed here, higher order statistics are obtained in closed-form formulas. More specifically, level-crossing rate, average fade duration, and joint statistics (joint probability density function, general joint moments, and general correlation coefficient) of correlated alpha-mu variates are obtained, and they are directly related to the physical fading parameters     

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.     

Statistical Characterization of Fading in LOS Wireless Channels with a Finite Number of Dominant Paths. Application in Millimeter Frequencies

Propagation Line Of Sight (LOS) indoor environment is studied through a new statistical model for the fast fading statistics which is based on the assumption of a small number of scatterrers. The analytical expression for the probability density function of fast fading statistics is presented and is applied in a mixture probability density function for the received signal envelope in order to incorporate shadowing. The new models are validated by measurements which have been conducted at NTUA in three different frequency bands, 1.8 GHz, 30 GHz and 60 GHz, in corridors. Finally the new models are compared with the traditional Rice and Rice-Lognormal respectively.     

A new simple model for land mobile satellite channels: first- and second-order statistics

We propose a new shadowed Rice (1948) model for land mobile satellite channels. In this model, the amplitude of the line-of-sight is characterized by the Nakagami distribution. The major advantage of the model is that it leads to closed-form and mathematically-tractable expressions for the fundamental channel statistics such as the envelope probability density function, moment generating function of the instantaneous power, and the level crossing rate. The model is very convenient for analytical and numerical performance prediction of complicated narrowband and wideband land mobile satellite systems, with different types of uncoded/coded modulations, with or without diversity. Comparison of the first- and the second-order statistics of the proposed model with different sets of published channel data demonstrates the flexibility of the new model in characterizing a variety of channel conditions and propagation mechanisms over satellite links. Interestingly, the proposed model provides a similar fit to the experimental data as the well-accepted Loo's (1985) model but with significantly less computational burden.     

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.     

Theoretical analysis and performance of OFDM signals in nonlinear fading channels

This paper presents an analytical framework to calculate the average symbol-error rate (SER) of uncoded orthogonal frequency-division multiplexing (OFDM) systems in realistic scenarios impaired by transmitter nonlinearity and frequency-selective fading channels. The results are applicable to cyclically extended OFDM signals characterized by a high number of carriers, which can be modeled as complex Gaussian processes. To avoid intercarrier interference, we also assume that the symbol duration is shorter than the channel coherence time. We derive analytical SER results in Rayleigh and Rice frequency-selective fading channels, for both the nonlinear amplification and the ideal predistortion case. Simulations results demonstrate the validity of the analytical results.