Formulation of spatial correlation statistics in Nakagami-Ricefading environments

Propagation environments in line-of-sight (LOS) communications, such as mobile-satellite communications and indoor radio communications, can be expressed by a Nakagami-Rice (or Rician) fading model. Since the Nakagami-Rice fading model also covers the Rayleigh fading model as an extreme case, it seems a very widely applicable model. This paper gives a theoretical formulation of spatial correlation characteristics in the Nakagami-Rice fading environment. Based on this theoretical model, spatial correlation characteristics of Nakagami-Rice fading are clarified comparing with those of Rayleigh fading. Moreover, the difference in spatial correlation characteristics between wide-band signals and narrow-band signals is discussed     

基于Kronecker法的MIMO信道模拟及硬件实现

针对多输入多输出（Multiple-Input Multiple-Output,MIMO）无线通信系统,在基于Kronecker 的MIMO信道模型中综合考虑了路径损耗、阴影衰落和多径衰落等因素,实现了基于现场可编程门阵列（Field Programmable Gate Array,FPGA）的MIMO信道模拟器,并分析了硬件设计方案以及MIMO信道模拟的实现方法。实测结果表明,设计的MIMO信道模拟器可以模拟瑞利衰落、莱斯衰落以及阴影衰落等常见的信道衰落类型,能够应用于3GPP、COST-207等标准信道模型的复现。该模拟器可作为无线通信系统研究的测试设备,辅助通信系统研究的算法验证、方案优化以及性能分析。     

Fading Channel Modeling via Variable-Length Markov Chain Technique

Channel characterization and modeling are essential to the wireless communication system design. A model that optimally represents a fading channel with a variable-length Markov chain (VLMC) is proposed in this paper. A VLMC offers a general class of Markov chains whose structure has a variable order and a parsimonious number of transition probabilities. The proposed model consists of two main components: 1) the optimal fading partition under the constraint of a transmission policy and 2) the derivation of the best VLMC representation with respect to the Kullback-Leibler (K-L) distance of fading samples. The fading partition is used to discretize a continuous fading channel gain. The optimal discretization criterion is developed based on the cost function of fading channel statistics and the transmission policy used in the system. Once a continuous fading channel gain is discretized, a VLMC is then used to model the channel. To obtain the optimal VLMC representation, we use the K-L distance of the discretized fading samples as the optimization criterion. The K-L distance of the discretized fading samples is used to determine the appropriate transition probabilities characterizing the optimal VLMC. Last, we show simulation results that demonstrate the accuracy and the effectiveness of the proposed fading channel representation in modeling the Rayleigh fading as well as the lognormal fading.     

Rayleigh fading channels in mobile digital communication systems.I. Characterization

The paper addresses Rayleigh fading, primarily in the UHF band, that affects mobile systems such as cellular and personal communication systems (PCS). The paper itemizes the fundamental fading manifestations and types of degradation. Two types of fading, large-scale and small-scale, are described. Two manifestations of small-scale fading (signal dispersion and fading rapidity) are examined, and the examination involves two aspects: time and frequency. Two degradation categories are defined for dispersion: frequency selective fading and flat fading. Two degradation categories are defined for fading rapidity: fast and slow. A mathematical model using correlation and power density functions is presented. This model yields a symmetry to help view the Fourier transform and duality relationships that describe the fading phenomena     

一种无线信道复合衰落模型的分析与仿真

移动通信过程中由于移动设备所处的环境不同,存在不同的信道衰落,从各种衰落模型的相互关系出发,提出了一种移动无线衰落信道混合应用模型。通过实现瑞利衰落分布和对数正态分布,经线性和非线性变换可以得到Nakagami和Suzuki等分布。对提出的复合衰落模型进行仿真,仿真结果符合理论值。该混合衰落模型设计和仿真方法可以用于指导信道模拟器设计和通信系统仿真。     

An Additive Model as a Physical Basis for Shadow Fading

Received signal power in mobile wireless communications is typically modeled as a product of three factors: distance-dependent average path loss law, variation in the local mean power (shadow fading), and small-scale fading. Of these three factors, the least investigated is the shadow fading, which is usually explained as a result of multiplication of large number of random attenuating factors in the radio channel. In this paper, the authors propose an additive model as an alternative physical basis for shadow fading within an "extended local area" where path loss is constant. Starting from a sum-of-sinusoids signal model, they show that under mild statistical assumptions on the powers of the sinusoids, the resulting signal power will have approximately Gaussian distribution in logarithmic scale. A cluster-based model for shadow fading emerges as a special instance of the general result. They present simulation and measurement results that support their theoretical findings. The new physical basis for shadow fading also provides insights into simulation and modeling of radio channels     

Modeling of signal envelope correlation of line-of-sight fadingwith applications to frequency correlation analysis

Based on the theoretical method developed by Clarke (1968) for the analysis of correlation characteristics in Rayleigh fading conditions, we develop a general model for envelope correlation statistics of line-of-sight fading known as Nakagami-Rice fading. The model developed here has a considerable degree of universality and can be applied to the analysis of correlation statistics in frequency and spatial domains for microcellular mobile radio, maritime and aeronautical mobile-satellite communications. Using this model, we examine the frequency correlation statistics of two typical Nakagami-Rice fading environments     

Multiple trellis coded frequency and phase modulation

Multiple trellis coded modulation of constant envelope frequency and phase modulated signal sets (MTCM/FPM) is investigated for performance on the additive white Gaussian noise (AWGN) channel and on the one-sided normal, Rayleigh and Rician fading channels. The Nakagami- m fading model is used as an alternative to the Rician fading model to calculate the error probability upper bound for trellis-coded schemes on the fading channel. The likeliness and the disparity between the upper bounds to the error probability for the two fading models are discussed. The design criteria for the one-sided normal fading channel, modeled by the Nakagami-m distribution, are observed to be the same as those for the Rayleigh-fading channel. For the MTCM/FPM schemes, it is demonstrated that the set partitioning designed to maximize symbol diversity (optimum for fading channels) is optimum for performance on the AWGN channel as well. The MTCM/FPM schemes demonstrate improved performance over MTCM/MPSK schemes and TCM/FPM schemes on the AWGN channel and the fading channel     

基于FDTD方法的无线信道衰落特性模拟研究

为了表述无线信道衰落的时变及远区分布特性，提出了利用时域有限差分(FDTD)方法研究由多径效应引起的时变无线信道衰落的方法。在此将无线信道的衰落建模为随机过程，而不是通常的确定性随机变量。首先基于Clarke统计模型，利用FDTD方法研究了时变无线信道的小尺度平坦衰落特征；然后利用Monte Carlo方法和FDTD方法产生了具有信道多普勒功率谱特性的色高斯随机过程，再基于无线信道的时变统计特性建模，用Suzuki模型研究了时变无线信道的快衰落；最后将无线信道衰落特性分布和理论分布做了比较，验证了方法的有效性。     

Moment Generating Function Based Performance Analysis of Maximal-Ratio Combining Diversity Receivers in the Generalized-K Fading Channels

In this paper, we have analyzed the performance of maximal ratio combing (MRC) diversity receiver of the wireless communication systems over the composite fading environment, which is modelled by using the generalized-K distribution. However, this distribution has been considered as a versatile distribution for the precise modelling of a great variety of the short-term fading in conjunction with the long-term fading (shadow fading) channel conditions. In this proposed analysis, we have derived the mathematical expression for the moment generating function (MGF) of the generalized-K fading channel model that is used to evaluate a novel closed-form expression of the average bit error rate for (BER) the binary phase-shift keying /binary frequency-shift keying and average symbol error rate (SER) for the rectangular quadrature amplitude modulation scheme. We have also derived the mathematical expressions for the outage probability as well as the channel capacity for the generalized-K fading channel model.     

复合衰落信道建模及模拟方法研究

针对传统信道模拟器仅考虑多径衰落的问题,建立了包含路径损耗、阴影衰落和多径衰落的复合衰落信道模型,提出了一种基于高斯变量分解和谐波叠加原理的硬件模拟方法,推导了该方法输出衰落幅值理论分布与仿真参数的内在联系,并详细分析了可编程逻辑器件定点化模型输出周期性及位宽选择等问题。针对原型化模拟器的实测结果表明,该模拟方法输出信道衰落的统计特性与理论值吻合,可用于实验室中无线通信系统的性能测试和验证。      

The union bound for turbo-coded modulation systems over fadingchannels

We derive performance bounds for turbo-coded modulation systems over fading channels. We consider a Ricean fading channel model both with and without channel-state information (CSI). This model obviously includes Rayleigh fading channel as a special case. The bounds are extensions of similar bounds derived for additive white Gaussian noise channels. For the special case of a Rayleigh fading channel with CSI, we also derive a tighter version of the bound. We illustrate the use of the new bounds via some numerical examples     

地空衰落信道建模与仿真

在对地空信道角度统计特性分析的基础上,得到非直视分量通用多普勒功率谱和天线空间相关系数数学表达式。将地空信道小尺度衰落和大尺度衰落结合起来,用Nakagami衰落来建模地空信道小尺度衰落。将Zheng模型仿真法和MSEM仿真法分别用来模拟地空小尺度衰落和大尺度衰落模型。仿真结果表明,信号经过信道后幅度和频率都将发生显著的变化。     

An Empirical Model for Nonstationary Ricean Fading

Ricean fading is common in dense urban cellular networks and, as a mobile moves through that environment, the K-factor of the Ricean fading will change. This paper presents a statistical model for dense urban vehicular nonstationary Ricean fading, where the K-factor gradually changes due to movement through changing surroundings. This model is empirical and is based on K-factor fluctuations that are observed in dense urban cellular radio channel measurements. The K -factor is modeled using a random process with a distribution that is fit to the measured K-factor values. An autoregressive (AR) model is also used to ensure that the autocorrelation of the simulated K-factor process matches the empirical data. The nonstationary Ricean fading envelope that is generated using this model is verified by comparing it with the fading envelope that is observed in the measurements.     

Characteristics of L-band multipath fading due to sea surface reflection

For lowG/Tship-based earth stations in future maritime satellite communications, the effect of multipath fading due to sea surface reflection will be very important at low elevation angles. However, a practical model of theL-band multipath fading for fade prediction has not been available so far. A practical fading model is presented based on the shadowed Kirchhoff approximation theory for the coherent and incoherent components of the scattered power as a function of sea surface conditions. Using this model, theoretical fading depths are presented as a function of elevation angle, wave height, and antenna gain. The results indicate that intense fading occurs for wave heights greater than 50 cm, and the dependence on wave height is small under these conditions atL-band frequencies. Theoretical results presented agree well with experimental results obtained by field experiments.     

Nakagami-m fading modeling in the frequency domain for OFDM system analysis

Nakagami-m fading modeling in the frequency domain is investigated. For frequency-selective Nakagami-m fading channels, we show the magnitudes of the channel frequency responses to be also Nakagami-m distributed random variables with fading and mean power parameters as explicit functions of the fading and mean power parameters of the channel impulse responses. Based on this new model, the bit error rate performance of an orthogonal frequency-division multiplexing system with receive diversity over correlated Nakagami-m fading channels is analytically evaluated and some numerical results are given.     

相关瑞利信道仿真方法的研究

在无线通信系统的仿真中,相关瑞利衰落信道扮演着重要的作用。一种基于对一系列统计独立的标准高斯随机过程进行线性变换,得到具有一定相关特性的瑞利衰落信道的仿真模型被提出。仿真结果及复杂度分析表明,由于本文提出的仿真模型采用了迭代算法,因此相对于传统的相关瑞利信道仿真模型,该模型具有准确,复杂度低,易实现等优点。     

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.     

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.     

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.