瑞利信道仿真模型及MATLAB实现

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"这篇文章主要介绍了瑞利信道的MATLAB仿真模型，提出了一种基于正弦函数的新统计仿真方法，该方法考虑了随机路径增益、随机初始相位和条件随机多普勒频率，适用于模拟瑞利衰落信道。" 在无线通信中，瑞利信道是描述信号在传播过程中遇到多重反射和散射时的一种重要模型，特别是在城市环境或移动通信场景下。MATLAB作为一个强大的数值计算和仿真平台，常被用于构建和分析各种通信系统模型，包括瑞利信道。该文作者Yahong Rosa Zheng和Chengshan Xiao提出了新的基于正弦函数的统计仿真模型，这些模型的核心在于引入了随机路径增益、随机初始相位以及条件随机多普勒频率，这使得每个正弦分量都能更准确地反映瑞利信道的实际特性。其中，随机路径增益模拟了信号在不同路径上的衰减；随机初始相位反映了信号在不同路径上的相位差；条件随机多普勒频率则考虑了由于移动物体导致的频率偏移，这是多普勒效应在通信中的体现。论文指出，即使只有极少数（如个位数）的正弦分量，新模型也能精确匹配所需的自相关和交叉相关性，这对于四阶统计量如平方衰落包络的自相关函数尤其重要。随着正弦分量数量的增加，新模型的概率密度函数（PDF）、包络和相位的级联率、平均衰落持续时间和平方衰落包络的自相关函数等关键性能指标都将渐近逼近理想值。实际上，即使正弦分量的数量仅为8，模型也能达到良好的收敛性。这一仿真模型的提出，不仅提高了瑞利信道仿真的精度，也降低了对计算资源的需求，对于理解和优化无线通信系统，尤其是在进行算法设计和性能评估时，提供了强大的工具。通过使用这种模型，工程师和研究人员可以更有效地预测和分析瑞利信道中的信号传输性能，从而改进通信系统的抗干扰能力和稳定性。

920 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 51, NO. 6, JUNE 2003

Simulation Models With Correct Statistical

Properties for Rayleigh Fading Channels

Yahong Rosa Zheng and Chengshan Xiao, Senior Member, IEEE

Abstract—In this paper, new sum-of-sinusoids statistical sim-

ulation models are proposed for Rayleigh fading channels. These

new models employ random path gain, random initial phase, and

conditional random Doppler frequency for all individual sinusoids.

It is shown that the autocorrelations and cross correlations of the

quadrature components, and the autocorrelation of the complex

envelope of the new simulators match the desired ones exactly, even

if the number of sinusoids is as small as asingle-digitinteger. More-

over, the probability density functions of the envelope and phase,

the level crossing rate, the average fade duration, and the auto-

correlation of the squared fading envelope which contains fourth-

order statistics of the new simulators, asymptotically approach the

correct ones as the number of sinusoids approaches infinity, while

good convergence is achieved even when the number of sinusoids is

as small as eight. The new simulators can be directly used to gen-

erate multiple uncorrelated fading waveforms for frequency selec-

tive fading channels, multiple-input multiple-output channels, and

diversity combining scenarios. Statistical properties of one of the

new simulators are evaluated by numerical results, finding good

agreements.

Index Terms—Channel models, fading channel simulator, fading

channels, high-order statistics, Rayleigh fading, second-order sta-

tistics.

I. INTRODUCTION

OBILE radio channel simulators are commonly used

in the laboratory because they allow system tests and

evaluations which are less expensive and more reproducible

than field trials. Many different approaches have been used for

the modeling and simulation of mobile radio channels [1]–[23],

[31], [32]. Among them, the well-known mathematical ref-

erence model due to Clarke [1] and its simplified simulation

model due to Jakes [6] have been widely used for Rayleigh

fading channels for about three decades. However, Jakes’ sim-

ulator is a deterministic model, and it has difficulty in creating

multiple uncorrelated fading waveforms for frequency-selective

fading channels and multiple-input multiple-output (MIMO)

channels, therefore, different modifications of Jakes’ simulator

have been reported in the literature [10], [16]–[19], [31].

Paper approved by R. A. Valenzuela, the Editor for Transmission Systems of

the IEEE Communications Society. Manuscript received April 1, 2002; revised

November 7, 2002. This work was supported in part by the University of Mis-

souri (UM)-Columbia Research Council under Grant URC-02-050 and in part

by the UM System Research Board under Grant URB-02-124. This paper was

presented in part at the IEEE Vehicular Technology Conference, Birmingham,

AL, May 6–9, 2002.

The authorsare with the Department of Electrical and Computer Engineering,

University of Missouri, Columbia, MO 65211 USA (e-mail: yzheng@ee.mis-

souri.edu; xiaoc@missouri.edu).

Digital Object Identifier 10.1109/TCOMM.2003.813259

Despite the extensive acceptance and application of Jakes’

simulator, some important limitations of the simulator were

determined and discussed in detail recently [22]. It was shown

in [22] that Jakes’ simulator is wide-sense nonstationary when

averaged across the physical ensemble of fading channels. Pop

and Beaulieu [22] proposed an improved simulator by intro-

ducing random phase shifts in the low-frequency oscillators to

remove the stationary problem. However, it was pointed out in

[22] that higher-order statistics of this improved simulator may

not match the desired ones. Consistent with Pop and Beaulieu’s

caution about higher-order statistics of the improved simulator,

it was further proved in [24] that second-order statistics of

the quadrature components and the envelope do not match the

desired ones. Moreover, even in the limit as the number of

sinusoids approaches infinity, the autocorrelations and cross

correlations of the quadrature components, and the autocorre-

lation of the squared envelope of the improved simulator, fail

to match the desired correlations. Jakes’ original simulator and

published modified versions of it, have similar problems with

these second-order statistics.

In this paper, new sum-of-sinusoids statistical simulation

models are proposed for Rayleigh fading channels. It is

shown that the autocorrelations and cross correlations of

the quadrature components, and the autocorrelation of the

complex envelope of the new simulators, match the desired

ones exactly even if the number of sinusoids is so small as

a single-digit integer. Furthermore, the autocorrelation of the

squared envelope which contains fourth-order statistics, the

probability density functions (PDFs) of the fading envelope

and the phase, the level-crossing rate, and the average fade

duration of our new simulators asymptotically approach the

desired ones as the number of sinusoids approaches infinity.

Moreover, convergence to the limiting (exact) values of these

properties, except for the fading phase’s PDF, is rapid and

close approximation is achieved even when the number of

sinusoids is as small an integer as eight, and the number of

random trials is only 50. Additionally, and importantly, the new

simulator can be directly used to generate multiple uncorrelated

fading waveforms, which are needed to simulate some realistic

frequency-selective fading channels, MIMO channels, and

diversity-combining scenarios.

The remainder of this paper is organized as follows. Section II

briefly reviews the mathematical reference model and the family

of Jakes’ simulators. Attention is given to the statistical proper-

ties of the reference model and an improved Jakes simulator.

Section III proposes a new sum-of-sinusoids simulation model

for Rayleigh fading channels, and the statistical properties of

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