Improved models for the generation of multiple uncorrelatedRayleigh fading waveforms

An improved sum-of-sinusoids simulation model is proposed for Rayleigh fading channels. The new model employs random initial phase, and conditional random Doppler frequency for all individual sinusoids. The second-order statistics of the new simulator match the desired ones exactly even if the number of sinusoids is a single-digit integer. Other key statistics of the new simulator approach the desired ones of Clarke's (1968) reference model as the number of sinusoids approaches infinity, while good convergence is achieved when the number of sinusoids is small. Moreover, the new simulator can be directly used to generate multiple uncorrelated fading waveforms; it is also pointed out that a class of 16 different simulators, which have identical statistical properties, can be developed for Rayleigh fading channels     

An Improved Deterministic SoS Channel Simulator for Multiple Uncorrelated Rayleigh Fading Channels

The generation of multiple uncorrelated Rayleigh fading waveforms is often demanded for simulating wideband fading channels, multiple-input multiple-output (MIMO) channels, and diversity-combined fading channels. In this letter, an improved deterministic sum-of-sinusoids (SoS) channel simulator with a new parameter computation method is proposed to simulate a large number of uncorrelated Rayleigh fading processes. Compared with the existing SoS channel simulators, the proposed deterministic SoS model yields a much better simulation efficiency while still preserving satisfactory approximations to the desired statistical properties of the reference model.     

STBC-Based (Turbo) STTC Codes Built by Set Partitioning for Three Transmit Antennas: Construction and Performances

Simulating wideband fading channels, multiple-input multiple-output (MIMO) channels, and diversity-combined fading channels often demands the generation of multiple uncorrelated Rayleigh fading waveforms. In this letter, two appropriate parameter computation methods, namely the method of exact Doppler spread (MEDS) and L_p -norm method (LPNM), for deterministic sum-of-sinusoids (SoS) channel simulators are investigated to guarantee the uncorrelatedness between different simulated Rayleigh fading processes. Numerical and simulation results show that the resulting deterministic SoS channel simulator can accurately and efficiently reproduce all the desired statistical properties of the reference model     

An Improved Simulator for the Correlation-Based MIMO Channel in Multiple Cluster Scattering Environments

An improved MIMO radio channel simulator is proposed, based on the most popular correlation-based MIMO channel model called Kronecker model and the sum-of-sinusoids (SoS) method which is widely used to generate Rayleigh fading waveforms with temporal correlation. Firstly, a simplified simulation model for generating multiple independent Rayleigh fading waveforms is presented, which employs only one random variable to set all Doppler frequency components in all waveforms. Next, a fast spatial correlation calculation technique, in a closed-form expression implemented by the Fourier Transform both for outdoor and indoor multiple cluster scattering environments, is introduced, which accurately reproduces the desired spatial correlation properties and indicates a direct dependence between spatial correlation and channel physical parameters. The ergodic and outage capacity of the simulated channel are also evaluated with respect to different azimuth of arrival and azimuth of departure (AoA/AoD) under the condition of 3GPP SCM (3rd Generation Partnership Project Spatial channel model) [23]. The presented simulator is therefore suitable for the theoretical analysis of MIMO radio systems, including dynamic system simulation.     

Analysis and Simulation of Second-Order Statistics with Modified Characteristic Function Parameters in a Multipath Fading Environment

In this paper, we analyse and implement a modified low pass filtering based characteristic function for a multipath Rayleigh fading channel. A new class of this modified filtering sequence based statistical simulation model is proposed for a Rayleigh fading environment. Comparing with the sum-of-sinusoids (SOS) deterministic model and its modifications as a new SOS model, the proposed model reintroduces the randomness to Doppler frequency and initial phase of the sinusoids to have non-deterministic simulators with desired statistical properties. The expressions and simulation results of level crossing rate (LCR) and average fade duration are derived and shown in this paper. Comparison of power spectra reveals that the spectrum spread is much less for our proposed method. Therefore, we would expect reduction in the rapidity of fading which is observed in LCR calculations.     

A multi-criteria comparative analysis of different Rayleigh fading channel simulators

In this paper, an in-depth comparative analysis of the most accepted and approved Rayleigh fading channel simulators is presented. Our study addresses the three common methods for generating time-correlated Rayleigh fading processes: the inverse discrete Fourier transform (IDFT) method, the filtering white Gaussian noise (FWGN) method and the sum-of-sinusoids (SOS) method. Totally seven models, including the recently proposed models, are analyzed and compared with Clarke's reference model. We use four quantitative measures for judicious assessment of the quality of generated processes in terms of both first-order and second-order statistics. Additionally, these measures cover analysis in time domain as well as in frequency domain. An evaluation of the computational effort is also depicted. The simulation results suggest that the recently published Wang's model is very attractive and it outperforms all SOS-based models. We conclude that Zheng and Xiao's first model remains the best choice among Zheng and Xiao's family models. Several other important remarks and conclusions about the accuracy and the capability of the different Rayleigh fading simulators are driven from this study.     

无线信道中一种新的瑞利波形仿真模型

该文提出了一种新的简单的产生满足任意自相关特性的瑞利波形的仿真模型,在此基础上得出无线信道中瑞利衰落波形的产生方法。该方法可以容易地产生多个相互独立的瑞利衰落波形,从而为研究各种频率分集无线通信系统提供了可能。仿真结果表明该模型能够有效地产生符合小尺度无线信道特征的瑞利衰落波形,满足自相关特性及平稳性的要求。     

Simulation models with correct statistical properties for Rayleigh fading channels

In this paper, new sum-of-sinusoids statistical simulation 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 a single-digit integer. Moreover, the probability density functions of the envelope and phase, the level crossing rate, the average fade duration, and the autocorrelation 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 generate multiple uncorrelated fading waveforms for frequency selective 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.     

Performance evaluation for cellular CDMA

The authors consider the performance of a cellular radio, direct-sequence code-division multiple access, (CDMA) system. The base-to-mobile link is modeled as a flat Rayleigh fading channel, with all signals transmitted from a given base station fading in unison. For the mobile-to-base link, the authors use a similar model, except that the waveforms from all users are assumed to experience independent fading. The effects of imperfect power control are shown     

Limitations of sum-of-sinusoids fading channel simulators

Rayleigh signal fading due to multipath propagation in wireless channels is widely modeled using sum-of-sinusoids simulators. In particular, Jakes' (1994) simulator and derivatives of Jakes' simulator have gained widespread acceptance. Despite this, few in-depth studies of the simulators' statistical behavior have been reported in the literature. Here, the extent to which Jakes' simulator adequately models the multipath Rayleigh fading propagation environment is examined. The results show that Jakes' simulator does not reproduce some important properties of the physical fading channel. Some possible improvements to Jakes' simulator are examined. The significances of the number and the symmetries of the Doppler frequency shifts on the validity of the simulator's reproduction of the physical fading channel are elucidated     

Jakes fading model revisited

The Jakes fading model is a deterministic method for simulating time-correlated Rayleigh fading waveforms and is still widely used today. However, since it is difficult to create multiple uncorrelated fading waveforms with this model, the authors propose modifications to the model which solve this problem.<>     

Space-Time Correlated Mobile-to-Mobile Channels: Modelling and Simulation

A single- and double-bounced two-ring parametric reference model is proposed for multiple-input multiple-output (MIMO) mobile-to-mobile (M-to-M) Ricean fading channels. From this model, a closed-form joint space-time correlation function and a space-Doppler power spectrum are derived for a two-dimensional (2D) non-isotropic scattering environment. Also, space-time correlation functions for the in-phase and quadrature components of the complex faded envelope are derived, assuming a 2D isotropic scattering environment. Finally, two new sum-of-sinusoids based simulation models for MIMO M-to-M Ricean fading channels are proposed. The statistics of the simulation models are verified by simulation. The results show that the simulation models are a good approximation of the reference model and that they outperform existing simulation models.     

一种新的多径相关瑞利信道的数学模型：理论分析及仿真比较

产生统计独立的多径相关瑞利信道是无线信道仿真的一个基本问题.Jakes模型得到了广泛应 用,但它在统计独立性方面还存在一些问题.该文提出一种新的相关瑞利信道的数学模型.理论分析和仿真 比较表明它在计算复杂度和统计独立性方面比最初的Jakes模型及其近来发现的改进模型更加简单有效.     

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     

On the Stationarity and Ergodicity of Fading Channel Simulators Based on Rice's Sum-of-Sinusoids

Channel simulators based on Rice's sum-of-sinusoids are playing an important role in fading channel modelling. However, the parameters of the sum-of-sinusoids have to be determined meticulously to fully exploit the potential that this powerful procedure has to offer. This paper presents general conditions under which the sum-of-sinusoids procedure results in a stationary and ergodic channel simulator. Moreover, with the help of the introduced conditions, several established parameter computations methods will be investigated with respect to their usability to design stationary and ergodic fading channel generators. It turns out that if and only if the gains and frequencies are constant quantities and the phases are random variables, then the sum-of-sinusoids defines a stationary and ergodic process.     

Stochastic Modeling and Simulation of Frequency-Correlated Wideband Fading Channels

For the simulation of practical frequency-diversity wireless communication systems, such as frequency-hopping systems, multicarrier code-division multiple-access systems, and orthogonal frequency-division multiplexing systems, it is often desirable to produce multiple Rayleigh fading processes with given frequency correlation properties. In this paper, a novel stochastic wide-sense stationary sum-of-sinusoids channel simulator is proposed to emulate frequency-correlated wideband fading channels, where the frequency correlation properties are controlled by only adjusting the constant phases. Closed-form expressions are provided for all the parameters of the simulation model. This enables us to investigate analytically the overall correlation properties (not only the correlation coefficients) of the simulated processes with respect to both time separation and frequency separation. It is shown that the wideband channel simulator will be reduced to a narrowband Rayleigh fading-channel simulator by removing the frequency selectivity. Furthermore, the COST 207 typical-urban and rural-area channels are applied to evaluate the performance of the resulting wideband and narrowband channel simulators, respectively. The correlation properties of the simulation models approach the desired ones of the underlying reference models as the number of exponential functions tends to infinity, while very good approximations are achieved with the chosen limited number of exponential functions     

Comparative analysis of statistical models for the simulation of Rayleigh faded cellular channels

Several new "sum-of-sinusoids" models have recently been introduced for the simulation of Rayleigh fading channels. These models are statistical in nature implying that their simulation parameters such as the Doppler frequencies are random. They have been shown to accurately reproduce some of the desired statistical properties of the faded envelope such as the time autocorrelation and the level crossing rate. However, a comparative analysis of these models, hitherto scattered throughout the literature, is not available. This paper compares these models in terms of their complexity and performance. The performance assessment is based upon the variance of the time average statistical properties from their ideal ensemble averages.     

一种新的Jakes模型参数计算方法

本文分析了小尺度无线衰落信道的理论参考模型—Clark模型,比较了两种较为重要的确定性仿真模型的参数计算方法—精确多普勒扩展法（MEDS）和随机精确多普勒扩展法（R_MEDS）,提出了一种新的用于仿真平坦衰落信道Jakes模型的参数计算方法,即在MEDS的基础上对离散多普勒频率引入随机抖动。仿真数据和图形表明,在模型复杂度较低的情况下,新的信道模型的自相关和互相关特性较R_MEDS有很大改善,而且与原始MEDS相比,新模型多普勒频率为随机变量,可以有效仿真瑞利衰落、多个不相关的瑞利衰落和频率选择性衰落信道等,并且可以结合工程需要设定随机抖动幅度,保证了衰落信道的不相关性和遍历性的有机统一。      

BER improvement of multilevel CPM in the mobile radio environment

An attractive modulation scheme, named accelerated phase-quaternary continuous phase modulation (AP-QCPM), is proposed for digital mobile radio applications. As AP-QCPM is a constant envelope modulation scheme, it is well suited to nonlinear power amplifier use in mobile equipment and handheld equipment of wireless LAN applications. The error performance of multilevel low-deviation frequency-shift keying (FSK) is severely degraded in the Rayleigh fading channel. On the other hand, the degradation of phase-shift keying (PSK) remains within a moderate amount. The paper is an attempt to clarify what kind of modification could be added to the conventional four-level FSK to achieve an error probability comparable with the QDPSK in the Rayleigh fading channel. The error probability of the proposed scheme and the power spectral characteristics are obtained to reveal critical values of the modification parameter. The analytical results are confirmed by the hardware simulation at 900 MHz