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

A Statistical Simulation Model for Mobile Radio Fading Channels

Recently, a Clarke\u27s model-based simulator was proposed for Rayleigh fading channels. However, that model, as shown in this paper, may encounter statistic deficiency. Therefore, an improved model is presented to remove the statistic deficiency. Furthermore, a new simulation model is proposed for Rician fading channels. This Rician fading simulator with finite number of sinusoids plus a zero-mean stochastic sinusoid as the specular (line-of-sight) component is different from all the existing Rician fading simulators, which have non-zero mean deterministic specular component. The statistical properties of the proposed Rayleigh and Rician fading channel models are analyzed in detail, which shows that these statistics either exactly match or quickly converge to the theoretically desired ones. Additionally and importantly, the probability density function of the Rician fading phase is not only independent from time but also uniformly distributed, which is fundamentally different from that of all the existing Rician fading models. The statistical properties of the new simulators are evaluated by numerical results, finding good agreement in all cases

Novel Sum-of-Sinusoids Simulation Models for Rayleigh and Rician Fading Channels

The statistical properties of Clarke\u27s fading model with a finite number of sinusoids are analyzed, and an improved reference model is proposed for the simulation of Rayleigh fading channels. A novel statistical simulation model for Rician fading channels is examined. The new Rician fading simulation model employs a zero-mean stochastic sinusoid as the specular (line-of-sight) component, in contrast to existing Rician fading simulators that utilize a non-zero deterministic specular component. The statistical properties of the proposed Rician fading simulation model are analyzed in detail. It is shown that the probability density function of the Rician fading phase is not only independent of time but also uniformly distributed over [-pi, pi). This property is different from that of existing Rician fading simulators. The statistical properties of the new simulators are confirmed by extensive simulation results, showing good agreement with theoretical analysis in all cases. An explicit formula for the level-crossing rate is derived for general Rician fading when the specular component has non-zero Doppler frequenc

Second-Order Statistical Properties of the WSS Jakes\u27 Fading Channel Simulator

An improved Jakes\u27 (1994) fading channel simulator was proposed by Pop and Beaulieu (see ibid., vol.49, p.699-708, Apr. 2001) to eliminate the stationarity problem occurring in Jakes\u27 original design. In this paper, second-order statistical properties of the improved Jakes\u27 simulator are analyzed. Consistent with Pop and Beaulieu\u27s caution about high-order statistics of the simulator, it is proved that some second-order statistics of both the quadrature components and the envelope do not match the desired ones even if the number of sinusoids approaches infinity. Therefore, care must be taken when the simulator is employed to evaluate algorithms and systems

A Novel Simulator of Nonstationary Random MIMO Channels in Rayleigh Fading Scenarios

For simulations of nonstationary multiple-input multiple-output (MIMO) Rayleigh fading channels in time-variant scattering environments, a novel channel simulator is proposed based on the superposition of chirp signals. This new method has the advantages of low complexity and implementation simplicity as the sum of sinusoids (SOS) method. In order to reproduce realistic time varying statistics for dynamic channels, an efficient parameter computation method is also proposed for updating the frequency parameters of employed chirp signals. Simulation results indicate that the proposed simulator is effective in generating nonstationary MIMO channels with close approximation of the time-variant statistical characteristics in accordance with the expected theoretical counterparts

Reduced Order Estimation of Time Varying Wireless Channels in Real Life Scattering Environment

This thesis deals with theoretical study and numerical simulation of 2x1 MISO system with Alamouti coding and imperfect channel estimation at the receiver. We adopt two channel models to represent scattering environment. One is Sum of Sinusoids model, which is simple, but does not properly reflect the geometry of scattering environment. The second model uses a set of Modulated Discrete Prolate Spheroidal Sequences to represent the channel in a scenario with scattering from one or more clusters with predefined geometry. The effect of clusters location on estimation quality is examined. Furthermore, we derive reduced complexity Wiener filters for slow flat fading channel estimation in pilot aided receiver. Our approach is based on the approximation of the channel covariance function to zero and second order Taylor series to reduce computational effort of the filter design. Theoretical MMSE is developed, verified through simulation and compared to one of a full Wiener filter

Research on 2×2 MIMO Channel with Truncated Laplacian Azimuth Power Spectrum

Multiple-input multiple-output (MIMO) Rayleigh fading channel with truncated Laplacian azimuth power spectrum (APS) is studied. By using the power correlation matrix of MIMO channel model and the modified Jakes simulator, into which with random phases are inserted, the effect of the azimuth spread (AS), angle of departure (AOD) and angle of arrival (AOA) on the spatial correlation coefficient and channel capacity are investigated. Numerical results show that larger AS generates smaller spatial correlation coefficient amplitude, while larger average AOD or AOA produces larger spatial correlation coefficient amplitude. The average capacity variation is comprehensively dominated by the average AOD, AOA and AS