On statistics of the mobile rayleigh fading channel in non-isotropic scattering environments (original) (raw)
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Wireless Communications and Mobile Computing, 2011
For the practical simulation and performance evaluation of mobile-to-mobile (M2M) communication systems, it is desirable to develop accurate M2M channel simulation models for more realistic scenarios of non-isotropic scattering. In this paper, by using a 'double-ring' concept to describe M2M non-isotropic scattering environments, we propose new deterministic and stochastic sum-of-sinusoids (SoS) based simulation models. The proposed simulation models extensively consider the distributions of the angle of arrival (AoA) and the angle of departure (AoD), and thus provide a good approximation to the desired statistical properties of the reference model.
Impact of Mobile Acceleration on the Statistics of Rayleigh Fading Channel
Clarke's model of the received signal statistics in a mobile isotropic scattering environment assumes a constant mobile velocity, a consequence of which is that the autocorrelation function of the received signal and the Power Spectral Density (PSD) are independent of the absolute time. In this contribution we relax the assumption of constant mobile velocity and analyze the statistics of the channel when the mobile receiver has a constant acceleration. First, we derive expressions for a general scattering environment and, then, specialize them to the case of isotropic scattering environment. The autocorrelation and PSD of the channel are not only a function of the lag, τ , but the absolute time index, n as well. There are now two kinds of PSDs: The conventional PSD , based on the well-known Wiener-Khintchine theorem, gives the spectrum in the τ domain. The second PSD is concerned with the variation of the channel with time and gives the spectrum in the n domain. The simulation results suggest that the two PSDs show a pattern of periodicity which can be explained by considering asymptotic approximation of the Bessel function. Moreover, the magnitudes of the PSDs diminish with increasing τ or n such that the conventional PSD approaches uniform distribution over 0 to 2π when time n is large whereas the PSD of channel variation with time approaches zero for large τ. We give results on the basis of simulations and justify analytically, or heuristically. We also discuss different implications of these results.
A generalisation of the Rayleigh distribution with applications in wireless fading channels
Wireless Communications and Mobile Computing, 2011
The signal received in a mobile radio environment exhibits rapid signal level fluctuations which are generally Rayleighdistributed. These result from interference by multiple scattered radio paths between the base station and the mobile receptor. Fading-shadowing effects in wireless channels are usually modelled by means of the Rayleigh-Lognormal distribution (RL), which has a complicated integral form. The K-distribution (K) is similar to RL but it has a simpler form and its probability density function admits a closed form; however, due to the Bessel function, parameter estimates are not direct. Another possible approach is that of the Rayleigh-inverse Gaussian distribution (RIG). In this paper, an alternative is presented, a generalisation of the Rayleigh distribution which is simpler than the RL, K and RIG distributions, and thus more suitable for the analysis and design of contemporary wireless communication systems. Closed-form expressions for the bit error rate (BER) for differential phase-shift keying (DPSK) and minimum shift keying (MSK) modulations with the proposed distribution are obtained. Theoretical results based on statistically well-founded distance measurements validate the new distribution for the cases analysed.
Geometry-Based Statistical Modeling of Non-WSSUS Mobile-to-Mobile Rayleigh Fading Channels
IEEE Transactions on Vehicular Technology
In this paper, we present a novel geometry-based statistical model (GBSM) for small-scale non-wide-sense stationary uncorrelated scattering (non-WSSUS) mobile-to-mobile (M2M) Rayleigh fading channels. The proposed model builds on the principles of plane wave propagation (PWP) to capture the temporal evolution of the propagation delay and Doppler shift of the received multipath signal. This is different from existing non-WSSUS geometry-based statistical channel models, which are based on a spherical wave propagation (SWP) approach, that in spite of being more realistic, is more mathematically intricate. By considering an arbitrary geometrical configuration of the propagation area, we derive general expressions for the most important statistical quantities of nonstationary channels, such as the first-order probability density functions (PDFs) of the envelope and phase, the four-dimensional (4D) time-frequency correlation function (TF-CF), local scattering function (LSF), and time-frequency (TF) dependent delay and Doppler profiles. We also present an approximate closed-form expression of the channel's 4D TF-CF for the particular case of the geometrical one-ring scattering model. The obtained results provide new theoretical insights into the correlation and spectral properties of non-WSSUS M2M Rayleigh fading channels. Index Terms-Fading channels, mobile-to-mobile communications, nonstationary processes, radiowave propagation, non-widesense stationary uncorrelated scattering (non-WSSUS) channels. I. INTRODUCTION T HE characterization of nonstationary time-frequency (TF) dispersive multipath fading channels is a topic of research that is receiving increasing attention due to the emergence of novel mobile communication systems that are conceived to operate under rapidly changing propagation conditions. Examples of such systems include high-speed railway communication systems [1], fourth (4G) [2] and fifth generation
Space-Time Channel Correlation of MIMO Rayleigh Fading Based on Non-isotropic 3D Scattering
2007
In this paper, a general space time correlation function is derived for narrowband (MIMO) Rayleigh fading channels assuming 3D scattering around the mobile station (MS). Non-isotropic scattering is assumed, and the Von Mises PDF of the angle of arrival (AOA) is used. The resulting 3D based correlation functions contain general non-isotropic 2D based functions, as well as isotropic 3D based functions as special cases. It has been shown that non-isotropic scattering increases the channel correlation as functions of the MS antenna spacing. Also, as means of proving the validity of the derived correlation functions, a multichannel autoregressive (AR) simulation method is used to generate channel samples possessing those correlation statistics.
A Generalised (M, NR) Mimo Rayleigh Channel Model for Non-Isotropic Scatterer Distributions
This paper extends a recently proposed space-time model for Rayleigh fading to include an arbitrary transmit antenna configuration of any shape and size transmitting simultaneously in a multiple-input multiple-output (MIMO) channel. The space-time correlation function and space-frequency cross spectrum function for a non-isotropic scatterer distribution around the receiver is derived for the arbitrary configuration as a further extension of a previous result of a multiple-input single-output Rayleigh wireless channel which used a ring of uniformly distributed scatterers model. Analysis based on achievable spectral efficiency for typical arbitrary transmit antenna configurations is given. The analysis demonstrates the utility of the correlation function.
Proceedings of the Tenth IEEE Workshop on Statistical Signal and Array Processing (Cat. No.00TH8496)
For the analysis and design of adaptive antenna arrays in mobile fading channels, we need a model for the spatio-temporal correlation among the array elements. In this paper we propose a general spatio-temporal correlation function, where non-isotropic scattering is modeled by von Mises distribution, an empiricallyverified model for non-uniformly distributed angle of arrival. The proposed correlation function has a closed form and is suitable for both mathematical analysis and numerical calculations. The utility of the new correlation function has been demonstrated by quantifying the effect of non-isotropic scattering on the performance of two applications of the antenna arrays for multiuser multichannel detection and single-user diversity reception. Comparison of the proposed correlation model with published data in the literature shows the flexibility of the model in fitting real data.
Simulation models with correct statistical properties for Rayleigh fading channels
IEEE Transactions on Communications, 2003
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 fourthorder 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.
On the second order statistics of the multihop rayleigh fading channel
IEEE Transactions on Communications, 2000
Second order statistics provides a dynamic representation of a fading channel and plays an important role in the evaluation and design of the wireless communication systems. In this paper, we present a novel analytical framework for the evaluation of important second order statistical parameters, as the level crossing rate (LCR) and the average fade duration (AFD) of the amplify-and-forward multihop Rayleigh fading channel. More specifically, motivated by the fact that this channel is a cascaded one and can be modeled as the product of N fading amplitudes, we derive novel analytical expressions for the average LCR and the AFD of the product of N Rayleigh fading envelopes (or of the recently so-called N * Rayleigh channel). Furthermore, we derive simple and efficient closed-form approximations to the aforementioned parameters, using the multivariate Laplace approximation theorem. It is shown that our general results reduce to the corresponding ones of the specific dual-hop case, previously published. Numerical and computer simulation examples verify the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations.