Matthias Pätzold

Mobile Fading Channels

From the Publisher: All relevant components of a mobile radio system, from digital modulation techniques over channel coding through to network aspects, are determined by the propagation characteristics of the channel. Therefore, a precise knowledge of mobile radio channels is crucial for the development, evaluation and test of current and future mobile radio communication systems. This volume deals with the modelling, analysis, and simulation of mobile fading channels and provides a fundamental understanding of many issues that are currently being investigated in the area of mobile fading channel modelling. The author strongly emphasises the detailed derivation of the presented channel models and conveys a high degree of mathematical unity to the reader. Introduces the fundamentals of stochastic and deterministic channel models Features the modelling and simulation of frequency-nonselective fading channels (Rayleigh channels, Rice channels, generalized Rice channels, Nakagami channels, various types of Suzuki channels, classical and modified Loo model) Presents the modelling and simulation of frequency-selective fading channels (WSSUS models, DGUS models, channel models according to COST 207) Discusses the methods used for the design and realization of efficient channel simulators Examines the design, realization, and analysis of fast channel simulators Includes MATLAB programs for the evaluation and simulation of mobile fading channels MATLAB is a registered trademark of The MathWorks, Inc. Telecommunication engineers, computer scientists, and physicists will all find this text both informative and instructive. It is also be an indispensable reference for postgraduate and senior undergraduate students of telecommunication and electrical engineering.

A study on the second order statistics of Nakagami-Hoyt mobile fading channels

In this paper, study of the second order statistics of the Nakagami-Hoyt fading channel model (Nakagami-q model) is considered. Expressions for the level crossing rate (LCR) as well as the average duration of fades (ADF) are derived. It is shown that the obtained analytical quantities best fit the corresponding measurement data for an equivalent mobile satellite channel in the case of an environment with heavy shadowing. This leads to the conclusion that the Nakagami-q model is applicable to realistic mobile communication channels. A simple and efficient deterministic simulation model based on the Rices sum of sinusoids, which enables the emulation of the fading envelope of the Nakagami-q model with the desired statistics, is also described. A very good agreement is obtained between the simulated, analytical, and experimental statistics.

A MIMO Mobile-To-Mobile Channel Model: Part I - The Reference Model

In this paper, we propose a multiple-input multiple-output (MIMO) channel model for mobile-to-mobile communications. This so-called MIMO mobile-to-mobile channel model is derived from the geometrical two-ring scattering model under the assumption that both the transmitter and the receiver are moving. In Part I of our paper, we focus on the reference model, which is based on the assumption that the transmitter and the receiver are surrounded by an infinite number of local scatterers. From a wave model, the complex channel gains are derived and their statistical properties are studied. General analytical solutions are provided for the three-dimensional (3-D) space-time cross-correlation function (CCF). We show that this 3-D function can be expressed as the product of two 2-D space-time CCFs, which are introduced as the transmit and receive CCF. Especially for the latter CCFs, closed-form expressions and numerical results are presented in case of isotropic scattering. The procedure presented in our paper provides an important framework for designers of future mobile-to-mobile communication systems to verify new transmission concepts under certain propagation conditions

Two new sum-of-sinusoids-based methods for the efficient generation of multiple uncorrelated rayleigh fading waveforms

This paper deals with the design of a set of multiple uncorrelated Rayleigh fading waveforms. The Rayleigh fading waveforms are mutually uncorrelated, but each waveform is correlated in time. The waveforms are generated by using the deterministic sum-of-sinusoids (SOS) channel modeling principle. Two new closed-form solutions are presented for the computation of the model parameters. Analytical and numerical results show that the resulting deterministic SOS-based channel simulator fulfills all main requirements imposed by the reference model with given correlation properties derived under two-dimensional isotropic scattering conditions. The proposed methods are useful for the design of simulation models for diversity-combined Rayleigh fading channels, relay fading channels, frequency-selective channels, and multiple-input multiple-output (MIMO) channels.

Level-crossing rate and average duration of fades of deterministic simulation models for Rice fading channels

The concept of Rices sum of sinusoids is often applied to the design of deterministic simulation models for Rice fading channels. This paper investigates in detail the level-crossing rate (LCR), average duration of fades (ADF), and cumulative distribution function (CDF) of such classes of simulation models. Exact and simple approximative formulas are deduced for these statistical quantities. Several numerical results for the derived expressions are presented by using different procedures for the design of the parameters of the deterministic simulation model. Moreover, comparisons with the corresponding simulation results-obtained by evaluating the deterministic simulation models output data-are also given.

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

A Wideband MIMO Channel Model Derived From the Geometric Elliptical Scattering Model

In this paper, we present a reference model for a wideband multiple-input multiple-output (MIMO) channel based on the geometric elliptical scattering model. The model takes into account the exact relationship between the angle of departure (AOD) and the angle of arrival (AOA). Based on this relationship, the statistical properties of the reference model are studied. Analytical solutions are presented for the three- dimensional (3D) space-time cross-correlation function (CCF), the temporal autocorrelation function (ACF), the 2D space CCF, and finally the frequency correlation function (FCF). The correlation properties are studied and visualized under the assumption of isotropic as well as non-isotropic scattering conditions. The proposed reference model can be used as a starting point for the derivation of a frequency-selective space-time MIMO channel simulator enabling the performance evaluation of multi-antenna wideband communication systems. The reference model is also quite useful for studying the MIMO channel capacity under various propagation conditions imposed by the geometry of the underlying scattering model.

A Mimo Mobile-To-Mobile Channel Model: Part II - The Simulation Model

In this paper, we propose a multiple-input multiple-output (IMIMO) mobile-to-mobile channel simulation model derived from a non-realizable reference model presented in Part I of our paper. The underlying reference model is based on the geometrical two-ring scattering model, where both the transmitter and the receiver are moving. A closed-form solution is provided for the three dimensional (3-D) space-time cross-correlation function (CCF) of the simulation model. An important result is that this CCF is ergodic. Also, our results show that this 3-D function can be expressed as a product of two 2-D space-time CCF, called the transmit and the receive CCF. It is shown that the parameters of the simulation model can be determined for any given space-time CCF describing the reference model. In case of isotropic scattering, we present a closed-form solution of the model parameters and illustrate some numerical results for the transmit and receive CCF. Finally, simulation results show an excellent correspondence between the statistical and time average of the MIMO channel capacity. This supports the hypothesis that the MIMO capacity is ergodic with respect to the mean

Exact Closed-Form Expressions for the Distribution, Level-Crossing Rate, and Average Duration of Fades of the Capacity of MIMO Channels

This paper deals with some important statistical properties of the multiple-input multiple-output (MIMO) channel capacity. We assume that all the subchannels are uncorrelated. In case of single-input multiple-output (SIMO) and multiple-input single-output (MISO) channels, exact closed-form expressions are derived for the probability density function (PDF), the cumulative distribution function (CDF), the level-crossing rate (LCR), and the average duration of fades (ADF) of the channel capacity. Furthermore, these exact closed-form expressions are extended to characterize the statistical properties of the maximum MIMO channel capacity. The correctness of the derived closed-form expressions is confirmed by simulations.

Methods for modeling of specified and measured multipath power-delay profiles

Five fundamental methods are proposed to model the multipath power-delay profile of frequency-selective indoor and outdoor wireless channels. Three of them are new, and the other two are well known, but their performance, however, has not been studied in detail up until now. All procedures are universally valid so that they can be applied to any specified or measured multipath power-delay profile. The performance of the proposed methods is investigated with respect to important characteristic quantities such as the frequency correlation function (FCF), average delay, and delay spread. The method found to perform best is the so-called L/sup P/-norm method (LPNM). This procedure is applied to measurement data of multipath power-delay profiles collected in different propagation environments. It is shown that the realization complexity of tapped-delay line-based simulation models for fading channels can be reduced considerably by using the LPNM. This is a great advantage for the development and specification of channel models for future wireless systems.