Frank Laue

On the statistical properties of deterministic simulation models for mobile fading channels

Rices (9144, 1945) sum of sinusoids can be used for an efficient approximation of colored Gaussian noise processes and is therefore of great importance to the software and hardware realization of mobile fading channel models. Although several methods can be found in the literature for the computation of the parameters characterizing a proper set of sinusoids, less is reported about the statistical properties of the resulting (deterministic) simulation model. In this paper, not only is the simulation models amplitude and phase probability density function (PDF) investigated, but also higher order statistics [e.g., level-crossing rate (LCR) and average duration of fades (ADFs)]. It is shown that due to the deterministic nature of the simulation model, analytical expressions for the PDF of the amplitude and phase, autocorrelation function (ACF), crosscorrelation function (CCF), LCR, and ADFs can be derived. We also propose a new procedure for the determination of an optimal set of sinusoids, i.e., the method results for a given number of sinusoids in an optimal approximation of Gaussian, Rayleigh, and Rice processes with given Doppler power spectral density (PSD) properties. It is shown that the new method can easily be applied to the approximation of various other kinds of distribution functions, such as the Nakagami (1960) and Weibull distributions. Moreover, a quasi-optimal parameter computation method is presented.

A deterministic digital simulation model for Suzuki processes with application to a shadowed Rayleigh land mobile radio channel

We present a novel computer simulation model for a land mobile radio channel. The underlying channel model takes for granted non-frequency-selective fading but considers the effects caused by shadowing. For such a channel model we design a simulation model that is based on an efficient approximation of filtered white Gaussian noise processes by finite sums of properly weighted sinusoids with uniformly distributed phases. In all, four completely different methods for the computation of the coefficients of the simulation model are introduced. Furthermore, the performance of each procedure is investigated on the basis of two quality criteria. All the presented methods have in common the fact that the resulting simulation model has a completely determined fading behavior for all time. Therefore, the simulation model can be interpreted as a deterministic model that approximates stochastic processes such as Rayleigh, log-normal, and Suzuki (1977) processes.

An extended Suzuki model for land mobile satellite channels and its statistical properties

This paper deals with the statistical characterization of a stochastic process which is a product of a Rice and lognormal process. Thereby, we consider the more general case where the two Gaussian noise processes describing the Rice process are correlated. The resulting process are named as extended Suzuki process, which can be used as a suitable statistical model for describing the fading behavior of large classes of frequency nonselective land mobile satellite channels. In particular, the statistical properties (e.g., probability density function (pdf) of amplitude and phase, level-crossing rate, and average duration of fades) of the Rice process with cross-correlated components as well as of the proposed extended Suzuki process are investigated. Moreover, all statistical model parameters are optimized numerically to fit the cumulative distribution function and the level-crossing rate of the underlying analytical model to measured data collected in different environments. Finally, an efficient simulation model is presented which is in excellent conformity with the proposed analytical model.

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.

Design of high-speed simulation models for mobile fading channels by using table look-up techniques

This paper describes a procedure for the design of fast simulation models for Rayleigh fading channels. The presented method is based on an efficient implementation of Rices sum of sinusoids by using table look-up techniques. The proposed channel simulator is composed of a few numbers of adders, storage elements, and simple modulo operators, whereas time-consuming operations like multiplications and trigonometric operations are not required. Such a multiplier-free simulation model is introduced as a high-speed channel simulator. It is shown that the high-speed channel simulator can be interpreted as a finite state machine which generates deterministic output envelope sequences with approximately Rayleigh distribution. The statistical properties of the designed high-speed channel simulator are investigated analytically and compared with the statistics of the underlying Rayleigh reference model. Results of experiments for measuring the speed of the presented and other types of channel simulators are also presented.

A new and optimal method for the derivation of deterministic simulation models for mobile radio channels

Stochastic multipath propagation models for indoor and outdoor mobile radio channels are in general derived by employing coloured Gaussian noise processes. Efficient design and realization techniques of such processes are therefore of particular importance in the area of mobile radio channel modelling. This paper presents especially for complex coloured Gaussian noise processes a deterministic simulation model that is based on Rices (1944) sum of sinusoids. A new method is introduced for the derivation of an optimal set of sinusoids, i.e., the procedure is such that for a given number of sinusoids an optimal approximation of Gaussian (Rayleigh, Rice) processes with given Doppler power spectral density shapes is obtained. Moreover, the statistical properties of the resulting (deterministic) simulation model are investigated.

Modeling, analysis, and simulation of nonfrequency-selective mobile radio channels with asymmetrical Doppler power spectral density shapes

What terrestrial and satellite land mobile radio channels have in common is that they are usually assumed to be nonfrequency selective. For such fading channels, a highly flexible analytical model is presented. Our model takes into account short-term fading with superimposed long-term lognormal variations of the local mean value of the received signal. It is assumed that the introduced complex stochastical process, which is used for modeling the short-term fading behavior, has a Doppler power spectral density with an asymmetrical shape. Closed solutions are presented showing the influence of asymmetrical Doppler power spectral density shapes on the statistical properties of the proposed channel model. A numerical optimization procedure is shown for the optimization of the model parameters in order to fit the statistics of the analytical model [amplitude probability density function (PDF), level-crossing rate (LCR), and average duration of fades (ADF)] to measurement results of an equivalent land mobile satellite channel for light and heavy shadowing environments. Finally, from the analytical model, an efficient simulation model is derived that enables the simulation of such realistic land mobile satellite channel scenarios on a digital computer.

A deterministic model for a shadowed Rayleigh land mobile radio channel

In this paper a computer simulation model for a land mobile radio fading channel is presented. The model assumes non frequency-selective fading but takes into consideration the effects caused by shadowing. The simulation model is based on an efficient approximation of filtered white Gaussian noise by a finite sum of weighted sinusoids with equally distributed phases. Two completely different methods for the computation of the coefficients of the simulation model are discussed. The design of a fading channel model by one of the presented methods leads always to a simulation model that is completely determined for all time, and therefore, it can be considered as a deterministic model that approximates a stochastic process.

On the problems of Monte Carlo method based simulation models for mobile radio channels

Propagation models for mobile radio channels are often derived by using Gaussian noise processes with given Doppler power spectral density shapes. Such stochastic processes can efficiently be realized by employing Rices sum of sinusoids. In the meantime, the Monte Carlo principle is widespread in use for designing the parameters of the sinusoids. This paper investigates the (higher order) statistical properties of Monte Carlo method based simulation models for Rice and Rayleigh channels. It will be shown analytically and experimentally that a single realization of the output sequence of the simulation model does in general not contain the aspired statistical information. Moreover, an alternative parameter computation method will be discussed, which avoids the disadvantages of the Monte Carlo method.

The performance of deterministic Rayleigh fading channel simulators with respect to the bit error probability

All Rayleigh fading channel simulators based on finite sums of weighted harmonic functions with determined frequencies and phases are constitutionally deterministic. We analyze the performance of this important class of fading channel simulators with respect to the bit error probability (BEP) of QPSK and DPSK systems. New exact and approximate formulas for the BEP are derived. Several analytical and simulation results for the BEP are presented by using a typical stochastic procedure (Monte Carlo method) and a typical deterministic procedure (method of exact Doppler spread) for the computation of the parameters of deterministic Rayleigh fading channel simulators.