Neji Youssef

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

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

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.

On the crossing statistics of phase processes and random FM noise in Nakagami-q mobile fading channels

The crossing statistics of phase processes and random frequency modulation (FM) noise are studied for Nakagami-q fading channels. Closed-form expressions are first derived for the probability density function (PDF) and the cumulative distribution function (CDF) of random FM noise. The crossing rate of the phase process is then obtained for any crossing level of the phase. Moreover, the conditional PDF of random FM noise and envelope processes-conditioned on the crossings of an arbitrary level of the phase-are investigated. Since the Rayleigh fading channel is a special case of the Nakagami-q fading channel, the derived expressions are verified by comparison with results known for Rayleigh fading channels. In addition, it is shown that the derived analytical results are in excellent agreement with those obtained by computer simulations. The presented results are useful, for example, for studying the statistics of noise spikes occurring in limiter-discriminator FM receivers and for investigating the cycle slipping phenomenon in phase-locked-loop schemes when considering the transmission over Nakagami-q mobile fading channels.

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

An efficient deterministic simulation model for the Nakagami-Hoyt (1960, 1947) fading channel model (Q model) is proposed by using the concept of Rices sum of sinusoids. Analytical formulas are derived for the amplitude and phase probability density functions (PDF), level-crossing rate (LCR) and average duration of fades (ADF). By using a numerical optimization procedure, we show how the statistical properties of the Q model and the corresponding simulation model can be adapted to those of an equivalent mobile satellite channel for an environment with heavy shadowing. It is demonstrated by several theoretical and simulation results that the Q model and the therefrom derived simulation model can provide excellent characterization for the corresponding measurement results with respect to the complementary cumulative distribution function (CDF), normalized LCR and ADF. Finally, it is shown that the Q model enables a better statistical fitting to the measurement data compared to the Rayleigh model due to the increased flexibility.

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

This paper deals with some important statistical properties of the channel capacity of multiple-input-multiple-output (MIMO) systems with orthogonal space-time block code (OSTBC) transmission. We assume that all the subchannels are uncorrelated. For OSTBC-MIMO systems, 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, it will be shown that these exact closed-form expressions can be used to characterize the channel capacity of single-input-multiple-output (SIMO) and multiple-input-single-output (MISO) systems. In addition, a Gaussian approximation to the exact LCR of the capacity of OSTBC-MIMO systems is derived. The correctness of the derived closed-form expressions and the approximation is confirmed by simulations.

A study on the statistical properties of double hoyt fading channels

This paper deals with a study on the statistical properties of narrowband amplify-and-forward relay fading channels for Hoyt multipath propagation environments. We consider the basic radio link topology, where only one fixed relay station is used for the amplification. In this case, the envelope of the signal received over the overall multipath channel is modeled by the so-called double Hoyt fading process. Considering this multipath propagation channel model, analytical expressions for the first and second order statistics are provided. Specifically, the mean value, variance, probability density function (PDF), level-crossing rate (LCR), and average duration of fades (ADF) of double Hoyt processes are derived. In addition, an expression for the PDF of the corresponding channel phase is also provided. Since the double Rayleigh fading channel is a special case of the double Hoyt model, it will be shown how the derived expressions can be reduced to the results known for the double Rayleigh fading channel. Moreover, the validity of the derived quantities is confirmed by computer simulations.

On the statistical properties of generalized Rice multipath fading channels

Statistical properties of generalized Rice multipath fading channels are studied. A closed-form expression for the probability density function (PDF) of the phase process is derived first. Second order statistics, in the form of the level-crossing rate (LCR) and the average duration of fades (ADF), are then investigated for an arbitrary crossing level of the fading amplitude. Additionally, it is shown that the generalized Rice model yields a good fit to available measurement data on mobile satellite channels in the case of an environment with light shadowing.

A Non-Stationary Mobile-to-Mobile Channel Model Allowing for Velocity and Trajectory Variations of the Mobile Stations

In mobile-to-mobile (M2M) communication systems, both the transmitter and the receiver are moving with a certain velocity, which is usually assumed to be constant over time. However, in realistic propagation scenarios, the velocity of the mobile stations (MSs) is subject to changes resulting in a non-stationary fading process. In this paper, we develop a non-stationary narrow-band M2M multipath fading channel model, where the transmitter and the receiver experience changes in their velocities and trajectories. For this model, we derive expressions for the local autocorrelation function (ACF), the Wigner–Ville spectrum, the local average Doppler shift, and the local Doppler spread under isotropic scattering conditions. In addition, we investigate the correlation properties of the proposed model assuming non-isotropic scattering around the MSs. By relaxing the standard assumption of constant velocities of the MSs, this paper shows that the local ACF and the Wigner–Ville spectrum differ completely from known expressions derived for wide-sense stationary M2M channel models. Furthermore, it is shown that our model provides consistent results with respect to the Doppler spread. The proposed channel model is useful for the performance analysis of M2M communication systems under non-stationary conditions caused by velocity variations of the MSs.