Alireza Borhani

Correlation and Spectral Properties of Vehicle-to-Vehicle Channels in the Presence of Moving Scatterers

This paper derives a vehicle-to-vehicle (V2V) channel model assuming a typical propagation scenario in which the local scatterers move with random velocities in random directions. The complex channel gain of the proposed V2V channel model is provided. Subsequently, for different scatterer velocity distributions, the corresponding autocorrelation function (ACF), power spectral density (PSD), and the Doppler spread of the channel are derived, shown, and confirmed by the available measurement data. It is shown that the Gaussian mixture (GM) and the exponential distribution can accurately describe the velocity distribution of relatively fast and slow moving scatterers, respectively. Since the proposed V2V channel model flexibly covers several communication scenarios as special cases, including fixed-to-vehicle (F2V) and fixed-to-fixed (F2F) scenarios in the presence of both fixed and moving scatterers, it is obvious that the presented results are important for the performance analysis of cutting-edge vehicular communication systems.

A Unified Disk Scattering Model and Its Angle-of-Departure and Time-of-Arrival Statistics

This paper proposes a novel probability density function (PDF) for the distribution of local scatterers inside a disk centered on the mobile station (MS). The new scattering model is introduced as the unified disk scattering model (UDSM), as it unifies a variety of typical circularly symmetric scattering models into one simple model. By adjusting a designated shape factor controlling the distribution of the scatterers, both the uniform circular and uniform ring scattering models can be obtained as special cases. Furthermore, the original Gaussian and uniform hollow-disk scattering models can be approximated with a high level of accuracy. In addition to these established scattering models, any continuous concentrations of local scatterers from a high density near the MS to a high density close to the outer edge of the disk can also be achieved. Under the assumption of single-bounce scattering, the joint PDF of the angle-of-departure and angle-of-arrival (AoA) and the joint PDF of the time-of-arrival and AoA are derived. Subsequently, the corresponding marginal PDFs are provided in closed form. Finally, the UDSM is validated by several measured channels, showing that the UDSM outperforms several other geometric models proposed in the literature. The proposed model is useful for the designers of cutting-edge vehicular communication technologies to study the system performance under different scattering conditions.

A non-stationary multipath fading channel model incorporating the effect of velocity variations of the mobile station

A standard assumption in mobile fading channel modelling is that the mobile station (MS) moves along a straight line with constant speed. In practice, this assumption is violated in most propagation scenarios. For the development of more realistic channel models, it is therefore important to relax this restriction by allowing the MS to change its velocity. In this paper, we study the effect of velocity changes on the statistical properties of multipath fading channels. Expressions will be derived for the local autocorrelation function (ACF), the Wigner-Ville spectrum, the average Doppler shift, and the Doppler spread. Our findings show that a variation of the speed and/or the direction of the MS results in a non-stationary channel model. The Wigner-Ville spectrum cannot be interpreted physically as a generalized Jakes (Clarke) power spectral density (PSD); although it includes the latter one for the special case that the MS moves with constant velocity.

Modeling of Vehicle-to-Vehicle Channels in the Presence of Moving Scatterers

In this paper, we derive a vehicle-to-vehicle (V2V) channel model assuming a typical propagation scenario in which the local scatterers move with random velocities in random directions. The complex channel gain of the proposed V2V channel model is provided. Subsequently, for different scatterer velocity distributions, the corresponding autocorrelation functions (ACFs) are derived, illustrated, and compared with the classical ACF derived under the assumption of fixed scatterers. Furthermore, under specific conditions, highly accurate approximations for the ACFs are provided in closed form. Since the proposed V2V channel model covers several communication scenarios as special cases, including fixed-to-vehicle (F2V) and fixed-to-fixed (F2F) scenarios in the presence of both fixed and moving scatterers, it is obvious that the presented results are important for the designers of cutting-edge vehicular communication systems.

A non-stationary one-ring scattering model

This paper introduces a non-stationary one-ring scattering model in which the mobile station (MS) can move along a straight line from the rings center to the border of the ring. This movement results in a time-variant angle-of-arrival (AOA), which is modeled by a stochastic process. We derive the first-order density of the AOA process in closed form. Subsequently, a closed-form expression is provided for the local power spectral density (PSD) of the channel. We also formulate the local autocorrelation function (ACF) of the complex channel gain in integral form, from which a highly accurate closed-form approximation is derived. Furthermore, the average Doppler shift and the Doppler spread of the channel are computed. The analytical results are illustrated and physically explained. It is shown that non-stationarity in time contradicts the common isotropic scattering assumption. The merit of this study is to open a new window to the performance analysis of mobile communication systems under non-stationary channel conditions.

Modelling of non-stationary mobile radio channels using two-dimensional brownian motion processes

The interdisciplinary idea of this paper is to employ a two-dimensional (2D) Brownian motion (BM) process to model non-stationary mobile fading channels. It is assumed that the mobile station (MS) starts moving from a fixed point along a random path in the 2D plane. We model such a moving scenario by a 2D BM process, in which the variance of the process determines the deviation of the MS from its starting point. The propagation area is modelled by a non-centred one-ring scattering model, where the local scatterers are uniformly distributed on a ring centred not necessarily on the MS. The random movement of the MS in the proposed scattering model results in local angles-of-arrival (AOAs) and local angles-of-motion (AOMs) characterized by stochastic processes rather than random variables. We derive the first-order density of the AOA and AOM processes in closed form. The local power spectral density (PSD) of the Doppler frequencies and the local autocorrelation function (ACF) of the complex channel gain are also provided. The numerical results show that the proposed non-targeted Brownian path model results in a non-stationary non-isotropic channel model. The proposed trajectory model is very useful for characterizing irregular movements of mobile users. Furthermore, the pioneering idea of the paper provides a new method for the modelling of mobile radio channels under non-stationary conditions.

A Random Trajectory Approach for the Development of Nonstationary Channel Models Capturing Different Scales of Fading

This paper introduces a new approach to developing stochastic nonstationary channel models, the randomness of which originates from a random trajectory of the mobile station (MS) rather than from the scattering area. The new approach is employed by utilizing a random trajectory model based on the primitives of Brownian fields (BFs), whereas the position of scatterers can be generated from an arbitrarily 2-D distribution function. The employed trajectory model generates random paths along which the MS travels from a given starting point to a fixed predefined destination point. To capture the path loss, the gain of each multipath component is modeled by a negative power law applied to the traveling distance of the corresponding plane wave, whereas the randomness of the path traveled results in large-scale fading. It is shown that the local received power is well approximated by a Gaussian process in logarithmic scale, even for a very limited number of scatterers. It is also shown that the envelope of the complex channel gain follows closely a Suzuki process, indicating that the proposed channel model superimposes small-scale fading and large-scale fading. The local power delay profile (PDP) and the local Doppler power spectral density (PSD) of the channel model are also derived and analyzed.

Time-of-arrival, angle-of-arrival, and angle-of-departure statistics of a novel simplistic disk channel model

This paper introduces a novel simplistic geometrical disk scattering model in which the local scatterers are uniformly distributed in polar coordinates within a disk centered on the mobile station (MS). The proposed joint uniform distribution in polar coordinates results in a higher concentration of scatterers around the disk center and a lower concentration far from it. Furthermore, it is assumed that the base station (BS) is elevated to a non-scattering region and that a wave transmitted from the BS reaches the MS after a single bounce by one of the randomly distributed scatterers. Under the above-mentioned assumptions, we derive closed-form expressions for the joint probability density function (PDF) of the time-of-arrival (ToA) and angle-of-arrival (AoA), as well as for the joint PDF of the angle-of-departure (AoD) and AoA. From the joint distributions, we derive the marginal PDFs of the ToA, AoA, and AoD. Finally, we analyze the average delay and the delay spread of the proposed disk scattering model. The results presented in this paper enable the designers of cutting-edge mobile communication systems to study the system performance under simple, yet realistic, scattering conditions.

A Highly Flexible Trajectory Model Based on the Primitives of Brownian Fields—Part I: Fundamental Principles and Implementation Aspects

A fundamental drawback of synthetic mobility models is that the spatial configuration of the path is determined by the temporal features of the mobile station (MS), such as its speed. This is, however, not true in reality. This first part of our paper establishes a new approach for generating fully spatial random trajectory (mobility) models to which different speed scenarios can be applied. We employ the new approach to the proposal of a highly flexible trajectory model based on the primitives (integrals) of Brownian fields (BFs). We construct a drifted partial random bridge from a given starting point to a random terminating point in the 2D plane. If the bridge is partially established, a target zone with a predefined radius and center can be reached via random paths. If the bridge is fully established, a certain destination point can be achieved by means of random bridges. For the broken bridge, completely random terminating points are obtained. The smoothness of the path can be controlled by the primitives of the employed BF. The implementation aspects of the path model in simulation environments are discussed. In wireless communications, the model can be used for tracking (estimating) the location of the MS, performance analysis of mobile ad hoc networks, and channel modeling under non-stationary conditions.

A Highly Flexible Trajectory Model Based on the Primitives of Brownian Fields—Part II: Analysis of the Statistical Properties

In the first part of our paper, we have proposed a highly flexible trajectory model based on the primitives of Brownian fields (BFs). In this second part, we study the statistical properties of that trajectory model in depth. These properties include the autocorrelation function (ACF), mean, and the variance of the path along each axis. We also derive the distribution of the angle-of-motion (AOM) process, the incremental traveling length process, and the overall traveling length. It is shown that the path process is in general non-stationary. We show that the AOM and the incremental traveling length processes can be modeled by the phase and the envelope of a complex Gaussian process with nonidentical means and variances of the quadrature components. In accordance with empirical studies, we prove that the AOM process does not follow the uniform distribution. As special cases, we show that the incremental traveling length process follows the Rice and Nakagami-q distributions, whereas the overall traveling path can be modeled by a random variable following either the Gaussian or the lognormal distribution. The flexibility of the results is demonstrated and discussed extensively. It is shown that the results are in line with those of real-world user tracings. The results can be used in many areas of wireless communications.