In the last decade, the nonstationary properties of channel models have attracted more and more attention for many scenarios, that is, vehicle-to-vehicle (V2V), mobile-to-mobile (M2M), and high-speed train (HST). However, little research has been done on the real-physical channel model. In this paper, we propose a generalized three-dimensional (3D) nonstationary channel model, in which the scatterers are assumed to be distributed around the transmitter (Tx) and receiver (Rx) on a two-sphere model. By employing the von Mises-Fisher distribution, the mean values of the azimuth angle of departure (AAoD) and elevation angle of departure (EAoD) and the azimuth angle of arrival (AAoA) and elevation angle of arrival (EAoA) are tracked by time-variant (TV) Brownian Markov (BM) motion paths, which ensure the nonstationarity of the proposed channel model. Moreover, the TV autocorrelation function (ACF) and Doppler power spectrum density (DPSD) of the proposed nonstationary channel model are calculated by using signal processing tools, for example, fast Fourier transform (FFT) and short-time Fourier transform (STFT). In addition, the simulation results show that the TV scatterer distribution results in a nonstationary nonisotropic channel model, and the proposed model can be employed to simulate the 3D nonstationary channel model.

The transmission channel is one of the most crucial parts in mobile communication systems, while the generation of an accurate and effective channel model for testing of communication systems represents a particular challenge. The majority of existing channel models in the literature rely on the assumption of wide-sense stationary (WSS) and uncorrelated scattering (US) [

The channel modeling can be classified into three categories, that is, deterministic, geometry, and correlation statistics [

In this paper, we propose a more general 3D geometric situation where the scatterers are assumed to be distributed around the user in a sphere area. By employing the von Mises-Fisher scattering distributions, the centers of the AoDs and AoAs scattering distribution are tracked by TV Brownian motion paths [

The remainder of this paper is organized as follows: Section

Let us consider a narrowband V2V communication channel with omnidirectional antennas. The radio propagation environment around the transmitter and the receiver is characterized by 3D nonisotropic scattering under line-of-sight (LoS) and none line-of-sight (NLoS) conditions. Figure

The proposed 3D two-sphere channel model.

Multiple uncorrelated fading processes bring the complex envelope, which can be written as

The normalized ACF between any two complex fading envelopes is defined as

The DPSD has been used for nonisotropic scattering channels and the theoretical expression DPSD is

The VMF distribution [

In this section, we will bring the temporal Brownian random process [

When

When

Due to the fact that the same statistical properties impact the receiver between the AoA distribution motion and the MS random movement, this paper proposes that the variation of the AoA distribution can be used for simulating a 3D nonstationary channel. To model the motion process of the AoA distribution in the 3D plane, we provide a path model with BM movement components along the elevation and azimuth plane. The fluctuations of the motion path especially are modeled by two independent temporal BM processes:

In this section, we consider the TV CIRs, ACF, and DPSD of the nonstationary process. At first, we introduce the BM process to the VMF scattering distribution, and the TV-VMF PDF can be rewritten as

Then the TV CIRs of the proposed model in (

It is noteworthy that the definition of the TV ACF keeps the symmetrical delay characteristic

In this section, simulations are carried out to illustrate the nonstationary properties of our proposed 3D TV channel model based on the VMF scatterer distribution. The impact of the model parameters on the VMF scatterer distribution is investigated first. Then, the nonstationary properties of the proposed two-sphere channel model are evaluated and analyzed in terms of the AoAs and AoDs motion path at the Tx and Rx, the TV ACF of the complex channel gain, and the TV DPSD.

Firstly, we consider the performance of the VMF scatterers distribution. From Figure

2D VM PDF.

Effect of the concentration parameter.

3D VMF PDF.

Secondly, Figure

The simulation of Brownian paths.

Thirdly, Figures

The absolute values of the temporal ACF for the proposed 3D TV channel model.

The PDF of amplitude.

The PDF of phase.

Figure

Finally, we assume that the mean elevation and azimuth angles are moving along the TV-BM motion paths shown in Figure

Time-variant ACF.

Time-variant DPSD (FFT for high VTD).

Time-variant DPSD (STFT for high VTD).

Time-variant ACF (low VTD).

Time-variant DPSD (FFT for low VTD).

Time-variant DPSD (STFT for low VTD).

In this paper, a novel 3D nonstationary channel model for V2V is proposed. By employing the proposed temporal BM process with the VMF PDF scatterer distribution, we derive a nonstationary nonisotropic channel model which can be applied to simulate the 3D channels in real time. Moreover, the dynamic changes of the local ACF and PSD have been provided. Lastly, the nonstationary properties of the proposed channel model are verified by simulation. In particular, we have proven that the STFT is also valid for analyzing nonstationary channel models.

The authors declare that they have no competing interests.

This research is supported in part by China Important National Science and Technology Specific Projects (no. 2013ZX03001020-002), by the National Key Technology Research and Development Program of China (no. 2012BAF14B01), by the National Natural Science Foundation of China (no. 61171105 and no. 61322110), by the 863 Program Project (no. 2015AA01A703), and by the Doctor Funding Program (no. 201300051100013).