We propose a wideband multipleinput multipleoutput (MIMO) cartocar (C2C) channel model based on the geometrical street scattering model. Starting from the geometrical model, a MIMO reference channel model is derived under the assumption of singlebounce scattering in lineofsight (LOS) and nonLOS (NLOS) propagation environments. The proposed channel model assumes an infinite number of scatterers, which are uniformly distributed in two rectangular areas located on both sides of the street. Analytical solutions are presented for the spacetimefrequency crosscorrelation function (STFCCF), the twodimensional (2D) space CCF, the timefrequency CCF (TFCCF), the temporal autocorrelation function (ACF), and the frequency correlation function (FCF). An efficient sumofcisoids (SOCs) channel simulator is derived from the reference model. It is shown that the temporal ACF and the FCF of the SOC channel simulator fit very well to the corresponding correlation functions of the reference model. To validate the proposed channel model, the mean Doppler shift and the Doppler spread of the reference model have been matched to realworld measurement data. The comparison results demonstrate an excellent agreement between theory and measurements, which confirms the validity of the derived reference model. The proposed geometrybased channel simulator allows us to study the effect of nearby street scatterers on the performance of C2C communication systems.
C2C communications is an emerging technology, which receives considerable attention due to new traffic telematic applications that improve the efficiency of traffic flow and reduce the number of road accidents [
In C2C communication systems, the underlying radio channel differs from traditional fixedtomobile and mobiletofixed channels in the way that both the transmitter and the receiver are in motion. In this connection, robust and reliable traffic telematic systems have to be developed and tested, which calls for new channel models for C2C communication systems. Furthermore, MIMO communication systems can also be of great interest for C2C communications due to their higher throughput [
All aforementioned channel models are narrowband M2M channel models. In contrast with narrowband channels, a channel is called a wideband channel or frequencyselective channel if the signal bandwidth significantly exceeds the coherence bandwidth of the channel. Owing to increasing demands for high data rate wideband communication systems employing MIMO technologies, such as MIMO orthogonal frequency division multiplexing (OFDM) systems, it is of crucial importance to have accurate and realistic wideband MIMO M2M channel models. According to IEEE 802.11p [
In the literature, numerous fundamental channel models with different scatterer distributions, such as the uniform, Gaussian, Laplacian, and von Mises distribution, have been proposed to characterize the angleofdeparture (AOD) and the angleofarrival (AOA) statistics. In [
In contrast to our previous work in [
In our model, we consider a 2D street scattering environment to reduce the computational cost by still guaranteeing a good match between the reference model and measured channels. A typical propagation scenario for the proposed model is illustrated in Figure
A typical propagation scenario along a straight street in urban areas.
The rest of this paper is organized as follows. Section
This section briefly describes the geometrical street scattering model for wideband MIMO C2C channels. The proposed geometrical model describes the scattering environment in an urban area, where the scatterers are located in two rectangular areas on both sides of the street as illustrated in Figure
The geometrical street scattering model with local scatterers uniformly distributed in two rectangular areas on both sides of the street.
In this section, we derive the reference model for the MIMO C2C channel under the assumption of LOS and NLOS propagation conditions. From Figure
Note that the singlebounce scattering components bear more energy than the doublebounce scattering components. Hence, in our analysis, we model the diffuse component
It is noteworthy that one can also find articles [
The TVTF of the LOS component is given by
In (
The position of all local scatterers
In this section, we derive a general analytical solution for the STFCCF, from which other correlation functions, such as the 2D space CCF, the TFCCF, the temporal ACF, and the FCF can easily be derived.
According to [
In Section
The infinitesimal power of the diffuse component corresponding to the differential axes
The 2D space CCF
The TFCCF of the transmission link from
The temporal ACF of the transmission link from
Computing the Fourier transform of the temporal ACF
The two most important statistical quantities characterizing the Doppler PSD
The Doppler spread
The frequency characteristics of the reference model are described by the FCF
The objective of this section is to determine the set of model parameters
In (
For the measured channels in [
Measurementbased parameters of the geometrical street scattering model and the resulting average Doppler shift and the Doppler spread.
Model parameters  Propagation environment  

Urban LOS  Urban NLOS  Rural LOS  Highway LOS  Highway NLOS  

546.28 (1249)  537.03 (908.3)  546.52 (1236)  547.69 (1207)  546.88 (1193) 

198.96 (198.77)  76.46 (1.1113)  20.89 (18.25)  199.8 (200)  0.01 (0.01) 

223.55 (219.77)  262.1 (209.97)  463.72 (491.65)  511.68 (442.62)  491.67 (481.97) 

10.42 ( 
2.12 (1.18)  15.28 (4.63)  17.62 (19.78)  1.3 (1.3) 

19.82 (6.6)  20 (7.06)  14.57 (9.4)  19.63 (25)  20 (9.4) 

238.6  236.7  186.77  896.7  749.6 

0.485  0  0.27  0.4  0 
Measured  
average Doppler  −20  103  201  209  −176 
shift 

Theoretical  
average Doppler  −20  102.67  200.55  208.8  −110 
shift 

Measured  
Doppler  341  298  782  761  978 
spread 

Theoretical  
Doppler  341  298  782.03  760.88  941 
spread 
The reference model described above is a theoretical model, which is based on the assumption that the number of scatterers (
This section illustrates the analytical results given by (
As an example for our geometrical street scattering model, we consider rectangular scattering areas on both sides of the street with a length of
In Figure
Absolute value of the 2D space CCF
Absolute value of the 2D space CCF
Figures
Absolute value of the TFCCF
Absolute value of the TFCCF
Figure
Absolute values of the ACFs
Finally, Figure
Absolute values of the FCFs
In this paper, a reference model for a wideband MIMO C2C channel has been derived by starting from the geometrical street scattering model. Taking both LOS and NLOS propagation conditions into account, we have analyzed the 2D space CCF and the TFCCF of the reference model. To find a proper simulation model, the SOC principle has been applied. It has been shown that the SOC channel simulator approximates the reference model with high accuracy with respect to the temporal ACF and the FCF. An excellent fitting of the average Doppler shift and the Doppler spread of the reference model to the corresponding quantities of measured channels has validated the usefulness of the proposed reference model. Further extensions of the proposed wideband MIMO C2C channel model incorporating the nonstationarity properties of realworld C2C channels are planned for future work.