**3. Related research work**

2 Will-be-set-by-IN-TECH

for IVC channels, a variety of applications, such as intelligent transportation systems and ad hoc networks, are based on mobile-to-mobile communications. Both the base station and mobile terminal are all in motion and the transmitted and received signals are all affected by the surrounded scatterers. So channel modeling in VANETs should be considered the both characteristics in I2V and IVC channels. More recently, infrastructure-to-vehicle (I2V) and inter-vehicle communication (IVC) links are being evaluated for VANETs and a LOS or NLOS environment should also be considered. The I2V and IVC channels can be distinguished by vehicle speed ratio and the difference of LOS and NLOS environment can also be represented by Rician K factor. Therefore, a comprehensive channel is needed to wholly describe the scene

An important factor of a vehicular channel model is the mobility (Gowrishankar et al., 2007; Yoon & Noble, 2006) by including the mobility of nodes and the channel variability. Channel variability, is not well modeled in today's wireless vehicle networks. (Pawlikowski et al., 2002) reports that simplistic models may not be practical and it is also different to draw conclusions on the real performance of the upper layers. Designers require statistical models that can accurately capture the characteristic of propagation behavior observed at both mobile vehicles

Currently, free space and two ray ground channel models are the most popular propagation models for simulation in vehicular wireless networks (NS, 2000). For the free space channel model, it describes an ideal propagation characteristic, and the received power depends on the transmitted power, the gain of antenna, and the distance of transmitter-receiver. While for the two way ground model, it assumes that the received signal is the sum of the direct line of sight path and the reflected path from the ground. However, the model does not take obstacles into consideration. It is also too ideal for short transmitter-receiver separation distances, as it assumes that signals have a perfect 250m radius range. On the other hand, QualNet supports open-space propagation as well as stochastic propagation models such as Rayleigh, Rician and Log-normal fading, in which all models describe the time-correlation of the received signal power. Rayleigh model considers indirect paths between the transmitter and the receiver, while Rician model considers when there is one dominant path and multiple indirect signals. OPNet supports open-space propagation models as well as an enhanced open-space model that accounts for hills, foliage and atmospheric affects(OPNET, 2000). Furthermore, obstacle effects are combined in (Jardosh et al., 2006; Jradosh et al., 2005; Mahajan et al., 2007), but the propagation characteristic is limited to line-of-sight. (Stepanoy & Rothermel, 2008) applies a radio planning tool and validates the evaluation for the impact of a more realistic propagation

In a dense urban area, path loss, shadow fading and short-term variants are the main factors affecting the communication quality. Path loss and shadowing fading determine the effective communication distance between two adjacent vehicles, while multi-path and Doppler spectrum caused by the sum of absolute speeds of individual nodes affect the quality of service (QoS) in inter-vehicle networks. However, it is noted that some of these effects can be avoided, such as by increasing the height of the antenna, and the inerratic variations is just relative to the distance between transmitter and receiver. Here, the model is focused on the short-term variants, especially for Doppler spectrum model caused by both high mobile vehicles. The Doppler spectrum model in (Clarke, 1968; Gans, 1972) for wireless cellular network cannot really be used for link between double mobile nodes. Akki and Haberp(Akki & Haber, 1989) consider a Doppler spectrum model for radio link between

of wave propagation for VANETs.

(Michelson & Chuang, 2006).

by a set of measurements.

A number of techniques have been proposed for the modeling and simulation of I2V channels. Among them, Clarke (Clarke, 1968) proposed the statistical theory of mobile-radio reception, and a power-spectral theory of propagation in the mobile-radio was developed by Gans in (Gans, 1972). The Jakes' simulator (Jakes, 1994; Dent et al., 1993), which is a simplified simulation model of Clarke's model (Clarke, 1968), has been widely used for frequency nonselective Rayleigh fading channels. Various modified models (Patzold et al., 1998)-(Li & Huang, 2002) and improvements (Xiao & Zheng, 2002)-(Zheng & Xiao, 2003) of Jakes' simulator for generating multiple uncorrelated fading waveforms needed for modeling frequency selective fading channels and multiple-input multiple-output (MIMO) channels have been reported. It is commonly perceived that Jakes' simulator (and its modifications) is more computationally efficient than Clarke's model since Jakes' simulator needs only one fourth the number of low-frequency oscillators as needed in Clarke's model. However, recently Pop and Beaulieu (Pop & Beaulieu, 2001) put forward a view that Jakes' simulator and its variants are not wide sense stationary (WSS), and that the reduction of simulator oscillators based on azimuthal symmetries lacks sufficient basis (Xiao et al., 2006). They improved the simulator by introducing random phase shifts in the low-frequency oscillators to remove the stationary problem in (Pop & Beaulieu, 2001). But Xiao and Zheng (Zheng & Xiao, 2003) gave a statistical analysis of Clarke's model with a finite number of sinusoids and showed that the Pop-Beaulieu simulator has also deficiencies in some of its higher-order statistics. it was further proved in (Xiao et al., 2002) that second-order statistics of the quadrature components and the envelope do not match the desired ones. Moreover, even in the limit as the number of sinusoids approaches infinity, the auto-correlations and cross-correlations of the quadrature components, and the auto-correlation of the squared envelope of the improved simulator, fail to match the desired correlations. Also, Jakes's

**4. The mathematical reference model**

*<sup>Y</sup>*(*t*) = <sup>2</sup>

1 *v*

**Definitions:**

follows.

*a* = |**v**1|/|**v**2|.

direction, respectively.

uniformly distributed over [−*π*,*π*).

a LOS component can be expressed as

where *f*<sup>0</sup> = (|**v**2| cos *θ*<sup>2</sup> − |**v**1| cos *θ*1)/*λ*.

complex channel envelope as (Akki & Haber, 1989)

*N*

*N* ∑ *n*=1

with Rician K-factor and Vehicle Speed Ratio in Vehicular Ad Hoc Networks

phase uniformly distributed on [−*π*,*π*), independent of *α*�

Fig. 1. IVC channel with a LOS component in VANETs

• the Doppler frequency caused by **v***x* and **v***y* are *fx*, *fy*.

*<sup>L</sup>* <sup>=</sup> <sup>√</sup>

Akki and Haber's simulation model for IVC channels with no LOS component gives the

<sup>161</sup> Sum-of-Sinusoids-Based Fading Channel Models

where *f*<sup>1</sup> and *f*<sup>2</sup> are the maximum Doppler frequencies due to the motion of the transmitter and the receiver, respectively. *N* is the number of propagation paths, *αn* and *βn* are the random angle of departure (AOD) and the angle of arrival (AOA) of the *nth* path measured with respect to the transmitter and the receiver velocity vectors, respectively, and *θn* is the random

Transmitter Receiver

*y*

Line-of-sight

• In Fig. 1, the velocities of transmitter and receiver are **v**1,**v**2, *λ* is the carrier wavelength,

• **v***x* and **v***y* are the relative velocity of receiver to the transmitter in the x-axis and y-axis

The angle between **v***x* and LOS component is 0◦ and the direction of **v***y* is perpendicular to the LOS component. From (Gregory, 2003), the Doppler frequency caused by LOS component in the IVC environment is | *fx*| = (|**v**2| cos *θ*<sup>2</sup> − |**v**1| cos *θ*1)/*λ*. The LOS component is given by

where *K* is the ratio of the specular power to the scattering power, and the initial phase *φ*<sup>0</sup> is

With reference to (1) and (2), the received complex envelope of the IVC fading channel with

*<sup>Z</sup>*(*t*) = *<sup>Y</sup>*(*t*) + <sup>√</sup>*<sup>K</sup>* exp(*j*2*<sup>π</sup> <sup>f</sup>*0*<sup>t</sup>* <sup>+</sup> *<sup>φ</sup>*0)

Assuming omnidirectional antennas and isotropic scattering conditions around the transmitter and the receiver, the statistical properties of the reference model are given as

• *θ*1,*θ*<sup>2</sup> are the angle between **v**1,**v**<sup>2</sup> and the LOS component, respectively.

exp{*j*[(2*π f*<sup>1</sup> cos(*αn*)*t* + 2*π f*<sup>2</sup> cos(*βn*)*t* + *θn*)]} (1)

*ns* and *β*�

*K* exp[*j*{2*π*(|**v**2| sin *θ*<sup>2</sup> − |**v**1| sin *θ*1)}*t* + *φ*0] (2)

<sup>√</sup><sup>1</sup> <sup>+</sup> *<sup>K</sup>* (3)

<sup>2</sup> <sup>1</sup>

2 *v* 

1 *v*  *ns* for all *n*.

*x*

original simulator and published modified versions, have similar problems with these second-order statistics. In (Xiao et al., 2006), Xiao and Zheng proposed a statistical SoS model for I2V channels which employs a zero-mean stochastic sinusoid as the specular LOS component, in contrast to previous Rician fading simulators that utilize a non-zero deterministic specular component. The statistical properties of the new simulators are confirmed by extensive simulation results, showing good agreement with theoretical analysis in all cases.

Channel modeling in VANETs should be considered the both characteristics in I2V and IVC channels. Those I2V channel models may not fully reflect the mobility characteristics of VANET channels. Several works in the open literature have been studied in this area (Akki & Haber, 1989)-(Patel et al., 2003). The theoretical analysis of the IVC channels for urban and suburban land communication channels was first developed by Akki and Haber (Akki & Haber, 1989; Akki, 1994), and was extended by Vatalaro and Forcella in (Vatalaro & Forcella, 1997) to account for scattering in three dimensions (3-D), and by Linnartz and Fiesta in (Linnartz & Fiesta, 1996) to include LOS scenarios. Some channel measurement results for narrowband IVC communications have been presented in (Kovacs et al., 2002; Maurer et al., 2002; Cheng et al., 2007). R.Wang and D.Cox (Wang & Cox, 2002) introduced the discrete line spectrum method to simulate the IVC channels. Whereas the accuracy of this method was assured only for short-duration waveforms, Moreover, the numerical integrations required in determining the discrete set of frequencies and corresponding Doppler spectrum make the implementation complex and not easily reconfigurable for different Doppler frequencies or the Doppler frequency ratio. So it is not always suitable for real time hardware channel emulation or software simulation. A method based on inverse fast Fourier transform (IFFT) was presented by D.J.Young and N.C.Beaulieu (Young & Beaulieu, 2000). This method was more accurate and efficient than the method of discrete line spectrum, but the IFFT-based method requires a complex elliptic integration. The authors in (Patel et al., 2003) proposed a "double-ring" scattering model to simulate the IVC scattering environment and developed modifications of two SoS models (statistical and deterministic SoS models) often used to simulate I2V channels in (Patel et al., 2005). More recently, Wang and Liu (Wang et al., 2009) presented a scattering Rician IVC fading model with a LOS component by SoS method, which is based on the Rayleigh model proposed in (Patel et al., 2005). A new statistical SoS in (Zajic & Stuber, 2006) model is proposed for Rayleigh IVC fading channel to directly generate multiple uncorrelated complex envelope, which shows faster convergence than the model in (Patel et al., 2005) and adequate statistics with small simulation trials.

The statistical properties of Xiao and Zheng's simulators in (Xiao et al., 2006) are confirmed by extensive simulation results, showing good agreement with theoretical analysis in all cases and is a typical model with high quality for I2V channels. But with the development of mobile ad hoc networks, VANET channel modeling often involves the IVC channels, which is generally considered as the common case of the I2V channels. Therefore, in this chapter, we mainly focus on the modeling for IVC channels in VANETs. This motivates us to extend the new statistical SoS model in (Zajic & Stuber, 2006) by employ a LOS component to characterize the IVC channels of VANETs. Furthermore, the deterministic SoS model, proposed in (Patel et al., 2005), are employed to simulate Rayleigh IVC channel for its reduced-complexity and theoretical and simulation results verified the usefulness of the model. Seeking to find a more suitable Rician simulation model for VANET channels, we also introduce a LOS component to extend the deterministic SoS model for comparison.
