**2. Background**

VANETs have been envisioned for safety, traffic management, and commercial applications, such as information notices of hazardous road conditions, traffic congestion, or sudden stops, furthermore, commercial services (e.g., data exchange, infotainment, rear-seat multiplayer games) (Boban et al., 2009)-(Abbas et al., 2010). Recently, the Quality of Service (QoS) and network security are used to determine the feasibility of such applications. To achieve the desirable QoS and network security, many techniques focusing on the design and optimization of routing protocol in VANETs have been proposed in (Lwinmuller et al., 2006)-(Saleet et al., 2010). However, the fundamental issue centers on the accurate description of the characteristics and mechanism of wave propagation in VANETs, so it is essential to establish a reasonable radio propagation model for VANET channels, which help to understand the characteristics of the channel and take some effective steps to improve the QoS and network security.

Direct communication between vehicles in VANETs may be supported by the deployment of Mobile Ad Hoc Networks (MANETs), which does not rely on fixed infrastructure and can accommodate a constantly evolving network topology (Boban et al., 2009; Vahid, 2009). More recently, infrastructure-to-vehicle (I2V) and inter-vehicle communication (IVC) links are being evaluated for a variety of applications. I2V channels is similar to the traditional cellular systems, the base station is stationary, and only the mobile terminal are in motion. However,

double mobile nodes in a two-dimensional (2-D) uniform scattering environment. It is a deterministic channel model without considering the specific characteristics, such as the effect

<sup>159</sup> Sum-of-Sinusoids-Based Fading Channel Models

Motivated by the recently presented IVC fading channel models in (Patel et al., 2005; Zajic & Stuber, 2006; Wang et al., 2009), we propose novel statistical and deterministic SoS models for Rician channels in VANETs. As described in (Patel et al., 2005), the properties, like auto-correlation and cross-correlation of the statistical models, differ for each simulation trial, but converge in a statistical sense to the desired properties over an infinite number of simulations. Therefore, such models are termed statistical models. In contrast, the properties of deterministic model, are identical for all simulation trials, hence, they can be predetermined, such models are called deterministic models. We provide detailed simulation results to verify and compare the performance of the proposed models in next sections.

The remainder of this chapter is organized as follows. Section 3 discusses the related work reported in the literature. In Section 4, we extend Akki and Haber's mathematical reference model for IVC channels by introducing the line-of-sight (LOS) components and derive the statistical properties of the extended model. Section 5 establishes new statistical and deterministic SoS simulation models. Their statistical properties are also derived and verified in this section. In Section 6, performance analysis is carried out through comparisons between the reference and the two SoS models. At last, the conclusion remarks are given in

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

of antenna and dynamic distribution of received multi-path wave.

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

Section 7.

**3. Related research work**

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 of wave propagation for VANETs.

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 (Michelson & Chuang, 2006).

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 by a set of measurements.

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 double mobile nodes in a two-dimensional (2-D) uniform scattering environment. It is a deterministic channel model without considering the specific characteristics, such as the effect of antenna and dynamic distribution of received multi-path wave.

Motivated by the recently presented IVC fading channel models in (Patel et al., 2005; Zajic & Stuber, 2006; Wang et al., 2009), we propose novel statistical and deterministic SoS models for Rician channels in VANETs. As described in (Patel et al., 2005), the properties, like auto-correlation and cross-correlation of the statistical models, differ for each simulation trial, but converge in a statistical sense to the desired properties over an infinite number of simulations. Therefore, such models are termed statistical models. In contrast, the properties of deterministic model, are identical for all simulation trials, hence, they can be predetermined, such models are called deterministic models. We provide detailed simulation results to verify and compare the performance of the proposed models in next sections.

The remainder of this chapter is organized as follows. Section 3 discusses the related work reported in the literature. In Section 4, we extend Akki and Haber's mathematical reference model for IVC channels by introducing the line-of-sight (LOS) components and derive the statistical properties of the extended model. Section 5 establishes new statistical and deterministic SoS simulation models. Their statistical properties are also derived and verified in this section. In Section 6, performance analysis is carried out through comparisons between the reference and the two SoS models. At last, the conclusion remarks are given in Section 7.
