LCR and AFD

Figure 6.6 shows the LCR of a mobile-to-mobile Rician channel fading enve-lope obtained using the sum-of-sinusoids method and that from theoretical analysis. As can be seen, LCR decreases with increase in the Rician fac-tor. This phenomenon can be explained by the fact that channel fading has greater correlation with larger amount of LOS components. Once the correlation arises, the change in channel fading decreases.

Figure 6.7 shows the analytical and simulated values of the normalized AFD for different Rician factors. As shown in the figure, the larger the Rician factor, the larger the AFD is. This property is caused by higher correlation of fading envelope for a larger Rician factor. Thus, if the signal envelope fades below a specified level, it is less likely that it will exceed the level.

The numerical results for LCR and AFD show some deviation of the simulation from the theoretical values, especially for small K (1 and 3). The

simulation curves consistently fall below the analytical curves, which do not occur for the larger values of K. This is because when K is small, the scatterers term will dominate the double-ring model. The simulation can only produce finite scatterers which cannot approach the ideal case enough, thus the deviation occurs. When K is large, the LOS term dominates the double-ring model, hence the problem of finite number of scatterers is not so significant compared to the cases of small values of K.

6.6 Conclusions

In this chapter, a sum-of-sinusoids-based mobile-to-mobile Rician fading sim-ulator is developed. The double-ring scattering model is proposed for char-acterizing the mobile-to-mobile communication environment with LOS com-ponents. Furthermore, the theoretical correlation functions of the mobile-to-mobile Rician channel are derived and its accuracy is verified by simulations.

The LCR and AFD of the mobile-to-mobile Rician fading channel are derived.

Finally, it is proved that the proposed sum-of-sinusoids approximation devel-oped from the double-ring with a LOS component model can approach the theoretical value more closely than the single-ring model at a slightly higher cost of computation loads.

Figure 6.1: Scattering environment in a mobile-to-mobile system with a LOS component.

Figure 6.2: Relative velocity v3 from the TX with velocity v1 to the RX with velocity v₂.

Figure 6.3: Single-ring scattering environment for a mobile-to-mobile Rician fading channel.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

−1

−0.8

−0.6

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1

Time delay τ (sec)

Re[R

(τ )]

Simulaiton Ideal K=9

K=3 K=1 K=0

Figure 6.4: The real part of the autocorrelation of the complex envelope Z(t), where N = M = 8 for K = 0, 1, 3, and 9.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

−1

−0.8

−0.6

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1

Time delay τ (sec)

Re[R

(τ )]

Single Ring N=8 Single Ring N=64 Double Ring N=M=8 ideal

Figure 6.5: The real part of the autocorrelation of the fading envelope of double-ring and single-ring scattering models for K = 1.

−12 −10 −8 −6 −4 −2 0 2 4 10⁻⁵

10⁻⁴ 10⁻³ 10⁻² 10⁻¹ 10⁰ 10¹

Level ρ (dB)

Normalized Envelope LCR L

/f

Analysis K = 1 Simulation K = 1 Analysis K = 3 Simulation K = 3 Analysis K = 7 Simulation K = 7 Analysis K = 10 Simulation K = 10

Figure 6.6: Normalized envelope level crossing rate for mobile-to-mobile Ri-cian fading. Solid line denotes the theoretical results and the dashed line denotes the simulation results, where ρ = √^R

Ω_p.

−12 −10 −8 −6 −4 −2 0 2 4 10⁻²

10⁻¹ 10⁰ 10¹ 10² 10³ 10⁴

Level ρ (dB)

Normalized Envelope AFD T

*f

Analysis K = 1 Simulation K = 1 Analysis K = 3 Simulation K = 3 Analysis K = 7 Simulation K = 7 Analysis K = 10 Simulation K = 10

Figure 6.7: Normalized average fade duration for a mobile-to-mobile Rician fading channel for K = 1, 3, 7, and 10.

Chapter 7

Modeling and Capacity Fades Analysis of MIMO Rician

Channels in Mobile Ad Hoc Networks

Multiple-input multiple-output (MIMO) mobile ad hoc networks have been receiving increasing attention in both commercial and military applications.

Just as in cellular networks, MIMO technologies can benefit ad hoc networks by providing the diversity and capacity advantages as well as the spatial degree of freedom in designing the media access control (MAC) protocol.

However, one fundamental issue of MIMO mobile ad hoc networks is how to accurately model the impact of spatial/temporal channel correlation in the mobile-to-mobile communication environment. In such a channel, a line-of-sight (LOS) component and different scattering environments will affect both ergodic capacity and average capacity fade duration of the MIMO system.

In this chapter, based on the correlated double-ring scattering model we

sug-gest a sum-of-sinusoids MIMO mobile-to-mobile channel simulation method, which can characterize the spatial/temporal channel correlation and Rician fading effect. We examine how often the MIMO capacity experiences the fades and relate this to the Rician factor.

7.1 Motivation

Multiple-input multiple-output (MIMO) antenna technique has recently emerged as one of the most significant breakthroughs in communications. The fourth generation (4G) cellular system [110] and the next generation high-speed IEEE 802.11n [111] wireless local area network (WLAN) all adopt the MIMO technique to deliver capacity and diversity gains.

Meanwhile, another communication paradigm – ad hoc networks – has become an important alternative for next generation wireless systems. In contrast to conventional cellular systems with a master-slave relation between the base station and mobile users, nodes in ad hoc networks adopt peer-to-peer communications. Specifically, this communication is supported by direct connection or multiple hop relays without fixed wireless infrastructure.

Ad hoc networks have been enabled in many standards such as Bluetooth and IEEE 802.11 WLAN. Ad hoc networking is considered the key enabling technique of many future wireless systems, such as wireless mesh networks [112] and cognitive radio [113].

Unlike conventional mobile-to-fixed base station systems that have been benefited from the MIMO technique, how and to what extent the ad hoc networks can benefit from the MIMO technique is still an open research area. One fundamental issue is how to accurately model the impact of spatial/temporal correlation on MIMO capacity from the viewpoint of the

mobile-to-mobile communication. Scattering model and the line-of-sight (LOS) component are two important factors that need to be considered.

First, in a mobile-to-mobile environment, the antenna heights of both the transmitter and the receiver are lower than the surrounding objects. Thus, the signal in a mobile-to-mobile environment will experience a richer scat-tering effect than in a mobile-to-base environment [20, 26, 114]. Second, an LOS component may more likely exist in a short distance mobile-to-mobile application than in a long-distance mobile-to-base environment. In [115], the distribution of the Rician K factor was modeled as lognormal, with the me-dian as a function of distance: K ∝ (distance)^−0.5. Implicitly, the K factor increases as the distance decreases. Thus, the Rician fading effect cannot be neglected in a short-distance mobile-to-mobile communication environment.