Wireless Network Design: Optimization Models and Solution ...

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3 Channel Models for Wireless Communication Systems 53 munication between the transmitter and receiver. This type of fading is also called Flat fading. Ricean channel: The amplitude of a channel which is modeled as a non-zero mean complex Gaussian random process has a Ricean distribution. Such channels are called Ricean channels and occur when there is Line-Of-Sight (LOS) communication between the transmitter and receiver. The Ricean pdf is given in [31]. The above channels are characterized by the mean and variance of the channel, which is modeled as a Gaussian random process. For the Ricean channel, an additional factor called the k − f actor is defined as the ratio of total power in the LOS path to the total scattered power received. If this ratio is zero, it implies Rayleigh fading. 3.4.3 Doppler Spread Due to Relative Motion Between Transmitter and Receiver and Coherence Time Consider a mobile receiver moving at a velocity v and receiving multiple signals from various directions (due to obstacles). Consider the case where there is no direct LOS path and hence Rayleigh fading is considered. The signal is assumed to be a narrowband signal centered around the carrier frequency fc. Considering the case that the signal is received from all directions and assuming that they are all of equal amplitude, the power spectrum of the Rayleigh fading channel is given by S( f ) = π fd b0 � 1 − { f / fd} 2 (3.14) where fd is the doppler frequency and the equation is valid for f < fd . The shape of the spectrum is like a ‘bathtub with infinitely high steep walls’. Jakes [50] proposed a technique to simulate a fading channel with the above doppler spectrum. The technique involves considering several oscillators and appropriately combined after suitable amplitude scaling. This is popularly known as the Jakes spectrum as shown in Figure 3.1. Consider the case where the receiver and transmitter are stationary. In this case too, one gets a Doppler spread due to the movement of the scatterers (for example, branches of trees, moving traffic) between the transmitter and receiver. The spectrum of such a channel was obtained through measurements carried out at Stanford University in the 2.5GHZ band [11]. A mathematical model, obtained from the measurement data, is given by � S f ixed( f ) = 1 − { f / fm} 2 (3.15) fm is the maximum doppler frequency (typically 2Hz to 4Hz). This spectrum shape is an ‘inverted cup’ as shown in Figure 3.2.
54 K. V. S. Hari Fig. 3.1 Normalized power spectral density for Rayleigh fading with Doppler spread of 277 Hz. Fig. 3.2 Normalized power spectral density for fading channel with transmitter and receiver at fixed locations with Doppler spread close to 3Hz. Coherence time, Tc, is the time during which the channel is assumed to be invariant with time. It can be approximately obtained from the Doppler spread characterization. One such approximation is given [34] as Tc = 0.423/ fd. where fd is the maximum Doppler frequency.
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International Series in Operations
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Editors Jeff Kennington Eli Olinick
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vi Preface assistance. The work of
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viii Contents 3.4.1 Experiments to
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x Contents 8.3.2 The Solution Proce
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xii Contents References . . . . . .
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List of Contributors Khaldoun Al Ag
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List of Contributors xvii Nitin Sal
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Chapter 1 Introduction to Optimizat
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104 Eli Olinick 93 85 160 16 38 21
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106 Eli Olinick Amaldi et al. [7] p
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108 Eli Olinick levels (possibly le
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110 Eli Olinick gmℓ ∑ ∑ m∈M
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112 Eli Olinick Using bk to denote
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114 Eli Olinick 5.3.5 Additional De
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116 Eli Olinick capacity, provide n
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118 Eli Olinick ficult optimization
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120 Eli Olinick and-bound so that t
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122 Eli Olinick solution times. Cai
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124 Eli Olinick 27. Glover, F.: Tab
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Chapter 6 Optimization Based WLAN M
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6 Optimization Based WLAN Modeling
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Chapter 7 Spectrum Auctions Karla H
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7 Spectrum Auctions 149 full value.
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7 Spectrum Auctions 151 also decide
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7 Spectrum Auctions 153 disclosed t
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7 Spectrum Auctions 155 focused on
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7 Spectrum Auctions 157 bidders to
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7 Spectrum Auctions 159 in the regi
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7 Spectrum Auctions 165 prior round
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7 Spectrum Auctions 169 lem has sup
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7 Spectrum Auctions 171 bidder on a
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7 Spectrum Auctions 173 some discus
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7 Spectrum Auctions 175 21. Dunford
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Chapter 8 The Design of Partially S
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8 The Design of Partially Survivabl
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Part III Optimization Problems in A
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200 Khaldoun Al Agha and Steven Mar
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Chapter 10 Compact Integer Programm
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10 Integer Programming Models for P
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Chapter 11 Improving Network Connec
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11 Improving Network Connectivity i
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Chapter 12 Simulation-Based Methods
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12 Simulation-Based Methods for Net
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296 Hang Jin and Li Guo formance in
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298 Hang Jin and Li Guo (ISI) as lo
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300 Hang Jin and Li Guo ARQ (HARQ)
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302 Hang Jin and Li Guo 13.3 Radio
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304 Hang Jin and Li Guo Table 13.2
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306 Hang Jin and Li Guo is transmit
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308 Hang Jin and Li Guo uplink powe
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310 Hang Jin and Li Guo The link ad
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314 Hang Jin and Li Guo 13.4.4.3 Ex
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316 Hang Jin and Li Guo Fig. 13.9 P
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318 Hang Jin and Li Guo 1. Guarante
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Chapter 14 Cross Layer Scheduling i
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14 Cross Layer Scheduling in Wirele
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Chapter 15 Major Trends in Cellular
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15 Major Trends in Cellular Network
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