Wireless Network Design: Optimization Models and Solution ...

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2 Introduction to Wireless Communications 41 lower than SIR ¯ and not changing their power when their SIR is greater than SIR ¯ all user powers would increase to infinity and the system would become unstable. However, it can be proved that in this case, there exists an optimum transmit power level for each user that results in a stable operating point. This optimum operating point can be obtained as the solution to the following optimization problem: min ∑ Pm m∈M (2.29) s.t.SIRmb ≥ SIR ¯ (2.30) As the keen reader might recognize, (2.29) is a centralized problem and requires global knowledge of all parameters to solve. However, it turns out that there exists a simple distributed and iterative solution to this problem. This solution only relies on each link observing its own SIR during iteration n and modifying its transmission power in iteration n + 1, as follows: Pm(n + 1) = ¯ SIR(m) SIRmb(n) Pm(n) (2.31) One of the features of this solution is that the updates for each user can occur independent of the other users and in a completely asynchronous manner. In most cases, the number of iterations required to achieve convergence is small. It is typically assumed that all system parameters including channel gains, network topology variations due to mobility, variation in the number of users occur on a time-scale that is larger than what is required to obtain convergence. Several variations of this problem and resulting solutions have been studied in the literature. For instance, problems that make the solution robust, opportunistic, and couple power control with beam-forming and scheduling have been investigated [13]. Ad-hoc Networks: The second example of power control is from ad-hoc networks. An ad-hoc network is a collection of nodes that communicate with each other in a multihop manner without the support of a backbone network. In an adhoc network, power control is also used for network topology control (for instance to achieve a fully connected network), or to improve the efficiency of the routing protocol or the MAC contention process. Further, the diverse nature of the nodes might cause a link to not have bidirectional connectivity. Let c1 i j be the indicator function for first order or direct connectivity between nodes i and j. That is, c1 i j = 1 if node i can directly communicate with node j. Set M denotes the set of all nodes. In the case of asymmetric links, c1 i j �= c1ji . Let cki j indicate whether a k−hop connection exists between nodes i and j. Then, c k i j = I[{ max 0≤n≤k,l∈M,l�=i, j (cn il + ck−n l j )} > 2] (2.32) where I[x] is the indicator function that equals 1 if the condition x is true, and equals 0, otherwise. Let the power of node i be denoted by Pi. In a more general
42 Dinesh Rajan setting, a node may choose to use a different power level to communicate with each of its neighboring nodes. At the other extreme, the protocol design may restrict all nodes in the network to use the same transmission power. Recognize that c 1 i j depends on the transmission power used by node i. Computing the minimum network power that ensures a fully connected network can be formally posed as the following optimization problem: min ∑ Pi i∈M (2.33) s.t. Pi and (2.36) ensures that the network is fully connected. Several protocols have been developed to solve problems of this nature in a distributed manner. We now describe a popular protocol, COMPOW [28], which selects a common transmit power for all nodes, thereby ensuring each link is bidirectional (Pi = Pj,∀i, j). COMPOW computes and maintains multiple routing tables at each node, one for each possible transmit power level. A routing table is essentially a look up table that a node uses to determine the next hop to forward the packets for each possible destination. COMPOW then determines the smallest power level at each node such that the list of nodes that can be reached (using a finite number of hops) from that particular node using the selected power, equals the list of nodes that can be reached from that node using the highest transmission power. In other words, network connectivity is not sacrificed in reducing the transmit power levels. The key features of COMPOW are: i) the authors show that there is no significant loss in asymptotic (large number of nodes) network capacity by using a common transmit power for all nodes, ii) existence of low power routes using a low common transmit power for all nodes, and iii) the contention at the data link layer is also minimized. 2.6 Advanced Transceiver Methods In this section we discuss selected advanced techniques used in state of the art wireless systems. These techniques are also an area of active research and form a critical component of future wireless networks.
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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
Page 11 and 12: x Contents 8.3.2 The Solution Proce
Page 13 and 14: xii Contents References . . . . . .
Page 16 and 17: List of Contributors Khaldoun Al Ag
Page 18: List of Contributors xvii Nitin Sal
Page 22 and 23: Chapter 1 Introduction to Optimizat
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Page 29 and 30: Part I Background
Page 31 and 32: 10 Dinesh Rajan The goal of this ch
Page 33 and 34: 12 Dinesh Rajan The source encoder
Page 35 and 36: 14 Dinesh Rajan ping (FH) CDMA, and
Page 37 and 38: 16 Dinesh Rajan of SNR is given in
Page 39 and 40: 18 Dinesh Rajan 2.3 Information The
Page 41 and 42: 20 Dinesh Rajan Perror ≤ e −nE
Page 43 and 44: 22 Dinesh Rajan For instance, for t
Page 45 and 46: 24 Dinesh Rajan 2.4.1 Block Codes I
Page 47 and 48: 26 Dinesh Rajan B(z) = 1 � (1 + z
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Page 53 and 54: 32 Dinesh Rajan 2.5.2 Physical laye
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Page 59 and 60: 38 Dinesh Rajan a length N Inverse
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Page 81 and 82: 60 K. V. S. Hari 3.5.2.4 Dominant R
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Page 87 and 88: 66 J. Cole Smith and Sibel B. Sonuc
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92 J. Cole Smith and Sibel B. Sonuc
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Part II Optimization Problems for N
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102 Eli Olinick carrying capacity.
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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 161 we suggest
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7 Spectrum Auctions 163 pays, since
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7 Spectrum Auctions 165 prior round
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7 Spectrum Auctions 167 and constra
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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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312 Hang Jin and Li Guo where ρ mi
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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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