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Wireless Network Design: Optimization Models and Solution ...

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2 Introduction to <strong>Wireless</strong> Communications 39<br />

2.5.3 Power Control<br />

Determining the transmission power to use in a wireless system is a crucial task<br />

which affects the overall performance. The transmission power is controlled to<br />

achieve a variety of desired objectives, such as: i) provide performance guarantees<br />

even in the presence of a time varying channel attenuation, ii) conserve battery<br />

power in mobile devices by regulating the transmission power to the bare minimum<br />

required to provide desired level of service, or iii) reduce the amount of interference<br />

caused to other users in a multiuser system.<br />

The variety <strong>and</strong> complexity of power control problems that arise in wireless systems<br />

are too numerous to cover in this chapter. For conciseness, we provide two<br />

examples of power control problems.<br />

Cellular Uplink: We will consider the uplink of a cellular network in which the<br />

mobile users attempt to minimize their transmission powers to meet their desired<br />

performance level. To keep the discussion general we will consider both orthogonal<br />

<strong>and</strong> non-orthogonal signaling schemes used by multiple users.<br />

Let set M <strong>and</strong> set B represent, respectively, the set of mobile users <strong>and</strong> base<br />

stations in the network. Mobile user m ∈ M is connected to base station bm ∈ B.<br />

Let set Km ⊂ M denote the set of mobile users whose transmissions interfere with<br />

Fig. 2.17 Simple illustration orthogonality in an OFDM system

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