Wireless Ad Hoc and Sensor Networks

Distributed Power Control of Wireless Cellular and Peer-to-Peer Networks 189PROOF The error in SIR of all links can be expressed as xi( l+ 1)=( 1− ki) xi( l) + ηi.With 0 < k i < 1for new links, the error system in SIR is astable linear system driven by a bounded input η i . Linear system theory(Lewis 1999) shows that the SIRs of the links reach their targets in a finite time.5.2.4 Distributed Power Control: Application to Cellular NetworksThe DPC is naturally applied to peer-to-peer networks in which communicationexists between a transmitter and a receiver, whereas in the caseof cellular networks, the base station would like to maintain a target SIRby acting as a receiver to all the mobile users. Normally, all the users ina cellular network have to achieve a target SIR value γ i . The SIR value isa measure of quality of received signal and can be used to determine thecontrol action that needs to be taken for the uplink process control. TheSIR, can be expressed as (Rappaport 1999)γ iγ i b= (( E / N0)/( W/ R))(5.18)where E b is the energy per bit of the received signal in watts, N 0 is theinterference power in watts per Hertz, R is the bit rate in bits per second,and W is the radio channel bandwidth in Hertz. In our case, the metricschosen to evaluate the performance of the power control scheme areoutage probability and the total power consumed by the users. The outageprobability is defined as the probability of failing to achieve adequatereception of the signal due to cochannel interference. It is defined as theratio of the number of disconnected or handed over users to that of thetotal number of users in the system.Example 5.2.1: Uplink Transmitter Power Controlof Cellular NetworksThe cellular network is considered to be divided into seven hexagonalcells covering an area of 10 × 10 km with 100 users randomly distributedin the cells. A base station, which is located at the center of the hexagonalcell, services a cell. It is assumed that there is no mobility in the networkinitially so that the performance of the DPC can be evaluated in thepresence of path loss. The system parameters used for the simulation aretaken from IS-95 system (Rappaport 1999). The receiver noise in thesystem κ is taken as 10 12 i ,. The threshold SIR, γ is selected as 0.04. TheEbratio of energy per bit to interference power per hertzNis taken as 5.120dB. Bit rate R b , is 9600 bps. Radio channel bandwidth is B c , and is consideredto be 1.2288 MHz.