Wireless Ad Hoc and Sensor Networks

Adaptive and Probabilistic Power Control Scheme 463interference measured at each reader is used as a local feedback parameterto dynamically adjust its transmission power. With the same underlyingconcept, decentralized adaptive power control uses SNR to adapt powerat discrete time steps, whereas PPC adapts the transmission power basedon a certain probability distribution. A Lyapunov-based approach is usedto show the convergence of the proposed DAPC scheme. Simulationresults demonstrate theoretical conclusions.10.2 Problem FormulationThe frequency interference problem needs to be fully understood beforea solution can be evolved. In this section, we present an analysis of thisproblem and the assumptions made.10.2.1 Mathematical RelationsIn a backscatter communication system, SNR must meet a required thresholdR required , which can be expressed asR = ( E N ) ( W D)requiredb0(10.1)where E b is the energy per bit of the received signal in watts, N 0 is thenoise power in watts per Hertz, D is the bit rate in bits per second, and Wis the radio channel bandwidth in Hertz. For a known modulation methodand BER, E N can be calculated. Hence, R required can be selected basedon desired a data rate and BER.For any reader i, the following must hold for successful tag detection:b/ 0PIbsi= R ≥Rirequired(10.2)where P bs is the backscatter power from a tag, I i is the interference at thetag backscatter frequency, and R i is the SNR at a given reader.In general, P bs can be evaluated in terms of the reader transmissionpower P i and tag distance r i−t . Other variables such as reader and tagantenna gains, modulation indexing, and wavelength, derived in Rappaport(1999), can be considered as constants and simplified in Equation 10.3as K 1 . Then,P K P ibs = 1 ⋅ = g Pq ii ⋅4iri−t(10.3)