Wireless Ad Hoc and Sensor Networks

464 Wireless Ad Hoc and Sensor Networkswhere q is an environment-dependent variable considering path loss,and g ii represents the channel loss from reader i to tag and back.Communication channel between the reader and interrogated tagshould be in a relatively short range; for this reason Rayleigh fadingand shadowing effects are not considered for the reader–tag link.Influence by reflection can also be considered as a constant merginginto g ii assuming the environment is relatively stable. Hence, P bs canbe evaluated using path loss alone and by ignoring other channeluncertainties. However, the channel uncertainites are consideredduring the calculation of interference as reader locations are relativelyfarther away compared to a reader and a tag, and readers are powersources.Interference caused by reader j at reader i is given asI K P j2ij = 2 ⋅ ⋅ ⋅ X g Pq ij = ij ⋅2jrij(10.4)10 0.1ζ 10 01where P j is the transmission power of reader j, r ij is the distance betweenthe two readers, K 2 represents all other constant properties, . ζ correspondsto the effect of shadowing, and X is a random variable withRayleigh distribution (Rappaport 1999) to account for Rayleigh fadingloss in the channel between reader j and reader i. After simplification, g ijrepresents the channel loss from reader j to reader i. Note that becausethe interference actually occurs at the tag backscatter sideband, onlypower at that particular frequency needs to be considered. This factor isalso accounted for in K 2 and g ij .Cumulative interference I i at any given reader i is essentially the sumof interferences introduced by all other readers plus the variance of thenoise η :I≠∑= g P + ηi ij jj i(10.5)Given the transmission power and interference, the actual detectionrange of a reader is given byrK=R⋅ Pi⋅ I4q1actualrequiredi(10.6)Received SNR for a tag at a desired range r d can be calculated asRrdK=r14qd⋅ Pi⋅ Ii(10.7)