In conclusion
(1) union of the 100a% read accuracy powering regions for each individual antenna
underestimates the real coverage volume because there might be points that would be
considered unreadable by each reader individually, yet would be readable when all of
the readers are considered jointly and (2) there is no straightforward process whereby one
can de?¬?ne the boundary of the powering region because of the absence of any direct
monotonicity result.
10.3.2 Integer Programming Formulation for Multiple Reader Coverage
In this section we formulate the reader antenna location problem as a mathematical
program by de?¬?ning a suitable objective, and translating our read accuracy requirements
and the corresponding powering region into mathematical relationships that de?¬?ne the
constraints of the math program. Suppose that the region within a portal where a tag can
lie is discretized into L distinct points and that each of these is a possible location for the
center of the tag??™s antenna (henceforth referred to as tag position; the entire set of L tag
positions will be referred to as the tag space). Suppose further that we are given N potential
locations along the portal for the center of any reader antenna (henceforth referred to as
reader position), and we have a maximum of n0 (
placement at these positions.
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