The tag??™s position is de?¬?ned as possessing 100a% read
accuracy as long as aM of the values computed are greater than a speci?¬?ed value Pmin, the
minimum operational power required to activate the tag.
Although it is true that evaluating the 100a% read accuracy powering region in a portal
can be done using Friis??™ equation, the computational effort could be overwhelming to
achieve suf?¬?ciently high precision: not only does one need to discretize the orientations in
three-dimensional space, but also the portal space. Discretizing a 1 m3 volume with 1 cm
search steps leads to 1 million search points, each of which presumably can take on as
many as M different orientations. With a 18 resolution, there will be M??64,800 values for
the gain for each point (18033608). Therefore, there are 64,8003106 evaluations for just
a 1 m3 space.
Greene has developed an ef?¬?cient algorithm to overcome this computational challenge
[2]. With a single reader antenna, we can ?¬?x the position and orientation of the reader
antenna, and the location and orientation of the tag can be uniquely de?¬?ned relative to this
point of reference. The reader antenna is assumed to be at the origin with its maximum
gain direction aligned with the x-axis, and the reader axis as per De?¬?nition 3. The monotonicity
of power received along the reader axis as a function of distance from the reader
yields the following corollary.
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