Mathematical Problems in Engineering
T : Denitions of the variables.
Var.
Denition
𝑘
𝑖
e actual interrogation radius of
𝑖
in th slot
𝑘
𝑖,th
e theoretical eective interrogation radius of
𝑖
in
th slot
𝑘
𝑖,max
e theoretical maximum interrogation radius of
𝑖
in th slot
where SINR
𝑘
𝑖
is the signal-to-interference-plus-noise ratio
(SINR) for
𝑖
in the th slot, SINR
min
is the desired minimum
value of SINR to identify tags,
𝑏𝜔
presents the normalized
spectrum power,
tg
presents reection coecient of eective
power,
𝑇
represents the gain of transmitting antenna,
𝑅
represents the gain of receiving antenna, PL
0
is the referenced
path loss at m distant from a reader, is the exponent of
path loss that is not less than two, and denotes the fading
coecient. e signal fading is ignored due to the line-of-
sight distance between readers. In addition,
𝑘
𝑖
represents the
operating power of
𝑖
in the th slot. According to EPC global
CG [],
𝑚
denotes the spectrum mask level and is also a
function with the arguments of the channel interval between
readers. CH
𝑘
𝑖
is the channel number used by
𝑖
in the th slot,
where CH
𝑘
𝑖
=1,2,...,
𝑆
.Notethat
𝑘
𝑗
is a -value function
which equals if
𝑗
is operating at the th slot and equals
otherwise. Please see [] for detailed derivations.
However,
𝑘
𝑖
must be not more than
𝑘
𝑖,max
;thatis,
𝑘
𝑖
≤
𝑘
𝑖,max
=
𝑘
𝑖
4
𝑘
𝑖
𝑇
𝑅
min
⋅
1−
4
𝑑
1+
𝑑
2
,
()
where
min
is the required minimum power for tag operation,
𝑑
means the modulation depth, and
𝑘
𝑖
is the wavelength of
𝑖
in the th slot.
Accordingly,
𝑘
𝑖
can be determined by
𝑘
𝑖
=min
𝑘
𝑖,th
,
𝑘
𝑖,max
.
()
InRRCAM,theutilityofanRFIDsystemisevaluatedbythe
interrogation region area of all the readers which is dened as
tt
. To maximize
tt
,RRCAMisformulatedas
maximize
tt
=
𝑁
𝑆
𝑘=1
𝑁
rd
𝑖=1
𝑘
𝑖
2
s.t. CH
𝑘
𝑖
∈1,
𝐹
,
∀∈1,
rd
,∈1,
𝑆
.
()
2.3. Articial Immune Network (aiNet). To solve theoreti-
cal or engineering problems which can be generalized as
optimization problems, for example, RRCAM, intelligent
algorithms are generally employed. aiNet is a main member in
articial immune systems, which is enlightened by biological
immune systems to solve real-world problems [].
Take the canonical opt-aiNet [] as an example to intro-
duce the structure of aiNet. e opt-aiNet uses real number
encoding and has ve operators, that is, cloning, mutation,
selection, suppression, and recruitment. In the cloning phase,
opt-aiNet uses the uniform cloning operator, where a x-
number cloning is conducted for each antibody individual,
and all the clones except the parent one experience the
Gaussian mutation following
Ab
=Ab +
⋅exp −A
∗
(
Ab
)
.
()
en, only one antibody, whose anity is the highest among
osprings, is selected to enter the next generation. In (),
is a random variable following Gaussian distribution whose
mean is zero and standard deviation is , is the control
coecient, Ab
is the mutated antibody of Ab, and A
∗
is
thefunctionofnormalizedanityintheinterval[0,1].Ifthe
average anity looks stable, the suppression operator will be
triggered. For any two antibodies, if their distance is smaller
than a suppression threshold
𝑆
,theonewithloweranity
will be removed. en, a number of antibodies are randomly
generated and merged into the antibody population to keep
the population diversity. Repeat the above process until it is
terminated.
3. The Proposed R2RCAM-IRO Optimized by
RA-IRO-aiNet
3.1. R2RCAM-IRO
3.1.1. Modeling of R2RCAM-IRO. To s olve theoretic al opti-
mization problem, let us assume that
tg
tags are distributed
uniformly in the deployment region and the maximum trans-
mitting power of readers is
max
. And the other assumptions
are the same as those of RRCAM.
Taking into account the identication capacity of a reader
in a slot,
𝑘
𝑖
must satisfy
tg
𝑘
𝑖
2
0
≤
𝑖
tg,max
,
()
where
𝑖
tg,max
is the maximum number of tags that
𝑖
can
identify in one slot. As a result, we can get
𝑘
𝑖
≤
0
𝑖
tg,max
tg
.
()
According to () and (),
𝑘
𝑖
is determined by
𝑘
𝑖
=min
𝑘
𝑖,th
,
𝑘
𝑖,max
,
0
𝑖
tg,max
tg
. ()
Tag identication rate (TIR) is a measure of the RFID system
performance. TIR is dened as the ratio of the number of
identiabletagstothetotalnumberoftags.Becauseofthe
assumption that the tags are distributed uniformly, TIR is