# An Effective Scheduling-Based RFID Reader Collision Avoidance Model and Its Resource Allocation via Artificial Immune Network

Authors: Shanjin Wang; Zhonghua Li; Chunhui He; Jianming Li
Journal: Mathematical Problems in Engineering
 (2016)

---

## Abstract

Radio frequency identification, that is, RFID, is one of important technologies in Internet of Things. Reader collision does impair the tag identification efficiency of an RFID system. Many developed methods, for example, the scheduling-based series, that are used to avoid RFID reader collision, have been developed. For scheduling-based methods, communication resources, that is, time slots, channels, and power, are optimally assigned to readers. In this case, reader collision avoidance is equivalent to an optimization problem related to resource allocation. However, the existing methods neglect the overlap between the interrogation regions of readers, which reduces the tag identification rate (TIR). To resolve this shortage, this paper attempts to build a reader-to-reader collision avoidance model considering the interrogation region overlaps (R2RCAM-IRO). In addition, an artificial immune network for resource allocation (RA-IRO-aiNet) is designed to optimize the proposed model. For comparison, some comparative numerical simulations are arranged. The simulation results show that the proposed R2RCAM-IRO is an effective model where TIR is improved significantly. And especially in the application of reader-to-reader collision avoidance, the proposed RA-IRO-aiNet outperforms GA, opt-aiNet, and PSO in the total coverage area of readers.


---

## Body

## 1. Introduction

As a wireless automatic identification and data capture technique, RFID (radio frequency identification) is employed to automatically identify the targets. With the main advantages of noncontact and fast reading rate for multiple targets, RFID has been applied widely in logistics, supply chain management, transportation, manufacturing, positioning, and many other fields [1, 2].For RFID applications with many tags within a large deployment region, multiple or even dense readers are necessary to enhance the identification efficiency. If R2RCP (reader-to-reader collision problem) happens, the identification efficiency of the systems will be reduced inevitably. Therefore, how to solve R2RCP has become one research focus. In general,scheduling-based reader collision avoidance methods are suitable for stationary reader scenarios. In the scheduling-based series, one or more kinds of communication resources, that is, time slots, channels, and power, are allocated to readers to maximize the tag identification efficiency of RFID systems. Further, intelligent algorithms are applied to optimize the utility of RFID systems. In [3], the reader collision problem is formulated as 0/1 integer programming problem and a simulated annealing algorithm is introduced to solve it. In [4], time slots are allocated by using color graphing and PSO. A resource allocation-based model is built in [5] and is optimized by using the genetic algorithm (RA-GA). Such model is improved as a reader-to-reader collision avoidance model (R2RCAM) by [6]. And a well designed artificial immune system is introduced to optimize R2RCAM, which has better performance in solving R2RCP by comparison with RA-GA and a random method (RM). These achievements indicate that intelligent algorithms are effective to deal with the reader collision problems from the viewpoint of resource scheduling. Note that a family ofcoverage-based methods [7, 8] deal with the reader collision problem by adaptively controlling the communication power of readers and minimizing the overlap between the interrogation region. Inspired by such spirit, it is worth to consider the overlap of the interrogation regions of readers and the resource of power, while R2RCAM without consideration about overlap is not suitable for the practice of RFID applications.In order to overcome the defects of canonical R2RCAM, this paper proposes an effective R2RCAM considering the interrogation region overlap (R2RCAM-IRO). The proposed R2RCAM-IRO takes into account not only the overlap but also the resource of power and the tag identification capacity of a reader. In addition, a revised artificial immune network (aiNet), namely, RA-IRO-aiNet, is designed to optimize R2RCAM-IRO. The proposed R2RCAM-IRO is expected to improve the tag identification rate with limited communication resources for multiple readers, where the proposed RA-IRO-aiNet is used.The rest of our paper is arranged as follows. Section2 reviews related theories and principles including R2RCP, R2RCAM, and the basic artificial immune network. Section 3 proposes R2RCAM-IRO and RA-IRO-aiNet. And Section 4 proves the effectiveness of the proposed model and compares RA-IRO-aiNet with RA-GA [5], PSO [4], and opt-aiNet [9] in the area of effective interrogation region by numerical simulations. And finally, the conclusions are made in Section 5.


## 2. Reviews of Related Theories and Principles

### 2.1. Reader-to-Reader Collision Problem (R2RCP)

A basic RFID system is composed of some tags, one or more readers, and an application system, as shown in Figure1. Multiple readers operating within a group become a reader network. When a tag attached to the objects to be identified enters the interrogation region of a reader, it will be powered and activated. Then, the tag sends its corresponding information to the reader. The reader identifies the tag by receiving information and sends the corresponding data to related application system for further processing and storage. And the readers operate according to the commands of the application system.Figure 1
Schematic description of a basic RFID system.In multiple-reader scenarios, the backscatter signal of a tag is easily disturbed. This is because the backscatter power is much weaker than the transmitting power of any neighboring interfering reader. As a result, R2RCP will happen and decrease the desired reader’s effective interrogation radius.Figure2 shows an example of R2RCP with two readers, where one is a desired reader R
i and the other is an interfering reader R
j. The distance between R
i and R
j is defined as d
i
,
j. If only R
i is operating, that is, R
i is not interfered; it can harvest a maximum interrogation radius with the value of r
m
a
x. However, if R
j is operating simultaneously with R
i, the interrogation radius of reader R
i will reduce to r. Further, strong enough interference from R
j will probably make r smaller than x which is the distance from the target tag T to R
i. Consequently, R
i is not able to detect T successfully. To sum up, the radius r
i of the desired reader R
i follows(1)
r
i
=
r
<
r
m
a
x
,
if
R
i
and
R
j
operates  at  the  same  time
r
m
a
x
,
otherwise
.Figure 2
Reader-to-reader collision problem.


### 2.2. Canonical Reader-to-Reader Collision Avoidance Model (R2RCAM)

Assume thatN
r
d readers are deployed randomly in a specified region with the area of S
0. N
C
h channels and N
S slots are available to be allocated for these readers.For clarification, three variables are defined as in Table1.Table 1
Definitions of the variables.
Var.
Definition
r
i
k
The actual interrogation radius ofR
i in k
t
h slot
r
i
,
t
h
k
The theoretical effective interrogation radius ofR
i in k
t
h slot
r
i
,
m
a
x
k
The theoretical maximum interrogation radius ofR
i in k
t
h slotAndr
i
,
t
h
k can be calculated by solving(2)
r
i
,
t
h
k
=
arg
max
x
⁡
S
I
N
R
i
k
x
≥
S
I
N
R
m
i
n
=
α
b
ω
E
t
g
P
i
k
G
T
G
R
P
L
0
2
S
I
N
R
m
i
n
h
G
T
G
R
∑
j
=
1
,
j
≠
i
N
r
d
ω
j
k
P
j
k
β
m
C
H
i
k
-
C
H
j
k
P
L
0
d
j
,
i
-
γ
+
N
s
i
1
/
2
γ
,where S
I
N
R
i
k is the signal-to-interference-plus-noise ratio (SINR) for R
i in the k
t
h slot, S
I
N
R
m
i
n is the desired minimum value of SINR to identify tags, α
b
ω presents the normalized spectrum power, E
t
g presents reflection coefficient of effective power, G
T represents the gain of transmitting antenna, G
R represents the gain of receiving antenna, P
L
0 is the referenced path loss at 1 m distant from a reader, γ is the exponent of path loss that is not less than two, and h denotes the fading coefficient. The signal fading is ignored due to the line-of-sight distance between readers. In addition, P
i
k represents the operating power of R
i in the k
t
h slot. According to EPC global C1G2 [10], β
m denotes the spectrum mask level and is also a function with the arguments of the channel interval between readers. C
H
i
k is the channel number used by R
i in the k
t
h slot, where C
H
i
k
=
1,2
,
…
,
N
S. Note that ω
j
k is a 2-value function which equals 1 if R
j is operating at the k
t
h slot and equals 0 otherwise. Please see [6] for detailed derivations.However,r
i
k must be not more than r
i
,
m
a
x
k; that is,(3)
r
i
k
≤
r
i
,
m
a
x
k
=
λ
i
k
4
π
P
i
k
G
T
G
R
P
m
i
n
·
1
-
M
d
4
1
+
M
d
2
,where P
m
i
n is the required minimum power for tag operation, M
d means the modulation depth, and λ
i
k is the wavelength of R
i in the k
t
h slot.Accordingly,r
i
k can be determined by(4)
r
i
k
=
m
i
n
r
i
,
t
h
k
,
r
i
,
m
a
x
k
.In R2RCAM, the utility of an RFID system is evaluated by the interrogation region area of all the readers which is defined as S
t
t. To maximize S
t
t, R2RCAM is formulated as(5)
m
a
x
i
m
i
z
e
S
t
t
=
∑
k
=
1
N
S
∑
i
=
1
N
r
d
π
r
i
k
2
s
.
t
.
C
H
i
k
∈
1
,
N
F
,
∀
i
∈
1
,
N
r
d
,
k
∈
1
,
N
S
.


### 2.3. Artificial Immune Network (aiNet)

To solve theoretical or engineering problems which can be generalized as optimization problems, for example, R2RCAM, intelligent algorithms are generally employed. aiNet is a main member in artificial immune systems, which is enlightened by biological immune systems to solve real-world problems [11].Take the canonical opt-aiNet [9] as an example to introduce the structure of aiNet. The opt-aiNet uses real number encoding and has five operators, that is, cloning, mutation, selection, suppression, and recruitment. In the cloning phase, opt-aiNet uses theuniform cloning operator, where a fix-number cloning is conducted for each antibody individual, and all the clones except the parent one experience theGaussian mutation following(6)
A
b
′
=
A
b
+
G
β
·
exp
⁡
-
A
f
f
∗
A
b
.Then, only one antibody, whose affinity is the highest among offsprings, is selected to enter the next generation. In (6), G is a random variable following Gaussian distribution whose mean is zero and standard deviation is 1, β is the control coefficient, A
b
′ is the mutated antibody of A
b, and A
f
f
∗ is the function of normalized affinity in the interval [
0,1
]. If the average affinity looks stable, the suppression operator will be triggered. For any two antibodies, if their distance is smaller than a suppression threshold δ
S, the one with lower affinity will be removed. Then, 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.


## 2.1. Reader-to-Reader Collision Problem (R2RCP)

A basic RFID system is composed of some tags, one or more readers, and an application system, as shown in Figure1. Multiple readers operating within a group become a reader network. When a tag attached to the objects to be identified enters the interrogation region of a reader, it will be powered and activated. Then, the tag sends its corresponding information to the reader. The reader identifies the tag by receiving information and sends the corresponding data to related application system for further processing and storage. And the readers operate according to the commands of the application system.Figure 1
Schematic description of a basic RFID system.In multiple-reader scenarios, the backscatter signal of a tag is easily disturbed. This is because the backscatter power is much weaker than the transmitting power of any neighboring interfering reader. As a result, R2RCP will happen and decrease the desired reader’s effective interrogation radius.Figure2 shows an example of R2RCP with two readers, where one is a desired reader R
i and the other is an interfering reader R
j. The distance between R
i and R
j is defined as d
i
,
j. If only R
i is operating, that is, R
i is not interfered; it can harvest a maximum interrogation radius with the value of r
m
a
x. However, if R
j is operating simultaneously with R
i, the interrogation radius of reader R
i will reduce to r. Further, strong enough interference from R
j will probably make r smaller than x which is the distance from the target tag T to R
i. Consequently, R
i is not able to detect T successfully. To sum up, the radius r
i of the desired reader R
i follows(1)
r
i
=
r
<
r
m
a
x
,
if
R
i
and
R
j
operates  at  the  same  time
r
m
a
x
,
otherwise
.Figure 2
Reader-to-reader collision problem.


## 2.2. Canonical Reader-to-Reader Collision Avoidance Model (R2RCAM)

Assume thatN
r
d readers are deployed randomly in a specified region with the area of S
0. N
C
h channels and N
S slots are available to be allocated for these readers.For clarification, three variables are defined as in Table1.Table 1
Definitions of the variables.
Var.
Definition
r
i
k
The actual interrogation radius ofR
i in k
t
h slot
r
i
,
t
h
k
The theoretical effective interrogation radius ofR
i in k
t
h slot
r
i
,
m
a
x
k
The theoretical maximum interrogation radius ofR
i in k
t
h slotAndr
i
,
t
h
k can be calculated by solving(2)
r
i
,
t
h
k
=
arg
max
x
⁡
S
I
N
R
i
k
x
≥
S
I
N
R
m
i
n
=
α
b
ω
E
t
g
P
i
k
G
T
G
R
P
L
0
2
S
I
N
R
m
i
n
h
G
T
G
R
∑
j
=
1
,
j
≠
i
N
r
d
ω
j
k
P
j
k
β
m
C
H
i
k
-
C
H
j
k
P
L
0
d
j
,
i
-
γ
+
N
s
i
1
/
2
γ
,where S
I
N
R
i
k is the signal-to-interference-plus-noise ratio (SINR) for R
i in the k
t
h slot, S
I
N
R
m
i
n is the desired minimum value of SINR to identify tags, α
b
ω presents the normalized spectrum power, E
t
g presents reflection coefficient of effective power, G
T represents the gain of transmitting antenna, G
R represents the gain of receiving antenna, P
L
0 is the referenced path loss at 1 m distant from a reader, γ is the exponent of path loss that is not less than two, and h denotes the fading coefficient. The signal fading is ignored due to the line-of-sight distance between readers. In addition, P
i
k represents the operating power of R
i in the k
t
h slot. According to EPC global C1G2 [10], β
m denotes the spectrum mask level and is also a function with the arguments of the channel interval between readers. C
H
i
k is the channel number used by R
i in the k
t
h slot, where C
H
i
k
=
1,2
,
…
,
N
S. Note that ω
j
k is a 2-value function which equals 1 if R
j is operating at the k
t
h slot and equals 0 otherwise. Please see [6] for detailed derivations.However,r
i
k must be not more than r
i
,
m
a
x
k; that is,(3)
r
i
k
≤
r
i
,
m
a
x
k
=
λ
i
k
4
π
P
i
k
G
T
G
R
P
m
i
n
·
1
-
M
d
4
1
+
M
d
2
,where P
m
i
n is the required minimum power for tag operation, M
d means the modulation depth, and λ
i
k is the wavelength of R
i in the k
t
h slot.Accordingly,r
i
k can be determined by(4)
r
i
k
=
m
i
n
r
i
,
t
h
k
,
r
i
,
m
a
x
k
.In R2RCAM, the utility of an RFID system is evaluated by the interrogation region area of all the readers which is defined as S
t
t. To maximize S
t
t, R2RCAM is formulated as(5)
m
a
x
i
m
i
z
e
S
t
t
=
∑
k
=
1
N
S
∑
i
=
1
N
r
d
π
r
i
k
2
s
.
t
.
C
H
i
k
∈
1
,
N
F
,
∀
i
∈
1
,
N
r
d
,
k
∈
1
,
N
S
.


## 2.3. Artificial Immune Network (aiNet)

To solve theoretical or engineering problems which can be generalized as optimization problems, for example, R2RCAM, intelligent algorithms are generally employed. aiNet is a main member in artificial immune systems, which is enlightened by biological immune systems to solve real-world problems [11].Take the canonical opt-aiNet [9] as an example to introduce the structure of aiNet. The opt-aiNet uses real number encoding and has five operators, that is, cloning, mutation, selection, suppression, and recruitment. In the cloning phase, opt-aiNet uses theuniform cloning operator, where a fix-number cloning is conducted for each antibody individual, and all the clones except the parent one experience theGaussian mutation following(6)
A
b
′
=
A
b
+
G
β
·
exp
⁡
-
A
f
f
∗
A
b
.Then, only one antibody, whose affinity is the highest among offsprings, is selected to enter the next generation. In (6), G is a random variable following Gaussian distribution whose mean is zero and standard deviation is 1, β is the control coefficient, A
b
′ is the mutated antibody of A
b, and A
f
f
∗ is the function of normalized affinity in the interval [
0,1
]. If the average affinity looks stable, the suppression operator will be triggered. For any two antibodies, if their distance is smaller than a suppression threshold δ
S, the one with lower affinity will be removed. Then, 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 solve theoretical optimization problem, let us assume thatN
t
g tags are distributed uniformly in the deployment region and the maximum transmitting power of readers is P
m
a
x. And the other assumptions are the same as those of R2RCAM.Taking into account the identification capacity of a reader in a slot,r
i
k must satisfy(7)
N
t
g
π
r
i
k
2
S
0
≤
N
t
g
,
m
a
x
i
,where N
t
g
,
m
a
x
i is the maximum number of tags that R
i can identify in one slot. As a result, we can get(8)
r
i
k
≤
S
0
N
t
g
,
m
a
x
i
π
N
t
g
.According to (3) and (8), r
i
k is determined by(9)
r
i
k
=
min
⁡
r
i
,
t
h
k
,
r
i
,
m
a
x
k
,
S
0
N
t
g
,
m
a
x
i
π
N
t
g
.Tag identification rate (TIR) is a measure of the RFID system performance. TIR is defined as the ratio of the number of identifiable tags to the total number of tags. Because of the assumption that the tags are distributed uniformly, TIR is equal to the ratio of the total interrogation area to the reader deployment region area. That is, (10)
T
I
R
=
S
t
t
S
0
.In the canonical R2RCAM, S
t
t is calculated easily by (5). However, there may be an overlap between the interrogation regions of some readers. Thus, the canonical R2RCAM does not meet the practice requirement and decreases TIR of the RFID system. Let R
g
i represent the interrogation region of the reader R
i. And in the proposed R2RCAM-IRO, the total interrogation region R
g follows(11)
R
g
=
⋃
i
=
1
N
r
d
R
g
i
=
⋃
i
=
1
N
r
d
⋃
k
=
1
N
S
R
g
i
k
,where R
g
i
k is the interrogation region of R
i in the k
t
h slot.Consequently, R2RCAM-IRO can be formulated as(12)
m
a
x
i
m
i
z
e
T
I
R
=
S
t
t
S
0
s
.
t
.
C
H
i
k
∈
1
,
N
F
,
P
i
k
∈
0
,
P
m
a
x
∀
i
∈
1
,
N
r
d
,
k
∈
1
,
N
S
.


#### 3.1.2. Analysis of R2RCAM-IRO

Assume that when the maximum TIR is obtained, a readerR
i works in k
i
,
1
t
h
,
k
i
,
2
t
h
,
…
,
k
i
,
p
t
h slot (2
≤
p
≤
N
S and k
i
,
p
1
≠
k
i
,
p
2
,
∀
p
1
≠
p
2) and the interrogation radii are r
i
k
i
,
1
,
r
i
k
i
,
2
,
…
,
r
i
k
i
,
p, respectively. Without loss of generality, it is assumed that r
i
k
i
,
1
≥
r
i
k
i
,
2
≥
⋯
≥
r
i
k
i
,
p. As a result,(13)
R
g
i
=
⋃
m
=
1
p
R
g
i
k
i
,
m
=
R
g
i
k
i
,
1
.This indicates that if R
i just works in k
1
t
h slot, its interrogation area will not change. Assume that another reader R
j (j
≠
i) works in k
j
,
1
t
h
,
k
j
,
2
t
h
,
…
,
k
j
,
q
t
h slot (1
≤
q
≤
N
S, k
j
,
q
1
≠
k
j
,
q
2, ∀
q
1
≠
q
2, and ∃
k
u
∈
{
k
i
,
1
,
k
i
,
2
,
…
,
k
i
,
p
}) and its interrogation radius in k
u
t
h slot is denoted by r
j
k
u. If R
i does not work in k
u
t
h slot, the theoretical interrogation radius of R
j will increase because its total interference decreases. With the constraints of the maximum reader interrogation radius and the identification capacity, the interrogation radius r
j
k
u
∗ may be unchanged. Thus, r
j
k
u
∗
≥
r
j
k
u and R
g
j
k
u
∗
⊇
R
g
j
k
u can be obtained. Thus, the total interrogation region R
g
j
∗ of R
j satisfies(14)
R
g
j
∗
=
R
g
j
k
u
∗
∪
⋃
m
=
1
,
m
≠
k
u
q
R
g
j
k
m
⊇
R
g
j
k
u
∪
⋃
m
=
1
,
m
≠
k
u
q
R
g
j
k
m
=
R
g
j
.Thus, the total area of the interrogation regions of all the readers satisfies(15)
R
g
∗
=
R
g
j
∗
∪
⋃
m
=
1
,
m
≠
j
N
r
d
R
g
m
⊇
R
g
j
∪
⋃
m
=
1
,
m
≠
j
N
r
d
R
g
m
=
R
g
.Clearly, the total interrogation area of an RFID system when each reader just works in one slot is not less than that when some readers operate in two or more slots. Thus, only one slot can be allocated to each operating reader in R2RCAM-IRO.


#### 3.1.3. Calculation Procedure ofS
t
t

Due to the interrogation region overlap,S
t
t cannot be calculated directly. Thus, agrid method is employed to compute S
t
t. Taking Figure 3 as an example, the details of the grid method are depicted as follows.Figure 3
Graphical representation of the grid method.Step 1.
Determine the region of all the circles shown as the red rectangle with the length ofL and the width of W.Step 2.
Divide the region intom
×
n (m
=
r
o
u
n
d
(
L
/
A
c
) and n
=
r
o
u
n
d
(
W
/
A
c
)) small rectangles with the area of S
s
r, where A
c determines the accuracy.Step 3.
Mark those small rectangles whose centers lie in any one of the circles as shown in yellow.Step 4.
Count the numberN
m
r of the marked small rectangles and use the total area of these rectangles as the result of S
t
t; that is, S
t
t
=
S
s
r
N
m
r.If the parameterA
c is large, the accuracy will be impaired. However, smaller A
c will result in a significant increase of the computational complexity. So, apreprocessing procedure is necessary to decrease the complexity by reducing the number of the circles and the area of the rectangular region. There are four situations for a single circle, where (S
1) it lies in some circle; (S
2) it is independent and does not intersect with any other circles; (S
3) it intersects with only one circle; or (S
4) it intersects with two or more circles. For any circle, if it is in S
1, it can be removed without having an impact on the result. If it is in S
2, its area can be calculated easily. If it is in S
3, its area without the overlap is added to the result. And then, this circle can be removed. It is assumed that a circle C
i with the centric point O
i intersects with the other circle C
j with the centric point O
j at point A and point B. And then the area S
o
l of the overlap can be obtained by(16)
S
o
l
=
t
i
r
i
2
+
t
j
r
j
2
-
r
i
d
i
j
sin
⁡
t
i
,
cos
⁡
t
i
=
r
i
2
+
d
i
j
2
-
r
j
2
2
r
i
d
i
j
,
cos
⁡
t
j
=
r
j
2
+
d
i
j
2
-
r
i
2
2
r
j
d
i
j
,where t
i is ∠
A
O
i
O
j, t
j is ∠
A
O
j
O
i, and d
i
j is the distance from the point O
i to the point O
j. For S
4, the grid method is employed.Taking Figure4 as an example, the details of the preprocessing procedure are depicted as follows.Figure 4
Example of the preprocessing procedure.Step 1.
Find the circles in some other circles, such as the one in the red solid box in Figure4(a). And then remove it.Step 2.
Find the independent circles, such as the two in the red solid box in Figure4(b). Calculate their area and add it to the result. And then remove them.Step 3.
Find the circles intersected with only one other circle, such as the one in the red solid box in Figure4(c). Calculate the area without the overlap as shown in green by (16) and add it to the result. And then remove it.Step 4.
If new independent circles or ones intersected with another circle appear, repeat Steps  2 and  3 until any circle intersects with two or more other ones.Step 5.
Separate the rest of the circles into groups, where the intersected circles belong to the same group and circles in different groups do not intersect with each other, as shown in Figure4(d). And the area of each group is calculated by the grid method.


### 3.2. RA-IRO-aiNet

By improving the main immune operators, artificial immune networks become efficient, adaptive, and suitable for the practical applications. To find the optimal scheme of time slots, channels, and power for an RFID reader network, this subsection designs RA-IRO-aiNet to solve R2RCAM-IRO. The technical details of the proposed algorithm are introduced in the following subsections.


#### 3.2.1. Encoding Format

A hybrid encoding format is used in RA-IRO-aiNet uses. Table2 presents the encoding format used by the i
t
h antibody. In Table 2, each antibody includes three segments of the slot, the channel, and the power, where T
i
,
j
∈
[
0
,
N
S
] is an integer and denotes the time slot, C
h
i
,
j
∈
[
1
,
N
F
] is an integer and denotes the channel, and P
i
,
j
∈
(
0
,
P
m
a
x
] is a real number and denotes the power. Note that T
i
,
j
=
0 means that R
j does not operate.Table 2
Encoding format for the antibody individual.
Slot segment
Channel segment
Power segment
T
i
,
1
,
T
i
,
2
,
…
,
T
i
,
N
r
d
C
h
i
,
1
,
C
h
i
,
2
,
…
,
C
h
i
,
N
r
d
P
i
,
1
,
P
i
,
2
,
…
,
P
i
,
N
r
d


#### 3.2.2. Affinity Function

To evaluate each antibody individual about the resource scheduling solution, an affinity function is designed according to R2RCAM-IRO presented in Section2, which is presented as(17)
A
f
f
A
b
=
S
t
t
S
0
.


#### 3.2.3. Initialization

In the initialization, an antibody population withN
a
b individuals is constructed randomly. And each antibody must be feasible, where T
i
,
j
∈
{
0,1
,
…
,
N
S
}, C
h
i
,
j
∈
{
1,2
,
…
,
N
C
h
}, and P
i
,
j
∈
(
0
,
P
m
a
x
] for i
∈
{
1,2
,
…
,
N
a
b
} and j
∈
{
1,2
,
…
,
N
r
d
}.


#### 3.2.4. Cloning Operator

Theuniform cloning operator is used, where each antibody is reproduced for a constant multiplier of N
C. The uniform cloning is simple to implement and can remarkably depress the computational consumption. All the cloned offsprings except the parent antibodies will execute the following mutation operator in order to increase the population diversity.


#### 3.2.5. Mutation Operator

Because the proposed RA-IRO-aiNet uses hybrid encoding, adifferentiated mutation operator is employed, in which different segments (i.e., the slot, the channel, and the power) of each antibody experience different mutation processes. In detail, therandom uniform mutation operator is employed for the slot segment and the channel segment, where a randomly selected bit is changed randomly in its set of feasible solutions. And for the power segment, the usedGaussian mutation operator is given in (6). Note that only one randomly selected segment experiences the mutation for each offspring. The pseudocode of the mutation process is shown in Pseudocode 1.Pseudocode 1:Pseudocode of the mutation process.
PROCEDURE Mutation Operator (A
b
i)
a
=
r
a
n
d
∈
1,2
,
3;
SWITCH
a
CASE 1:
b
=
r
a
n
d
∈
1,2
,
…
,
N
r
d;
T
i
,
b
=
r
a
n
d
∈
0,1
,
…
,
N
S;
CASE 2:
b
=
r
a
n
d
∈
1,2
,
…
,
N
r
d;
C
h
i
,
b
=
r
a
n
d
∈
1,2
,
…
,
N
F;
CASE 3:
P
i
,
j
=
P
i
,
j
+
exp
⁡
(
-
A
f
f
∗
(
A
b
i
)
)
G
(
0,1
)
/
β
,
j
=
1,2
,
…
,
N
r
d;
END SWITCH
END PROCEDURE


#### 3.2.6. Suppression Operator and Recruitment

The similarity between any two antibodies is evaluated by the measure ofhybrid distance (D
H
y
b). It is obtained by the sum of the normalized distance of each segment. The corresponding formula is given in (18)(18)
D
H
y
b
A
b
i
,
A
b
j
=
D
H
a
m
,
T
A
b
i
,
A
b
j
N
r
d
+
D
H
a
m
,
C
h
A
b
i
,
A
b
j
N
r
d
+
D
E
u
c
,
P
A
b
i
,
A
b
j
D
m
a
x
,where D
H
a
m
,
T
(
·
,
·
) and D
H
a
m
,
C
h
(
·
,
·
) are the Hamming distance of the slot segment and the channel segment, respectively, D
E
u
c
,
P
(
·
,
·
) is the Euclidean distance of the power segment, and D
m
a
x is the maximum Euclidean distance which equals P
m
a
x
N
r
d. The higher the hybrid distance is, the better diversity the antibody population has. Thus, in order to keep the diversity of the antibody population, once the hybrid distance of two antibodies is smaller than a threshold δ
S, the antibody with lower affinity will be suppressed. The threshold is determined by such defined similarity following(19)
δ
S
=
min
⁡
D
H
y
b
A
b
i
,
A
b
j
,
i
≠
j
+
ξ
max
⁡
D
H
y
b
A
b
i
,
A
b
j
-
min
⁡
D
H
y
b
A
b
i
,
A
b
j
.The desired goal is to adjust the threshold dynamically and to remove those ξ
(
0
<
ξ
<
1
) of similar antibodies. After the suppression operator, some new antibodies are randomly produced to keep the antibody population at the number of N
a
b.The flowchart of our proposed RA-IRO-aiNet is shown in Figure5. The left orange box shows the flowchart of opt-aiNet, while the right green box highlights the revised immune operators of RA-IRO-aiNet. In RA-IRO-aiNet, each antibody experiences the uniform cloning operator, the differentiated mutation operator, the hybrid similarity evaluation, the similarity-based suppression operator, and the recruitment in each generation. Repeat the above process until it is terminated.Figure 5
Flowchart of the proposed RA-IRO-aiNet.


## 3.1. R2RCAM-IRO

### 3.1.1. Modeling of R2RCAM-IRO

To solve theoretical optimization problem, let us assume thatN
t
g tags are distributed uniformly in the deployment region and the maximum transmitting power of readers is P
m
a
x. And the other assumptions are the same as those of R2RCAM.Taking into account the identification capacity of a reader in a slot,r
i
k must satisfy(7)
N
t
g
π
r
i
k
2
S
0
≤
N
t
g
,
m
a
x
i
,where N
t
g
,
m
a
x
i is the maximum number of tags that R
i can identify in one slot. As a result, we can get(8)
r
i
k
≤
S
0
N
t
g
,
m
a
x
i
π
N
t
g
.According to (3) and (8), r
i
k is determined by(9)
r
i
k
=
min
⁡
r
i
,
t
h
k
,
r
i
,
m
a
x
k
,
S
0
N
t
g
,
m
a
x
i
π
N
t
g
.Tag identification rate (TIR) is a measure of the RFID system performance. TIR is defined as the ratio of the number of identifiable tags to the total number of tags. Because of the assumption that the tags are distributed uniformly, TIR is equal to the ratio of the total interrogation area to the reader deployment region area. That is, (10)
T
I
R
=
S
t
t
S
0
.In the canonical R2RCAM, S
t
t is calculated easily by (5). However, there may be an overlap between the interrogation regions of some readers. Thus, the canonical R2RCAM does not meet the practice requirement and decreases TIR of the RFID system. Let R
g
i represent the interrogation region of the reader R
i. And in the proposed R2RCAM-IRO, the total interrogation region R
g follows(11)
R
g
=
⋃
i
=
1
N
r
d
R
g
i
=
⋃
i
=
1
N
r
d
⋃
k
=
1
N
S
R
g
i
k
,where R
g
i
k is the interrogation region of R
i in the k
t
h slot.Consequently, R2RCAM-IRO can be formulated as(12)
m
a
x
i
m
i
z
e
T
I
R
=
S
t
t
S
0
s
.
t
.
C
H
i
k
∈
1
,
N
F
,
P
i
k
∈
0
,
P
m
a
x
∀
i
∈
1
,
N
r
d
,
k
∈
1
,
N
S
.


### 3.1.2. Analysis of R2RCAM-IRO

Assume that when the maximum TIR is obtained, a readerR
i works in k
i
,
1
t
h
,
k
i
,
2
t
h
,
…
,
k
i
,
p
t
h slot (2
≤
p
≤
N
S and k
i
,
p
1
≠
k
i
,
p
2
,
∀
p
1
≠
p
2) and the interrogation radii are r
i
k
i
,
1
,
r
i
k
i
,
2
,
…
,
r
i
k
i
,
p, respectively. Without loss of generality, it is assumed that r
i
k
i
,
1
≥
r
i
k
i
,
2
≥
⋯
≥
r
i
k
i
,
p. As a result,(13)
R
g
i
=
⋃
m
=
1
p
R
g
i
k
i
,
m
=
R
g
i
k
i
,
1
.This indicates that if R
i just works in k
1
t
h slot, its interrogation area will not change. Assume that another reader R
j (j
≠
i) works in k
j
,
1
t
h
,
k
j
,
2
t
h
,
…
,
k
j
,
q
t
h slot (1
≤
q
≤
N
S, k
j
,
q
1
≠
k
j
,
q
2, ∀
q
1
≠
q
2, and ∃
k
u
∈
{
k
i
,
1
,
k
i
,
2
,
…
,
k
i
,
p
}) and its interrogation radius in k
u
t
h slot is denoted by r
j
k
u. If R
i does not work in k
u
t
h slot, the theoretical interrogation radius of R
j will increase because its total interference decreases. With the constraints of the maximum reader interrogation radius and the identification capacity, the interrogation radius r
j
k
u
∗ may be unchanged. Thus, r
j
k
u
∗
≥
r
j
k
u and R
g
j
k
u
∗
⊇
R
g
j
k
u can be obtained. Thus, the total interrogation region R
g
j
∗ of R
j satisfies(14)
R
g
j
∗
=
R
g
j
k
u
∗
∪
⋃
m
=
1
,
m
≠
k
u
q
R
g
j
k
m
⊇
R
g
j
k
u
∪
⋃
m
=
1
,
m
≠
k
u
q
R
g
j
k
m
=
R
g
j
.Thus, the total area of the interrogation regions of all the readers satisfies(15)
R
g
∗
=
R
g
j
∗
∪
⋃
m
=
1
,
m
≠
j
N
r
d
R
g
m
⊇
R
g
j
∪
⋃
m
=
1
,
m
≠
j
N
r
d
R
g
m
=
R
g
.Clearly, the total interrogation area of an RFID system when each reader just works in one slot is not less than that when some readers operate in two or more slots. Thus, only one slot can be allocated to each operating reader in R2RCAM-IRO.


### 3.1.3. Calculation Procedure ofS
t
t

Due to the interrogation region overlap,S
t
t cannot be calculated directly. Thus, agrid method is employed to compute S
t
t. Taking Figure 3 as an example, the details of the grid method are depicted as follows.Figure 3
Graphical representation of the grid method.Step 1.
Determine the region of all the circles shown as the red rectangle with the length ofL and the width of W.Step 2.
Divide the region intom
×
n (m
=
r
o
u
n
d
(
L
/
A
c
) and n
=
r
o
u
n
d
(
W
/
A
c
)) small rectangles with the area of S
s
r, where A
c determines the accuracy.Step 3.
Mark those small rectangles whose centers lie in any one of the circles as shown in yellow.Step 4.
Count the numberN
m
r of the marked small rectangles and use the total area of these rectangles as the result of S
t
t; that is, S
t
t
=
S
s
r
N
m
r.If the parameterA
c is large, the accuracy will be impaired. However, smaller A
c will result in a significant increase of the computational complexity. So, apreprocessing procedure is necessary to decrease the complexity by reducing the number of the circles and the area of the rectangular region. There are four situations for a single circle, where (S
1) it lies in some circle; (S
2) it is independent and does not intersect with any other circles; (S
3) it intersects with only one circle; or (S
4) it intersects with two or more circles. For any circle, if it is in S
1, it can be removed without having an impact on the result. If it is in S
2, its area can be calculated easily. If it is in S
3, its area without the overlap is added to the result. And then, this circle can be removed. It is assumed that a circle C
i with the centric point O
i intersects with the other circle C
j with the centric point O
j at point A and point B. And then the area S
o
l of the overlap can be obtained by(16)
S
o
l
=
t
i
r
i
2
+
t
j
r
j
2
-
r
i
d
i
j
sin
⁡
t
i
,
cos
⁡
t
i
=
r
i
2
+
d
i
j
2
-
r
j
2
2
r
i
d
i
j
,
cos
⁡
t
j
=
r
j
2
+
d
i
j
2
-
r
i
2
2
r
j
d
i
j
,where t
i is ∠
A
O
i
O
j, t
j is ∠
A
O
j
O
i, and d
i
j is the distance from the point O
i to the point O
j. For S
4, the grid method is employed.Taking Figure4 as an example, the details of the preprocessing procedure are depicted as follows.Figure 4
Example of the preprocessing procedure.Step 1.
Find the circles in some other circles, such as the one in the red solid box in Figure4(a). And then remove it.Step 2.
Find the independent circles, such as the two in the red solid box in Figure4(b). Calculate their area and add it to the result. And then remove them.Step 3.
Find the circles intersected with only one other circle, such as the one in the red solid box in Figure4(c). Calculate the area without the overlap as shown in green by (16) and add it to the result. And then remove it.Step 4.
If new independent circles or ones intersected with another circle appear, repeat Steps  2 and  3 until any circle intersects with two or more other ones.Step 5.
Separate the rest of the circles into groups, where the intersected circles belong to the same group and circles in different groups do not intersect with each other, as shown in Figure4(d). And the area of each group is calculated by the grid method.


## 3.1.1. Modeling of R2RCAM-IRO

To solve theoretical optimization problem, let us assume thatN
t
g tags are distributed uniformly in the deployment region and the maximum transmitting power of readers is P
m
a
x. And the other assumptions are the same as those of R2RCAM.Taking into account the identification capacity of a reader in a slot,r
i
k must satisfy(7)
N
t
g
π
r
i
k
2
S
0
≤
N
t
g
,
m
a
x
i
,where N
t
g
,
m
a
x
i is the maximum number of tags that R
i can identify in one slot. As a result, we can get(8)
r
i
k
≤
S
0
N
t
g
,
m
a
x
i
π
N
t
g
.According to (3) and (8), r
i
k is determined by(9)
r
i
k
=
min
⁡
r
i
,
t
h
k
,
r
i
,
m
a
x
k
,
S
0
N
t
g
,
m
a
x
i
π
N
t
g
.Tag identification rate (TIR) is a measure of the RFID system performance. TIR is defined as the ratio of the number of identifiable tags to the total number of tags. Because of the assumption that the tags are distributed uniformly, TIR is equal to the ratio of the total interrogation area to the reader deployment region area. That is, (10)
T
I
R
=
S
t
t
S
0
.In the canonical R2RCAM, S
t
t is calculated easily by (5). However, there may be an overlap between the interrogation regions of some readers. Thus, the canonical R2RCAM does not meet the practice requirement and decreases TIR of the RFID system. Let R
g
i represent the interrogation region of the reader R
i. And in the proposed R2RCAM-IRO, the total interrogation region R
g follows(11)
R
g
=
⋃
i
=
1
N
r
d
R
g
i
=
⋃
i
=
1
N
r
d
⋃
k
=
1
N
S
R
g
i
k
,where R
g
i
k is the interrogation region of R
i in the k
t
h slot.Consequently, R2RCAM-IRO can be formulated as(12)
m
a
x
i
m
i
z
e
T
I
R
=
S
t
t
S
0
s
.
t
.
C
H
i
k
∈
1
,
N
F
,
P
i
k
∈
0
,
P
m
a
x
∀
i
∈
1
,
N
r
d
,
k
∈
1
,
N
S
.


## 3.1.2. Analysis of R2RCAM-IRO

Assume that when the maximum TIR is obtained, a readerR
i works in k
i
,
1
t
h
,
k
i
,
2
t
h
,
…
,
k
i
,
p
t
h slot (2
≤
p
≤
N
S and k
i
,
p
1
≠
k
i
,
p
2
,
∀
p
1
≠
p
2) and the interrogation radii are r
i
k
i
,
1
,
r
i
k
i
,
2
,
…
,
r
i
k
i
,
p, respectively. Without loss of generality, it is assumed that r
i
k
i
,
1
≥
r
i
k
i
,
2
≥
⋯
≥
r
i
k
i
,
p. As a result,(13)
R
g
i
=
⋃
m
=
1
p
R
g
i
k
i
,
m
=
R
g
i
k
i
,
1
.This indicates that if R
i just works in k
1
t
h slot, its interrogation area will not change. Assume that another reader R
j (j
≠
i) works in k
j
,
1
t
h
,
k
j
,
2
t
h
,
…
,
k
j
,
q
t
h slot (1
≤
q
≤
N
S, k
j
,
q
1
≠
k
j
,
q
2, ∀
q
1
≠
q
2, and ∃
k
u
∈
{
k
i
,
1
,
k
i
,
2
,
…
,
k
i
,
p
}) and its interrogation radius in k
u
t
h slot is denoted by r
j
k
u. If R
i does not work in k
u
t
h slot, the theoretical interrogation radius of R
j will increase because its total interference decreases. With the constraints of the maximum reader interrogation radius and the identification capacity, the interrogation radius r
j
k
u
∗ may be unchanged. Thus, r
j
k
u
∗
≥
r
j
k
u and R
g
j
k
u
∗
⊇
R
g
j
k
u can be obtained. Thus, the total interrogation region R
g
j
∗ of R
j satisfies(14)
R
g
j
∗
=
R
g
j
k
u
∗
∪
⋃
m
=
1
,
m
≠
k
u
q
R
g
j
k
m
⊇
R
g
j
k
u
∪
⋃
m
=
1
,
m
≠
k
u
q
R
g
j
k
m
=
R
g
j
.Thus, the total area of the interrogation regions of all the readers satisfies(15)
R
g
∗
=
R
g
j
∗
∪
⋃
m
=
1
,
m
≠
j
N
r
d
R
g
m
⊇
R
g
j
∪
⋃
m
=
1
,
m
≠
j
N
r
d
R
g
m
=
R
g
.Clearly, the total interrogation area of an RFID system when each reader just works in one slot is not less than that when some readers operate in two or more slots. Thus, only one slot can be allocated to each operating reader in R2RCAM-IRO.


## 3.1.3. Calculation Procedure ofS
t
t

Due to the interrogation region overlap,S
t
t cannot be calculated directly. Thus, agrid method is employed to compute S
t
t. Taking Figure 3 as an example, the details of the grid method are depicted as follows.Figure 3
Graphical representation of the grid method.Step 1.
Determine the region of all the circles shown as the red rectangle with the length ofL and the width of W.Step 2.
Divide the region intom
×
n (m
=
r
o
u
n
d
(
L
/
A
c
) and n
=
r
o
u
n
d
(
W
/
A
c
)) small rectangles with the area of S
s
r, where A
c determines the accuracy.Step 3.
Mark those small rectangles whose centers lie in any one of the circles as shown in yellow.Step 4.
Count the numberN
m
r of the marked small rectangles and use the total area of these rectangles as the result of S
t
t; that is, S
t
t
=
S
s
r
N
m
r.If the parameterA
c is large, the accuracy will be impaired. However, smaller A
c will result in a significant increase of the computational complexity. So, apreprocessing procedure is necessary to decrease the complexity by reducing the number of the circles and the area of the rectangular region. There are four situations for a single circle, where (S
1) it lies in some circle; (S
2) it is independent and does not intersect with any other circles; (S
3) it intersects with only one circle; or (S
4) it intersects with two or more circles. For any circle, if it is in S
1, it can be removed without having an impact on the result. If it is in S
2, its area can be calculated easily. If it is in S
3, its area without the overlap is added to the result. And then, this circle can be removed. It is assumed that a circle C
i with the centric point O
i intersects with the other circle C
j with the centric point O
j at point A and point B. And then the area S
o
l of the overlap can be obtained by(16)
S
o
l
=
t
i
r
i
2
+
t
j
r
j
2
-
r
i
d
i
j
sin
⁡
t
i
,
cos
⁡
t
i
=
r
i
2
+
d
i
j
2
-
r
j
2
2
r
i
d
i
j
,
cos
⁡
t
j
=
r
j
2
+
d
i
j
2
-
r
i
2
2
r
j
d
i
j
,where t
i is ∠
A
O
i
O
j, t
j is ∠
A
O
j
O
i, and d
i
j is the distance from the point O
i to the point O
j. For S
4, the grid method is employed.Taking Figure4 as an example, the details of the preprocessing procedure are depicted as follows.Figure 4
Example of the preprocessing procedure.Step 1.
Find the circles in some other circles, such as the one in the red solid box in Figure4(a). And then remove it.Step 2.
Find the independent circles, such as the two in the red solid box in Figure4(b). Calculate their area and add it to the result. And then remove them.Step 3.
Find the circles intersected with only one other circle, such as the one in the red solid box in Figure4(c). Calculate the area without the overlap as shown in green by (16) and add it to the result. And then remove it.Step 4.
If new independent circles or ones intersected with another circle appear, repeat Steps  2 and  3 until any circle intersects with two or more other ones.Step 5.
Separate the rest of the circles into groups, where the intersected circles belong to the same group and circles in different groups do not intersect with each other, as shown in Figure4(d). And the area of each group is calculated by the grid method.


## 3.2. RA-IRO-aiNet

By improving the main immune operators, artificial immune networks become efficient, adaptive, and suitable for the practical applications. To find the optimal scheme of time slots, channels, and power for an RFID reader network, this subsection designs RA-IRO-aiNet to solve R2RCAM-IRO. The technical details of the proposed algorithm are introduced in the following subsections.


### 3.2.1. Encoding Format

A hybrid encoding format is used in RA-IRO-aiNet uses. Table2 presents the encoding format used by the i
t
h antibody. In Table 2, each antibody includes three segments of the slot, the channel, and the power, where T
i
,
j
∈
[
0
,
N
S
] is an integer and denotes the time slot, C
h
i
,
j
∈
[
1
,
N
F
] is an integer and denotes the channel, and P
i
,
j
∈
(
0
,
P
m
a
x
] is a real number and denotes the power. Note that T
i
,
j
=
0 means that R
j does not operate.Table 2
Encoding format for the antibody individual.
Slot segment
Channel segment
Power segment
T
i
,
1
,
T
i
,
2
,
…
,
T
i
,
N
r
d
C
h
i
,
1
,
C
h
i
,
2
,
…
,
C
h
i
,
N
r
d
P
i
,
1
,
P
i
,
2
,
…
,
P
i
,
N
r
d


### 3.2.2. Affinity Function

To evaluate each antibody individual about the resource scheduling solution, an affinity function is designed according to R2RCAM-IRO presented in Section2, which is presented as(17)
A
f
f
A
b
=
S
t
t
S
0
.


### 3.2.3. Initialization

In the initialization, an antibody population withN
a
b individuals is constructed randomly. And each antibody must be feasible, where T
i
,
j
∈
{
0,1
,
…
,
N
S
}, C
h
i
,
j
∈
{
1,2
,
…
,
N
C
h
}, and P
i
,
j
∈
(
0
,
P
m
a
x
] for i
∈
{
1,2
,
…
,
N
a
b
} and j
∈
{
1,2
,
…
,
N
r
d
}.


### 3.2.4. Cloning Operator

Theuniform cloning operator is used, where each antibody is reproduced for a constant multiplier of N
C. The uniform cloning is simple to implement and can remarkably depress the computational consumption. All the cloned offsprings except the parent antibodies will execute the following mutation operator in order to increase the population diversity.


### 3.2.5. Mutation Operator

Because the proposed RA-IRO-aiNet uses hybrid encoding, adifferentiated mutation operator is employed, in which different segments (i.e., the slot, the channel, and the power) of each antibody experience different mutation processes. In detail, therandom uniform mutation operator is employed for the slot segment and the channel segment, where a randomly selected bit is changed randomly in its set of feasible solutions. And for the power segment, the usedGaussian mutation operator is given in (6). Note that only one randomly selected segment experiences the mutation for each offspring. The pseudocode of the mutation process is shown in Pseudocode 1.Pseudocode 1:Pseudocode of the mutation process.
PROCEDURE Mutation Operator (A
b
i)
a
=
r
a
n
d
∈
1,2
,
3;
SWITCH
a
CASE 1:
b
=
r
a
n
d
∈
1,2
,
…
,
N
r
d;
T
i
,
b
=
r
a
n
d
∈
0,1
,
…
,
N
S;
CASE 2:
b
=
r
a
n
d
∈
1,2
,
…
,
N
r
d;
C
h
i
,
b
=
r
a
n
d
∈
1,2
,
…
,
N
F;
CASE 3:
P
i
,
j
=
P
i
,
j
+
exp
⁡
(
-
A
f
f
∗
(
A
b
i
)
)
G
(
0,1
)
/
β
,
j
=
1,2
,
…
,
N
r
d;
END SWITCH
END PROCEDURE


### 3.2.6. Suppression Operator and Recruitment

The similarity between any two antibodies is evaluated by the measure ofhybrid distance (D
H
y
b). It is obtained by the sum of the normalized distance of each segment. The corresponding formula is given in (18)(18)
D
H
y
b
A
b
i
,
A
b
j
=
D
H
a
m
,
T
A
b
i
,
A
b
j
N
r
d
+
D
H
a
m
,
C
h
A
b
i
,
A
b
j
N
r
d
+
D
E
u
c
,
P
A
b
i
,
A
b
j
D
m
a
x
,where D
H
a
m
,
T
(
·
,
·
) and D
H
a
m
,
C
h
(
·
,
·
) are the Hamming distance of the slot segment and the channel segment, respectively, D
E
u
c
,
P
(
·
,
·
) is the Euclidean distance of the power segment, and D
m
a
x is the maximum Euclidean distance which equals P
m
a
x
N
r
d. The higher the hybrid distance is, the better diversity the antibody population has. Thus, in order to keep the diversity of the antibody population, once the hybrid distance of two antibodies is smaller than a threshold δ
S, the antibody with lower affinity will be suppressed. The threshold is determined by such defined similarity following(19)
δ
S
=
min
⁡
D
H
y
b
A
b
i
,
A
b
j
,
i
≠
j
+
ξ
max
⁡
D
H
y
b
A
b
i
,
A
b
j
-
min
⁡
D
H
y
b
A
b
i
,
A
b
j
.The desired goal is to adjust the threshold dynamically and to remove those ξ
(
0
<
ξ
<
1
) of similar antibodies. After the suppression operator, some new antibodies are randomly produced to keep the antibody population at the number of N
a
b.The flowchart of our proposed RA-IRO-aiNet is shown in Figure5. The left orange box shows the flowchart of opt-aiNet, while the right green box highlights the revised immune operators of RA-IRO-aiNet. In RA-IRO-aiNet, each antibody experiences the uniform cloning operator, the differentiated mutation operator, the hybrid similarity evaluation, the similarity-based suppression operator, and the recruitment in each generation. Repeat the above process until it is terminated.Figure 5
Flowchart of the proposed RA-IRO-aiNet.


## 3.2.1. Encoding Format

A hybrid encoding format is used in RA-IRO-aiNet uses. Table2 presents the encoding format used by the i
t
h antibody. In Table 2, each antibody includes three segments of the slot, the channel, and the power, where T
i
,
j
∈
[
0
,
N
S
] is an integer and denotes the time slot, C
h
i
,
j
∈
[
1
,
N
F
] is an integer and denotes the channel, and P
i
,
j
∈
(
0
,
P
m
a
x
] is a real number and denotes the power. Note that T
i
,
j
=
0 means that R
j does not operate.Table 2
Encoding format for the antibody individual.
Slot segment
Channel segment
Power segment
T
i
,
1
,
T
i
,
2
,
…
,
T
i
,
N
r
d
C
h
i
,
1
,
C
h
i
,
2
,
…
,
C
h
i
,
N
r
d
P
i
,
1
,
P
i
,
2
,
…
,
P
i
,
N
r
d


## 3.2.2. Affinity Function

To evaluate each antibody individual about the resource scheduling solution, an affinity function is designed according to R2RCAM-IRO presented in Section2, which is presented as(17)
A
f
f
A
b
=
S
t
t
S
0
.


## 3.2.3. Initialization

In the initialization, an antibody population withN
a
b individuals is constructed randomly. And each antibody must be feasible, where T
i
,
j
∈
{
0,1
,
…
,
N
S
}, C
h
i
,
j
∈
{
1,2
,
…
,
N
C
h
}, and P
i
,
j
∈
(
0
,
P
m
a
x
] for i
∈
{
1,2
,
…
,
N
a
b
} and j
∈
{
1,2
,
…
,
N
r
d
}.


## 3.2.4. Cloning Operator

Theuniform cloning operator is used, where each antibody is reproduced for a constant multiplier of N
C. The uniform cloning is simple to implement and can remarkably depress the computational consumption. All the cloned offsprings except the parent antibodies will execute the following mutation operator in order to increase the population diversity.


## 3.2.5. Mutation Operator

Because the proposed RA-IRO-aiNet uses hybrid encoding, adifferentiated mutation operator is employed, in which different segments (i.e., the slot, the channel, and the power) of each antibody experience different mutation processes. In detail, therandom uniform mutation operator is employed for the slot segment and the channel segment, where a randomly selected bit is changed randomly in its set of feasible solutions. And for the power segment, the usedGaussian mutation operator is given in (6). Note that only one randomly selected segment experiences the mutation for each offspring. The pseudocode of the mutation process is shown in Pseudocode 1.Pseudocode 1:Pseudocode of the mutation process.
PROCEDURE Mutation Operator (A
b
i)
a
=
r
a
n
d
∈
1,2
,
3;
SWITCH
a
CASE 1:
b
=
r
a
n
d
∈
1,2
,
…
,
N
r
d;
T
i
,
b
=
r
a
n
d
∈
0,1
,
…
,
N
S;
CASE 2:
b
=
r
a
n
d
∈
1,2
,
…
,
N
r
d;
C
h
i
,
b
=
r
a
n
d
∈
1,2
,
…
,
N
F;
CASE 3:
P
i
,
j
=
P
i
,
j
+
exp
⁡
(
-
A
f
f
∗
(
A
b
i
)
)
G
(
0,1
)
/
β
,
j
=
1,2
,
…
,
N
r
d;
END SWITCH
END PROCEDURE


## 3.2.6. Suppression Operator and Recruitment

The similarity between any two antibodies is evaluated by the measure ofhybrid distance (D
H
y
b). It is obtained by the sum of the normalized distance of each segment. The corresponding formula is given in (18)(18)
D
H
y
b
A
b
i
,
A
b
j
=
D
H
a
m
,
T
A
b
i
,
A
b
j
N
r
d
+
D
H
a
m
,
C
h
A
b
i
,
A
b
j
N
r
d
+
D
E
u
c
,
P
A
b
i
,
A
b
j
D
m
a
x
,where D
H
a
m
,
T
(
·
,
·
) and D
H
a
m
,
C
h
(
·
,
·
) are the Hamming distance of the slot segment and the channel segment, respectively, D
E
u
c
,
P
(
·
,
·
) is the Euclidean distance of the power segment, and D
m
a
x is the maximum Euclidean distance which equals P
m
a
x
N
r
d. The higher the hybrid distance is, the better diversity the antibody population has. Thus, in order to keep the diversity of the antibody population, once the hybrid distance of two antibodies is smaller than a threshold δ
S, the antibody with lower affinity will be suppressed. The threshold is determined by such defined similarity following(19)
δ
S
=
min
⁡
D
H
y
b
A
b
i
,
A
b
j
,
i
≠
j
+
ξ
max
⁡
D
H
y
b
A
b
i
,
A
b
j
-
min
⁡
D
H
y
b
A
b
i
,
A
b
j
.The desired goal is to adjust the threshold dynamically and to remove those ξ
(
0
<
ξ
<
1
) of similar antibodies. After the suppression operator, some new antibodies are randomly produced to keep the antibody population at the number of N
a
b.The flowchart of our proposed RA-IRO-aiNet is shown in Figure5. The left orange box shows the flowchart of opt-aiNet, while the right green box highlights the revised immune operators of RA-IRO-aiNet. In RA-IRO-aiNet, each antibody experiences the uniform cloning operator, the differentiated mutation operator, the hybrid similarity evaluation, the similarity-based suppression operator, and the recruitment in each generation. Repeat the above process until it is terminated.Figure 5
Flowchart of the proposed RA-IRO-aiNet.


## 4. Simulations and Results

### 4.1. Environment for Simulation

In the numerical simulations, suppose that readers are randomly deployed in a square area of 100 × 100 m2 and in the multiple-reader scenarios, where readers and tags transmit in the same channels following EPCglobal C1G2 [10]. All parameters in R2RCAM-IRO are listed in Table 3.Table 3
Parameters in R2RCAM-IRO.
Parameter
Value
Operating frequency
902–928 MHz
Bandwidth
500 KHz
Normalized spectrum power,α
b
ω
0.86
Reader antenna gain,G
T, G
R
6 dBi
Reflection coefficient of effective power,E
t
g
0.1
Required minimum power for tag operation,P
m
i
n
−15 dBm
Reference path loss,P
L
0
−31.6 dB
Minimum SINR,S
I
N
R
m
i
n
11.6 dB
Exponent of the path loss,γ
2.5
Noise power,N
S
−90 dBm
Modulation depth,M
d
0.1
Number of the tags,N
t
g
100000
Maximum identifiable tag number of a reader in a slot,N
t
g
,
m
a
x
4000
Accuracy,A
c
0.01
Spectrum mask,β
m
(
Δ
C
H
)
Δ
C
H
=
0
0 dB
Δ
C
H
=
1
−20 dB
Δ
C
H
=
2
−50 dB
Δ
C
H
=
3
−60 dB
Δ
C
H
>
3
−65 dB


### 4.2. Simulation Results and Discussion

The effectiveness of the proposed R2RCAM-IRO optimized by the designed RA-IRO-aiNet is discussed in this subsection. And furthermore, the efficiency of the designed RA-IRO-aiNet is examined by comparison with RA-GA [5], PSO [4], and opt-aiNet [9] in the total coverage area of the readers.For all algorithms in the simulations, the population size is set to 50, the maximum number of generations is set to 1000, and all the numerical simulations are repeated for 50 runs. In the proposed RA-IRO-aiNet, the encoding format has been introduced in Section3.2.1, the cloned multiplier N
C is 10, the control parameter of mutation β is 100, and the suppression parameter ξ is 10%. RA-GA uses hybrid encoding; in other words, the integer encoding is used in both the slot segment and the channel segment, and the 6-bit binary encoding for P
i
,
j is used in the power segment. PSO uses real number encoding. And, opt-aiNet also uses real number encoding and has the same cloned copies and control parameters of mutation to the proposed RA-IRO-aiNet. Other parameters of RA-GA, opt-aiNet, and PSO used in the simulations are referred to in [4, 5] and [9], respectively.


#### 4.2.1. Effectiveness of the Proposed R2RCAM-IRO

Figure6 shows TIRs from two different models: the proposed R2RCAM-IRO and R2RCAM. Note that the overlap is considered in R2RCAM-IRO but not in R2RCAM. As shown in Figure 6, TIRs grow nonlinearly as the number of readers increases and is less than 24. When more readers are added, R2RCP become more serious, and thus the solution dimension increases more. It heavily degrades the convergence performance of RA-IRO-aiNet. Consequently, TIRs begin to decrease. These two models have similar TIR with less than 10 readers, while TIR of the proposed R2RCAM-IRO is much better than that of R2RCAM. For example, with 20 readers, the proposed R2RCAM-IRO harvests an improvement of 11.9%.Figure 6
Tag identification rate.Assume that 10 channels are available for 20 readers, and the maximum power is 1 W. In this case, Figure7 shows the effect of the number of available time slots on TIR. Seen from Figure 7, when the slot number increases from 3 to 15, TIR increases nonlinearly and is gradually approximate to 38% optimized by the proposed R2RCAM-IRO, while TIR is lower than 36%, if R2RCAM is used.Figure 7
Effect of the number of available time slots.Assume that 5 time slots are available for 20 readers, and the maximum power is 1 W. In this case, Figure8 presents the effect of the number of available channels. In Figure 8, TIRs of the two models are similar when the number available channels is less than 6, while the proposed R2RCAM-IRO shows its superiority obviously with more available channels. In particular, with 20 channels, TIR of the proposed R2RCAM-IRO can reach 33.6%, which improves R2RCAM by 16.7%.Figure 8
Effect of the number of available channels.Assume that 5 time slots and 10 channels are available for 20 readers. In this case, Figure9 describes the effect of the power. As shown in Figure 9, TIR increases when the power becomes greater and is approaching 31% for the proposed R2RCAM-IRO, while it is approaching 29% for R2RCAM. The proposed R2RCAM-IRO improves TIR by 7.9% with the maximum power of 2 W compared with R2RCAM.Figure 9
Effect of the power.The results from Figures6–9 illustrate that R2RCAM-IRO is effective and outperforms R2RCAM, where the overlap is ignored in the tag identification rate with limited resources.


#### 4.2.2. Comparison in the Total Coverage Area of the Readers

Assume that 5 time slots and 10 channels are available for 20 readers, and the maximum power is 1 W. In this case, Figure10 shows the total coverage area of readers based on the proposed model optimized by RA-GA, opt-aiNet, PSO, and the proposed RA-IRO-aiNet.Figure 10
Total coverage area.As shown in Figure10, these four algorithms perform similarly to some extent in the optimal total coverage area with less than 6 readers. This is because the dimension of the solution is so low that each algorithm can capture the global optima and some desired solution. However, as more readers are added, the dimension of the solution becomes higher, which degrades the convergence performance. And the total coverage area optimized by RA-IRO-aiNet is much better than those obtained by the other algorithms. In particular, with 30 readers, the proposed algorithm has an improvement of 14.69%, 49.15%, and 74.43% compared with RA-GA, opt-aiNet, and PSO, respectively.Figure11 gives the graphical representations of interrogation regions with 30 readers for the best solutions optimized by RA-GA, opt-aiNet, PSO, and the proposed RA-IRO-aiNet, respectively.Figure 11
Graphical representation of the readers’ interrogation regions.
(a)
RA-GA
(b)
opt-aiNet
(c)
PSO
(d)
The proposed RA-IRO-aiNetAs shown in Figure11, it is clear that the readers, where the proposed RA-IRO-aiNet is used, have much larger interrogation region than those by the other three algorithms. The proposed RA-IRO-aiNet has 16 operating readers with the average radius of 3.9887 m, while RA-GA has 15 operating readers with the average radius of 3.4899 m, PSO has 14 operating readers with the average radius of 3.6659 m, and opt-aiNet has 15 operating readers with the average radius of 3.0091 m. This indicates that the proposed RA-IRO-aiNet has larger average radius with more operating readers and outperforms the other three algorithms in interrogation regions especially in dense reader scenarios.


## 4.1. Environment for Simulation

In the numerical simulations, suppose that readers are randomly deployed in a square area of 100 × 100 m2 and in the multiple-reader scenarios, where readers and tags transmit in the same channels following EPCglobal C1G2 [10]. All parameters in R2RCAM-IRO are listed in Table 3.Table 3
Parameters in R2RCAM-IRO.
Parameter
Value
Operating frequency
902–928 MHz
Bandwidth
500 KHz
Normalized spectrum power,α
b
ω
0.86
Reader antenna gain,G
T, G
R
6 dBi
Reflection coefficient of effective power,E
t
g
0.1
Required minimum power for tag operation,P
m
i
n
−15 dBm
Reference path loss,P
L
0
−31.6 dB
Minimum SINR,S
I
N
R
m
i
n
11.6 dB
Exponent of the path loss,γ
2.5
Noise power,N
S
−90 dBm
Modulation depth,M
d
0.1
Number of the tags,N
t
g
100000
Maximum identifiable tag number of a reader in a slot,N
t
g
,
m
a
x
4000
Accuracy,A
c
0.01
Spectrum mask,β
m
(
Δ
C
H
)
Δ
C
H
=
0
0 dB
Δ
C
H
=
1
−20 dB
Δ
C
H
=
2
−50 dB
Δ
C
H
=
3
−60 dB
Δ
C
H
>
3
−65 dB


## 4.2. Simulation Results and Discussion

The effectiveness of the proposed R2RCAM-IRO optimized by the designed RA-IRO-aiNet is discussed in this subsection. And furthermore, the efficiency of the designed RA-IRO-aiNet is examined by comparison with RA-GA [5], PSO [4], and opt-aiNet [9] in the total coverage area of the readers.For all algorithms in the simulations, the population size is set to 50, the maximum number of generations is set to 1000, and all the numerical simulations are repeated for 50 runs. In the proposed RA-IRO-aiNet, the encoding format has been introduced in Section3.2.1, the cloned multiplier N
C is 10, the control parameter of mutation β is 100, and the suppression parameter ξ is 10%. RA-GA uses hybrid encoding; in other words, the integer encoding is used in both the slot segment and the channel segment, and the 6-bit binary encoding for P
i
,
j is used in the power segment. PSO uses real number encoding. And, opt-aiNet also uses real number encoding and has the same cloned copies and control parameters of mutation to the proposed RA-IRO-aiNet. Other parameters of RA-GA, opt-aiNet, and PSO used in the simulations are referred to in [4, 5] and [9], respectively.


### 4.2.1. Effectiveness of the Proposed R2RCAM-IRO

Figure6 shows TIRs from two different models: the proposed R2RCAM-IRO and R2RCAM. Note that the overlap is considered in R2RCAM-IRO but not in R2RCAM. As shown in Figure 6, TIRs grow nonlinearly as the number of readers increases and is less than 24. When more readers are added, R2RCP become more serious, and thus the solution dimension increases more. It heavily degrades the convergence performance of RA-IRO-aiNet. Consequently, TIRs begin to decrease. These two models have similar TIR with less than 10 readers, while TIR of the proposed R2RCAM-IRO is much better than that of R2RCAM. For example, with 20 readers, the proposed R2RCAM-IRO harvests an improvement of 11.9%.Figure 6
Tag identification rate.Assume that 10 channels are available for 20 readers, and the maximum power is 1 W. In this case, Figure7 shows the effect of the number of available time slots on TIR. Seen from Figure 7, when the slot number increases from 3 to 15, TIR increases nonlinearly and is gradually approximate to 38% optimized by the proposed R2RCAM-IRO, while TIR is lower than 36%, if R2RCAM is used.Figure 7
Effect of the number of available time slots.Assume that 5 time slots are available for 20 readers, and the maximum power is 1 W. In this case, Figure8 presents the effect of the number of available channels. In Figure 8, TIRs of the two models are similar when the number available channels is less than 6, while the proposed R2RCAM-IRO shows its superiority obviously with more available channels. In particular, with 20 channels, TIR of the proposed R2RCAM-IRO can reach 33.6%, which improves R2RCAM by 16.7%.Figure 8
Effect of the number of available channels.Assume that 5 time slots and 10 channels are available for 20 readers. In this case, Figure9 describes the effect of the power. As shown in Figure 9, TIR increases when the power becomes greater and is approaching 31% for the proposed R2RCAM-IRO, while it is approaching 29% for R2RCAM. The proposed R2RCAM-IRO improves TIR by 7.9% with the maximum power of 2 W compared with R2RCAM.Figure 9
Effect of the power.The results from Figures6–9 illustrate that R2RCAM-IRO is effective and outperforms R2RCAM, where the overlap is ignored in the tag identification rate with limited resources.


### 4.2.2. Comparison in the Total Coverage Area of the Readers

Assume that 5 time slots and 10 channels are available for 20 readers, and the maximum power is 1 W. In this case, Figure10 shows the total coverage area of readers based on the proposed model optimized by RA-GA, opt-aiNet, PSO, and the proposed RA-IRO-aiNet.Figure 10
Total coverage area.As shown in Figure10, these four algorithms perform similarly to some extent in the optimal total coverage area with less than 6 readers. This is because the dimension of the solution is so low that each algorithm can capture the global optima and some desired solution. However, as more readers are added, the dimension of the solution becomes higher, which degrades the convergence performance. And the total coverage area optimized by RA-IRO-aiNet is much better than those obtained by the other algorithms. In particular, with 30 readers, the proposed algorithm has an improvement of 14.69%, 49.15%, and 74.43% compared with RA-GA, opt-aiNet, and PSO, respectively.Figure11 gives the graphical representations of interrogation regions with 30 readers for the best solutions optimized by RA-GA, opt-aiNet, PSO, and the proposed RA-IRO-aiNet, respectively.Figure 11
Graphical representation of the readers’ interrogation regions.
(a)
RA-GA
(b)
opt-aiNet
(c)
PSO
(d)
The proposed RA-IRO-aiNetAs shown in Figure11, it is clear that the readers, where the proposed RA-IRO-aiNet is used, have much larger interrogation region than those by the other three algorithms. The proposed RA-IRO-aiNet has 16 operating readers with the average radius of 3.9887 m, while RA-GA has 15 operating readers with the average radius of 3.4899 m, PSO has 14 operating readers with the average radius of 3.6659 m, and opt-aiNet has 15 operating readers with the average radius of 3.0091 m. This indicates that the proposed RA-IRO-aiNet has larger average radius with more operating readers and outperforms the other three algorithms in interrogation regions especially in dense reader scenarios.


## 4.2.1. Effectiveness of the Proposed R2RCAM-IRO

Figure6 shows TIRs from two different models: the proposed R2RCAM-IRO and R2RCAM. Note that the overlap is considered in R2RCAM-IRO but not in R2RCAM. As shown in Figure 6, TIRs grow nonlinearly as the number of readers increases and is less than 24. When more readers are added, R2RCP become more serious, and thus the solution dimension increases more. It heavily degrades the convergence performance of RA-IRO-aiNet. Consequently, TIRs begin to decrease. These two models have similar TIR with less than 10 readers, while TIR of the proposed R2RCAM-IRO is much better than that of R2RCAM. For example, with 20 readers, the proposed R2RCAM-IRO harvests an improvement of 11.9%.Figure 6
Tag identification rate.Assume that 10 channels are available for 20 readers, and the maximum power is 1 W. In this case, Figure7 shows the effect of the number of available time slots on TIR. Seen from Figure 7, when the slot number increases from 3 to 15, TIR increases nonlinearly and is gradually approximate to 38% optimized by the proposed R2RCAM-IRO, while TIR is lower than 36%, if R2RCAM is used.Figure 7
Effect of the number of available time slots.Assume that 5 time slots are available for 20 readers, and the maximum power is 1 W. In this case, Figure8 presents the effect of the number of available channels. In Figure 8, TIRs of the two models are similar when the number available channels is less than 6, while the proposed R2RCAM-IRO shows its superiority obviously with more available channels. In particular, with 20 channels, TIR of the proposed R2RCAM-IRO can reach 33.6%, which improves R2RCAM by 16.7%.Figure 8
Effect of the number of available channels.Assume that 5 time slots and 10 channels are available for 20 readers. In this case, Figure9 describes the effect of the power. As shown in Figure 9, TIR increases when the power becomes greater and is approaching 31% for the proposed R2RCAM-IRO, while it is approaching 29% for R2RCAM. The proposed R2RCAM-IRO improves TIR by 7.9% with the maximum power of 2 W compared with R2RCAM.Figure 9
Effect of the power.The results from Figures6–9 illustrate that R2RCAM-IRO is effective and outperforms R2RCAM, where the overlap is ignored in the tag identification rate with limited resources.


## 4.2.2. Comparison in the Total Coverage Area of the Readers

Assume that 5 time slots and 10 channels are available for 20 readers, and the maximum power is 1 W. In this case, Figure10 shows the total coverage area of readers based on the proposed model optimized by RA-GA, opt-aiNet, PSO, and the proposed RA-IRO-aiNet.Figure 10
Total coverage area.As shown in Figure10, these four algorithms perform similarly to some extent in the optimal total coverage area with less than 6 readers. This is because the dimension of the solution is so low that each algorithm can capture the global optima and some desired solution. However, as more readers are added, the dimension of the solution becomes higher, which degrades the convergence performance. And the total coverage area optimized by RA-IRO-aiNet is much better than those obtained by the other algorithms. In particular, with 30 readers, the proposed algorithm has an improvement of 14.69%, 49.15%, and 74.43% compared with RA-GA, opt-aiNet, and PSO, respectively.Figure11 gives the graphical representations of interrogation regions with 30 readers for the best solutions optimized by RA-GA, opt-aiNet, PSO, and the proposed RA-IRO-aiNet, respectively.Figure 11
Graphical representation of the readers’ interrogation regions.
(a)
RA-GA
(b)
opt-aiNet
(c)
PSO
(d)
The proposed RA-IRO-aiNetAs shown in Figure11, it is clear that the readers, where the proposed RA-IRO-aiNet is used, have much larger interrogation region than those by the other three algorithms. The proposed RA-IRO-aiNet has 16 operating readers with the average radius of 3.9887 m, while RA-GA has 15 operating readers with the average radius of 3.4899 m, PSO has 14 operating readers with the average radius of 3.6659 m, and opt-aiNet has 15 operating readers with the average radius of 3.0091 m. This indicates that the proposed RA-IRO-aiNet has larger average radius with more operating readers and outperforms the other three algorithms in interrogation regions especially in dense reader scenarios.


## 5. Conclusions

In this paper, the problem of RFID reader-to-reader collision is studied. And an enhanced collision avoidance model (i.e., R2RCAM-IRO) related to time slots, channels, and power is formulated. In the proposed model, the overlap between the interrogation regions of readers and the tag identification capacity of readers are considered. This makes R2RCAM-IRO suitable for the practice of RFID applications. In addition, a revised artificial immune network (i.e., RA-IRO-aiNet) is designed to optimize the proposed R2RCAM-IRO. In RA-IRO-aiNet, the hybrid encoding, uniform cloning, differentiated mutation, hybrid distance based similarity evaluation, and similarity-based suppression are helpful to optimize the proposed R2RCAM-IRO. The simulation results show that the proposed R2RCAM-IRO is effective in tag identification rate with limited communication resources and the proposed RA-IRO-aiNet outperforms RA-GA, opt-aiNet, and PSO in the total coverage area of readers.



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*Source: 7854154-2016-01-19.xml*