Geometric Distribution-Based Readers Scheduling Optimization Algorithm Using Artificial Immune System

Abstract

In the multiple-reader environment (MRE) of radio frequency identification (RFID) system, multiple readers are often scheduled to interrogate the randomized tags via operating at different time slots or frequency channels to decrease the signal interferences. Based on this, a Geometric Distribution-based Multiple-reader Scheduling Optimization Algorithm using Artificial Immune System (GD-MRSOA-AIS) is proposed to fairly and optimally schedule the readers operating from the viewpoint of resource allocations. GD-MRSOA-AIS is composed of two parts, where a geometric distribution function combined with the fairness consideration is first introduced to generate the feasible scheduling schemes for reader operation. After that, artificial immune system (including immune clone, immune mutation and immune suppression) quickly optimize these feasible ones as the optimal scheduling scheme to ensure that readers are fairly operating with larger effective interrogation range and lower interferences. Compared with the state-of-the-art algorithm, the simulation results indicate that GD-MRSOA-AIS could efficiently schedules the multiple readers operating with a fairer resource allocation scheme, performing in larger effective interrogation range.

1. Introduction

Radio Frequency Identification (RFID) is one of the Auto Identification and Data Capture (AIDC) techniques, which enable objects to be automatically identified. With the advantages such as automation, no-contract, easy-to-implement and enough-durability, passive RFID is widely applied in various applications such as supply chain management [1], manufacturing management [2] and warehouse management [3] with objects localization [4].

According to most applications, a single reader cannot totally cover a specific area (i.e., in a warehouse, every product has a tag attached to by automatically taking stock). Correspondingly, a classical RFID scenario is usually composed of multiple readers and large quantity of passive tags: the so-called Multiple-reader Environment (MRE). In classical MRE, multiple readers are deployed in different densities with known positions to interrogate the randomized tags with fixed positions under the same RFID system. To dynamically allocate the operating resources (i.e., available time slots and frequency channels) and manage readers, centralized mechanism is usually designed to be executed by a coordinator device (i.e., polling server), which is connected to the readers through a wired or wireless network [5,6]. During this process, signal interference problem degrades the operating performance in efficiency and reliability, which is caused by multiple readers operating at the same time. Correspondingly, the multiple-reader interference avoidance algorithms are proposed to help coordinator device to schedule the readers operating non-simultaneously or simultaneously but at different frequency channels, which could be clustered in two categories: the control-mechanism-based ones and the scheduling-based ones.

Control-mechanism-based algorithms [7,8,9] allow each reader to detect the status of other readers in order to avoid the simultaneous operating. For example, Neighbor Friendly Reader Interference Avoidance Algorithm (NFRIA) utilized readers with two bistatic antennas, where one antenna is for data transmitting and the other one is for continuously receiving to detect if other readers are using the same channel when they are operating. However, NFRIA did not take full advantage of centralized mechanism and, meanwhile, it is based on a hardware assumption that makes it hard to implement in real MRE.

Scheduling-based algorithms transform the multiple-reader interference problem into an optimization problem with respect to the allocation of operating resources (e.g., [10,11]). Based on this, the number of time slots, the number of frequency channels and the position of readers are optimally allocated by using some heuristic algorithms such as genetic algorithm [12], swarm optimization algorithm [13] and artificial immune algorithms [14,15,16,17]. Among these, the artificial immune algorithms output the best performance when compared with other heuristic ones, the advantage of which is mainly embodied in outputting a larger interrogation range. In [14,15,16,17], the author introduced a reader-to-reader avoidance model formulizing from the signal-to-interference-plus-noise (SINR) view, which could perfectly describe the interference process. However, the author did not consider the non-uniformity distribution of multiple readers deployment in MRE, resulting in the unfairness of scheduling schemes since the readers with no interferences are always operating while the ones dramatically affected by interferences are almost never operating. Therefore, part of the interrogation range is actually thriftless and, meanwhile, the interfering readers are not effectively scheduled to operate as well.

In the view of scheduling-based mechanism, a Geometric Distribution-based Multiple-reader Scheduling Optimization Algorithm using Artificial Immune System (GD-MRSOA-AIS) is proposed as a resource allocation algorithm to fairly schedule the readers operating with low interferences and large effective interrogation ranges in centralized MRE. GD-MRSOA-AIS first produces several fair feasible scheduling schemes using geometric probability distribution to allocate the operating time slot and frequency channel, which could minimize the collisions among the readers contending for operating resources and therefore maximize the probability that one reader successfully gains the opportunity to operate. To optimize these feasible scheduling schemes with the objective of maximizing the total effective interrogation range, the artificial immune system optimization with immune clone, immune mutation and immune suppression is further introduced. During the mutation process in artificial immune system optimization, there are two alternative mutation operators for different cloned antibodies, where the single-bit mutation is suitable for the superior ones and the region-bits mutation is appropriate for the regular ones.

Summarizing, the contributions of this paper are as follows:

• By using signal-to-interference-plus-noise (SINR) to explain the reduction in interrogation range, a resource allocation model is constructed with two constraint conditions which are used to decrease the multiple-reader interference.
• A geometric probability function is introduced to replace the uniform probability function to produce the feasible scheduling schemes, which ensures that readers could operate in a fair way.
• Artificial immune system with clone operator, mutation operator and suppression operator is introduced to optimize the feasible scheduling schemes. In mutation process, both of the single-bit mutation operator and the region-bits mutation operator are imported to deal with the different cloned antibodies to accelerate the optimization process and convergence speed.

The remainder of this paper is organized as follows. In Section 2, the formulized resource allocation model is constructed in the view of signal-to-interference-plus-noise (SINR) to efficiently avoid the multiple-reader interference in MRE. The structure of GD-MRSOA-AIS is introduced in details in Section 3, where a geometric distribution probability is first utilized to generate the feasible scheduling schemes and then an artificial immune system is designed to optimize these feasible scheduling schemes as optimal ones. Simulation results for GD-MRSOA-AIS are provided in Section 4 as well as a series of comparative results between the proposed one and the state-of-the-art algorithm (i.e., LIs [14]). Finally, the conclusions and future works are drawn in Section 5.

2. Resource Allocation Model in Centralized MRE under EPCGlobal C1G2

2.1. General Description with Assumptions

In MRE, each reader transmits electromagnetic wave to create the interrogation range, where the size and shape of interrogation range depends on many factors [5,18] such as the antennas design (radiation pattern, gain, polarization and impedance), tag parameters (e.g., gain, matching features and IC sensitivity), external factors (ambient conditions, and noise) and readers output power suited. In most literatures [5,14,15,16,17,19], the interrogation range is defined as a perfect circumstance where the radius only depends on the reader’s output power. In this paper, we also follow this assumption as UHF RFID readers with known positions and passive RFID tags with fixed positions in centralized MRE:

• Readers are randomly distributed over an area in two dimensions.
• Any reader has only two states, active and inactive, where only the readers in active operate and interfere with other active ones.
• The interference power from multiple interfering readers seen by the desired reader is additive.

2.2. Multiple-Reader Interference Problem in Centralized MRE

A simple centralized MRE is illustrated as Figure 1 according to the above assumptions, which is composed of one polling server, four readers in the same rated power and two target tags. Suppose that R₁ is the desired reader, R₁ could reach to the red circle as its maximum interrogation radius of r_max,1 without any interference. When R₁ attempts to detect the target tag A, if the signal is masked by the interfering reader R₂ and R₃ (the interfering range is represented by the black circle), the effective interrogation range r₁ (blue circle) of R₁ will decrease from r_max,1. If r₁ is smaller than the distance x between R₁ and tag A, R₁ could not detect this target tag A. Moreover, target tag B located in the overlapped range of r₁ and r₃ is hardly detected due to the multiple electromagnetic waves from R₁ and R₃ simultaneously operating.

The maximum interrogation radius r_max,i of R_i is related to the hardware design [20], which is obtained by Equation (1), where λ_i is the wavelength of R_i, P_min is the minimum power required for the tag to operate, P_i is the signal transmission power of R_i, M_d is the modulation depth, and G_T and G_R are the gains of the transmit antenna and the receive antenna, respectively.

$$r_{max,i}=\left(\frac{{\lambda }_i}{4\mathsf{\pi }}\right)\sqrt{\frac{G_T{G}_R{P}_i}{P_{min}}\times \frac{1-M_d{}^4}{{(1+M_d)}^2}}$$

(1)

However, the effective interrogation radius r_i of R_i is variable as a function of signal interfering. For reader R_i interrogating the target tag at a given time slot (i.e., at the kth time slot), R_i receives the backscatter signal from the tag and, meanwhile, it is also interfered by other simultaneous operating readers signal among N_Reader readers, where a 0–1 function ω_j(k) (as Equation (3)) is to indicate if the reader R_j is operating at the kth slot or not. To ensure that R_i could successfully detect the target tag in distance of x, Signal-to-Interference-Plus-Noise ratio (SINR) [21] has to exceed the minimum one of SINR_min as Equation (2):

$$SIN{R}_i(x,d_{j,i})=\frac{B{P}_i(x)}{{\displaystyle {\sum }_{j=1\&j\ne i}^{N_{Reader}}{\omega }_j(k)I_j(d_{j,i})}+N{o}_i}\ge SIN{R}_{min}$$

(2)

$${\omega }_j(k)=\{\begin{array}{ll}1,& {\mathrm{R}}_j\mathrm{operates}\mathrm{at}k\mathrm{th}\mathrm{slot}\\ 0,& \mathrm{Otherwise}\end{array}$$

(3)

where No_i represents the noise power of R_i, BP_i(x) represents backscatter signal power from the target tag as a function of the distance x between the desired reader and the target tag, I_j(d_j,i) represents the interference from any other R_j as a function of the relative distance d_i,j (as Equation (6)) between the desired reader R_i and the other interfering reader R_j. The function [19] of BP_i(x) and I_j(d_j,i) are defined as Equations (4) and (5), respectively.

$$B{P}_i(x)={\alpha }_{bw}{E}_{tag}{P}_i{G}_T{G}_R{(P_0{x}^{-\gamma })}^2$$

(4)

$$\begin{array}{l}{I}_j(d_{j,i})=h{P}_j{G}_T{G}_R{\beta }_{mask}(\Delta C{H}_{j,i}(k))P_0{d}_{j,i}^{-\gamma },\\ \Delta C{H}_{j,i}(k)=|C{H}_i(k)-C{H}_j(k)|\end{array}$$

(5)

$$d_{j,i}=\sqrt{{(x_i-x_j)}^2+{(y_i-y_j)}^2}$$

(6)

where α_bw is the normalized spectrum power, E_tag is the effective power reflection coefficient of the tag, P_i denotes the signal transmission power of R_i, G_T and G_R are the gains of the transmit antenna and the receive antenna, respectively, P₀ is the referenced path loss at the distance of 1 m, γ is the path loss exponent, x is the distance between R_i and the target tag, h is a fading coefficient in the channel between R_i and R_j, β_mask(·) is the function of a spectrum mask defined in EPCGlobal Class1 Generation2 standard [22], ΔCH_j,i(k) is the frequency channel interval between R_i (CH_i(k) denotes the frequency channel numbers selected by R_i at the kth time slot) and R_j (CH_j(k) denotes the frequency channel numbers selected by R_j at the kth time slot) selected, and d_j,i is the relative distance between R_i and R_j.

By Equations (1)–(6), the effective interrogation range r_i (i.e., blue circle in Figure 1) of R_i could be finally obtained by solving Equation (7) to ensure that the backscatter signal from target tag could be correctly recovered.

$$r_i=min(\arg \underset{x}{\max }SINR(x,d_{j,i})\ge SIN{R}_{min},r_{max,i})$$

(7)

According to d_j,i and r_i (i, j∈[1, N_Reader]), R_i may face two kinds of interference scenarios [23] at one time slot when it tries to detect the target tags:

• Multiple readers are simultaneously operating at the same frequency channel, which leads to the signals generated by multiple readers interfere with the reception system of the desired reader. In Figure 1, R₁ suffers from this kind of interference if R₂ and R₃ are simultaneously operating with R₁ at the same frequency channel. As a result, r₁ is smaller than the distance x between R₁ and the target tag A, R₁ could not successfully detect A. To ensure that R₁ could operate with a larger interrogation range to cover tag A, R₁ with R₂ and R₃ should be scheduled to operate at different frequency channels and/or at different times by polling server.
• Multiple readers operating at independently frequency channels try to simultaneously detect the same tag located in the overlapped area of their effective interrogation ranges. In Figure 1, tag B locates in the overlapped interrogation area of R₁ and R₃, where B receives electromagnetic waves from both R₁ and R₃ simultaneously, it is not able to select a particular reader to communicate even if R₁ and R₃ are operating at the different frequency channels. To avoid this scenario, R₁ and R₃ should operate asynchronously which are scheduled by polling server as well.

2.3. The Proposed Resource Allocation Model in Centralized MRE

In order to construct the resource allocation model for a centralized MRE, it is necessary to efficiently decrease the above two interference scenarios. Accordingly,

Table 1. Readers operating restrictions versus d_j,i.

	=Frequency Channel	≠Frequency Channel
=time slot	dj,i > df-min	df-min ≥ dj,i > ds-min(ΔCHj,i(k))
≠time slot	ds-min(ΔCHj,i(k)) ≥ dj,i > 0	ds-min(ΔCHj,i(k))≥ dj,i > 0

summarizes the restrictions set for any R_i and R_j operating in MRE, where d_f-min represents the threshold of reader-to-reader range for selecting different operating frequency channel, d_s-min(ΔCH_j,i(k)) is the threshold of reader-to-reader range for selecting different operating time slot which depends on the selected frequency channel.

Based on Table 1, two constraint conditions are proposed to restrict the resource allocation for readers operating as:

• CH_i(k) ≠ CH_j(k) if d_j,i < d _f-min

Based on the relative distance d_j,i between R_j and R_i, every R_i exists a neighbor set (denoted as IS_Ri = {j|j∈[1, N_Reader], d_j,i < d_f-min} with cardinality |IS_Ri| = N_Neighbor(i), i∈[1, N_Reader]) to mark the readers located in the range of d_f-min, where R_i is suffered from the first kind interference if the readers from IS_Ri are simultaneously operating at the same frequency channel with R_i (i.e., R₁ and R₂ in Figure 1). According to LIs [14], d_f-min is set as 16.79 m (the transmitting signal power of reader is 1 W, and the frequency is 902–928 MHz) for any two R_i and R_j. Therefore, R_i with any R_j in its IS_Ri (j ≠ i) should be operating at different frequency channels as: CH_i(k) ≠ CH_j(k) if j∈IS_Ri and j ≠ i, where CH_i(k) denotes the frequency channel numbers selected by R_i at the kth time slot.

• ω_j(k) = 0 if d_j,i ≤ d_s-min(ΔCH_j,i(k))

Further, in d_f-min, another smaller distance denoted as d_s-min exists, where R_i is suffered from the second kind interference if readers located in d_s-min are operating simultaneously even if they are at different frequency channels because they are overlapped in the effective interrogation range (i.e., R₁ and R₃ in Figure 1). Usually, d_s-min for R_i and R_j is variable along with the correspondingly selected frequency channels interval ΔCH_j,i(k), which is listed in

Table 2. Influence of frequency channel interval to d_s-min.

ΔCHj,i(k)	0	1	2	3	≥4
ds-min(ΔCHj,i(k))	0.0269 m	0.8452 m	2.6970 m	6.7458 m	10.339 m

. The calculation process is attached in Appendix A.

Therefore, R_i with R_j in d_s-min should be operating non-simultaneously as: ω_j(k) = 0 if d_j,i ≤ d_s-min(ΔCH_j,i(k)), where ω_j(k) denotes the 0–1 function of Equation (3).

Constricted by the constraint conditions, the resource allocation model is finally constructed as Equation (8) with the objective of maximizing the total effective interrogation range (denoted as S) to schedule N_Reader readers operating with N_Slot time slots and N_Freq frequency channels. Note that NR = {1, 2, 3, …, N_Reader}, NS = {1, 2, 3, …, N_Slot}, CH = {1, 2, 3, …, N_Freq}, WS = {(x_i, y_i)|x_i∈[0, L_x], y_i∈[0, L_y]} and IS_Ri = {j|j∈NR, d_j,i < d_f-min}.

$$\{\begin{array}{l}MaximizeS={\displaystyle \sum _{i=1}^{N_{Reader}}{\displaystyle \sum _{k=1}^{N_{Slot}}{\omega }_i(k)\pi (}}{r}_i(k){)}^2,\\ \begin{array}{l}s.t.\begin{array}{cccc}\forall i,j\in NR,& \forall k\in NS,& C{H}_i(k),C{H}_j(k)\in CH,(x_i,y_j)\in WS,\Delta C{H}_{j,i}(k)\ne 0& \mathrm{if}\end{array}\begin{array}{c}j\in I{S}_{R_i},\end{array}\\ \begin{array}{cc}{\omega }_j(k)=0& \begin{array}{cc}\mathrm{if}& d_{j,i}\le d_{s-min}\end{array}\end{array}(\Delta C{H}_{j,i}(k))\end{array}\end{array}$$

(8)

3. Geometric Distribution-Based Multiple-Reader Scheduling Optimization Algorithm Using Artificial Immune System (GD-MRSOA-AIS)

According to the proposed resource allocation model, GD-MRSOA-AIS is proposed to fairly allocate the operating resources with lower reader interference and larger effective interrogation range. In GD-MRSOA-AIS, it is composed of two parts:

• GD: Geometric distribution function (GD) combined with the fairness consideration is introduced to randomize the feasible scheduling schemes with lower interferences which satisfy the constraint conditions in Equation (8). Details are described in Section 3.1;
• AIS: Artificial immune system optimization (AIS) is to optimize these feasible scheduling schemes as the optimal scheduling scheme for readers fairly operating with larger effective interrogation range. Details are presented in Section 3.2.

3.1. Feasible Scheduling by Geometric Distribution Function

According to the constraint conditions in Equation (8), GD-MRSOA-AIS will first produce several feasible solutions as the feasible scheduling schemes to ensure that readers could fairly operate with low signal interference.

In centralized MRE, both the interference-reader (i.e., R₁, R₂ and R₃ in Figure 1) and the isolation-reader (i.e., R₄ in Figure 1) exist, where the isolated readers could operate at any time while the interfering readers have to be scheduled by polling server to decrease the interferences as much as possible. On the other hand, it is obvious that the isolated readers keeping on operating is thriftless since the number of deployed tags in the interrogation range is constant. Therefore, it is unfair to allocate the interfering readers and isolated readers with same opportunities to operate. To enhance the fairness, the interfering readers should gain more opportunities to operate.

To efficiently and fairly allocate the available operating time slots, a geometric probability distribution function called Sift [24,25] is imported to replace the typical uniform distribution. Based on the character of Sift distribution, it could increase the probability that one contender selects one resource in a low position, winning the contention quickly. Therefore, if R_i contends for the operating time slot with large quantity of neighbor readers simultaneously, most neighbors will tend to select the last few time slots, and only the minority will contend for the first few time slots, decreasing the probability of collision in slots selection and increasing the probability that R_i successfully selects one of the first few time slots. On the contrary, if R_j contends for the operating time slots with small quantity of neighbor readers, the probability of selecting one slot almost obeys uniform distribution.

For Sift_Function, the probability that the ith reader gains the opportunity to operate at the kth time slot from N_Slot time slots is denoted as Equation (9). Here, N_Neighbor(i) is the cardinality of IS_Ri for R_i, where N_Neighbor(i) = 1 denotes that there is no neighbors located around R_i and therefore R_i is an isolated reader without any possible interference.

$$p{(k)}_i=\frac{(1-{\alpha }_i){\alpha }_i^{N_{Slot}}}{1-{\alpha }_i^{N_{Slot}}}{\alpha }_i^{-k},\begin{array}{c}1\le k\le N_{Slot},\end{array}\begin{array}{c}0<{\alpha }_i<1,\end{array}{\alpha }_i=N_{Neighbor}{(i)}^{-1/(N_{Slot}-1)}$$

(9)

Note that when N_Neighbor(i) = 1, then α_i = 1, and $\underset{\alpha \to 1}{\lim }p{\left(k\right)}_i=1/N_{Slot}$, becoming the uniform probability distribution. Consequently, R_i with bigger N_Neighbor(i) could easily wins the kth time slot as a higher p(k)_i while R_j with smaller N_Neighbor(j) has to select the operating time slot like uniform distribution as a lower p(k)_j.

By using Sift_Function, it generates several feasible scheduling schemes for readers operating with the allocated time slots and frequency channels, where the feasible scheduling schemes are restricted by the constraint conditions in Equation (8). Therefore, each feasible scheduling scheme produced by Sift_Function is actually a feasible solution for Equation (8), where the pseudocode is summarized as Algorithm 1.

Algorithm 1: Pseudocode for Feasible Solutions Generation by Sift_Function

Sift_Function

1 set i = 1;

2 while i ≤ NReader do

3  set ${\alpha }_i=N_{Neighbor}{(i)}^{-1/(N_{Slot}-1)}$;

4  set $l_i=random(0,1)$;

5  set ki = NSlot;

6   for z = 1 to NSlot do

7    if $p_z=\frac{(1-{\alpha }_i){\alpha }_i^{N_{Slot}}}{1-{\alpha }_i^{N_{Slot}}}{\alpha }_i^{-z}$ >li then // Contend for operating time slot

8      set ki = z; // Ri is operating at zth time slot

9      break;

10     end if

11    end for

12    randomize CHi(ki) from CH; // Allocate a frequency channel for Ri

13    for j = 1 to NReader and j ≠ i do

14      if j∈ISRi then // Constraint Condition: CHi(k) ≠ CHj(k) if j ∈ISRi

15     randomize CHj(ki) from CH-{CHi(ki)};

16     if dj,i ≤ ds-min(|CHj(ki)-CHi(ki)|) then // ωj(k) = 0 if dj,i ≤ ds-min(ΔCHj,i(k))

17        set CHj(ki) = 0;

18     end if

19     end if

20     end for

21     i++;

22  end while

For each feasible solution of Equation (8), the total effective interrogation range might be not large enough. Therefore, this feasible scheduling scheme might be not the optimal one to maximize the global effective interrogation range. To optimize these feasible scheduling schemes, the artificial immune system optimization is introduced in the following section.

3.2. Optimal Scheduling by Artificial Immune System Optimization

For the produced feasible scheduling schemes, they could be optimized by using artificial immune system optimization, where each candidate antibody corresponds to one feasible solution of Equation (8) produced by Sift_Function and the antigen corresponds to the objective function of Equation (8) with the constraint conditions. According to this, the affinity function could be formulated as Equation (10), where the process for optimizing the feasible solutions of Equation (8) is transformed to find the maximum affinity value of Equation (10) and its corresponding optimum antibody.

$$\{\begin{array}{l}Affinity(Ab)={\displaystyle \sum _{i=1}^{N_{Reader}}{\displaystyle \sum _{k=1}^{N_{Slot}}{\omega }_i(k)\times (}}{r}_i(k){)}^2,\\ \begin{array}{l}s.t.\begin{array}{cccc}\forall i,j\in NR,& \forall k\in NS,& C{H}_i(k),C{H}_j(k)\in CH,(x_i,y_j)\in WS,\Delta C{H}_{j,i}(k)\ne 0& \mathrm{if}\end{array}\begin{array}{c}j\in I{S}_{R_i},\end{array}\\ \begin{array}{cc}{\omega }_j(k)=0& \begin{array}{cc}\mathrm{if}& d_{j,i}\le d_{s-min}\end{array}\end{array}(\Delta C{H}_{j,i}(k))\end{array}\end{array}$$

(10)

The proposed artificial immune system optimization is predefined to iterate N_Gen generations, where it exists three phases in every iterative generation as: immune clone, immune mutation and immune suppression/recruitment. In the clone phase, each antibody is acted as a parent to be correspondingly cloned for a fixed number of N_Clone children antibodies, and all children antibodies go through the mutation process but only one child antibody with the highest affinity-value among the children antibodies is selected to compare with its parent antibody. If this selected child antibody is superior to its parent antibody in affinity value, it will replace its parent antibody as a new generation. Once the affinity value of this new generation is not significantly different from that of the previous generation, the suppression will be triggered, where the P_S antibodies with lowest affinity-values are suppressed. Then, the corresponding numbers of antibodies produced by Sift_Function are recruited. This process is repeated until N_Gen iteration is met. The related symbols and their descriptions are listed in

Table 3. Symbol and description in artificial immune system optimization.

Symbol	Description
AB	The candidate antibody population
Ab(u)	The uth antibody
ab(u)i	The ith antibody segment in Ab(u)
ABRemain	The set for remained antibodies
Ab(u)Clone	The clone pool for Ab(u)
Affinity(·)	Affinity function
Aff_old	The mean affinity value of the previous generation
Aff_new	The mean affinity value of the current generation
CHi(k)	The kth bit in ab(u)i
NIni	The population size of AB
NClone	The cloned multiplier
NGen	The generation multiplier
L	Region-bits mutation length
PS	The suppression percentage

.

3.2.1. Initialization

To initialize the optimizing process by using artificial immune system, N_Ini antibodies (feasible solutions) are randomized by repeatedly run Sift_Function in N_Ini times to construct the candidate antibody population set as AB = {Ab(u)|u∈[1, N_Ini]}.

For each antibody Ab(u) in AB, it is encoded as integer type since both frequency channels and time slots are discrete distribution as integer type. Seen from Figure 2a, Ab(u) consists of N_Reader segments as ab(u)₁, ab(u)₂, ab(u)₃,…, ab(u)_NReader, where each ab(u)_i is actually corresponding to a reader R_i and it includes a sequence of bits as CH_i(1), CH_i(2), CH_i(3),…, CH_i(N_Slot) where each CH_i(k) is denoted as the selected frequency channel of reader R_i at the kth time slot. CH_i(k) = 0 means that reader R_i does not operate at this kth slot.

3.2.2. Clone Operation

After producing the candidate antibody population set as AB = {Ab(u)|u∈[1, N_Ini]}, each Ab(u) is regarded as an parent antibody. For each parent antibody Ab(u), N_Clone cloned antibodies with the same encodings are produced as its children antibodies, in which these children antibodies will go through the mutation operation to increase the diversity and therefore they have more potential to evolve as excellent individuals. Here, N_Clone is required to be predefined as the cloned multiplier, and each Ab(u) has a clone pool as AB(u)_Clone = {Abc(c)|c∈[1, N_Clone]} to store its children antibodies, where each Abc(c) in AB(u)_Clone is encoded as Figure 2b.

Note that each child antibody Abc(c) from the clone pool AB(u)_Clone is totally the same as its parent antibody Ab(u) in every bit before the mutation operation.

3.2.3. Mutation Operation

For each child antibody Abc(c) (i.e., Figure 2b) from the clone pool AB(u)_Clone = {Abc(c)|c∈[1, N_Clone]} of its parent Ab(u), there are two optional mutation operators as: single-bit mutation operator is applied for the ones with higher affinity values and region-bits mutation operator is applied for the ones with lower affinity values.

For single-bit mutation operator, only one bit CH_i(k) is randomly selected as a hotspot to be mutated following the constraint conditions, which belongs to a reader R_i (i.e., Figure 2b). As a result, this mutated Abc(c) is also a feasible scheduling scheme as well.

For region-bits mutation operator, a contiguous region bits are selected to be mutated starting from a hotspot of CH_i(k) increasing L-bit length, note that L is less than N_Slot minus k to guarantee the mutation is happened in one reader R_i (i.e., Figure 2b). In addition, this mutation is restricted by the constraint conditions. As a result, this mutated Abc(c) is also a feasible scheduling scheme.

By single-bit mutation, the children antibody could extremely inherit the superior bits of the parent antibody while the children antibody would have more potential to mutate as the superior ones by region-bits mutation. Both of them could fast the convergence and quickly reach to the global optimization.

The single-bit and region-bit mutation operator run as in Algorithms 2 and 3 respectively.

After the mutation operations, for each parent antibody Ab(u) (u∈[1, N_Ini]), its children antibodies Abc(c) from the clone pool AB(u)_Clone = {Abc(c)|c∈[1, N_Clone]} are totally different: some Abc(c) surpasses Ab(u) in affinity value while some of Abc(c) are identical or inferior to Ab(u). To distinguish them, all Abc(c) (c∈[1, N_Clone]) should be sorted by affinity value. Select the Abc(c) with highest affinity value and compare it with its parent antibody Ab(u): if this Abc(c) is superior to its parent antibody Ab(u), it will replace its parent antibody as a new candidate antibody in AB.

Algorithm 2: Pseudocode for Single-bit Mutation

Single-bit _Operator ()

1 Randomly determine a bit CHi(k) of Ri from Abc(c) to be mutated;

2 for j = 1 to NReader and j ≠ i

3   if ISRj∩ISRi ≠ ∅

4   CH = CH-{CHj(k)};

5   end if

6 end for

7 if CH ≠ ∅

8   Randomize CHi(k) from CH;

9 else

10   CHi(k) = 0;

11 end if

Algorithm 3: Pseudocode for Region-bits Mutation

Region-bits _Operator ()

1 Randomly determine a bit CHi(k) of Ri from Abc(c) to be mutated;

2 for(q = k; q ≤ k + L; q++)

3 for j = 1 to NReader and j ≠ i

4 if ISRj∩ISRi ≠ ∅

5 CH = CH-{CHj(q)};

6 end if

7 end for

8 if CH ≠ ∅

9 Randomize CHi(q) from CH;

10 else

11 CHi(q) = 0;

12 end if

13 end for

3.2.4. Suppression Operation

After the mutation operation, the candidate antibodies are changed. If the affinity value of new candidate antibody population set AB is significantly increased, this AB will be directly regarded as a new generation and go through the same immune process via clone operation, mutation operation and suppression operation.

On the contrary, the candidate antibodies with highest affinity values should be promoted while the antibodies with lowest affinity values should be suppressed. Sorted by the affinity value, it will suppress P_S percentage of antibodies with lowest affinity values. After that, P_S of N_Ini antibodies (feasible solutions) are produced by Sift_Function, where these fresh candidate antibodies are recruited in AB to compose a new generation population. In addition, this new generation population will go through the same immune process via clone operation, mutation operation and suppression operation.

When the iteration reaches the predefined maximum generations N_gen, GD-MRSOA-AIS terminates. Finally, the pseudocode for proposed artificial immune system (proposed-AIS) optimization in GD-MRSOA-AIS is listed as Algorithm 4, where the corresponding flowchart is shown in Figure 3.

Algorithm 4: Pseudocode for Optimal Scheme Generation by using proposed-AIS Optimization

AIS_Optimization

1  Set NIni, NClone, NGen, PS;

2  int t, u, c;

3  float aff_old, aff_new;

4  Initialization: Run Sift_Function in NIni times to construct set AB;

5       Evaluate the affinity value of all elements in AB and average them as aff_old;

6  while t< NGen do

7   for(u = 1; u ≤ NIni; u++)

8    Produce NClone clones for uth antibody as its children antibodies; // Clone Operation

9    for(c = 1; c ≤ NClone; c++)

10      Mutate cth child antibody following the Mutation Operation;

11    end for

12    Evaluate the affinity value of all children antibodies and their parent antibody;

13    Remain the antibody with the highest affinity value;

14   Evaluate the affinity value of all candidate antibodies and average them as aff_new;

15   end for

16   if(aff_new is not significantly bigger than aff_old) // Suppression Operation

17     Sort the candidate antibodies by their affinity values;

18     Suppress PS antibodies with lowest affinity values;

19     Produce PS new recruited antibodies by Sift_Function satisfying the constraint conditions;

20   end if

21 end while

4. Simulations and Results

In this section, the total effective interrogation range using the proposed-AIS optimization with Sift_Function (denoted as GD-MRSOA-AIS) and without Sift_Function (denoted as MRSOA-AIS) will be simulated and compared with the state-of-the-art algorithm (LIs [14]) in two scenarios:

• The number of readers N_Reader = 15 with fixed positions among GD-MRSOA-AIS, MRSOA-AIS and LIs. Meanwhile, the advantage of Sift_Function and proposed-AIS optimization is illustrated by comparisons of GD-MRSOA-AIS, MRSOA-AIS and LIs.
• Variable N_Reader with randomized positions among GD-MRSOA-AIS, MRSOA-AIS and LIs.

During the simulations, readers are randomly distributed over an area in two dimensions with 100 × 100 m² (i.e., L_x = 100 m, L_y = 100 m). As readers communicate with tags by means of EPCGlobal C1G2, the parameter settings are same with the ones listed in

Table A1. Parameter value under EPCGlobal C1G2 standard.

Parameter	Description		Value
Etag	The effective power reflection coefficient of the tag		0.1
αbw	The normalized spectrum power		0.86
γ	The path loss exponent		2.5
Md	The modulation depth		0.1
H	The fading coefficient in the channel between Ri and Rj		1
Pmin	The minimum required power for tag operation		−15 dB m
Pi	The signal power of Ri		30 dB m
P0	The referenced path loss at the distance of 1 m		−31.6 dB m
Noi	The noise power of Ri		−90 dB m
SINRmin	The minimum SINR		11.6 dB
GT	The reader antenna transmitting gain		6 dB
GR	The reader antenna receiving gain		6 dB
βmask(·) for MRE	The function of the spectrum mask in multiple-reader environment	ΔCHj,i(k) = 0	0 dB
		ΔCHj,i(k) = 1	−20 dB
		ΔCHj,i(k) = 2	−50 dB
		ΔCHj,i(k) = 3	−60 dB
		ΔCHj,i(k) ≥ 4	−65 dB

in Appendix A.

Given a certain number of readers, as the number of available time slots increases, the readers have more options to avoid simultaneously operation. In other words, for a specific number of time slots, as the number of readers increases, the total effective interrogation range will be smaller, which is caused by the heavy interferences. Without the loss of generality, N_Slot is finally assigned as 5 in the following simulations. In addition, as the number of available frequency channels increases, the total effective interrogation range always increases since each reader has more options for selecting an available frequency channel to simultaneously operate with other readers at different frequency channels. Usually, the number of available frequency channels is set to no more than 10. Consequently, N_Freq is assigned as 10 in the simulation. The parameters setting of proposed-AIS optimization in simulation are listed in

Table 4. Parameter settings of proposed AIS optimization process.

Parameter	Value
The number of available time slots (NSlot)	5
The number of available frequency channels (NFreq)	10
Initialized candidate population size (NIni)	40
Cloned Multiplier (NClone)	5
Maximum generation (NGen)	150
Suppression percentage (PS)	25%

.

4.1. Case Study: N_Reader = 15, N_Slot = 5, N_Freq = 10

When N_Reader = 15, the fixed positions of readers are randomized in Figure 4, where the corresponding neighbor set for each reader is IS_R1 = {1, 3}, IS_R2 = {2, 5, 6}, IS_R3 = {1, 3}, IS_R4 = {4, 7}, IS_R5 = {5, 6, 8, 9}, IS_R6 = {2, 5, 6, 8}, IS_R7 = {4, 7}, IS_R8 = {5, 6, 8, 9, 10, 11}, IS_R9 = {5, 8, 9, 10, 11}, IS_R10 = {8, 9, 10, 11}, IS_R11 = {8, 9, 10, 11}, IS_R12 = {12, 13}, IS_R13 = {12, 13}, IS_R14 = {14}, and IS_R15 = {15}. Here, R₁₄ and R₁₅ are isolated readers since IS_R14∩IS_Rj = ∅ (any j∈NR and j ≠ 14) and IS_R15∩IS_Rl = ∅ (any l∈NR and l ≠ 15). On the contrary, i.e., IS_R5∩IS_R8∩IS_R9∩IS_R10∩IS_R11 = {5, 8, 9, 10, 11}, these readers should be scheduled to operate at different time slots or simultaneously operate but at different frequency channels.

Figure 5 shows the graphical representation of effective interrogation range for each reader with its corresponding operation time slots (where the five time slots are represented by Green, Red, Blue, Cyan and Magenta) under the operating scheduling scheme. Correspondingly, the operating scheduling scheme for each algorithm is listed in

Table 5. The operating schedule for 15 readers with N_Slot = 5 and N_Freq = 10 among three algorithms.

			GD-MRSOA-AIS					MRSOA-AIS					LIs
		TSk	TS1	TS2	TS3	TS4	TS5	TS1	TS2	TS3	TS4	TS5	TS1	TS2	TS3	TS4	TS5
	CHi(k)
Ri
R1			0	0	0	0	0	0	6	7	1	1	7	0	0	3	5
R2			0	1	0	7	10	0	0	0	10	7	0	1	8	7	1
R3			0	10	0	5	1	0	3	0	0	0	0	0	5	0	0
R4			0	0	10	0	0	0	0	0	0	0	1	3	1	1	3
R5			0	0	1	0	0	0	0	0	0	0	0	0	0	0	1
R6			0	5	0	0	0	0	0	0	0	0	0	0	0	0	0
R7			5	0	0	0	0	0	0	0	0	0	0	0	0	0	0
R8			0	0	5	0	0	0	0	0	0	0	0	10	0	0	0
R9			7	0	0	0	0	0	2	10	5	0	0	0	0	0	8
R10			0	8	0	0	0	0	0	0	0	0	0	0	3	0	0
R11			0	0	0	0	8	9	0	0	0	5	0	0	0	0	0
R12			0	0	8	0	0	0	0	0	0	0	0	0	0	0	0
R13			0	3	0	0	0	7	0	0	3	0	10	7	7	10	7
R14			1	0	0	9	6	1	9	2	0	0	0	0	0	0	10
R15			10	0	3	3	3	5	0	5	7	10	3	5	10	5	9

* In the table, TS_k stands for the kth time slot from the optional values of {TS₁, TS₂, TS₃, TS₄, TS₅} in N_Slot = 5. R_i stands for the ith reader from the optional values of {R₁, R₂, …, R₁₅} in N_Reader = 15. The operating frequency channel for ith reader at kth time slot (CH_i(k)) is listed from the optional values of CH = {0, 1, 2, 3, …, 10} when N_Freq = 10, where CH_i(k) = 0 means that the ith reader does not work at kth time slot.

, where CH_i(k) = 0 means that the ith reader does not operate at this kth time slot. At the first time slot (TS₁) as green circles in Figure 5a–c, {R₇, R₉, R₁₄, R₁₅} are operating at the frequency channel of {CH₇(1) = 5, CH₉(1) = 7, CH₁₄(1) = 1, CH₁₅(1) = 10} using GD-MRSOA-AIS as in Table 5; {R₁₁, R₁₃, R₁₄, R₁₅} are operating at the frequency channel of {CH₁₁(1) = 9, CH₁₃(1) = 7, CH₁₄(1) = 1, CH₁₅(1) = 5} using MRSOA-AIS; and {R₁, R₄, R₁₃, R₁₅} are operating at the frequency channel of {CH₁(1) = 7, CH₄(1) = 1, CH₁₃(1) = 10, CH₁₅(1) = 3} using LIs algorithm. Take {R₄, R₇} as an example, IS_R4∩IS_R7 = {4, 7}. According to Table 5, R₄ is scheduled to operate at TS₃ with the frequency channel of CH₄(3) = 10 and R₇ is scheduled to operate at TS₁ with the frequency channel of CH₇(1) = 5 by GD-MRSOA-AIS while R₄ is scheduled to operate at every time slot as {CH₄(1) = 1, CH₄(2) = 3, CH₄(3) = 1, CH₄(4) = 1, CH₄(5) = 3} and R₇ is scheduled to be inactive at every time slot by LIs. Therefore in LIs, R₄ is actually operating in uselessness especially for the last few time slots and it is unfair for R₇. On the contrary, GD-MRSOA-AIS schedules R₄ and R₇ corporately operating in a fair way. The same scenario is also happened in {R₁₂, R₁₃}.

On average, the effective interrogation radius using GD-MRSOA-AIS is 2.142 m, 2.0881 m using MRSOA-AIS and 1.909 m using LIs algorithm. It seems like that the effective interrogation ranges of these three algorithms are similar. However, by introducing Sift_Function, GD-MRSOA-AIS is obviously fairer since almost all readers (except for R₁) are scheduled to operate at different time slots and frequency channels while both of MRSOA-AIS and LIs could not. For example, {R₄, R₅, R₆, R₇, R₈, R₁₀, R₁₂} are always inactive in MRSOA-AIS and {R₆, R₇, R₁₁, R₁₂} are inactive in LIs (shown in Table 5 and Figure 5b,c), especially that R₆, R₁₀, R₁₁ are posited in crowed with more neighbors (shown in Figure 4).

To evaluate the fairness of readers during the operating scheduling, a general purpose quantitative measure of fairness called Jain Index [26] is imported as Equation (11), where N_Reader denotes the number of readers, ω_i is the 0–1 function to indicate whether the reader R_i operates at least once at these N_Slot time slots or not, and N_Neighbor(i) is the cardinality of IS_Ri. The I_Jain ranges from 0 to 1: the higher I_Jain means that the corresponding optimal scheduling scheme is fairer. Obviously, R_i with larger N_Neighbor(i) will make more contribution to obtain a bigger I_Jain. Therefore, the Jain Index could express the fairness of an optimal scheduling scheme.

$$I_{Jain}=\frac{{\displaystyle \sum _{i=1}^{N_{Reader}}{\omega }_i\times N_{Neighbor}(i)}}{N_{Reader}\times N_{Reader}}$$

(11)

As a result, GD-MRSOA-AIS becomes the fairest one with highest Jain Index of I_Jain = 18.22%, while the I_Jain of MRSOA-AIS is 8.89% and the I_Jain of LIs is 14.67% in the same scenario.

In Figure 6, the initial average affinity value of GD-MRSOA-AIS starts from 450, which is much higher than that of the other two from 200. This obvious difference is owing to the contending mechanism of Sift_Function for time slots selection. Additionally, the average affinity value of both GD-MRSOA-AIS and MRSOA-AIS are much higher than LIs, where MRSOA-AIS rockets up to a high affinity value and then it stabilizes in the similar average affinity value like GD-MRSOA-AIS, which dues to the multiple mutation operations in the proposed-AIS. To achieve the average affinity value of 600, with GD-MRSOA-AIS and MRSOA-AIS, it costs around 50 generations while with LIs it is more than 150 generations. Therefore, the proposed-AIS also reduces the time consumption of optimization process.

4.2. Variable N_Reader with Fixed N_Slot = 5 and N_Freq = 10 in Randomized Positions

For a given N_Reader readers with N_Slot = 5 and N_Freq = 10 in the area of 100 × 100 m², the position of each reader is randomly located. To ensure the convergence of the results, all the simulations are repeated for 50 times with 50 randomly positions. For an easier understanding, the results are listed in five indices (the best, the worst, and the mean of total effective interrogation area, the average radius and Jain Index) among GD-MRSOA-AIS, MRSOA-AIS and LIs algorithm, which are represented in

Table 6. The comparison results of the total effective interrogation range with N_Slot = 5 and N_Freq = 10.

NReader	Algorithm	Best (Unit: m2)	Worst (Unit: m2)	Mean (Unit: m2)	Average Radius (Unit: m)	Jain Index (IJain)
4	GD-MRSOA-AIS	3886.166	2459.977 *	3190.954 *	6.906 *	-
	MRSOA-AIS	3976.631 *	1918.756	3078.580	6.784	-
	LIs	3570.661	1512.397	3041.527	6.573	-
8	GD-MRSOA-AIS	4392.362 *	3287.613 *	3907.504 *	4.308 *	42.19% *
	MRSOA-AIS	4293.650	3180.301	3790.565	4.174	25.00%
	LIs	4316.239	3263.520	3859.630	4.252	29.69%
12	GD-MRSOA-AIS	3910.000 *	3328.207 *	3539.014 *	2.670 *	27.08% *
	MRSOA-AIS	3765.571	3014.043	3481.625	2.620	13.89%
	LIs	3671.977	2977.352	3428.592	2.639	18.06%
16	GD-MRSOA-AIS	3780.408 *	3356.667 *	3533.103 *	2.027 *	27.34% *
	MRSOA-AIS	3612.826	2901.954	3471.431	1.974	19.92%
	LIs	3437.009	3128.828	3270.978	1.963	21.88%
20	GD-MRSOA-AIS	3331.845	2935.414 *	3133.686	1.443	70.50% *
	MRSOA-AIS	3369.615 *	2901.954	3160.941 *	1.463 *	40.25%
	LIs	2869.225	2297.590	2528.864	1.346	45.50%
24	GD-MRSOA-AIS	3232.966 *	2550.474 *	2909.812 *	1.229 *	68.06% *
	MRSOA-AIS	3206.098	2279.184	2830.733	1.195	43.75%
	LIs	2151.093	1874.913	2035.651	1.020	42.36%
28	GD-MRSOA-AIS	3068.395 *	2436.688	2737.177 *	0.999 *	64.29% *
	MRSOA-AIS	2675.789	2586.912 *	2616.538	0.923	35.71%
	LIs	1859.409	1532.377	1670.742	0.814	32.14%

* The best one for each comparison.

.

When N_Reader = 4 with N_Slot = 5 available time slots and N_Freq = 10 frequency channels, readers are easily scheduled to operate at different time slots and frequency channels. Additionally, they could be deployed so sparsely that they are hardly interfered each other in such a large zone (100 × 100 m²). Therefore, the Jain Index is failed to measure the fairness. However, limited by the self-rated-power, the interrogation range is also finite. As a result, the total effective interrogation range is not large enough. As the number of readers increases, such as N_Reader = 24 and N_Reader = 28, positions of readers become much denser, the readers could not make full use of the frequency channels and the time slots, and then the individual effective interrogation range is declining and the total effective interrogation range relies on the cooperation among readers operating.

From Table 6, we can see that the Jain Index is fluctuated up and down. For the former situations (i.e., N_Reader = 8, N_Reader = 12, N_Reader = 16), each reader has fewer neighbors since they are sparsely distributed, which declines the Jain Index value even if all of the readers are scheduled to operate at least once. For the latter situations (i.e., N_Reader = 24, N_Reader = 28), readers are located in denser positions and so each reader has more neighbors, but some readers might be not scheduled to operate even once (ω_i = 0) which also decreases the Jain Index value. Even so, the Jain Index value of GD-MRSOA-AIS is also higher than MRSOA-AIS and LIs with the same number of readers.

In addition, Table 6 shows that the best, the worst and the mean of total effective interrogation range between GD-MRSOA-AIS and MRSOA-AIS are similar but larger than the ones of LIs; meanwhile, the average radius of effective interrogation range for each operating readers with GD-MRSOA-AIS and MRSOA-AIS is also larger than that with LIs. The total effective interrogation range is declined fast by using LIs when the number of readers increases while it is much slower by using both GD-MRSOA-AIS and MRSOA-AIS. For example, when N_Reader = 20, the mean effective interrogation range with GD-MRSOA-AIS is 3133.686 m², the best one as 3331.845 m² and the worst one as 2935.414 m²; the mean value with LIs is only 2528.864 m², the best one as 2869.225 m² and the worst one as 2297.590 m². When N_Reader = 28, with GD-MRSOA-AIS, the mean value is glided down to 2737.177 m², the best one as 3068.395 m² and the worst one as 2436.688 m²; with LIs, the mean value is slumped down as 1670.742 m², the best one as 1859.409 m² and the worst one as 1532.377 m².

In conclusion, GD-MRSOA-AIS could schedule multiple readers operating in fairness with lower multiple-reader interfering and large effective interrogation range, where the fairness with lower multiple-reader interfering dues to the geometric distribution of Sift_Function and the large effective interrogation range dues to the proposed-AIS optimization process. As a result, the deployment of eight readers with five available time slots and 10 available frequency channels is the most economical way to maximize the total effective interrogation range in 100 × 100 m², especially using GD-MRSOA-AIS.

5. Conclusions

This paper refers to the multiple-reader interference problem in the multiple-reader environment (MRE) and formulates a resource allocation model with the consideration of interference avoidance in SINR under EPCGlobal C1G2 standard, where the allocable resources include available time slots and frequency channels. Based on this resource allocation model, GD-MRSOA-AIS is further proposed. In GD-MRSOA-AIS, geometric distribution replaces the uniform distribution to produce the feasible scheduling schemes, where the reader, which is interfered by large quantity of readers, has more opportunities to be allocated in an operating time slot. To optimize these feasible scheduling schemes, the artificial immune system optimization including immune clone, immune mutation and immune suppression is further introduced. During the mutation operation for antibodies, there are two optional mutation operators depending on the affinity values. According to the simulation results, GD-MRSOA-AIS could obtain an optimal and fairer readers collaboratively operating scheduling scheme, and it could output a larger total effective interrogation range with higher convergence than the state-of-the-art one.

Although GD-MRSOA-AIS indeed enhances the effective interrogation range with lower interferences by fairer operating scheme, it still has shortcomings:

• It only focuses on the scenario of multiple readers in known position with randomized tags in fixed positions, and ignores the new entrancing tags with variable population.
• It only solves the resource allocation problem for multiple readers scheduling to interrogate the tags in centralized MRE, but ignores the identification problem (i.e., tag-to-tag collision) in data transmission process.

Therefore, the next work will reconstruct a resource allocation model by considering the variable population of tags and identification problem with an enhanced scheduling-based algorithm.