Modeling RFID readers deployment in three-dimensional space

3.1 The difficulty of modeling RFID reader’s reading space

In this paper, reading space refers to the largest communication range of readers, which is the largest space where RFID tags can be read. We also use the reading region to denote communication range and reading range, which refers the largest distance from the reader to the end of reading space where tags could be read by reader.

For most coverage problems in 3D space, researchers simplified the communication range of a RFID reader as a formal sphere or an ellipsoid. Then, the coverage problem can be viewed as the use of one or more regular spheres or ellipsoids to fill the 3D space. By this idealization model, the RFID coverage problem can be solved by many network planning methods used in wireless sensor network and wireless communication system. For example, geometry theory based planning method is one of these network planning tools.

The analysis of RFID reader’s electromagnetic field proves that the read region shape likes an oval on a plane. However, studies on RFID reader show that the read region is an irregular ellipsoid-like space (Huang and Boyle, 2008; Grover and Berghel, 2011) (Fig. 1). Thus, it is necessary to propose a new model to describe the non-sphere or non-ellipsoid irregular reading space of RFID readers.

3.2 Cube-based reading region model

In our proposed cube-based model (CBM), we imagine that the reading space of reader R is placed into a cube, A, where A’s edges are size of L. Additionally, A is large enough to contain the whole reading space of the reader. Cube A is called container of R. Then, cube A is cut into n × n × n small cubes along each edge of A. That is, each edge of A is equally divided into n parts, where the size of each part is l and thus L = nl. By this way, the container is equally divided into n × n × n small cubes.

Similarly, because reader R is inside of A, the reading space of the reader in cube A is also divided into many small parts, some of them are cubes and some of them are in irregular shapes. Obviously, the irregular parts are those around the whole border of R. While the size of l is smaller enough, those irregular parts can also be approximately denoted by cubes. That means the reading space of R can be computed as the sum of a set of small cubes. Obviously, the smaller l is, the more precise the cube-based reading region model is.

The strong point of our cube-based model of R is that we can use a 3D matrix to denote the reading model. We assume l = 1 where “1” means a unit length. Cube A is denote by a matrix M _r  = M (nl, nl, nl). The value of each element in M could be either 0 or 1. When the value of the element is 1, the corresponding cube of A is overlapped with a cube in R. It means that this cube is covered by a RFID reader. When the value of the element is 0, it means this cube is not covered by any reader. Therefore, the whole reading region of R is a set of elements whose value is 1:R ={ R|M _r  (L, W, H) =1 }.

For example, in Fig. 1 we set n = 55, then the Cube A is divided into 166375 small cubes. Consequently, the reading region of R is also cut into some small cubes which are the dark shadow in the center of A. Similarly, the shadow of R is also denoted by a set of elements in M _r where the value is 1.

3.3 Model RFID antennas rotation with cube-based reading region model

In practical RFID applications, we could rotate RFID antennas. The rotation of the antenna can be any direction in 3D space, either clockwise or counter-clockwise, up or down. In Fig. 2, we show that R is deployed with different angles. Actually, it is very complex while readers can be installed in any angle. In this paper, it assumes that we can only rotate RFID antennas around a line which is parallel with the z axis. Then, we can compute the reading space deployed in any direction by matrixcalculation.

The reading space model of reader R in practical deployment is denoted as R (x,  y,  z,  θ), where x, y, z are the x axis, the y axis and the z axis, θ is the angle of radiation of R in horizontal plane. In theory, the value of θ could be any value of [0, 2π]. However, R with differently value of θ must be described by different reading model. Therefore, if the value of θ could be any value of [0, 2π], there will be an infinite number of reading model for only one readers. This means that it is impossible to model reading space in practical deployment.

In this paper, we assume that the rotation angle of R is limited to a set of values. We set θ = k (π/8), where k is a positive integer. For example, if k ∈ [0, 15], we get 16 different rotation angles of R, which means we can rotate R with 16 different angles in horizontal plane. Then, we can get 16 different reading space models of one reader. The mathematical matrix of these different reading space models M _r  (θ) can be easily compute from the reading matrix M _r of R constructed in our CBM model. In order to compute M _r  (θ), we first rotate R with θ degree along a line parallel the z axis. Then, the element in M _r with value of 1 is re-calculated as the following formula: ( x ′ y ′ z ′ 1 ) = ( x y z 1 ) [ cos θ sin θ 0 0 - sin θ cos θ 0 0 0 0 1 0 0 0 0 1 ](1)

Finally, the newly elements with (x′, y′, z′) is set to 1. The new matrix M _r  (θ) for new reading space with θ degree is constructed by this way. While θ is changed, we can get different M _r  (θ). For example, in our above assumption, we can get 16 different M _r  (θ) which denote 16 rotation angles in practical deployment.

We summarize our novel CBM model as following:

Reading spaces in any shape could be modeled by CBM.

5.1 Reader deployment in CBM model

After constructing M _r , M _r  (θ) in CBM, the deployment of readers into a coverage area with any shape and size is very easy. Firstly, we imagine that the whole coverage space is situated inside a cube whose size of edge is at least twice as long as the reader’s communication distance. That is, the outside cube should be large enough to not only hold the whole reader’s reading space, but provide more space to install readers (see Fig. 4). In our CBM model, we set the edge size of outside cube to twice of the reader’s communication distance, because if most of the reading space of a reader does not cover any coverage space, this deployment is not reasonable. Actually, although we can use a cube which is much larger than the reader’s reading space, much memory space will be wasted to store the information of deployment space, coverage space and reading space. Then, the deployment matrix M _d could be constructed by our CBM. In M _d , all elements with value of 1 refer to those spaces that should be covered by at least one RFID reader.

After constructing the reading space model and the deployment space model, we can imagine one or more readers are installed at the mount point inside of the deployment space. Obviously, some of these mount points will be located inside of coverage space and some of them should be outside of coverage space. In order to improve the totally coverage of readers, we can rotate the antenna of each reader. Intuitively, deploying a reader into the deployment space is to superimpose the reader on the deployment. The superimposition of a reader on the deployment space is an addition operation of two matrices: M _r  (θ) + M _d .

The mathematically meaning of M _r  (θ) + M _d is to add the value of elements in M _d with the elements in M _r  (θ). According to our CBM model, any element c _d  = (x, y, z, 1) in M _d with a value of 1 means that it belongs to the coverage space and should be covered by readers. Any element c _r  = (x, y, z, 1) in M _r  (θ) with value of 1 means that the reader can cover the corresponding cube in deployment space. So after one reader is deployed, all values of elements which are covered by one reader will be change. However, the value of element not covered by readers will not change.

In Fig. 3, we show one reader is deployed into the deployment space. It is clearly that the mount point of this reader is inside the coverage space, so the whole reading space of this reader can cover the coverage space. However, if the mount point of a reader is located outside of the coverage space or at the border of coverage space, only parts of reading space can cover the coverage space.

Obviously, when a lots of readers are required for a give coverage space, the key issue is how to deploy all readers into deployment space while maximizing coverage and minimizing overlap. We summarize the process of reader deployment in CBM as following.

Step 1: Set initial parameters of L and l, where L is the size of edge of the largest cube we estimate that should be used in a RFID application, l is the size of edge of the smallest cube we want to divide the largest cube. These two parameters are set according to the size of deployment area and the accuracy we want to achieve.

Step 2: Model the reading space, the deployment space and the coverage space by our CBM. Then, M _r , M _r  (θ) and M _d are all initialized. In M _r , all elements, corresponding to the small cubes within the communication range of the reader, are set to value of 1. Then, according to the initialization of θ, different values of M _r  (θ) can also be calculated. Similarly, with CBM, all elements in M _d are set to value of 1 if the corresponding cubes should be covered.

Step 3: One or more readers are superimposed on the development space. While we want to deploy a reader in deployment space, we first chose the reader’s mount point, p (x, y, x). Then, the reader is superimposed on the development with a rotation angle θ. By this way, any other readers could all be deployed into the predefined space. Obviously, how to choose the deployment policy is the key issue of this step. In this paper we use the particle swarm optimization (PSO) to optimize coverage problem. We will discuss PSO in the simulation section.

Step 4: Then, the coverage and the overlap of this deployment scheme is calculated. If the coverage and the overlap meet the requirement, then we get the deployment scheme and the process finishes. Otherwise, we should go to step 3 to change the deployment. The key issue in this step is how to compute the coverage and the overlap. We will discuss this problem in the next section.

5.2 Computing coverage and overlap rates

There are two important factors, coverage and overlapping, which can be used to evaluate the effectiveness of the deployment. The coverage rate denotes the rate of total covered area to the whole deployment area. The overlapping rate indicates the rate of the overlapping area to the whole coverage area. In this section, we will address how to calculate coverage and overlap in CBM model.

When the first reader is deployed, which is the sub-space of the coverage space that is covered by reader’s reading signals from at least one reader, by multiplying matrices M _r  (θ) and M _D . The value of each element in the product matrix of M _r  (θ) + M _d could be either 0 or 1 or 2. If the value is 0, the corresponding space is not required to be covered by readers. That is, this space is outside of coverage space. If the value is 1, the corresponding space is within the coverage space but not covered by any reader. If the value if 2, it means that the space is covered by a reader.

Suppose that the reader matrices for readers 1 and 2 are M _{r 1}  (θ₁) and M _{r 2}  (θ₂), respectively. When two readers 1 and 2 are deployed, the deployment matrix M _d is the addition of matrices M _{r 1}  (θ₁) and M _{r 1}  (θ₁). Therefore, we can find the effective coverage space by multiplying matrices M _d and M _r  (θ), then both the coverage and the overlap can be easily calculated.

(1) Computing the coverage rate

In our cube-based model, the coverage rate is defined as follows: ρ = S c A S = ⋃ k = 1 n A k A S(2) where ρ is the coverage of a deployment space, S _c is the space covered by RF signals from at least one RFID reader, A _S is the coverage space, and n is the number of RFID readers. Take Fig. 3 as an example, n equals to 1, S _c is the shadow space inside the cube, A _S is the area of the inside cube.

When the number of readers is large, the calculation of S _c is very difficult because one read region may overlap with several other read regions. However, with our CBM model, we can compute the coverage as: ρ = count ( find ( M r ( θ ) + M d ) > 1 ) count ( find ( M D ) = 1 )(3) where the function find (M _r  (θ) + M _d ) >1 finds out those elements in the product matrix M _r  (θ) + M _d whose value is no less than 1, which are corresponding to those cubes covered by at least one RFID readers. The function count (find (M _r  (θ) + M _d ) >1) counts the number of cubes covered by at least one reader. The function count (find (M _D ) =1) counts the number of cubes that need to be covered.

(2) Computing the overlapping

A tag covered by two or more RFID readers may fail to read or write RFID tags due to the RFID reader collisions. Thus, it is important to calculate the overlapping among readers. In our CBM model, we define the overlapping as follows: ∂ = S o A S = ⋃ i = 1 , j = 1 i = n , j = n ( A i ⋂ i ≠ j A j ) A S(4) where ∂ is the overlapping, S _o is the total space covered by at least two RFID readers, A _S is the space need to be covered, and n is the number of RFID readers. In our CBM model, the overlapping rate can be given by: ∂ = count ( find ( M D · M C ) > 2 ) count ( find ( M C ) = 1 )(5)

The function count (find (M _D  · M _C ) >2) counts the number of cubes covered by more than one RFID readers.

6.1 The choice of optimization algorithm

Many existing works choose the genetic algorithm (GA) to solve the coverage problem in RFID systems (Guan et al., 2006; Yang et al., 2009). However, the drawback of the GA is its expensive computational cost. The research on the comparison between GA and PSO has shown that PSO has the same effectiveness (finding the true global optimal solution) as the GA but with significantly better computational efficiency (less function evaluations) by implementing statistical analysis and formal hypothesis testing (Xue et al., 2007; Zhou and Luo, 2014). Therefore, in this paper we adopt the improved particle swarm optimization to optimize the deployment of readers in intensive RFID based applications.

The particle swarm optimization (PSO) optimizes a problem by having a population of candidate solutions, here dubbed particles, and moving these particles in the searching space according to simple mathematical formulae over the particle’s position and velocity (Xue et al., 2007; Zhou and Luo, 2014). Each particle’s movement is impacted by its local best known position and is also guided toward the best known positions in the searching space, which are updated as better positions are found by otherparticles.

In PSO, it assumes that there are n particles in a D-dimensional space. The position and the velocity of each particle denote as X _i  = (x_i1, x_i2, …, x _iD ) and V _i  = (v_i1, v_i2, …, v _iD ). The best position of particle i, pbest, in the whole searching space is P _{pbest i}  = (p_i1, p_i2, ⋯ , p _iD ). The best position of the best particle g in N, gbest, denotes as P _gbest  = (p_g1, p_g2, ⋯ , p _gD ). The fitness function is f (x). Therefore, at the (t + 1) iteration, the best position P _pbest  (t + 1) of particle i is computed by following formula: P pbest i ( t + 1 ) = { P pbest i ( t ) , if f ( x i ( t + 1 ) ) ≤ f ( P pbest i ( t ) ) x i ( t + 1 ) , if f ( x i ( t + 1 ) ) ≥ f ( P pbest i ( t ) ) , t is iterations(6)

That is, at iteration t + 1, the best position of each particle will be changed according to fitness function f (x). If the fitness is good than the fitness at the t iteration, pbest will be update to the new value of t + 1 iteration; otherwise the value of the t iteration will be keep. The value of gbest after t iterations can be calculated by following formula: P gbest ( t ) = max { f ( P pbest 1 ( t ) ) , f ( P pbest 2 ( t ) ) , f ( P pbest 3 ( t ) ) , … , f ( P pbest N ( t ) ) }(7)

In this paper, we define the fitness function as the position and the velocity of each particle. Therefore, the fitness function determine how to move the reader. After the each reader is moved a new position, the overlap rate and the overlap should be recomputed to determine if it is a more optimized deployment scheme. The fitness functions are defined in (8) and (9).

At the t + 1 iteration, the formulas for updating the position and the velocity of each particle are listed as follows: v id t + 1 = wv id t + c 1 r 1 ( p id - x id t ) + c 2 r 2 ( p gd - x id t )(8) x id t + 1 = x id t + v id t + 1(9) where x id t ∈ [ L d , U d ], L _d , U _d are respectively the lower and the upper limits of the d-dimensional space; v id t ∈ [ v min , d , v max , d ], v_min,d, v_max,d are respectively the minimum and maximum speed of particle i.

In above formulas, i = 1, 2, …, N, r₁ and r₂ are two random between [0, 1], c₁ and c₂ are two constants which are called acceleration constants or learning factors. c₁ is call the particle acceleration constant of a particle itself, and c₂ is the global acceleration constant in system. w is inertia weight.

The possibility of finding the best particle locally or globally is guaranteed by the movement of each particle and its fitness function. In this paper, we regard a possible deployment as a particle, which includes parameters of all readers. Therefore, each particle is denoted as:

P = { R 1 , R 2 , … … , R n } = { x 1 , y 1 , z 1 , p 1 , θ 1 x 2 , y 2 , z 2 , p 2 , θ 2 … … x n , y n , z n , p n , θ n }(10)

where P is a particle (an candidate solution), n is the number of RFID readers, and {x _k ,  y _k ,  z _k , p _k ,  θ _k } (k = 1,  2,   ⋯ ,  n) represents the kth RFID reader, R _k  (k = 1,  2,   … ,  n) represents the parameters of RFID reader k (x _k is the horizontal coordinate of reader, y _k is the vertical coordinate of reader, z _k is the z coordinate of reader, p _k is the size of the read region, and θ _k is orientation of the antenna.

The optimizing process is to adjust all reader parameters. The position and the velocity of all particles are determined by fitness functions defined in Equations (8) and (9). We list all parameters of the PSO-based algorithm that used in our simulations in Table 1.

We assume that the read region is also regular or irregular area, and the orientation of the antenna is k (π/8), where k ranges from 0 to 15. Let UB and LB be upper and lower bounds of the read region. Referring to the parameter setting in the PSO algorithm, we define UB and LB as follows if there are n readers:

LB = { x r 1 min y r 1 min z r 1 min θ r 1 min x r 2 min y r 2 min z r 2 min θ r 2 min … … … … x rn min y rn min z rn min θ rn min }(11) UB = { x r 1 max y r 1 max z r 1 max θ r 1 max x r 2 max y r 2 max z r 2 max θ r 2 max … … … … x rn max y rn max z rn max θ rn max }(12)

In our simulation, Matlab is used and all simulations are done on a PC with 2.5 G Hz CPU and 2 G memories on Windows 7 operation system. We will test our CBM model in regular and irregular space. We will show that our CBM model also applies to the condition where the mount points of readers are limited to some special positions. In all simulations, we only consider coverage ρ and overlap ∂ metrics to evaluate the deployment scheme. Although we will get the value of (x, y, z, θ) for each reader, we only give a virtual view of the deployment in our simulation.

(1) Simulation in regular coverage space

In this simulation, we consider how to deploy a group of RFID readers into a cuboid with length = 200, width = 150 and high = 120. According to our CBM mode, M _c  = (200, 150, 120), M _d  = (400, 400, 400). Although all shape of reading space apply to our CBM mode, we assume M _r  = (55, 55, 35) in this simulation (see Fig. 1).

Before starting simulation, we estimate the minimum number of readers, n_min, when ρ = 100% and ∂=0% to improve the performance of simulation. That is, the initial condition in simulation is that we do not consider overlap among reader. According to our CBM model, n_min is calculated by following formula: n min = n c n r(13) where n _r is the number of cubes in reader’s reading space, n _c is the number of cubes that should be covered in deployment space. The values of n _r and n _c can easily calculated by finding the number of elements in M _r and M _d whose values are 1. In this simulation, n _r  = 16617, n _c  = 1800000, so n_min ≈ 109. In order to reduce overlap among readers, we increase the number of reader gradually to reduce overlap as far as possible to keep coverage higher. The simulation results are shown in Fig. 5. One of the deployment schemes is shown in Fig. 6.

In Fig. 5, the number of the maximum iterations of simulations is set to 5000. While 147 readers are deployed, the coverage and the overlap converge to about 90% and 20% respectively. While the deployed number of readers is increased to 200, the coverage and the overlap converge to about 97% and 35% respectively. Therefore, the simulation results in regular space show that our CBM model and PSO optimization algorithm can archive high coverage in intensive RFID-based applications. However, as the simulation results in Fig. 5 show that the overlap keeps relative high, especially when coverage is approached to full covering when we increase the number of readers deployed.

(2) Simulation in irregular coverage space

In practical intensive RFID-based applications, the coverage space is not regular. In this simulation, we consider the coverage problem in a sphere-like irregular 3D space. We also assume the reading space is the same as the one in the first simulation where M _r  = (55, 55, 35).

While we deploy a reader, we really hope the final deployment of this reader will produce more coverage as far as possible. Obviously, if a reader is totally located inside of coverage space, its value of the coverage is max. However, practically we cannot ensure all readers are deployed into the interior of coverage space. Although some reader will not be deployed totally inside of the coverage space, we also do not want the reader cross the border of coverage space too much. If a reader cross the border of coverage space, its effective coverage should be decreased rapidly. In order to keep the effective coverage of each reader higher, we should check that whether the deployment of a reader oversteps the boundary or not. During simulation, we should set a boundary limit to ensure that there is no violation of border constrain.

In regular deployment, we can check the coordinate constrain of each dimension to ensure that the install position for each reader is within the boundary limit of the coverage space. However, in irregular coverage problem, we cannot exploit coordinates to limit the deployment of readers. Fortunately, we can define an approximate value to determine if the position of a reader is out of the coverage space. In this simulation, if the diameter of the sphere-like space is approximate denoted as d and the mount point of reader is (x, y, z, θ), then we can assume x ≤ d, y ≤ d, z ≤ d.

Although this method solve the border constrain problem in CBM, we should find out the mathematical method to determine whether a reader is deployed out of the limited region or not. By our CBM model, when reader r is superimposed on the deployment space, we can get a sub-matrix, M _ds , whose size is the same as the M _r  (θ). Then, we calculate the multiplication of these two metrics: M _r  (θ) · M _ds . The value of the element in M _r  (θ) · M _ds can be used to determine whether the deployment is valid or not. Theoretically, if there is one element in M _r  (θ) · M _ds with value of 1, then the deployment is valid because at least one cube of coverage space is coved by the reader. However, we set a threshold value λ = count (find (M _r  (θ) · M _ds ) ≥1) to decide if the deployment is valid, where λ is the number of elements in M _r  (θ) · M _ds whose values are 1. By this way, we can adjust the value of λ to evaluate and change the simulation results.

In Fig. 7, the final deployment scheme shows that all readers are deployed into the coverage space. No reader is out of the border of coverage space. Therefore, the simulation result proved that our position-limit method is practical and correct.

In Fig. 7, while 107 readers are deployed, the coverage and the overlap converge to about 85% and 30% respectively. While the deployed number of readers is increased to 160, the coverage and the overlap converge to about 95% and 45% respectively. According to above simulation results, we can get following conclusions:

(a) By our CBM model and PSO optimization algorithm, high coverage could be obtained. That is, our scheme is also suitable for the coverage problem in irregular space. However, compared to coverage problem in regular space, the overlap is increased rapidly when the coverage reaches about 70%. This means that it is more difficult to solve the coverage problem in irregular 3D space than in regular3D space.

(b) In Fig. 7, both the coverage and the overlap initially keep constant and are very low. However, they are rapidly increased along with simulation time. At the beginning of simulation, all readers are randomly deployed to the whole deployment area. Obviously, some of them will be out of the border of coverage space. So the coverage and the overlap are very low. However, because we adopted a border constrain checking mechanism to ensure that as many as possible number of readers will not violate the border constrain, some or all of the readers out of coverage space will be re-deployed to a new mount point which may not violate the border constrains. Consequently, the coverage rapidly rises to a higher value. Similarly, when more and more readers are deployed inside of the coverage space, the overlap among readers will also be increased.

(3) Simulation in irregular coverage space

In this simulation, we consider a much more complicated application scene in which a set of readers can only be installed at limited sub-space of the deployment space. In many application scenarios, all or parts of RFID readers cannot be placed in the arbitrary position of the deployment or coverage space. For example, while we plan to place many readers in a large warehouse in which many items are placed on the shelves, all readers must be placed in the corresponding shelves. Otherwise, the reader cannot monitor the item if they are fixed in some vacant position. We call such coverage problem as position-limit deployment.

In order to study the position-limit coverage problem, we consider how to place readers in a cuboid warehouse with 7 shelves. All readers must be placed on these shelves. The simulation result is shown in Fig. 10.

As shown in Fig. 9, finally 280 readers are deployed. All readers are deployed in 7 shelves and no reader is placed outside of the shelves. Although initially the coverage is only 71%, it converges to 85%. Compared to the non-restriction reader deployment, more readers should be placed in order to achieve the same coverage. One interesting thing in position-limit coverage problem is that with the increase of the number of readers, the value of coverage is also increased. However, the overlap is decreased and finally converges to 20% while its initial value is about 35%. That is, with CBM model, we can get high coverage while keep the overlap low.

(4) Comparison simulations

In this section, we will compare our cube-based model with the planar-based model (PBM) which are used in (Danev et al., 2012; O’rourke, 1987; Melissen and Osehuu, 1996). In planar-based model, the 3D coverage problem is simplified to a planar coverage problem. That is, the coverage problem in the 3D space can be described as a two-dimensional plane with the surface. The coverage area will be projected to the two-dimensional plane.

Consequently, the problem of RFID reader deployment in the 3D space can be transformed into the problem of RFID reader deployment in the two-dimensional plane, which can be solved by using two-dimensional deployment algorithms of the RFID readers (see Fig. 8). Clearly, because PBM maps the space to six two-dimensional planes, there will be a ‘hole’ while is not covered by any reader when the 3D apace is large.

In this simulation, after the 3D space is mapped to planar, the lattice based model proposed in (Zhou and Luo, 2014) is used to deploy readers in two-dimensional space. While considering how to deploy readers in two dimensional space, we also adopted the PSO algorithm. The number of iterations in PSO is set to 5000. The RFID reader’s coverage model is simplified to a sphere with radius R. The deployment area is a large cube with size of nR × nR × nR, where n is integer.

The simulation results are shown in Tables 2 and 3. According to the simulation, in planar based model, the coverage decreases with the size of space. However, in our cube based model the coverage keep constant high. It is clearly our cube based model can achieve higher coverage than planar-based model in a large space. As shown in Table 3, in large spaces, planar based model can achieve lower overlap than our cube based model, although in small space our model can achieve lower overlap than planar based model.

Why does PBM achieve lower overlap than our CBM? We think the ‘hole’ in PBM based simple model decrease the overlap. According to the PBM model, while the 3D space is map to six planes, the central parts of the 3D space is a ‘hole’ which is not covered while calculating the RFID readers. The larger the 3D space is, the larger the discovered hole will be.

However, as we pointed out, the simplification of three dimensions to two planes ignores many special features in 3D space and is not practical. So we think the deployment solution obtained by our CBM is more practical than that by PBM. Certainly, the high overlap in our CBM indicates the RFID coverage problem in 3D space is more difficult than the one in two dimensional planar. Eventually, as point out by anonymous reviewers, how to avoid this reader collision or overlapping problem in three dimensional space is a hard work.