# Improvement of the Communication between RFID Sensor Network Devices Used to Control and Monitor a Building

Authors: Abdelhamid Bou-El-Harmel; Ali Benbassou; Jamal Belkadid
Journal: Journal of Sensors
 (2021)

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## Abstract

In the RFID sensor network (RSN), the devices communicate with each other by RF waves using the antennas through a propagation channel. A poor communication between these devices results in either a significant economic loss or security threats. The communication problems can have several origins depending on the type of antenna used and the nature of the propagation channel. In this work, our objective is to limit the communication problems between the nodes of this network that are linked to the characteristics of an indoor propagation channel. The goal is to predict the channel characteristics using the 3D ray tracing method in order to select the appropriate transmission parameters such as transmission power and duration of a symbol. To achieve this, we have modeled a building that is sectioned as a propagation channel where network devices are deployed for control and monitoring. The communication was made at 915 MHz using the quasi-isotropic 3D cubic antenna that we designed as well as a conventional dipole antenna in order to compare the results. We have found that the use of the 3D cubic antenna gives several advantages to the RFID sensor network compared to the most commonly used conventional dipole antenna, such as a transmission power of 0 dBm which automatically leads to an increase in the lifetime of the devices, as well as a minimum symbol duration of around 219.78 ns which gives a high bit rate.


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## Body

## 1. Introduction

The RSN network is a new research field for industrialists and academics. It combines the properties of RFID technology to WSN technology and vice versa [1, 2]. This association makes it possible to extend the operational and functional capabilities of the devices in order to respond to the needs of the applications.In RSN applications, the devices communicate with each other by RF waves using the antennas through a propagation channel. A poor communication between these devices results in either a significant economic loss or security threats. The communication problems can have several origins depending on the type of antenna used and the nature of the propagation channel.The antennas are fundamental and essential elements in communication between devices of the RSN network. Each antenna has different radiation characteristics. The most commonly used antennas are dipoles and monopoles [3, 4]. The latter produce radiation in the form of a doughnut with zero field strength areas along their axis. In these areas, poor communication occurs between network nodes.In order to ensure reliable communication between RSN nodes at the antennas level, we have designed in previous work new antennas in 3D form that produce quasi-isotropic radiation, such as the cubic [5, 6] and spherical [7] antennas.Regarding the propagation channel, it corresponds to the environment traversed by the RF waves during the transmission of information between the transmitting and receiving antennas of the nodes of the RSN network. Most RSN applications are deployed inside buildings, which constitutes a multipath propagation channel. These multiple paths can generate destructive interference at the receiving node which produces a fading of the received signal. Thus, the long propagation delays between the different paths and their variation with time can cause intersymbol interference (ISI) and symbol estimation errors (SEE), respectively. All of these problems contribute to poor RF transmission between network nodes.A good transmission then requires a good choice of transmission parameters such as the transmission powerPt and the symbol duration Ts. These parameters are directly linked to the characteristics of the propagation channel, i.e., received power Pr, coherence band Bc, and coherence time Tc.In previous work [8], we have studied the effects of the orientation of two different antennas on the characteristics of the multipath propagation channel in a typical indoor environment. The propagation channel characteristics are compared in terms of received power level (Pr) and delay spread (τRMS) for the 3D cubic antenna and the conventional dipole in the LOS, NLOS, and OLOS scenarios.In this work, our objective is to predict the appropriate transmission parameters (Pt and Ts) using our 3D cubic antenna and the conventional dipole antenna as transmitting and receiving antenna of the RSN network and to compare the results obtained. For this purpose, we will in “Environment, Location, and Antennas” model the indoor environment (building) that has been selected as the propagation channel where the RSN network will be deployed, as well as specify the location of the nodes and determine the antennas used with their radiation characteristics. In “3D Ray Tracing Method”, we will present the 3D ray tracing method. In “Results and Analysis”, we will present the predicted propagation channel characteristics as well as the appropriate transmission parameters with a comparison between the results obtained.


## 2. Environment, Location, and Antennas

### 2.1. Selected Environment

The selected environment as the propagation channel where the RSN network is deployed is the one we have already modeled in the work [8]. We remind that this environment is a building within our university [9] (see Figure 1).Figure 1
A view of the building taken by Google Maps.The complete modeling of this two-floor building is very complex. We were only interested in modeling the north wing of the first floor (see Figure2) where our laboratory is located. This floor consists of reinforced-concrete and brick walls, glass partitions, iron and wooden doors, and glass windows.Figure 2
First floor of the north wing of the building in 3D.All the constituents of our environment are considered homogeneous and having complex dielectric constants (see Table1) obtained from a free space method using transmission measurements at normal incidence [10]. Obstacles such as cupboards, machines, and desks are not modeled because of the complexity of their design.Table 1
Dielectric constants of materials.
Typesεr=εr′+jϵr′′εr′εr′′Reinforced-concrete wall6.7−1.2Brick wall5.1−0.2Glass partition50Iron door10Wood door30Glass window50Ground10−1.2Roof10−1.2


### 2.2. Location of RSN Nodes

The RSN network is used for control and monitoring of the building with a star topology, as shown in Figure3. The terminal nodes are deployed and fixed above the doors and windows with a height from the ground of 2.5m. This position is most optimal for integrating several types of sensors (motion sensor, temperature sensor, gas sensor, camera, etc.) with the magnetic contact sensor which is used to monitor the opening and closing of doors and windows. All detected information is transmitted to the coordinator node which is located in the middle of the corridor with a height above the ground of 2.5m. In the star topology, the network is controlled by the coordinator node, so we choose it as a transmitter (Tx) and the terminal nodes as receivers (Rx).Figure 3
Location of the nodes of the RSN network according to the star topology.


### 2.3. Used Antennas

In this study, we use, for RF communication between the nodes of the network, the 3D cubic antenna that we designed and the conventional half-wave dipole antenna. We remind that the 3D cubic antenna produces a quasi-isotropic radiation pattern with a maximum gain of1.29dBi and circular polarization; on the other hand, the dipole antenna produces a radiation in the form of a doughnut with a maximum gain of 2.14dBi and a polarization linear. The position of these two antennas relative to the environment is shown in Figure 4.Figure 4
Position of the antennas in relation to the environment.During communication, the frequency and power of transmission used are, respectivelyf=915MHz (the resonant frequency of the two antennas) and Pt=0dBm (the minimum transmission power of the RSN devices).


### 2.4. 3D Ray Tracing Method

The 3D ray tracing method is an asymptotic method based on the following:(i)
The Geometric Optics (GO) method [11] to describe the direct, reflected and transmitted fields by the concept of rays, as shown in Figure 5(a)(ii)
The Uniform Diffraction Theory (UDT) [12] to describe the diffracted fields by the concept of rays (see Figure 5(b)).Figure 5
(a) Reflection and transmission of an incident wave and (b) diffraction of an incident wave.
(a)(b)To identify the rays (paths) that propagate between the antennas, the RT-3D method uses the image method and the folding method [13]. The implementation of the RT-3D method is very complex but offers a complete description of the received waves [14]. Once all propagation rays are determined, the received power in dB is calculated by [15]:
(1)PrdB=10logEtotη02A,where
(i)
η0=μ0/ϵ0=120π is the intrinsic impedance of air with μ0 and ϵ0 being the permeability and permittivity of the vacuum, respectively(ii)
A=λ2Gr/4π is the effective area of the receiving antenna with λ being the wavelength and Gr the gain of the receiving antenna(iii)
Etot=∑iEi is the combination of the direct field between the Tx node and the Rx node, the fields reflected by obstacles, the fields transmitted through obstacles, and the fields diffracted by the edges of obstacles. With(2)Ei=E0ftfre−jkdidi∏a=1nRa∏b=1mTb∏c=1lDc,where
(i)
E0=PtGe/4π is the reference field(ii)
ft and fr are the characteristic functions of the radiation in the ray direction between transmitting and receiving antennas, respectively(iii)
k=2π/λ is the constant of propagation(iv)
di is the length of path i(v)
n, m, and l are the total numbers of reflections, transmissions, and diffractions, respectively(vi)
Ra, Tb, and Dc are the reflection coefficient of the ath reflection, the transmission coefficient for the bth transmission, and the diffraction coefficient for the cth diffraction, respectively.During the simulation, the maximum number of reflections, transmissions, and diffractions is in the order of5. The receivers of the RSN node are capable of achieving a sensitivity between −92dBm and −107.5dBm [16, 17]. Therefore, we will choose the −92dBm value as the sensitivity threshold of the Rx.


## 2.1. Selected Environment

The selected environment as the propagation channel where the RSN network is deployed is the one we have already modeled in the work [8]. We remind that this environment is a building within our university [9] (see Figure 1).Figure 1
A view of the building taken by Google Maps.The complete modeling of this two-floor building is very complex. We were only interested in modeling the north wing of the first floor (see Figure2) where our laboratory is located. This floor consists of reinforced-concrete and brick walls, glass partitions, iron and wooden doors, and glass windows.Figure 2
First floor of the north wing of the building in 3D.All the constituents of our environment are considered homogeneous and having complex dielectric constants (see Table1) obtained from a free space method using transmission measurements at normal incidence [10]. Obstacles such as cupboards, machines, and desks are not modeled because of the complexity of their design.Table 1
Dielectric constants of materials.
Typesεr=εr′+jϵr′′εr′εr′′Reinforced-concrete wall6.7−1.2Brick wall5.1−0.2Glass partition50Iron door10Wood door30Glass window50Ground10−1.2Roof10−1.2


## 2.2. Location of RSN Nodes

The RSN network is used for control and monitoring of the building with a star topology, as shown in Figure3. The terminal nodes are deployed and fixed above the doors and windows with a height from the ground of 2.5m. This position is most optimal for integrating several types of sensors (motion sensor, temperature sensor, gas sensor, camera, etc.) with the magnetic contact sensor which is used to monitor the opening and closing of doors and windows. All detected information is transmitted to the coordinator node which is located in the middle of the corridor with a height above the ground of 2.5m. In the star topology, the network is controlled by the coordinator node, so we choose it as a transmitter (Tx) and the terminal nodes as receivers (Rx).Figure 3
Location of the nodes of the RSN network according to the star topology.


## 2.3. Used Antennas

In this study, we use, for RF communication between the nodes of the network, the 3D cubic antenna that we designed and the conventional half-wave dipole antenna. We remind that the 3D cubic antenna produces a quasi-isotropic radiation pattern with a maximum gain of1.29dBi and circular polarization; on the other hand, the dipole antenna produces a radiation in the form of a doughnut with a maximum gain of 2.14dBi and a polarization linear. The position of these two antennas relative to the environment is shown in Figure 4.Figure 4
Position of the antennas in relation to the environment.During communication, the frequency and power of transmission used are, respectivelyf=915MHz (the resonant frequency of the two antennas) and Pt=0dBm (the minimum transmission power of the RSN devices).


## 2.4. 3D Ray Tracing Method

The 3D ray tracing method is an asymptotic method based on the following:(i)
The Geometric Optics (GO) method [11] to describe the direct, reflected and transmitted fields by the concept of rays, as shown in Figure 5(a)(ii)
The Uniform Diffraction Theory (UDT) [12] to describe the diffracted fields by the concept of rays (see Figure 5(b)).Figure 5
(a) Reflection and transmission of an incident wave and (b) diffraction of an incident wave.
(a)(b)To identify the rays (paths) that propagate between the antennas, the RT-3D method uses the image method and the folding method [13]. The implementation of the RT-3D method is very complex but offers a complete description of the received waves [14]. Once all propagation rays are determined, the received power in dB is calculated by [15]:
(1)PrdB=10logEtotη02A,where
(i)
η0=μ0/ϵ0=120π is the intrinsic impedance of air with μ0 and ϵ0 being the permeability and permittivity of the vacuum, respectively(ii)
A=λ2Gr/4π is the effective area of the receiving antenna with λ being the wavelength and Gr the gain of the receiving antenna(iii)
Etot=∑iEi is the combination of the direct field between the Tx node and the Rx node, the fields reflected by obstacles, the fields transmitted through obstacles, and the fields diffracted by the edges of obstacles. With(2)Ei=E0ftfre−jkdidi∏a=1nRa∏b=1mTb∏c=1lDc,where
(i)
E0=PtGe/4π is the reference field(ii)
ft and fr are the characteristic functions of the radiation in the ray direction between transmitting and receiving antennas, respectively(iii)
k=2π/λ is the constant of propagation(iv)
di is the length of path i(v)
n, m, and l are the total numbers of reflections, transmissions, and diffractions, respectively(vi)
Ra, Tb, and Dc are the reflection coefficient of the ath reflection, the transmission coefficient for the bth transmission, and the diffraction coefficient for the cth diffraction, respectively.During the simulation, the maximum number of reflections, transmissions, and diffractions is in the order of5. The receivers of the RSN node are capable of achieving a sensitivity between −92dBm and −107.5dBm [16, 17]. Therefore, we will choose the −92dBm value as the sensitivity threshold of the Rx.


## 3. Results and Analysis

### 3.1. Received Power

After the simulations, Figure6 presents the prediction results of the received power PrdBm at each Rx using the two antennas ((a) 3D cubic and (b) dipole). According to the results, we observe that the received power Pr varies randomly as a function of the distance between Tx and each Rx, which is due to the different paths received at each Rx.Figure 6
Pr predicted as a function of the distance between Tx and each Rx when using (a) the 3D cubic antenna and (d) the dipole antenna.
(a)(b)When using the 3D cubic antenna, we have obtained a minimum power value of−77.35dBm at distance 14.03m. However, during the use of the conventional dipole antenna, the minimum value of the power is −74.18dBm at the distance of 14.44m.In this study, we have positioned the 3D cubic antenna of the RSN nodes in the same way throughout the environment. The orientation of the antennas relative to each other changes the values of the powerPr as we have found in the work [8]. Table 2 summarizes the maximum differences between the levels of the power Pr obtained during all the orientations of the 3D cubic and dipole antennas in the LOS, NLOS, and OLOS scenarios.Table 2
Maximum differences between the levels of thePr during the orientations of the 3D cubic and dipole antennas [8].
Scenarios3D cubic antennaDipole antennaLOS6.85dBm27.81dBmNLOS6.07dBm25.08dBmOLOS4.6dBm27.97dBmAs shown in Table2, the two maximum power differences obtained when orienting the 3D cubic antenna and the dipole antenna are 6.85dBm and 27.97dBm, respectively. Therefore, the minimum value of the power obtained when using the 3D cubic antenna becomes −84.2dBm and when using the dipole antenna becomes −102.15dBm.As regards the fight against the fading of the received signal, the minimum value of the powerPr must be greater than the sensitivity threshold 4of the Rx (−92dBm). This implies that the value of the transmission power Pt (0dBm) chosen at the outset is satisfactory to ensure reliable RF transmission between the nodes of the RSN network using the 3D cubic antenna. On the contrary, the power Pt must be increased when using the dipole antenna, which will decrease the lifespan of the devices.


### 3.2. Coherence Band

The coherence bandBc is obtained from the maximum delay Tm by the following relation:
(3)Bc=1Tm,with Tm being the delay between the first and last pulse of the impulse response (IR) of each channel, as shown in Figure 7 which represents three predicted IRs at the level of three Rx using the 3D cubic antenna.Figure 7
Impulse responses (IRs) at the level of threeRx using the 3D cubic antenna.In the case where the transmission powerPt is insufficient, the increase of this one leads to an increase in the number of paths received, which implies an increase in the values of the delay Tm. Therefore, we will use the delay dispersion τRMS which takes into account the importance of the paths in order to calculate the coherence band:
(4)τRMS=∑iPiτi2∑iPi−∑iPiτi∑iPi2.The relationship between the coherence bandBc and the delay spread τRMS has been proposed by [18] as follows:
(5)Bc≈1ατRMS,where α is a coefficient that depends on the nature of the propagation channel. In work [19], the authors found that α=1/0.15 in an indoor radio channel.Figure8 displays the levels of τRMS as a function of the distance between the Tx and each Rx when using the two antennas ((a) 3D cubic and (b) dipole).Figure 8
Dispersion of delaysτRMS as a function of the distance between Tx and each Rx using the antenna: (a) 3D cubic and (b) dipole.
(a)(b)According to the results and when using the 3D cubic antenna, we have obtained a maximum value ofτRMS of 23.66ns at a distance 14.03m. On the other hand, the maximum value of the τRMS obtained when using the conventional dipole antenna is 39.76ns at the same distance.The values ofτRMS change depending on the orientation of the antennas as we have shown in the work [8]. Table 3 summarizes the maximum differences between the levels of τRMS obtained during all orientations of the 3D cubic and dipole antennas in the LOS, NLOS, and OLOS scenarios.Table 3
Maximum deviations between the levels ofτRMS during the orientations of the 3D cubic and dipole antennas [8].
Scenarios3D cubic antennaDipole antennaLOS6.48ns28.49nsNLOS4.64ns23.62nsOLOS9.34ns27.97nsAccording to the table, the two maximum differences ofτRMS obtained when orienting the 3D cube antenna and the dipole antenna are9.34ns and 28.49ns, respectively. Therefore, the maximum value of τRMS obtained when using the 3D cube antenna becomes 33ns and when using the dipole antenna becomes 68.25ns.Then, the minimum value ofBc obtained using the 3D cubic antenna and the conventional dipole antenna are 4.55MHz and 2.2MHz, respectively. Therefore, the signal bandwidth Bs must be lower than the coherence band Bc in order to limit intersymbol interference (ISI).For digital modulation, theBs is calculated from the symbol duration Ts by
(6)Bs=1Ts.So, to limit ISI, theTs duration must be greater than 219.78ns when using the 3D cubic antenna. On the other hand, the Ts duration must be greater than 454.55ns when using the conventional dipole antenna.


### 3.3. Coherence Time

To limit symbol estimation errors (SEE), the durationTs must be less than the coherence time Tc resulting from the mobility of network nodes and obstacles. In our case, the nodes are fixed, and the obstacles that are always moving are humans. The influence of obstacle mobility is very negligible compared to that of node mobility.Consequently, we can consider that the human wears nodes, in order to know only the maximum value of the durationTs that we will not exceed. From Equation (7), we can plot the variation of Tc (see Figure 9) as a function of the human speed V, which normally does not exceed 1m/s.
(7)Tc≈916πfV/C.Figure 9
Coherence timeTc as a function of speed V.According to the results, the minimumTc is 6.52ms, which implies that the duration Ts must be less than this value in order to limit SEE.To conclude, the durationTs must be between 219.78ns and 6.52ms to limit ISI and EES during the use of the 3D cubic antenna. On the other hand, it must be between 454.55ns and 6.52ms when using the conventional dipole antenna.The limit of durationTs also limits the bit rate D because D is the product of the inverse of Ts (modulation rate R) and the logarithm to the base 2 of the number of possible states of a symbol (valence V) [20]:
(8)D=1Tslog2V.Tables4 and 5 list the limiting values of D as a function of V when using the 3D cubic antenna and the conventional dipole antenna, respectively.Table 4
Limiting values of bit rateD as a function of valence V when using the 3D cubic antenna.
Minimum valueParametersMaximum value153.37bit/s<DV=2<4.55Mbit/s306.75bit/s<DV=4<9.1Mbit/s460.12bit/s<DV=8<13.65Mbit/sTable 5
Limiting values of bit rateD as a function of valence V when using the conventional dipole antenna.
Minimum valueParametersMaximum value153.37bit/s<DV=2<2.2Kbit/s306.75bit/s<DV=4<4.4Mbit/s460.12bit/s<DV=8<6.6Mbit/sUsually, the bit rateD must be high to ensure low data transfer time. Therefore, the duration Ts must be chosen close to the minimum value. This implies that we will not have SEE whatever the movement of nodes and obstacles.From both Tables4 and 5, we have a very high bit rate when using the 3D cubic antenna compared to using the conventional dipole antenna. Then, the use of our 3D cubic antenna is better than the conventional dipole antenna.


## 3.1. Received Power

After the simulations, Figure6 presents the prediction results of the received power PrdBm at each Rx using the two antennas ((a) 3D cubic and (b) dipole). According to the results, we observe that the received power Pr varies randomly as a function of the distance between Tx and each Rx, which is due to the different paths received at each Rx.Figure 6
Pr predicted as a function of the distance between Tx and each Rx when using (a) the 3D cubic antenna and (d) the dipole antenna.
(a)(b)When using the 3D cubic antenna, we have obtained a minimum power value of−77.35dBm at distance 14.03m. However, during the use of the conventional dipole antenna, the minimum value of the power is −74.18dBm at the distance of 14.44m.In this study, we have positioned the 3D cubic antenna of the RSN nodes in the same way throughout the environment. The orientation of the antennas relative to each other changes the values of the powerPr as we have found in the work [8]. Table 2 summarizes the maximum differences between the levels of the power Pr obtained during all the orientations of the 3D cubic and dipole antennas in the LOS, NLOS, and OLOS scenarios.Table 2
Maximum differences between the levels of thePr during the orientations of the 3D cubic and dipole antennas [8].
Scenarios3D cubic antennaDipole antennaLOS6.85dBm27.81dBmNLOS6.07dBm25.08dBmOLOS4.6dBm27.97dBmAs shown in Table2, the two maximum power differences obtained when orienting the 3D cubic antenna and the dipole antenna are 6.85dBm and 27.97dBm, respectively. Therefore, the minimum value of the power obtained when using the 3D cubic antenna becomes −84.2dBm and when using the dipole antenna becomes −102.15dBm.As regards the fight against the fading of the received signal, the minimum value of the powerPr must be greater than the sensitivity threshold 4of the Rx (−92dBm). This implies that the value of the transmission power Pt (0dBm) chosen at the outset is satisfactory to ensure reliable RF transmission between the nodes of the RSN network using the 3D cubic antenna. On the contrary, the power Pt must be increased when using the dipole antenna, which will decrease the lifespan of the devices.


## 3.2. Coherence Band

The coherence bandBc is obtained from the maximum delay Tm by the following relation:
(3)Bc=1Tm,with Tm being the delay between the first and last pulse of the impulse response (IR) of each channel, as shown in Figure 7 which represents three predicted IRs at the level of three Rx using the 3D cubic antenna.Figure 7
Impulse responses (IRs) at the level of threeRx using the 3D cubic antenna.In the case where the transmission powerPt is insufficient, the increase of this one leads to an increase in the number of paths received, which implies an increase in the values of the delay Tm. Therefore, we will use the delay dispersion τRMS which takes into account the importance of the paths in order to calculate the coherence band:
(4)τRMS=∑iPiτi2∑iPi−∑iPiτi∑iPi2.The relationship between the coherence bandBc and the delay spread τRMS has been proposed by [18] as follows:
(5)Bc≈1ατRMS,where α is a coefficient that depends on the nature of the propagation channel. In work [19], the authors found that α=1/0.15 in an indoor radio channel.Figure8 displays the levels of τRMS as a function of the distance between the Tx and each Rx when using the two antennas ((a) 3D cubic and (b) dipole).Figure 8
Dispersion of delaysτRMS as a function of the distance between Tx and each Rx using the antenna: (a) 3D cubic and (b) dipole.
(a)(b)According to the results and when using the 3D cubic antenna, we have obtained a maximum value ofτRMS of 23.66ns at a distance 14.03m. On the other hand, the maximum value of the τRMS obtained when using the conventional dipole antenna is 39.76ns at the same distance.The values ofτRMS change depending on the orientation of the antennas as we have shown in the work [8]. Table 3 summarizes the maximum differences between the levels of τRMS obtained during all orientations of the 3D cubic and dipole antennas in the LOS, NLOS, and OLOS scenarios.Table 3
Maximum deviations between the levels ofτRMS during the orientations of the 3D cubic and dipole antennas [8].
Scenarios3D cubic antennaDipole antennaLOS6.48ns28.49nsNLOS4.64ns23.62nsOLOS9.34ns27.97nsAccording to the table, the two maximum differences ofτRMS obtained when orienting the 3D cube antenna and the dipole antenna are9.34ns and 28.49ns, respectively. Therefore, the maximum value of τRMS obtained when using the 3D cube antenna becomes 33ns and when using the dipole antenna becomes 68.25ns.Then, the minimum value ofBc obtained using the 3D cubic antenna and the conventional dipole antenna are 4.55MHz and 2.2MHz, respectively. Therefore, the signal bandwidth Bs must be lower than the coherence band Bc in order to limit intersymbol interference (ISI).For digital modulation, theBs is calculated from the symbol duration Ts by
(6)Bs=1Ts.So, to limit ISI, theTs duration must be greater than 219.78ns when using the 3D cubic antenna. On the other hand, the Ts duration must be greater than 454.55ns when using the conventional dipole antenna.


## 3.3. Coherence Time

To limit symbol estimation errors (SEE), the durationTs must be less than the coherence time Tc resulting from the mobility of network nodes and obstacles. In our case, the nodes are fixed, and the obstacles that are always moving are humans. The influence of obstacle mobility is very negligible compared to that of node mobility.Consequently, we can consider that the human wears nodes, in order to know only the maximum value of the durationTs that we will not exceed. From Equation (7), we can plot the variation of Tc (see Figure 9) as a function of the human speed V, which normally does not exceed 1m/s.
(7)Tc≈916πfV/C.Figure 9
Coherence timeTc as a function of speed V.According to the results, the minimumTc is 6.52ms, which implies that the duration Ts must be less than this value in order to limit SEE.To conclude, the durationTs must be between 219.78ns and 6.52ms to limit ISI and EES during the use of the 3D cubic antenna. On the other hand, it must be between 454.55ns and 6.52ms when using the conventional dipole antenna.The limit of durationTs also limits the bit rate D because D is the product of the inverse of Ts (modulation rate R) and the logarithm to the base 2 of the number of possible states of a symbol (valence V) [20]:
(8)D=1Tslog2V.Tables4 and 5 list the limiting values of D as a function of V when using the 3D cubic antenna and the conventional dipole antenna, respectively.Table 4
Limiting values of bit rateD as a function of valence V when using the 3D cubic antenna.
Minimum valueParametersMaximum value153.37bit/s<DV=2<4.55Mbit/s306.75bit/s<DV=4<9.1Mbit/s460.12bit/s<DV=8<13.65Mbit/sTable 5
Limiting values of bit rateD as a function of valence V when using the conventional dipole antenna.
Minimum valueParametersMaximum value153.37bit/s<DV=2<2.2Kbit/s306.75bit/s<DV=4<4.4Mbit/s460.12bit/s<DV=8<6.6Mbit/sUsually, the bit rateD must be high to ensure low data transfer time. Therefore, the duration Ts must be chosen close to the minimum value. This implies that we will not have SEE whatever the movement of nodes and obstacles.From both Tables4 and 5, we have a very high bit rate when using the 3D cubic antenna compared to using the conventional dipole antenna. Then, the use of our 3D cubic antenna is better than the conventional dipole antenna.


## 4. Conclusions

In this work, we have modeled a building that has been selected as a propagation channel where the RSN network is deployed for control and monitoring. For the transmission, we have used the 3D cubic antenna that we have designed and the conventional dipole antenna which is the most used in the RSN network. By means of the 3D ray tracing method, we have predicted the characteristics of the propagation channel in order to improve the communication between the devices of the RSN network in terms of the appropriate transmission parameters such as the transmission powerPt and the duration of a symbol Ts. We have found as results to fight against fading of the received signal that a transmission power of 0dBm is sufficient when using our 3D cube antenna. However, it is necessary to increase this power during the use of the conventional dipole antenna, which automatically leads to a decrease in the lifetime of the devices, which is a disadvantage. To limit ISI and EES, the symbol duration must be close to a minimum value of the order of 219.78 ns when using our 3D cubic antenna and of the order of 454.55 ns when using the conventional dipole antenna. These two values result in different bit rates. The use of our antenna provides a high bit rate in order to ensure a low data transfer time. To conclude, our antenna gives several advantages for the RFID sensor array compared to the most commonly used antennas.



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*Source: 8883005-2021-01-29.xml*