# Optimization of Wireless Communication Coverage in Underground Tunnels Based on Zone Division

Authors: Yu Huo; Qingsong Hu; Yanjing Sun; Xiwang Guo; Liang Qi; Xiaohu Zhao; Enjie Ding
Journal: International Journal of Antennas and Propagation
 (2020)

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## Abstract

In order to reduce the path loss of the wireless communication signal in the underground tunnel, a scheme for configuring the antenna polarization of wireless systems based on a zone-division method is proposed. A multimodal method is used to estimate the effect of antenna polarization on the wireless propagation. When the optimal polarization of the antenna leading to low path loss is different in the zones near and far from the transmitting antenna, a dividing point is used to separate the zones. Experiments are conducted in an underground mine. It shows that the results by the multimodal method are consistent with the real data. Compared with the existing coverage schemes, the proposed scheme can obtain better coverage. Meanwhile, zone division has an important influence on the optimized performance of the wireless coverage. The zones divided based on Fresnel zone clearance and system identification are too small or too large, which result in incorrect polarization switching and high path loss.


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## Body

## 1. Introduction

Mining is very important in modern life by supporting mankind with energy and various mineral resources. A large proportion of mining operations take place underground. The operating environment is very dangerous because underground hazards (e.g., roof falls and toxic gases) occur from time to time [1–3]. With the development of smart technologies, wireless communication is used at every stage of mining operations, such as personnel positioning, environmental monitoring, remote operation, and emergency rescue [4–8]. With the aid of wireless communication, working safety, productivity, and emergency response efficiency in underground mines can be greatly improved. The effectiveness and reliability of coverage play a significant role in the quality of wireless communications. In underground mines, radio waves do not propagate well [1–3]. Wireless devices are powered by batteries with limited capacity. Therefore, optimizing the coverage of energy-constrained devices in underground mines is a challenging and significant task.In [9], the attenuation of the signal power is reduced by optimizing the position of the antenna. In [10], radio wave coverage is optimized by using the spatial diversity and polarization diversity of the transceiver antennas. In [11], the optimal polarization is analysed by measuring radio propagation, so as to obtain the minimum attenuation of the signal power in the tunnel. In [12], it is reported that the optimal antenna polarization relies on the antenna position. The coverage schemes studied in [9–12] usually focus on the deployment optimization of wireless devices, so the signal power can be improved only when the antenna is in a certain position. In addition, the authors in [9–12] use the same antenna polarization to communicate in the whole tunnel. However, it is found that the effect of antenna polarization on signal propagation is different in the zones near and far from the transmitter [13]. In underground mines and tunnels, only the horizontally polarized antenna can achieve low path loss when the electromagnetic signal is propagated in the zone far from the transmitter [13–15]. When the wireless signal is propagated in the zone near the transmitter, the vertically polarized antenna can also obtain low path loss [12, 13]. In underground mines, many wireless users are mobile, such as miners, vehicles, and some mining machines. Hence, in order to reduce the power loss of the signal for communication, it is necessary to distinguish the different propagation regions of the wireless system and configure different optimal antenna polarization as the user moves. This paper expands the work in [13]. It employs region division and polarization switching to realize dynamic coverage optimization of wireless systems at any position in the tunnel.In studies [16–20], a dividing point is used to separate the propagation regions near and far from the transmitting antenna. This point is determined by the first Fresnel zone clearance. In [21, 22], the dividing point of the regions is determined by system identification. It has been proved to be reasonable for path loss modeling and prediction [16–22], whereas existing methods of zone division do not take into account the axial variation of the optimal polarization. Whether the antenna polarization configuration and coverage optimization based on the existing zone-division methods are reasonable has not been verified.The major contributions of this paper are as follows:(1)
A multimodal method is proposed to quickly estimate the axial variation of the optimal antenna polarization and the dividing point of the propagation zones in the tunnel. The method depends on the solution of the propagation equation.(2)
Zone division and polarization switching are applied to dynamic coverage optimization of the wireless system for communication in underground mines and tunnels. The effectiveness and feasibility of the coverage optimization are validated by experiments in real mines.In addition, from empirical studies, it shows the difference in zone division between our proposed method and existing methods. The significant effect of zone division on the performance of coverage optimization is also shown.The rest of this paper is organized as follows. The related work is introduced in Section2. The optimization strategy for coverage is described in Section 3. It also presents the proposed zone-division method. Sections 4 and 5 conduct numerical experiments for zone division and coverage optimization examples and analyse experimental results. Section 6 concludes this work and discusses the future works.


## 2. Related Work

Radio field coverage in underground tunnels can be improved by the positions, polarization, and radiation patterns of the antennas [1]. Table 1 summarizes some existing efforts to optimize wireless communication coverage in underground tunnels.Table 1
Examples of wireless coverage optimization scheme in underground tunnels.
Research groupOptimization schemeCharacteristicsLimitationsLi and Wang [9]Antenna beam width and antenna deployment(1) Use antennas with narrow beam widthOptimal configuration of antenna parameters is not given(2) Deploy antennas on proper locationsZhao et al. [10]Antenna diversityUse spatial and polarization diversities of two antennas(1) Optimization is limited by antenna locations(2) Scheme cannot be adjusted dynamically as the user movesZhou et al. [11]Antenna polarizationUse the horizontally polarized antenna to communicate(1) Scheme cannot be adjusted dynamically as the user moves(2) Optimization is restricted to the case where the receiver is in the far-field region of the transmitterBashir [12]Antenna deploymentConsider the interaction of the effects of antenna polarization and location on field propagation(1) Optimization is limited by antenna locations(2) Scheme cannot be adjusted dynamically as the user moves(3) Optimization is restricted to the case where the receiver is in the near-field region of the transmitterHuo et al. [13]Antenna deploymentConsider the different effects of antenna polarization on field propagation in the near-field and far-field zones(1) Optimization is limited by antenna locations(2) Scheme cannot be adjusted dynamically as the user movesLi and Wang [9] use a modal method to discuss the effects of the antenna on the field coverage in tunnels. The results indicate that the attenuation of the signal power can be reduced by narrow beam width and proper location of the transmitting antenna. However, the optimal configuration of antenna parameters is not given in this study. Besides, Li and Wang [9] suggest that the deep fading of radio waves in a tunnel can be suppressed by the spatial diversity of the transceiver antennas. This work is extended in [10]. Two antennas are used to realize spatial diversity. The locations of the antennas are determined by finding the smallest correlation coefficient. By combining polarization with diversity, the field intensity and uniformity can be further improved.Zhou et al. [11] discuss the effect of antenna polarization on radio propagation by extensive measurements in mines and tunnels. Results show that horizontal polarization gives the minimum attenuation in the tunnel which has a larger width than its height.Bashir [12] reports that the optimal antenna polarization for ultrawideband (UWB) propagation channel relies on the antenna position. Analysis is based on channel measurements. The results show that the horizontally polarized antenna can obtain low average path loss when it is mounted on the ceiling, whereas the vertically polarized antenna can obtain low average path loss when it is mounted on a side wall of the tunnel.Based on multimode theory, Huo et al. [13] find that the results reported in [12] are valid when the receiver is located near the transmitter. However, when the receiver is located far from the transmitter, only the horizontally polarized antenna can achieve low path loss. The optimal mounting location of the antenna is the center of the ceiling and the center of the side wall. Besides, both horizontally and vertically polarized antennas have the weakest signal strength at the corner of the tunnel cross-section.On one hand, existing coverage optimization studies [9–13] mainly focus on the deployment of wireless devices. The power of wireless signal can be improved only when the antenna is in a certain position. However, it is also necessary to solve the coverage optimization problem of the wireless devices in nonoptimal locations because wireless devices may not always be installed in the theoretically optimal locations in practice. The real deployment of wireless nodes and sensors should also consider the location of monitored objects (e.g., hazard sources), deployment of mining infrastructure, influence of industrial electromagnetic noise generated by mining machine, and so on. On the other hand, the coverage schemes in [9–12] usually use the same antenna polarization to communicate in the whole tunnel. In underground mines, some wireless communication devices are carried by miners and some mining machines. Their locations change dynamically as miners and mining machines move. In this nonstatic scenario, it is essential to develop a dynamic configuration strategy in which the polarization changes with the user’s movement. The reason is that the optimal antenna polarization for radio propagation is different in the zones near and far from the transmitter [13].Usually, zones for wireless propagation along the tunnel axis are separated by a dividing point [16–20]. On one side of the dividing point, the zone is close to the transmitter and is known as a near-field region. On the other side, the zone is far from the transmitter and is known as a far-field region. This point can be determined by the following two methods.Method 1: most researchers use the Fresnel break point (FBP) to divide the near-field region and the far-field region [16–20]. The dividing point is given by(1)zDV=maxw2λ,h2λ,whereλ is the wavelength; w and h denote the width and the height of the rectangular tunnel, respectively. If the tunnel is nonrectangular, it can be equivalently surrogated by a rectangular tunnel [16–20], by using the method reported in [23, 24].Method 2: system identification (SI) is used to estimate the parameters in the models that depict wireless propagation in the near-field region and the far-field region [21, 22]. In the near-field region, the electromagnetic field has the lognormal distribution, and the path loss model is estimated by nonlinear optimization [21, 22]. In the far-field region, the field exhibits an exponential fall-off, and the path loss model is estimated by linear optimization [21, 22]. The dividing point is the tangent point of the optimized nonlinear curve and the optimized linear curve of the field [21, 22].Existing methods, which distinguish the near-field region and the far-field region of the source, are mainly based on the law of the field fading [16–22]. The difference in field power between horizontal polarization and vertical polarization is not captured by these methods.In this paper, we focus on the dynamic coverage optimization of wireless devices at any position in the tunnel. Locations of the receiver and transmitter are the key parameters at every stage of the coverage procedure. User positioning and zone division are used to guide the polarization switching of the transceiver. The propagation zones are divided based on a multimodal method, which can quickly estimate the axial variation of the optimal antenna polarization in a tunnel.


## 3. Methodology

### 3.1. Coverage Optimization for Wireless Communication

#### 3.1.1. Variation of Optimal Antenna Polarization for Wireless Communication

According to multimodal theory, the wireless propagation in the near-field region is dominated by multiple modes [18–21]. The modes that are significant for propagation and the optimal polarization with lower path loss are determined by the location of the antenna [9, 13]. For example, n (n = 1, 2, and 3) modes can be effectively excited and play significant roles in the propagation when the transceivers are close to the side walls of the tunnel [13]. Compared with the horizontally polarized excitation, these modes have lower path loss under the vertically polarized excitation [12, 13], whereas m (m = 1, 2, and 3) modes can be effectively excited when the transceivers are close to the ceiling of the tunnel [13]. Compared with the vertically polarized excitation, these modes have lower path loss under the horizontally polarized excitation [12, 13]. The horizontally polarized antenna is parallel to the floor. The vertically polarized antenna is parallel to the side walls of the tunnel.In the far-field region, the field is dominated only by the fundamental mode [18–21]. The power attenuation of the fundamental mode is lower for horizontal polarization than vertical polarization [13–15]. Only horizontal polarization is optimal for signal propagation [13–15].When the optimal polarization changes along the tunnel axis, we define the near-field region is the zone where the vertically polarized signal has a lower path loss. The far-field region is the zone where the horizontally polarized signal has a lower path loss. According to the propagation mechanism revealed by the multimodal theory [13], we consider the dividing point of both regions as the point where the high-order mode (the horizontally polarized and the vertically polarized wave) has greater power attenuation than the fundamental mode (the horizontally polarized wave).


#### 3.1.2. Coverage Optimization

This work studies peer-to-peer communication. The antenna position of the fixed wireless system is known. A Cartesian coordinate system is set with its origin located at the center of the tunnel.x, y, and z axes denote the width, height, and length of the tunnel, respectively. The coordinate of the antenna of the fixed wireless system is expressed as (x0, y0, 0).The optimization process is as follows:(1)
Estimate the location of the user through positioning algorithms. (x1, y1, z1) denotes the coordinates of the antenna of the user.(2)
Estimate the variation of the optimal polarization with the axial distance in the tunnel.(3)
Divide the propagation zones:If horizontal polarization has lower path loss in the propagation zones, there is no need to divide the zones. The fixed wireless system and the user use horizontally polarized antennas to send and receive signals;Otherwise, the near-field region and the far-field region are divided by a dividing point. The location of the dividing point is indicated by its longitudinal coordinatezDV. The range of the near-field zone is from 0 to zDV.(4)
If the propagation zones are divided, configure the optimal polarization for the communication systems by comparing the position of the dividing point with the position of the user:If0≤z1≤zDV, the user is in the near-field region. Wireless systems use vertically polarized antennas to send and receive signals [12, 13]; if z1>zDV, the user is in the far-field region. Wireless systems use horizontally polarized antennas to send and receive signals [13];(5)
If the communication does not end, return to step (1). Continue steps (1)–(4) until the communication end.The procedure of coverage optimization for wireless communication in underground tunnels is shown in Figure1. It can be used for most tunnels with their width being larger than their height. If the tunnel has a shorter width than its height, the polarization configuration for coverage optimization should be reversed [13]. If the width of the tunnel is equivalent to its height, there is no need to divide the communication cell to switch polarizations during the communication.Figure 1
Procedure of coverage optimization for communication systems in underground tunnels.


### 3.2. Optimal Polarization Estimation and Zone Division

#### 3.2.1. Multimodal Method

The proposed zone-division method is a multimodal method (MM). Table2 lists the symbols used in the paper.Table 2
List of symbols used in this paper.
SymbolQuantitywWidth of the rectangular tunnelhHeight of the rectangular tunnel(x0, y0, 0)Coordinate of the antenna of the wireless device(x1, y1, z1)Coordinate of the antenna of the userm, nOrder of the waveguide modeλWavelengthLmnPath loss of the (m, n) modeCopmnCoupling loss of signal power at both the transmitting and receiving antennasMAFmnPower loss of the (m, n) mode as it propagates along the tunnelηmnTCoupling fraction of the transmitting antenna power along the (m, n) modeηmnRCoupling fraction of the receiving antenna power along the (m, n) modeαmnAttenuation coefficient of the (m, n) modezDVLongitudinal coordinate of the location of the dividing pointZmnVBoundary of the zone where the attenuation of the vertically polarized (m, n) mode is larger than that of the horizontally polarized (1,1) modeZmnHBoundary of the zone where the attenuation of the horizontally polarized (m, n) mode is larger than that of the horizontally polarized (1,1) modePvVertically polarized field powerPhHorizontally polarized field powerΔPPower difference between vertical polarization and horizontal polarizationΔP¯Mean value ofΔP per unit lengthpPseudoperiod of the field variationz0.5Longitudinal coordinate of the location of the observation intervalThe path loss of each modeLmn is given by [13, 25–28](2)Lmn=Copmn+MAFmn,where Copmn is the loss of signal power at both the transmitter and receiver due to the inefficient coupling of the antennas to the (m, n) mode and MAFmn is the power loss of the (m, n) mode as it propagates along the tunnel.The restrictions ofm and n in (2) are as follows [28]:(3)1<m≤2wλ,1<n≤2hλ.The (1, 1) mode is the fundamental mode [28].Copmn is given as(4)Copmn=−10log10ηmnTηmnR,where ηmnT is the fraction of the transmitting antenna radiated power that is coupled to the (m, n) mode; ηmnR is the coupling fraction for the power of the receiving antenna. The function of ηmn is reported in [13]. ηmnT and ηmnR change with antenna current density and antenna positions with respect to the tunnel cross-section, but change little with antenna polarization and communication distance [13].MAFmn is a function of antenna polarization and the distance [13, 26, 28]:(5)MAFmn=−20log10e−αmnz=8.686αmnz,where αmn is the attenuation coefficient of the (m, n) mode. αmn can be calculated by functions reported in [28].According to the definition of the dividing point in Section3.2.1, we can get the following relationship when the waves travel to the dividing point:(6)LmnV≥L11H,LmnH≥L11H,where LmnVand LmnH are the path loss of the (m, n) mode for vertical polarization and horizontal polarization, respectively.By combining (2) and (4)–(6), for wireless communication in the far-field region, the axial distance between the receiver and the sender should satisfy the following conditions:(7)z≥ZmnV=Cop11−Copmn8.686αmnV−α11H,z≥ZmnH=Cop11−Copmn8.686αmnH−α11H,where ZmnV is the boundary of the zone where the attenuation of the vertically polarized (m, n) mode is larger than that of the horizontally polarized (1, 1) mode; similarly, ZmnH is the boundary for the horizontally polarized (m, n) mode.The optimal polarization estimation and zone division are as follows:(1)
IfmaxZmnH<maxZmnV, it can be inferred that higher-order modes for horizontal polarization attenuate more quickly than that for vertical polarization. Hence, before maxZmnV, vertical polarization is optimal due to smaller path loss. There is a change in optimal polarization when the waves propagate along the tunnel axis.In order to configure optimal polarization for the communication system, different propagation regions need to be distinguished. The location of the point dividing the regions is(8)zDV=maxZmnV.(2)
IfmaxZmnH≥maxZmnV, it means that higher-order modes for vertical polarization attenuate more quickly than that for horizontal polarization. Therefore, horizontally polarized field has a lower path loss in the zone close to the source. Then, there is no change in optimal polarization along the tunnel axis. It is unnecessary to divide the propagation regions and change the antenna polarization.


#### 3.2.2. Statistical Methods

In order to verify the prediction, the following statistical method (SM) is used to identify the measured polarization difference and dividing point:(1)
Measure the distance-dependent signal power along the tunnel, and record the field power in decibels.(2)
Calculate the difference between the vertically polarized field powerPv and the horizontally polarized field power Ph. The power difference is represented as ΔP, and ΔP=Pv−Ph.(3)
Calculate the mean value ofΔP per unit length. The mean value of ΔP per unit length is represented asΔP¯.The observation interval is the pseudoperiod of the field variation along the tunnel axis [23, 24]. The pseudoperiod of the field variation is expressed as p and is deduced from the minima locations of ΔP [24]:(9)p=1V∑v=2Vzv−zv−12,wherezv is the location of the vth minimum of the power difference and V is the total number of minima.(4)
Move the observation interval along the tunnel axis. Search the location of the observation interval, whereΔP¯ is equal to 0. The location of the observation interval refers to the center of the interval, and its longitudinal coordinate is expressed as z0.5.(5)
Search the furthestz0.5, where the average ΔP is smaller than 0 before z0.5 and greater than 0 after z0.5. The furthest z0.5 is the location of the dividing point between the near-field region and the far-field region. If there is no furthest z0.5 that meets the aforementioned condition, it can be obtained that horizontal polarization is optimal in the both propagation zones, and there is no need to split the zones.


## 3.1. Coverage Optimization for Wireless Communication

### 3.1.1. Variation of Optimal Antenna Polarization for Wireless Communication

According to multimodal theory, the wireless propagation in the near-field region is dominated by multiple modes [18–21]. The modes that are significant for propagation and the optimal polarization with lower path loss are determined by the location of the antenna [9, 13]. For example, n (n = 1, 2, and 3) modes can be effectively excited and play significant roles in the propagation when the transceivers are close to the side walls of the tunnel [13]. Compared with the horizontally polarized excitation, these modes have lower path loss under the vertically polarized excitation [12, 13], whereas m (m = 1, 2, and 3) modes can be effectively excited when the transceivers are close to the ceiling of the tunnel [13]. Compared with the vertically polarized excitation, these modes have lower path loss under the horizontally polarized excitation [12, 13]. The horizontally polarized antenna is parallel to the floor. The vertically polarized antenna is parallel to the side walls of the tunnel.In the far-field region, the field is dominated only by the fundamental mode [18–21]. The power attenuation of the fundamental mode is lower for horizontal polarization than vertical polarization [13–15]. Only horizontal polarization is optimal for signal propagation [13–15].When the optimal polarization changes along the tunnel axis, we define the near-field region is the zone where the vertically polarized signal has a lower path loss. The far-field region is the zone where the horizontally polarized signal has a lower path loss. According to the propagation mechanism revealed by the multimodal theory [13], we consider the dividing point of both regions as the point where the high-order mode (the horizontally polarized and the vertically polarized wave) has greater power attenuation than the fundamental mode (the horizontally polarized wave).


### 3.1.2. Coverage Optimization

This work studies peer-to-peer communication. The antenna position of the fixed wireless system is known. A Cartesian coordinate system is set with its origin located at the center of the tunnel.x, y, and z axes denote the width, height, and length of the tunnel, respectively. The coordinate of the antenna of the fixed wireless system is expressed as (x0, y0, 0).The optimization process is as follows:(1)
Estimate the location of the user through positioning algorithms. (x1, y1, z1) denotes the coordinates of the antenna of the user.(2)
Estimate the variation of the optimal polarization with the axial distance in the tunnel.(3)
Divide the propagation zones:If horizontal polarization has lower path loss in the propagation zones, there is no need to divide the zones. The fixed wireless system and the user use horizontally polarized antennas to send and receive signals;Otherwise, the near-field region and the far-field region are divided by a dividing point. The location of the dividing point is indicated by its longitudinal coordinatezDV. The range of the near-field zone is from 0 to zDV.(4)
If the propagation zones are divided, configure the optimal polarization for the communication systems by comparing the position of the dividing point with the position of the user:If0≤z1≤zDV, the user is in the near-field region. Wireless systems use vertically polarized antennas to send and receive signals [12, 13]; if z1>zDV, the user is in the far-field region. Wireless systems use horizontally polarized antennas to send and receive signals [13];(5)
If the communication does not end, return to step (1). Continue steps (1)–(4) until the communication end.The procedure of coverage optimization for wireless communication in underground tunnels is shown in Figure1. It can be used for most tunnels with their width being larger than their height. If the tunnel has a shorter width than its height, the polarization configuration for coverage optimization should be reversed [13]. If the width of the tunnel is equivalent to its height, there is no need to divide the communication cell to switch polarizations during the communication.Figure 1
Procedure of coverage optimization for communication systems in underground tunnels.


## 3.1.1. Variation of Optimal Antenna Polarization for Wireless Communication

According to multimodal theory, the wireless propagation in the near-field region is dominated by multiple modes [18–21]. The modes that are significant for propagation and the optimal polarization with lower path loss are determined by the location of the antenna [9, 13]. For example, n (n = 1, 2, and 3) modes can be effectively excited and play significant roles in the propagation when the transceivers are close to the side walls of the tunnel [13]. Compared with the horizontally polarized excitation, these modes have lower path loss under the vertically polarized excitation [12, 13], whereas m (m = 1, 2, and 3) modes can be effectively excited when the transceivers are close to the ceiling of the tunnel [13]. Compared with the vertically polarized excitation, these modes have lower path loss under the horizontally polarized excitation [12, 13]. The horizontally polarized antenna is parallel to the floor. The vertically polarized antenna is parallel to the side walls of the tunnel.In the far-field region, the field is dominated only by the fundamental mode [18–21]. The power attenuation of the fundamental mode is lower for horizontal polarization than vertical polarization [13–15]. Only horizontal polarization is optimal for signal propagation [13–15].When the optimal polarization changes along the tunnel axis, we define the near-field region is the zone where the vertically polarized signal has a lower path loss. The far-field region is the zone where the horizontally polarized signal has a lower path loss. According to the propagation mechanism revealed by the multimodal theory [13], we consider the dividing point of both regions as the point where the high-order mode (the horizontally polarized and the vertically polarized wave) has greater power attenuation than the fundamental mode (the horizontally polarized wave).


## 3.1.2. Coverage Optimization

This work studies peer-to-peer communication. The antenna position of the fixed wireless system is known. A Cartesian coordinate system is set with its origin located at the center of the tunnel.x, y, and z axes denote the width, height, and length of the tunnel, respectively. The coordinate of the antenna of the fixed wireless system is expressed as (x0, y0, 0).The optimization process is as follows:(1)
Estimate the location of the user through positioning algorithms. (x1, y1, z1) denotes the coordinates of the antenna of the user.(2)
Estimate the variation of the optimal polarization with the axial distance in the tunnel.(3)
Divide the propagation zones:If horizontal polarization has lower path loss in the propagation zones, there is no need to divide the zones. The fixed wireless system and the user use horizontally polarized antennas to send and receive signals;Otherwise, the near-field region and the far-field region are divided by a dividing point. The location of the dividing point is indicated by its longitudinal coordinatezDV. The range of the near-field zone is from 0 to zDV.(4)
If the propagation zones are divided, configure the optimal polarization for the communication systems by comparing the position of the dividing point with the position of the user:If0≤z1≤zDV, the user is in the near-field region. Wireless systems use vertically polarized antennas to send and receive signals [12, 13]; if z1>zDV, the user is in the far-field region. Wireless systems use horizontally polarized antennas to send and receive signals [13];(5)
If the communication does not end, return to step (1). Continue steps (1)–(4) until the communication end.The procedure of coverage optimization for wireless communication in underground tunnels is shown in Figure1. It can be used for most tunnels with their width being larger than their height. If the tunnel has a shorter width than its height, the polarization configuration for coverage optimization should be reversed [13]. If the width of the tunnel is equivalent to its height, there is no need to divide the communication cell to switch polarizations during the communication.Figure 1
Procedure of coverage optimization for communication systems in underground tunnels.


## 3.2. Optimal Polarization Estimation and Zone Division

### 3.2.1. Multimodal Method

The proposed zone-division method is a multimodal method (MM). Table2 lists the symbols used in the paper.Table 2
List of symbols used in this paper.
SymbolQuantitywWidth of the rectangular tunnelhHeight of the rectangular tunnel(x0, y0, 0)Coordinate of the antenna of the wireless device(x1, y1, z1)Coordinate of the antenna of the userm, nOrder of the waveguide modeλWavelengthLmnPath loss of the (m, n) modeCopmnCoupling loss of signal power at both the transmitting and receiving antennasMAFmnPower loss of the (m, n) mode as it propagates along the tunnelηmnTCoupling fraction of the transmitting antenna power along the (m, n) modeηmnRCoupling fraction of the receiving antenna power along the (m, n) modeαmnAttenuation coefficient of the (m, n) modezDVLongitudinal coordinate of the location of the dividing pointZmnVBoundary of the zone where the attenuation of the vertically polarized (m, n) mode is larger than that of the horizontally polarized (1,1) modeZmnHBoundary of the zone where the attenuation of the horizontally polarized (m, n) mode is larger than that of the horizontally polarized (1,1) modePvVertically polarized field powerPhHorizontally polarized field powerΔPPower difference between vertical polarization and horizontal polarizationΔP¯Mean value ofΔP per unit lengthpPseudoperiod of the field variationz0.5Longitudinal coordinate of the location of the observation intervalThe path loss of each modeLmn is given by [13, 25–28](2)Lmn=Copmn+MAFmn,where Copmn is the loss of signal power at both the transmitter and receiver due to the inefficient coupling of the antennas to the (m, n) mode and MAFmn is the power loss of the (m, n) mode as it propagates along the tunnel.The restrictions ofm and n in (2) are as follows [28]:(3)1<m≤2wλ,1<n≤2hλ.The (1, 1) mode is the fundamental mode [28].Copmn is given as(4)Copmn=−10log10ηmnTηmnR,where ηmnT is the fraction of the transmitting antenna radiated power that is coupled to the (m, n) mode; ηmnR is the coupling fraction for the power of the receiving antenna. The function of ηmn is reported in [13]. ηmnT and ηmnR change with antenna current density and antenna positions with respect to the tunnel cross-section, but change little with antenna polarization and communication distance [13].MAFmn is a function of antenna polarization and the distance [13, 26, 28]:(5)MAFmn=−20log10e−αmnz=8.686αmnz,where αmn is the attenuation coefficient of the (m, n) mode. αmn can be calculated by functions reported in [28].According to the definition of the dividing point in Section3.2.1, we can get the following relationship when the waves travel to the dividing point:(6)LmnV≥L11H,LmnH≥L11H,where LmnVand LmnH are the path loss of the (m, n) mode for vertical polarization and horizontal polarization, respectively.By combining (2) and (4)–(6), for wireless communication in the far-field region, the axial distance between the receiver and the sender should satisfy the following conditions:(7)z≥ZmnV=Cop11−Copmn8.686αmnV−α11H,z≥ZmnH=Cop11−Copmn8.686αmnH−α11H,where ZmnV is the boundary of the zone where the attenuation of the vertically polarized (m, n) mode is larger than that of the horizontally polarized (1, 1) mode; similarly, ZmnH is the boundary for the horizontally polarized (m, n) mode.The optimal polarization estimation and zone division are as follows:(1)
IfmaxZmnH<maxZmnV, it can be inferred that higher-order modes for horizontal polarization attenuate more quickly than that for vertical polarization. Hence, before maxZmnV, vertical polarization is optimal due to smaller path loss. There is a change in optimal polarization when the waves propagate along the tunnel axis.In order to configure optimal polarization for the communication system, different propagation regions need to be distinguished. The location of the point dividing the regions is(8)zDV=maxZmnV.(2)
IfmaxZmnH≥maxZmnV, it means that higher-order modes for vertical polarization attenuate more quickly than that for horizontal polarization. Therefore, horizontally polarized field has a lower path loss in the zone close to the source. Then, there is no change in optimal polarization along the tunnel axis. It is unnecessary to divide the propagation regions and change the antenna polarization.


### 3.2.2. Statistical Methods

In order to verify the prediction, the following statistical method (SM) is used to identify the measured polarization difference and dividing point:(1)
Measure the distance-dependent signal power along the tunnel, and record the field power in decibels.(2)
Calculate the difference between the vertically polarized field powerPv and the horizontally polarized field power Ph. The power difference is represented as ΔP, and ΔP=Pv−Ph.(3)
Calculate the mean value ofΔP per unit length. The mean value of ΔP per unit length is represented asΔP¯.The observation interval is the pseudoperiod of the field variation along the tunnel axis [23, 24]. The pseudoperiod of the field variation is expressed as p and is deduced from the minima locations of ΔP [24]:(9)p=1V∑v=2Vzv−zv−12,wherezv is the location of the vth minimum of the power difference and V is the total number of minima.(4)
Move the observation interval along the tunnel axis. Search the location of the observation interval, whereΔP¯ is equal to 0. The location of the observation interval refers to the center of the interval, and its longitudinal coordinate is expressed as z0.5.(5)
Search the furthestz0.5, where the average ΔP is smaller than 0 before z0.5 and greater than 0 after z0.5. The furthest z0.5 is the location of the dividing point between the near-field region and the far-field region. If there is no furthest z0.5 that meets the aforementioned condition, it can be obtained that horizontal polarization is optimal in the both propagation zones, and there is no need to split the zones.


## 3.2.1. Multimodal Method

The proposed zone-division method is a multimodal method (MM). Table2 lists the symbols used in the paper.Table 2
List of symbols used in this paper.
SymbolQuantitywWidth of the rectangular tunnelhHeight of the rectangular tunnel(x0, y0, 0)Coordinate of the antenna of the wireless device(x1, y1, z1)Coordinate of the antenna of the userm, nOrder of the waveguide modeλWavelengthLmnPath loss of the (m, n) modeCopmnCoupling loss of signal power at both the transmitting and receiving antennasMAFmnPower loss of the (m, n) mode as it propagates along the tunnelηmnTCoupling fraction of the transmitting antenna power along the (m, n) modeηmnRCoupling fraction of the receiving antenna power along the (m, n) modeαmnAttenuation coefficient of the (m, n) modezDVLongitudinal coordinate of the location of the dividing pointZmnVBoundary of the zone where the attenuation of the vertically polarized (m, n) mode is larger than that of the horizontally polarized (1,1) modeZmnHBoundary of the zone where the attenuation of the horizontally polarized (m, n) mode is larger than that of the horizontally polarized (1,1) modePvVertically polarized field powerPhHorizontally polarized field powerΔPPower difference between vertical polarization and horizontal polarizationΔP¯Mean value ofΔP per unit lengthpPseudoperiod of the field variationz0.5Longitudinal coordinate of the location of the observation intervalThe path loss of each modeLmn is given by [13, 25–28](2)Lmn=Copmn+MAFmn,where Copmn is the loss of signal power at both the transmitter and receiver due to the inefficient coupling of the antennas to the (m, n) mode and MAFmn is the power loss of the (m, n) mode as it propagates along the tunnel.The restrictions ofm and n in (2) are as follows [28]:(3)1<m≤2wλ,1<n≤2hλ.The (1, 1) mode is the fundamental mode [28].Copmn is given as(4)Copmn=−10log10ηmnTηmnR,where ηmnT is the fraction of the transmitting antenna radiated power that is coupled to the (m, n) mode; ηmnR is the coupling fraction for the power of the receiving antenna. The function of ηmn is reported in [13]. ηmnT and ηmnR change with antenna current density and antenna positions with respect to the tunnel cross-section, but change little with antenna polarization and communication distance [13].MAFmn is a function of antenna polarization and the distance [13, 26, 28]:(5)MAFmn=−20log10e−αmnz=8.686αmnz,where αmn is the attenuation coefficient of the (m, n) mode. αmn can be calculated by functions reported in [28].According to the definition of the dividing point in Section3.2.1, we can get the following relationship when the waves travel to the dividing point:(6)LmnV≥L11H,LmnH≥L11H,where LmnVand LmnH are the path loss of the (m, n) mode for vertical polarization and horizontal polarization, respectively.By combining (2) and (4)–(6), for wireless communication in the far-field region, the axial distance between the receiver and the sender should satisfy the following conditions:(7)z≥ZmnV=Cop11−Copmn8.686αmnV−α11H,z≥ZmnH=Cop11−Copmn8.686αmnH−α11H,where ZmnV is the boundary of the zone where the attenuation of the vertically polarized (m, n) mode is larger than that of the horizontally polarized (1, 1) mode; similarly, ZmnH is the boundary for the horizontally polarized (m, n) mode.The optimal polarization estimation and zone division are as follows:(1)
IfmaxZmnH<maxZmnV, it can be inferred that higher-order modes for horizontal polarization attenuate more quickly than that for vertical polarization. Hence, before maxZmnV, vertical polarization is optimal due to smaller path loss. There is a change in optimal polarization when the waves propagate along the tunnel axis.In order to configure optimal polarization for the communication system, different propagation regions need to be distinguished. The location of the point dividing the regions is(8)zDV=maxZmnV.(2)
IfmaxZmnH≥maxZmnV, it means that higher-order modes for vertical polarization attenuate more quickly than that for horizontal polarization. Therefore, horizontally polarized field has a lower path loss in the zone close to the source. Then, there is no change in optimal polarization along the tunnel axis. It is unnecessary to divide the propagation regions and change the antenna polarization.


## 3.2.2. Statistical Methods

In order to verify the prediction, the following statistical method (SM) is used to identify the measured polarization difference and dividing point:(1)
Measure the distance-dependent signal power along the tunnel, and record the field power in decibels.(2)
Calculate the difference between the vertically polarized field powerPv and the horizontally polarized field power Ph. The power difference is represented as ΔP, and ΔP=Pv−Ph.(3)
Calculate the mean value ofΔP per unit length. The mean value of ΔP per unit length is represented asΔP¯.The observation interval is the pseudoperiod of the field variation along the tunnel axis [23, 24]. The pseudoperiod of the field variation is expressed as p and is deduced from the minima locations of ΔP [24]:(9)p=1V∑v=2Vzv−zv−12,wherezv is the location of the vth minimum of the power difference and V is the total number of minima.(4)
Move the observation interval along the tunnel axis. Search the location of the observation interval, whereΔP¯ is equal to 0. The location of the observation interval refers to the center of the interval, and its longitudinal coordinate is expressed as z0.5.(5)
Search the furthestz0.5, where the average ΔP is smaller than 0 before z0.5 and greater than 0 after z0.5. The furthest z0.5 is the location of the dividing point between the near-field region and the far-field region. If there is no furthest z0.5 that meets the aforementioned condition, it can be obtained that horizontal polarization is optimal in the both propagation zones, and there is no need to split the zones.


## 4. Experimental Setup and Configuration

For validation purposes, the distance-dependent field power is measured in two arched underground tunnels located at Xinglongzhuang Coal Mine, Shandong Province, China. One of the tunnels is wide. The tunnel has a cross-section radius of 2.69 m, a flat bottom width of 5.12 m, and a maximum height of 3.56 m. The other tunnel is narrow. The tunnel has a cross-section radius of 1.54 m, a flat bottom width of 2.82 m, and a maximum height of 2.16 m.The grid-based system introduced in [13] is used to measure the electromagnetic field. The grid-based system can carry out multiple transceiver tests at the same time to improve the testing efficiency [13, 29]. The diagram of the grid-based system is shown in Figure 2(b). Long-range measurements (up to 500 m in the wide tunnel) are needed in order to analyse the propagation characteristics in both near-field and far-field regions [20, 21]. High transmitting power and low receiving sensitivity are conducive to long-range measurements [30, 31]. 21 dBm AS32-TTL and E22-900T nodes are used in the grid-based system. Their receiving sensitivities are −130 dBm and −148 dBm, respectively. AS32-TTL and E22-900T nodes operate at 433 MHz and 900 MHz frequencies, respectively. The antennas of the nodes are linearly polarized. The gain of the antennas is 4 dBi. Other antennas with different gains are also considered. Experimental results show that the antenna types and characteristics do not influence the effectiveness and feasibility of the proposed coverage optimization scheme. For the purpose of this paper, we do not describe the parameters of other antennas and the corresponding experimental results. Figure 2 and Tables 3–5 how the configuration of the measurements.Figure 2
Measurement configuration. (a) Inside views of the tunnels. (b) Diagram of the measurement setup reported in [13]. (c) Details of LoRa nodes.
(a)(b)(c)Table 3
Experimental settings: parameters of the measure tunnel.
Parameters of cross-sectionWide tunnelNarrow tunnelShapeArchedArchedRadius2.69 m1.54 mFloor width5.12 m2.82 mMaximum height3.56 m2.16 mTable 4
Experimental settings: details of LoRa nodes.
ParametersAS32-TTL nodeE22-900T nodeCenter frequency433 MHz900 MHzSending power21 dBm21 dBmReceiving sensitivity−130 dBm−148 dBmAntenna polarizationLinearLinearAntenna gain4 dBi4 dBiTable 5
Experimental settings: locations of antennas.
AntennaPosition of CPosition of CCPosition of COPosition of WCPosition of WWMeasurements in wide tunnelSending antenna(0, 0.94,z1)————Receiving antenna(−0.28,0.89,0)(−0.04,2.40,0)(−1.62,1.90,0)(−2.30,0.90,0)(−2.45, 0.02,0)Measurements in narrow tunnelSending antenna(0, 0.46,z1)Receiving antenna(0,0.46,0)(0,1.29,0)(0.89,1.06,0)(−1.20,0.46,0)(−1.20, 0,0)In the measurements, five fixed nodes simultaneously receive signals and provide the Received Signal Strength Indication (RSSI). The antenna nodes are, respectively, mounted at the tunnel center (C), ceiling center (CC), corner (CO), sidewall center (WC), and the widest part of the sidewall (WW). One node broadcasted signals at C point. The antenna position parameters are shown in Table5. For each test, the average RSSI was recorded by calculation over 300 packets for 2 times. The average RSSI varied at most ±1 dBm from the mean value of the set of the test nodes. After each test, the transmitting node is moved backward along the tunnel by 1.40 m distance in the wide tunnel and 0.6 m distance in the narrow tunnel. The detailed description of the experimental system, node calibration, the signal transmitting and receiving, and the data recording can be found in [13].


## 5. Results and Discussion

Figure3 shows 900 MHz and 433 MHz distance-dependent signal power measured in the wide tunnel and the narrow tunnel. The field is measured only by the horizontally polarized antennas or only by the vertically polarized antennas. Figure 3(b) has been reported in [13], and other data is expanded in this paper.Figure 3
Distance-dependent signal power measured in the coal mine tunnel.V indicates vertical polarization, and H indicates horizontal polarization. (a) 900 MHz signal in wide tunnel; (b) 433 MHz signal in wide tunnel; (c) 900 MHz signal in narrow tunnel; (d) 433 MHz signal in narrow tunnel.
(a)(b)(c)(d)


### 5.1. Optimal Polarization Estimation and Zone Division

To simplify the solution of the proposed method, the measured tunnels are equivalently surrogated by rectangular tunnels by using the method reported in [23]. The simulation parameters are presented in Figure 4.Figure 4
Simulation parameters of the equivalently surrogated tunnel.Firstly, we show an example of the optimal polarization estimation and zone division by using the proposed method for 900 MHz field coverage in the wide tunnel.


#### 5.1.1. MM

The boundary of the zones where the power attenuation of the higher-order mode is larger than the fundamental mode is calculated by using (7). The maximum boundaries for horizontal polarization and vertical polarization are shown in Table 6.Table 6
Maximum boundary for horizontal polarization modes and vertical polarization modes at 900 MHz frequency in the wide tunnel (in m).
PolarizationPosition of CPosition of CCPosition of COPosition of WCPosition of WWHorizontal0269.94268.0879.0979.28Vertical025.03293.29307.97308.70Compare the results in Table6. It can be observed that the maximum boundary for horizontal polarization is smaller than that for vertical polarization, when the signal is received at the position of CO, WC, and WW. The opposite results appear when the signal is received at the position of C and CC.As illustrated in Section3.2.1, when the signal is received at the position of CO, WC, and WW, vertical polarization is optimal in the near-field region. There is a change in optimal polarization when the signal travels along the tunnel axis. When the receiver is fixed at the position of C and CC, horizontal polarization is optimal, and there is no change in optimal polarization when the signal travels along the tunnel axis.For the receiver mounted at the position of CO, WC, and WW, the propagation regions are divided into a near-field region and a far-field region by a dividing point at 293.29 m, 307.97 m, and 308.70 m, respectively. The corresponding range of the near-field region is from 0 m–293.29 m, 0 m–307.97 m, and 0 m–308.70 m, respectively. For the receiver mounted at C and CC positions, zone division is unnecessary.


#### 5.1.2. SM

900 MHz measured field distribution in the wide tunnel is shown in Figure3(a).The difference between the vertically and the horizontally polarized field powerΔPis plotted in Figure 5. The smoothing spline filter is used to reduce the influence of the noise on the data and to facilitate the analysis of the field variation. The pseudoperiod of the field variation measured at the positions of C, CC, CO, WC, and WW are 103.88 m, 81.19 m, 62.68 m, 71.64 m, and 63.50 m, respectively.Figure 5
Difference between the vertically polarized and the horizontally polarized field power.Take the pseudoperiod of the field variation as the observation unit, and then calculate the mean value ofΔP per unit length. The results are shown in Figure 6.Figure 6
Average difference between the vertically polarized and the horizontally polarized field power.It can be noted that when the receiver is located at the position of CO, WC, and WW, vertical polarization results in less average path loss in the near-field region, while horizontal polarization results in less average path loss in the far-field region. The corresponding measured dividing points of the regions are located at 274.20 m, 248.60 m, and 317.30 m, respectively. The corresponding range of the near-field region is from 0 m–274.20 m, 0 m−248.60 m, and 0 m−317.30 m, respectively. When the receiver is located at the point of C and CC, there is no change in optimal polarization along the tunnel axis, and it is unnecessary to divide the propagation regions.Table7 lists the separation of the zones in all experimental scenarios. In comparison, the prediction by MM is close to the measurement. The difference between the theory and the measurements may be due to the influence of the industrial electromagnetic interference, the nonuniformity of scatters, materials, and shapes present in coal mine tunnels.Table 7
Location of dividing point (in m).
MethodReceiver PositionCCCCOWCWW900 MHz-wide tunnelMM——293.28307.97308.70SM——274.20248.60317.30FBP77.9877.9877.9877.9877.98SI-H143.50200.90350.70454.30469.70SI-V46.9091.70101.5095.9076.30433 MHz-wide tunnelMM——67.5370.9271.09SM——62.1857.2183.76FBP37.5137.5137.5137.5137.51SI-H13.3051.1067.9062.3069.30SI-V120.3038.50118.3094.5094.50900 MHz-narrow tunnelMM——61.3063.2259.76SM———>34.80>34.80FBP25.6625.6625.6625.6625.66SI-H—————SI-V—————433 MHz-narrow tunnelMM——13.7514.5013.64SM———17.1914.34FBP12.3412.3412.3412.3412.34SI-H5.407.2013.2013.80—SI-V—7.203.60——The dividing points estimated by the proposed method are also compared with the existing methods based on FBP [16–20] and SI [21, 22]. There are two dividing points determined by SI for each experimental scenario. One is deduced from the horizontally polarized field, and the other is deduced from the vertically polarized field. As listed in Table 7, the dividing points determined by FBP and SI are usually different from the measured dividing points. The reason is that FBP and SI do not capture the polarization difference in the path loss.From Table7, the dividing point is farther from the transmitter for larger tunnel or higher frequency. This result is consistent with the previous study in [18–21]. The reason is that larger tunnel size and higher frequencies can excite more modes with lower path loss [18–21]. The near-field region where the field consists of many modes is expanded.


### 5.2. Coverage Optimization

According to the aforementioned results obtained from MM and SM, zone division is unnecessary for nodes installed at C and CC points, but necessary for nodes installed at CO, WC, and WW points. By using coverage optimization introduced in Section3.1, we adopt horizontal polarization to communicate with the nodes fixed at C and CC points. We optimize the field coverage of the nodes fixed at CO, WC, and WW through polarization switching. The proposed coverage scheme and other coverage schemes [11–13] are also compared in this section. Table 8 lists the coverage schemes for comparison.Table 8
List of coverage schemes for comparison.
Coverage schemeDescriptionStrategy-H [11, 13]Coverage without zone division; use the horizontally polarized antennasStrategy-V [12]Coverage without zone division; use the vertically polarized antennasStrategy-MMCoverage with zone division by using MMStrategy-SMCoverage with zone division by using SMStrategy-FBPCoverage with zone division by using FBP [16–20]Strategy-SI-HCoverage with zone division by using SI [21, 22]; SI is performed based on the horizontally polarized fieldStrategy-SI-VCoverage with zone division by using SI [21, 22]; SI is performed based on the vertically polarized fieldFigure7 shows an example of 900 MHz field distribution covered by a node fixed at the WW point in the wide tunnel. In Figure 7, DP-MM/SM/FBP/SI represents the dividing point determined by MM/SM/FBP/SI. SI–H/V represents SI based on the horizontally/vertically polarized field. Figure 7(a) provides the cumulative probability of RSSI. It can be seen that the signal power covered by the proposed strategy (Strategy-MM/SM) is much larger than that covered by other strategies. Figure 7(b) shows the distance-dependent signal power. It can be seen that Strategy-FBP and Strategy-SI-H/V lead to unreasonable zone division and polarization switching and obtain higher path loss in some propagation regions. To further analyse the significant impact of zone division on the optimized performance of the wireless coverage, Tables 9 and 10 list the average path loss covered by different strategies in different propagation regions. In all experimental scenarios, the results by Strategy-MM are consistent with Strategy-SM. For Strategy-FBP, the average path loss from DP-MM to DP-FBP tends to be larger because the estimated near-field region is usually smaller (Table 7), and the antenna polarization is changed earlier. From DP-MM to DP-FBP, the average path loss of Strategy-FBP can exceed that of Strategy-MM 8.99 dBm. For Strategy-SI, the average path loss from DP-MM to DP-SI is usually larger because the estimated near-field region is either smaller or larger (Table 7), and the antenna polarization is switched either earlier or later. From DP-MM to DP-SI, the average path loss of Strategy-SI can exceed that of Strategy-MM 9.39 dBm.Figure 7
900 MHz coverage with and without coverage optimization. (a) Cumulative probability of RSSI. (b) Distance-dependent signal power.
(a)(b)Table 9
Average field power in different propagation regions (in dBm): coverage in the wide tunnel.
Coverage strategyPosition of COPosition of WCPosition of WWPropagation regionDP-MM to DP-FBPDP-MM to DP-SI-HDP-MM to DP-SI-VDP-MM to DP-FBPDP-MM to DP-SI-HDP-MM to DP-SI-VDP-MM to DP-FBPDP-MM to DP-SI-HDP-MM to DP-SI-V900 MHz-wide tunnelStrategy-MM−49.85−55.26−50.41−49.83−55.37−50.26−43.14−50.35−43.09Strategy-SM−50.36−55.26−50.99−47.94−55.37−48.22−43.21−50.88−43.09Strategy-FBP−51.88−55.26−52.33−51.42−55.37−51.32−48.41−50.35−48.53Strategy-SI-H−49.85−64.65−50.41−49.83−61.27−50.26−43.21−56.16−43.09Strategy-SI-V−51.55−55.26−52.33−50.80−55.37−51.32−48.41−50.35−48.71Strategy-H−51.88−55.26−52.33−51.42−55.37−51.32−48.41−50.35−48.71Strategy-V−49.85−64.65−50.41−49.83−61.27−50.26−43.21−56.16−43.09433 MHz-wide tunnelStrategy-MM−37.11−43.95−44.41−38.44−40.51−42.97−32.68−35.78−41.60Strategy-SM−37.40−43.95−44.41−37.37−42.02−42.97−32.68−35.78−41.35Strategy-FBP−39.68−43.95−44.41−38.73−42.02−42.97−38.34−37.34−41.60Strategy-SI-H−37.11−42.62−44.40−38.45−42.02−42.97−32.74−37.34−41.60Strategy-SI-V−37.11−49.54−51.40−38.44−40.51−49.83−32.68−35.78−41.86Strategy-H−39.68−43.95−44.41−38.73−42.02−42.97−38.34−37.34−41.60Strategy-V−37.11−49.54−51.40−38.44−40.51−49.83−32.68−35.78−41.86Table 10
Average field power in different propagation regions (in dBm): coverage in the narrow tunnel.
Coverage strategyPosition of COPosition of WCPosition of WWPropagation regionDP-MM to DP-FBPDP-MM to DP-SI-HDP-MM to DP-SI-VDP-MM to DDP-MM to DP-SI-HDP-MM to DP-SI-VDP-MM to DP-FBPDP-MM to DP-SI-HDP-MM to DP-SI-V900 MHz-narrow tunnelStrategy-MM−41.13——−31.15——−32.37——Strategy-SM−41.93——−31.15——−32.37——Strategy-FBP−41.93——−40.14——−38.74——Strategy-SI-H−41.93——−40.14——−38.74——Strategy-SI-V−41.93——−40.14——−38.74——Strategy-H−41.93——−40.14——−38.74——Strategy- V−41.13——−31.15——−32.37——433 MHz-narrow tunnelStrategy-MM−30.53−32.99−32.01−25.27−25.14—−24.65——Strategy-SM−33.04−30.25−29.40−25.27−25.14—−24.65——Strategy-FBP−33.04−30.25−32.32−26.55−25.76—−24.85——Strategy-SI-H−30.53−32.99−32.01−25.42−25.76—−24.85——Strategy-SI-V−33.04−30.25−29.40−26.55−25.76—−24.85——Strategy-H−33.04−30.25−29.40−26.55−25.76—−24.85——Strategy-V−30.53−32.99−32.01−25.27−25.14—−24.65——


## 5.1. Optimal Polarization Estimation and Zone Division

To simplify the solution of the proposed method, the measured tunnels are equivalently surrogated by rectangular tunnels by using the method reported in [23]. The simulation parameters are presented in Figure 4.Figure 4
Simulation parameters of the equivalently surrogated tunnel.Firstly, we show an example of the optimal polarization estimation and zone division by using the proposed method for 900 MHz field coverage in the wide tunnel.


### 5.1.1. MM

The boundary of the zones where the power attenuation of the higher-order mode is larger than the fundamental mode is calculated by using (7). The maximum boundaries for horizontal polarization and vertical polarization are shown in Table 6.Table 6
Maximum boundary for horizontal polarization modes and vertical polarization modes at 900 MHz frequency in the wide tunnel (in m).
PolarizationPosition of CPosition of CCPosition of COPosition of WCPosition of WWHorizontal0269.94268.0879.0979.28Vertical025.03293.29307.97308.70Compare the results in Table6. It can be observed that the maximum boundary for horizontal polarization is smaller than that for vertical polarization, when the signal is received at the position of CO, WC, and WW. The opposite results appear when the signal is received at the position of C and CC.As illustrated in Section3.2.1, when the signal is received at the position of CO, WC, and WW, vertical polarization is optimal in the near-field region. There is a change in optimal polarization when the signal travels along the tunnel axis. When the receiver is fixed at the position of C and CC, horizontal polarization is optimal, and there is no change in optimal polarization when the signal travels along the tunnel axis.For the receiver mounted at the position of CO, WC, and WW, the propagation regions are divided into a near-field region and a far-field region by a dividing point at 293.29 m, 307.97 m, and 308.70 m, respectively. The corresponding range of the near-field region is from 0 m–293.29 m, 0 m–307.97 m, and 0 m–308.70 m, respectively. For the receiver mounted at C and CC positions, zone division is unnecessary.


### 5.1.2. SM

900 MHz measured field distribution in the wide tunnel is shown in Figure3(a).The difference between the vertically and the horizontally polarized field powerΔPis plotted in Figure 5. The smoothing spline filter is used to reduce the influence of the noise on the data and to facilitate the analysis of the field variation. The pseudoperiod of the field variation measured at the positions of C, CC, CO, WC, and WW are 103.88 m, 81.19 m, 62.68 m, 71.64 m, and 63.50 m, respectively.Figure 5
Difference between the vertically polarized and the horizontally polarized field power.Take the pseudoperiod of the field variation as the observation unit, and then calculate the mean value ofΔP per unit length. The results are shown in Figure 6.Figure 6
Average difference between the vertically polarized and the horizontally polarized field power.It can be noted that when the receiver is located at the position of CO, WC, and WW, vertical polarization results in less average path loss in the near-field region, while horizontal polarization results in less average path loss in the far-field region. The corresponding measured dividing points of the regions are located at 274.20 m, 248.60 m, and 317.30 m, respectively. The corresponding range of the near-field region is from 0 m–274.20 m, 0 m−248.60 m, and 0 m−317.30 m, respectively. When the receiver is located at the point of C and CC, there is no change in optimal polarization along the tunnel axis, and it is unnecessary to divide the propagation regions.Table7 lists the separation of the zones in all experimental scenarios. In comparison, the prediction by MM is close to the measurement. The difference between the theory and the measurements may be due to the influence of the industrial electromagnetic interference, the nonuniformity of scatters, materials, and shapes present in coal mine tunnels.Table 7
Location of dividing point (in m).
MethodReceiver PositionCCCCOWCWW900 MHz-wide tunnelMM——293.28307.97308.70SM——274.20248.60317.30FBP77.9877.9877.9877.9877.98SI-H143.50200.90350.70454.30469.70SI-V46.9091.70101.5095.9076.30433 MHz-wide tunnelMM——67.5370.9271.09SM——62.1857.2183.76FBP37.5137.5137.5137.5137.51SI-H13.3051.1067.9062.3069.30SI-V120.3038.50118.3094.5094.50900 MHz-narrow tunnelMM——61.3063.2259.76SM———>34.80>34.80FBP25.6625.6625.6625.6625.66SI-H—————SI-V—————433 MHz-narrow tunnelMM——13.7514.5013.64SM———17.1914.34FBP12.3412.3412.3412.3412.34SI-H5.407.2013.2013.80—SI-V—7.203.60——The dividing points estimated by the proposed method are also compared with the existing methods based on FBP [16–20] and SI [21, 22]. There are two dividing points determined by SI for each experimental scenario. One is deduced from the horizontally polarized field, and the other is deduced from the vertically polarized field. As listed in Table 7, the dividing points determined by FBP and SI are usually different from the measured dividing points. The reason is that FBP and SI do not capture the polarization difference in the path loss.From Table7, the dividing point is farther from the transmitter for larger tunnel or higher frequency. This result is consistent with the previous study in [18–21]. The reason is that larger tunnel size and higher frequencies can excite more modes with lower path loss [18–21]. The near-field region where the field consists of many modes is expanded.


## 5.1.1. MM

The boundary of the zones where the power attenuation of the higher-order mode is larger than the fundamental mode is calculated by using (7). The maximum boundaries for horizontal polarization and vertical polarization are shown in Table 6.Table 6
Maximum boundary for horizontal polarization modes and vertical polarization modes at 900 MHz frequency in the wide tunnel (in m).
PolarizationPosition of CPosition of CCPosition of COPosition of WCPosition of WWHorizontal0269.94268.0879.0979.28Vertical025.03293.29307.97308.70Compare the results in Table6. It can be observed that the maximum boundary for horizontal polarization is smaller than that for vertical polarization, when the signal is received at the position of CO, WC, and WW. The opposite results appear when the signal is received at the position of C and CC.As illustrated in Section3.2.1, when the signal is received at the position of CO, WC, and WW, vertical polarization is optimal in the near-field region. There is a change in optimal polarization when the signal travels along the tunnel axis. When the receiver is fixed at the position of C and CC, horizontal polarization is optimal, and there is no change in optimal polarization when the signal travels along the tunnel axis.For the receiver mounted at the position of CO, WC, and WW, the propagation regions are divided into a near-field region and a far-field region by a dividing point at 293.29 m, 307.97 m, and 308.70 m, respectively. The corresponding range of the near-field region is from 0 m–293.29 m, 0 m–307.97 m, and 0 m–308.70 m, respectively. For the receiver mounted at C and CC positions, zone division is unnecessary.


## 5.1.2. SM

900 MHz measured field distribution in the wide tunnel is shown in Figure3(a).The difference between the vertically and the horizontally polarized field powerΔPis plotted in Figure 5. The smoothing spline filter is used to reduce the influence of the noise on the data and to facilitate the analysis of the field variation. The pseudoperiod of the field variation measured at the positions of C, CC, CO, WC, and WW are 103.88 m, 81.19 m, 62.68 m, 71.64 m, and 63.50 m, respectively.Figure 5
Difference between the vertically polarized and the horizontally polarized field power.Take the pseudoperiod of the field variation as the observation unit, and then calculate the mean value ofΔP per unit length. The results are shown in Figure 6.Figure 6
Average difference between the vertically polarized and the horizontally polarized field power.It can be noted that when the receiver is located at the position of CO, WC, and WW, vertical polarization results in less average path loss in the near-field region, while horizontal polarization results in less average path loss in the far-field region. The corresponding measured dividing points of the regions are located at 274.20 m, 248.60 m, and 317.30 m, respectively. The corresponding range of the near-field region is from 0 m–274.20 m, 0 m−248.60 m, and 0 m−317.30 m, respectively. When the receiver is located at the point of C and CC, there is no change in optimal polarization along the tunnel axis, and it is unnecessary to divide the propagation regions.Table7 lists the separation of the zones in all experimental scenarios. In comparison, the prediction by MM is close to the measurement. The difference between the theory and the measurements may be due to the influence of the industrial electromagnetic interference, the nonuniformity of scatters, materials, and shapes present in coal mine tunnels.Table 7
Location of dividing point (in m).
MethodReceiver PositionCCCCOWCWW900 MHz-wide tunnelMM——293.28307.97308.70SM——274.20248.60317.30FBP77.9877.9877.9877.9877.98SI-H143.50200.90350.70454.30469.70SI-V46.9091.70101.5095.9076.30433 MHz-wide tunnelMM——67.5370.9271.09SM——62.1857.2183.76FBP37.5137.5137.5137.5137.51SI-H13.3051.1067.9062.3069.30SI-V120.3038.50118.3094.5094.50900 MHz-narrow tunnelMM——61.3063.2259.76SM———>34.80>34.80FBP25.6625.6625.6625.6625.66SI-H—————SI-V—————433 MHz-narrow tunnelMM——13.7514.5013.64SM———17.1914.34FBP12.3412.3412.3412.3412.34SI-H5.407.2013.2013.80—SI-V—7.203.60——The dividing points estimated by the proposed method are also compared with the existing methods based on FBP [16–20] and SI [21, 22]. There are two dividing points determined by SI for each experimental scenario. One is deduced from the horizontally polarized field, and the other is deduced from the vertically polarized field. As listed in Table 7, the dividing points determined by FBP and SI are usually different from the measured dividing points. The reason is that FBP and SI do not capture the polarization difference in the path loss.From Table7, the dividing point is farther from the transmitter for larger tunnel or higher frequency. This result is consistent with the previous study in [18–21]. The reason is that larger tunnel size and higher frequencies can excite more modes with lower path loss [18–21]. The near-field region where the field consists of many modes is expanded.


## 5.2. Coverage Optimization

According to the aforementioned results obtained from MM and SM, zone division is unnecessary for nodes installed at C and CC points, but necessary for nodes installed at CO, WC, and WW points. By using coverage optimization introduced in Section3.1, we adopt horizontal polarization to communicate with the nodes fixed at C and CC points. We optimize the field coverage of the nodes fixed at CO, WC, and WW through polarization switching. The proposed coverage scheme and other coverage schemes [11–13] are also compared in this section. Table 8 lists the coverage schemes for comparison.Table 8
List of coverage schemes for comparison.
Coverage schemeDescriptionStrategy-H [11, 13]Coverage without zone division; use the horizontally polarized antennasStrategy-V [12]Coverage without zone division; use the vertically polarized antennasStrategy-MMCoverage with zone division by using MMStrategy-SMCoverage with zone division by using SMStrategy-FBPCoverage with zone division by using FBP [16–20]Strategy-SI-HCoverage with zone division by using SI [21, 22]; SI is performed based on the horizontally polarized fieldStrategy-SI-VCoverage with zone division by using SI [21, 22]; SI is performed based on the vertically polarized fieldFigure7 shows an example of 900 MHz field distribution covered by a node fixed at the WW point in the wide tunnel. In Figure 7, DP-MM/SM/FBP/SI represents the dividing point determined by MM/SM/FBP/SI. SI–H/V represents SI based on the horizontally/vertically polarized field. Figure 7(a) provides the cumulative probability of RSSI. It can be seen that the signal power covered by the proposed strategy (Strategy-MM/SM) is much larger than that covered by other strategies. Figure 7(b) shows the distance-dependent signal power. It can be seen that Strategy-FBP and Strategy-SI-H/V lead to unreasonable zone division and polarization switching and obtain higher path loss in some propagation regions. To further analyse the significant impact of zone division on the optimized performance of the wireless coverage, Tables 9 and 10 list the average path loss covered by different strategies in different propagation regions. In all experimental scenarios, the results by Strategy-MM are consistent with Strategy-SM. For Strategy-FBP, the average path loss from DP-MM to DP-FBP tends to be larger because the estimated near-field region is usually smaller (Table 7), and the antenna polarization is changed earlier. From DP-MM to DP-FBP, the average path loss of Strategy-FBP can exceed that of Strategy-MM 8.99 dBm. For Strategy-SI, the average path loss from DP-MM to DP-SI is usually larger because the estimated near-field region is either smaller or larger (Table 7), and the antenna polarization is switched either earlier or later. From DP-MM to DP-SI, the average path loss of Strategy-SI can exceed that of Strategy-MM 9.39 dBm.Figure 7
900 MHz coverage with and without coverage optimization. (a) Cumulative probability of RSSI. (b) Distance-dependent signal power.
(a)(b)Table 9
Average field power in different propagation regions (in dBm): coverage in the wide tunnel.
Coverage strategyPosition of COPosition of WCPosition of WWPropagation regionDP-MM to DP-FBPDP-MM to DP-SI-HDP-MM to DP-SI-VDP-MM to DP-FBPDP-MM to DP-SI-HDP-MM to DP-SI-VDP-MM to DP-FBPDP-MM to DP-SI-HDP-MM to DP-SI-V900 MHz-wide tunnelStrategy-MM−49.85−55.26−50.41−49.83−55.37−50.26−43.14−50.35−43.09Strategy-SM−50.36−55.26−50.99−47.94−55.37−48.22−43.21−50.88−43.09Strategy-FBP−51.88−55.26−52.33−51.42−55.37−51.32−48.41−50.35−48.53Strategy-SI-H−49.85−64.65−50.41−49.83−61.27−50.26−43.21−56.16−43.09Strategy-SI-V−51.55−55.26−52.33−50.80−55.37−51.32−48.41−50.35−48.71Strategy-H−51.88−55.26−52.33−51.42−55.37−51.32−48.41−50.35−48.71Strategy-V−49.85−64.65−50.41−49.83−61.27−50.26−43.21−56.16−43.09433 MHz-wide tunnelStrategy-MM−37.11−43.95−44.41−38.44−40.51−42.97−32.68−35.78−41.60Strategy-SM−37.40−43.95−44.41−37.37−42.02−42.97−32.68−35.78−41.35Strategy-FBP−39.68−43.95−44.41−38.73−42.02−42.97−38.34−37.34−41.60Strategy-SI-H−37.11−42.62−44.40−38.45−42.02−42.97−32.74−37.34−41.60Strategy-SI-V−37.11−49.54−51.40−38.44−40.51−49.83−32.68−35.78−41.86Strategy-H−39.68−43.95−44.41−38.73−42.02−42.97−38.34−37.34−41.60Strategy-V−37.11−49.54−51.40−38.44−40.51−49.83−32.68−35.78−41.86Table 10
Average field power in different propagation regions (in dBm): coverage in the narrow tunnel.
Coverage strategyPosition of COPosition of WCPosition of WWPropagation regionDP-MM to DP-FBPDP-MM to DP-SI-HDP-MM to DP-SI-VDP-MM to DDP-MM to DP-SI-HDP-MM to DP-SI-VDP-MM to DP-FBPDP-MM to DP-SI-HDP-MM to DP-SI-V900 MHz-narrow tunnelStrategy-MM−41.13——−31.15——−32.37——Strategy-SM−41.93——−31.15——−32.37——Strategy-FBP−41.93——−40.14——−38.74——Strategy-SI-H−41.93——−40.14——−38.74——Strategy-SI-V−41.93——−40.14——−38.74——Strategy-H−41.93——−40.14——−38.74——Strategy- V−41.13——−31.15——−32.37——433 MHz-narrow tunnelStrategy-MM−30.53−32.99−32.01−25.27−25.14—−24.65——Strategy-SM−33.04−30.25−29.40−25.27−25.14—−24.65——Strategy-FBP−33.04−30.25−32.32−26.55−25.76—−24.85——Strategy-SI-H−30.53−32.99−32.01−25.42−25.76—−24.85——Strategy-SI-V−33.04−30.25−29.40−26.55−25.76—−24.85——Strategy-H−33.04−30.25−29.40−26.55−25.76—−24.85——Strategy-V−30.53−32.99−32.01−25.27−25.14—−24.65——


## 6. Conclusions

This paper applies zone division and polarization switching to coverage optimization of the wireless system in underground tunnels. A multimodal approach is proposed to estimate the axial variation of the optimal antenna polarization along the tunnel for zone division. Extensive measurements are conducted to validate the effectiveness and feasibility of the coverage optimization. Compared with coverage that only uses a single polarization in the entire propagation region, polarization switching based on reasonable zone division can reduce the power attenuation of the signal. Meanwhile, we compare the performance of our proposed method with that of the existing zone-division methods based on the Fresnel breakpoint and system identification. Results show that zone division has an important influence on the optimized performance of the wireless coverage. The zones divided by the existing methods are too small or too large, which results in incorrect polarization switching and higher average path loss. It is more reasonable to switch polarization based on the proposed zone-division method.The proposed coverage scheme requires repeated user positioning, zone division, and polarization configuration. However, there is no need to repeatedly call the coverage optimization procedure, when the user is relatively static or is always in one of the propagation zones during communication. The efficiency of the coverage optimization program can be further improved by optimizing the repetition cycle of the program with the information of the user’s movement direction and speed.The proposed coverage optimization and zone division can also provide solutions for other wireless energy efficiency related problems in underground tunnels such as wireless charging and network connectivity.



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*Source: 8826546-2020-11-23.xml*