# Scattering of Electric Field from Leaky Coaxial Cable in Confined Area

Authors: Asad Saleem; Min Wang; Guoxin Zheng
Journal: International Journal of Antennas and Propagation
 (2017)

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## Abstract

The new radiation model for the electric field scattering of single leaky coaxial cable (LCX) being a transmitting antenna in the rectangular blind zone at 1.8 GHz is reported. The effect of varying the receiving antenna distance from the LCX on the fluctuation of radiated field using Ray-Tracing Method is examined. The line of sight and reflected paths between the LCX and receiving antenna for both horizontal and vertical polarizations are considered. Furthermore, it is inferred that the selection of appropriate period of slots and distance of the receiver reduce the fluctuations of electric field. The theory and procedures used in this paper can be extrapolated in different slot patterns of the LCX and zones which have many valuable applications for mobile communication in underground mines, tunnels, and railways.


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## Body

## 1. Introduction

Leaky coaxial cables have found many useful applications in communication systems both as feeders and as transmitting antennas such as Communication Based Train Control (CBTC) systems, for high speed railway, automated highway, wireless LAN retrieving, location of train, and underground conveyance [1]. Mobile edge service platform delivers dynamical sensor networks (SNS) in the high speed rail (HSR). Passengers acquire information about train location and environment by interacting with a virtual crew through dynamical SNS application via their smartphones [2]. The Long Term Evolution for Metro (LTE-M) method using the LCX for the CBTC system has been found to be an important communication technique for upcoming urban rail transit system. The LTE-M is designed for high speed wireless communications in confined areas. The key requirements for the LTE-M are high peak data rates, high spectral efficiency, less processing time, and flexibility in bandwidth [3]. Experimental visualization of the LCX MIMO system in tunnel environment is demonstrated in [4] and it is inferred that the LCX MIMO system performance is not fully dependent on the LCX spacing. The Finite-Difference Time-Domain (FDTD) is a method to visualize the whole wireless radio frequency (RF) connection of the LCX in a tunnel environment. The FDTD method is used to predict the radiation patterns of cylindrical coordinates and it covers a wide range of frequencies with a single simulation run [5].LCX is modeled in different shapes according to requirements. In order to avoid transmission loss inside tunnel environment, Fujikura has developed a lightweight and thin LCX-5D that is capable of securing a stable communication region near the LCX [6]. In [7], patched leaky coaxial cable (PLCX) is considered as a substitute for the conventional LCX for a wireless connection in a composite environment to acquire smoother radiated field coverage. Leaky cable has slots on its outer conductor, which allows radio signals to pass in and out of its surface along the whole length of the cable [8]. Radio communication in the rectangular blind zone depends on the magnitude of the electromagnetic field intensity (EMI), environmental conditions nearby the leaky cable, and installation methods [9]. By increasing the number of slots of the LCX, it brings down the resonance center-frequency and provides broad radiation bandwidth and good radiation efficiency [10].The influence of slot period on the performance of the LCX MIMO system in terms of capacity, correlation, and channel matrix rank is discussed in [11], when single LCX is used as two transmitting antennas. Ray-Tracing (RT) method is used for precise prediction of radio channel constraints and significant accuracy of near-field computations for indoor environment. In [12], the authors describe the importance of the RT propagation modeling for the forthcoming small-cell millimeter-wave schemes and emphasize the significance of the application potential. In [13], two major kinds of LCXs, coupled mode and radiating mode, are explained concisely for an indoor building environment. The Akaike information criterion (AIC) can be used to find out the model of small-scale fading. It is revealed that lognormal distribution is appropriate for small-scale fading, and the representing parameters of lognormal distribution are also found from the experimental results. The field distribution in the tunnel area is discussed under the excitations of the LCX and BSA. To include the Tx/Rx nearby environment, an IMT including the UPML technique and the FDTD method is applied [14]. In [15], the authors explained the tunnel antenna which develops circularly polarized waves alongside its axis and has an improved directivity. Though the literature conveys several studies, many of these works lack experimental validations of real time dimensions of tunnel and practical antenna location.The objective of this study is to propose a radiation model of the LCX, which explore the insights of the LTE used in China’s metro at 1.8 GHz. Radiation from a leaky coaxial cable in a tunnel environment is studied for both line of sight (LOS) path and reflected paths (NLOS) based on RT method. We studied the effect of varying the period of slots on radiated field and compared theoretically the design in an actual environment for both horizontally and vertically polarized radio waves. The measurement results may be useful to identify the shortcomings in LTE systems and to determine an optimum system design based on the LCX deployment in a real time tunnel environment.


## 2. Theory of Radiations

Theory of radiation deals with transmission or emission of energy in the form of waves from a medium such as electromagnetic radiation. The intensity of these radiations follows the inverse square law of distance from their origin. Generally, these radiations depend on two factors: (1) scattering of magnetic current of a slot and (2) radiated field of a slot. The following section will explain these two problems briefly.


### 2.1. Scattering of Magnetic Current of Slot

The procedure of calculating the scattered magnetic current of a slot is complex. In this paper, we deal only with the vertical and horizontal slotted leaky coaxial cable as shown in Figures1(a) and 1(b). The LCX slots are vertical in shape and they are perpendicular to z-axis. Here, we considered the slot angle as 2a, where L represents length of cable, l is the length of slot, a and b represent the inner and outer radius of the conductor, and w denotes the width of the slot. The magnetic current of the cable is described in the following equations [9].(1)M=C1-cos⁡K0bφcos⁡kobα,where(2)C=-jV0εr2φk0bln⁡b/a,φ=∫-bαbαe-jK0R2πRdl,R=l2+w22.Figure 1
The slot structure of LCX.
(a)
(b)ε
r is the dielectric coefficient of cable, k0 is the wave number of the free space, and V0 is excited voltage of LCX.


### 2.2. Radiated Field of Slot

Field produced along leaky cable due to static and moving charges is considered as an electric and magnetic field, respectively. The LCXs have two types of emitting modes which are surface mode and radiating mode. The waves exist around the LCX in emitting mode and the waves radiate in far field only in radiating mode [16]. On the basis of cylindrical Fourier transforms of Ez and Eφ, we can find the distribution of the electric field due to the slot on the outer conductor of LCX [9] as shown in Figure 2.(3)Ezφ,z=Vw1-cos⁡k0bφcos⁡k0bα,where V=-jV0εr/2k0bln⁡b/a, Ez shows the electric field along z-axis, and o represents the location of slot.Figure 2
Radiated field of the LCX.Distance from pointo to one point in space is r whose projection in xoy plane is r′. θ is the angle between r and z-axis while φ is the angle between r′ and x-axis.(4)Eφ=-jk0e-Jk0rπrϵ0sin⁡θ∑n=-∞∞ejnφjn+1gn-k0cos⁡θ,gnω=ϵ0nωEz~n,ωbK02-ω23/2Hn2′bk02-ω2,where ω is the angular frequency, ϵ0 is dielectric coefficient of free space, and Hn2 is Hankel function of 2nd type of rank nth. Ez~ is cylindrical Fourier transform of Ez.(5)Ez~n,ω=12π∫02πdφ∫-∞∞dzEzφ,ze-jnφe-jωz.From the above formulation, we can write it as(6)Eφ=Vθ,φe-jk0rrsin⁡θ,where(7)Vθ,φ=jVcos⁡θπ2bk0sin3⁡θ∑n=-5n=+5nejnφjn+1Hn2′bk0sin⁡θsin⁡nαn-msin⁡mαcos⁡nα-ncos⁡mαsin⁡nαm2-n2cos⁡mα,where m=k0b. Ez remains invariable along z-axis because width w of slot is very small. The scattered field due to circumferential polarization can be calculated from (6) and (7).


### 2.3. The Pathway of Electric Waves in Rectangular Blind Zone

We placed the LCX alongz-axis and the receiver (Rx) is placed at a far distance from the LCX. The pathway of electric waves is shown in three-dimensional spaces in Figures 3(a), 3(b), and 3(c). Distance between the LCX and Rx is considered along x-axis and LCX is placed at 1.1 m higher than the receiving antenna along y-axis as shown in Figure 4. The vertically polarized components of Eφ can be written by using Ray-Tracing Method [17–19].(8)Ey=Vθi,φie-jk0ri+ri1-jβiPri+ri1sin⁡θicos⁡φiΓh,where(9)ri=xo2+y02+z02,ri1=x02+h-h02+ip-z02,φi=arccos⁡x0x02+h02,θi=arctan⁡x02+h02z0,β=k0ϵr,γ=arctan⁡x0z02+h02.Figure 3
The three-dimensional view of radiations: (a) the nether view, (b) the side view, and (c) the obverse view.
(a)
(b)
(c)Figure 4
The visualization of Nantong Tunnel area.Height of receiving antenna ish = 1.6 m, while the height of the LCX is h0 = 2.7 m. Γh is a reflection coefficient of horizontally polarized waves, ϵ1-jϵ1′ is a complex dielectric coefficient of the wall, and z0 is the remaining distance starting from current slot to the remaining z-axis. The reflection coefficient for the vertically polarized waves is given below.(10)Γv=ϵ1-jϵ1′sin⁡γ-ϵ1-jϵ1′-cos2⁡γϵ1-jϵ1′sin⁡γ+ϵ1-jϵ1′-cos2⁡γ.The reflection coefficient of a horizontally polarized wave is written as(11)Γh=sin⁡γ-ϵ1-jϵ1′-cos2⁡γsin⁡γ+ϵ1-jϵ1′-cos2⁡γ.The total radiated field is calculated by adding the effect of all slots of the leaky coaxial cable:(12)Ey∑=∑i=1NVθi,φie-jk0ri+ri1-jβiPri+ri1sin⁡θicos⁡φiΓv.For reflected waves, this method is also applicable. By using superposition principle, we obtain the total radiated field produced by the LCX at the receiving antenna.


## 2.1. Scattering of Magnetic Current of Slot

The procedure of calculating the scattered magnetic current of a slot is complex. In this paper, we deal only with the vertical and horizontal slotted leaky coaxial cable as shown in Figures1(a) and 1(b). The LCX slots are vertical in shape and they are perpendicular to z-axis. Here, we considered the slot angle as 2a, where L represents length of cable, l is the length of slot, a and b represent the inner and outer radius of the conductor, and w denotes the width of the slot. The magnetic current of the cable is described in the following equations [9].(1)M=C1-cos⁡K0bφcos⁡kobα,where(2)C=-jV0εr2φk0bln⁡b/a,φ=∫-bαbαe-jK0R2πRdl,R=l2+w22.Figure 1
The slot structure of LCX.
(a)
(b)ε
r is the dielectric coefficient of cable, k0 is the wave number of the free space, and V0 is excited voltage of LCX.


## 2.2. Radiated Field of Slot

Field produced along leaky cable due to static and moving charges is considered as an electric and magnetic field, respectively. The LCXs have two types of emitting modes which are surface mode and radiating mode. The waves exist around the LCX in emitting mode and the waves radiate in far field only in radiating mode [16]. On the basis of cylindrical Fourier transforms of Ez and Eφ, we can find the distribution of the electric field due to the slot on the outer conductor of LCX [9] as shown in Figure 2.(3)Ezφ,z=Vw1-cos⁡k0bφcos⁡k0bα,where V=-jV0εr/2k0bln⁡b/a, Ez shows the electric field along z-axis, and o represents the location of slot.Figure 2
Radiated field of the LCX.Distance from pointo to one point in space is r whose projection in xoy plane is r′. θ is the angle between r and z-axis while φ is the angle between r′ and x-axis.(4)Eφ=-jk0e-Jk0rπrϵ0sin⁡θ∑n=-∞∞ejnφjn+1gn-k0cos⁡θ,gnω=ϵ0nωEz~n,ωbK02-ω23/2Hn2′bk02-ω2,where ω is the angular frequency, ϵ0 is dielectric coefficient of free space, and Hn2 is Hankel function of 2nd type of rank nth. Ez~ is cylindrical Fourier transform of Ez.(5)Ez~n,ω=12π∫02πdφ∫-∞∞dzEzφ,ze-jnφe-jωz.From the above formulation, we can write it as(6)Eφ=Vθ,φe-jk0rrsin⁡θ,where(7)Vθ,φ=jVcos⁡θπ2bk0sin3⁡θ∑n=-5n=+5nejnφjn+1Hn2′bk0sin⁡θsin⁡nαn-msin⁡mαcos⁡nα-ncos⁡mαsin⁡nαm2-n2cos⁡mα,where m=k0b. Ez remains invariable along z-axis because width w of slot is very small. The scattered field due to circumferential polarization can be calculated from (6) and (7).


## 2.3. The Pathway of Electric Waves in Rectangular Blind Zone

We placed the LCX alongz-axis and the receiver (Rx) is placed at a far distance from the LCX. The pathway of electric waves is shown in three-dimensional spaces in Figures 3(a), 3(b), and 3(c). Distance between the LCX and Rx is considered along x-axis and LCX is placed at 1.1 m higher than the receiving antenna along y-axis as shown in Figure 4. The vertically polarized components of Eφ can be written by using Ray-Tracing Method [17–19].(8)Ey=Vθi,φie-jk0ri+ri1-jβiPri+ri1sin⁡θicos⁡φiΓh,where(9)ri=xo2+y02+z02,ri1=x02+h-h02+ip-z02,φi=arccos⁡x0x02+h02,θi=arctan⁡x02+h02z0,β=k0ϵr,γ=arctan⁡x0z02+h02.Figure 3
The three-dimensional view of radiations: (a) the nether view, (b) the side view, and (c) the obverse view.
(a)
(b)
(c)Figure 4
The visualization of Nantong Tunnel area.Height of receiving antenna ish = 1.6 m, while the height of the LCX is h0 = 2.7 m. Γh is a reflection coefficient of horizontally polarized waves, ϵ1-jϵ1′ is a complex dielectric coefficient of the wall, and z0 is the remaining distance starting from current slot to the remaining z-axis. The reflection coefficient for the vertically polarized waves is given below.(10)Γv=ϵ1-jϵ1′sin⁡γ-ϵ1-jϵ1′-cos2⁡γϵ1-jϵ1′sin⁡γ+ϵ1-jϵ1′-cos2⁡γ.The reflection coefficient of a horizontally polarized wave is written as(11)Γh=sin⁡γ-ϵ1-jϵ1′-cos2⁡γsin⁡γ+ϵ1-jϵ1′-cos2⁡γ.The total radiated field is calculated by adding the effect of all slots of the leaky coaxial cable:(12)Ey∑=∑i=1NVθi,φie-jk0ri+ri1-jβiPri+ri1sin⁡θicos⁡φiΓv.For reflected waves, this method is also applicable. By using superposition principle, we obtain the total radiated field produced by the LCX at the receiving antenna.


## 3. Experimental Description and Numerical Results

The measurements were carried out in the subway-like tunnel of Zhongtian RF Cable Co., Ltd., at Nantong, China. The length of the tunnel was 100 m, with the cross-section of the first 50 m arch and the following 50 m rectangle, but we considered the first 50 m arch area for measurements. The wall of the tunnel was covered with concrete material. Nobody was moving throughout the experiments. The parameters of the measurement setup are given in Table1. In these calculations, the radius of outer conductor of LCX was 16 mm and radius of inner conductor was 6 mm. The volume of the rectangular blind zone was 50 m (length) × 5 m (width) × 3 m (height). The length of the cable was 50 m along the z-axis and the minimum distance between the Rx point and the LCX along x-axis was 2 m.Table 1
Measuring parameters.
Unit
Parameter
Slots distance of LCX
0.6 m
Transmitted power
23 dBm
Bandwidth
40.8 MHz
Tx-antenna
ZTT-LCX of 50 m length
Rx-antenna
UHA9125D dipole antenna
Antenna gain
2.15 dBi
Height of Tx-antenna
2.7 m
Height of Rx-antenna
1.6 m
Sampling rate
81.6 MHz
Resistance
50 ohm
Measurement time
50 msWe divided the measurement area into three different regions as Region 1, Region 2, and Region 3. Each region has 15 observing points. We further divided these points into 3 × 5 matrix formats; the distance between each observing point was 0.5 m as illustrated in Figure4. The LCX was 1.1 m higher than a conventional receiving antenna. Height of LCX was 2.7 m and the slot angle was taken as π/4. The complex dielectric coefficient was 4-j0.3 and the dielectric coefficient of dielectric sheet was 1.25. The frequency was considered 1.8 GHz because this frequency spectrum provides broader LTE coverage as well as improved indoor signal strength, whereas the excitation voltage was considered as unity.The required number of slots can be determined using the relationN=L/P-1. Period of slots of the LCX have great impact on the radiated field. Desired results can be obtained by adjusting the proper period of slots. Minimum slots period of the LCX provide better radiated field such that P=0.4 m shows improved performance more than others, as specified in Figure 5.Figure 5
The distribution ofEy for different period of slots of horizontally polarized LCX in Region 1 for LOS path.By using MATLAB Software, we analyzed the effect of radiated fieldEy due to fastened LCX and compared it with different positions along all three regions of subway-like tunnel.


### 3.1. Horizontal Polarization

In this experiment, we considered the horizontally polarized radio waves radiated from the leaky coaxial cable along thez-axis and evaluated its effect on the receiving antenna which was horizontally polarized and it was located at minimum distance of 2 m away from the LCX along the x-axis. We extracted the LOS path from the total radiated path using the Ricean K-factor method [20]. This estimated moment method provides a satisfactory resemblance with the actual experimental data. To save space, mathematical formulas for the moment method are not covered here. Further details can be determined in [20]. We only give final results here; that is,(13)K=V2σ2,where(14)V2=Ga2-Gv21/2,σ2=Ga-Ga2-Gv21/2.Here|V|2 and σ2 give LOS and NLOS received powers, respectively. Further, Ga represents the first moment of received power gain and Gv is the real value of the second moment which is the root mean square (rms) variation of the corresponding power gain around Ga. First path contains only the LOS path which is illustrated as Path 1, while the second part (Path 2) consists of the NLOS paths containing reflection from roof, wall, and floor as illustrated in Figure 4. Transmitted power and resistance (R) along LCX were considered, respectively, as 23 dBm and 50 ohm. The height of the LCX was 2.7 m from floor and the height of receiving antenna was 1.6 m. We divided the concern area into three different regions of same length. We further compared these theoretical results with the experimental data which was conducted in the Nantong subway-like tunnel. First comparison consists of the LOS path components extracted from the real time data evaluation of the Nantong tunnel and simulated results (MATLAB results based on theory), while second comparison consists of both the LOS and NLOS components of simulations and Nantong tunnel experimental data as illustrated in Figure 6(a). Results show good agreement between the simulated and real time calculated data. From Figure 6(a), it is evident that in Region 1 when period of slots is 0.6 m and length of cable is 50 m then Ey variations of vertically slotted LCX are stable. Same procedure was repeated for Region 2 and Region 3 as given in Figures 6(b) and 6(c), respectively, and the results show similarity with the former experiments of Region 1.Figure 6
The distribution ofEy of horizontally polarized LCX for the LOS and NLOS paths and its comparison with the Nantong Tunnel different measuring locations such as in (a) Region 1, (b) Region 2, and (c) Region 3, respectively.
(a)
(b)
(c)


### 3.2. Vertical Polarization

In order to further investigate the effect of radiated electric field, we considered the vertically polarized LCX of 0.6 m of period of slots and 50 m alongz-axis, locating a receiving antenna of vertically polarized radio waves at 2 m distance from the LCX along x-axis following Path 1 and Path 2 as clarified in previous experiment. Then the overall radiated field can be achieved by accumulating the effect of all the slots on LCX using (12). The theory and measurement data are compared for both the LOS and NLOS paths and it proves resemblance in behavior as given in Figure 7. In Region 1, Region 2, and Region 3, Ey shows variations as the distance of reference points of respective regions increase along z-axis as specified in Figures 7(a), 7(b), and 7(c).Figure 7
The distribution ofEy of vertically polarized LCX for the LOS and NLOS paths and its comparison with the Nantong Tunnel different measuring locations such as in (a) Region 1, (b) Region 2, and (c) Region 3, respectively.
(a)
(b)
(c)From Figures6 and 7, it is evident that the period of slots, length of cable, and the separation between antennas have a significant impact on the magnitude of radiated field. By proper selection of slots period, stable Ey can be achieved which is essential for radio communication. It is also clear that, in Region 2, we have a strong radiated field as compared to Region 1 and Region 3 in both horizontally polarized and vertically polarized cases, whereas Region 1 has lowest radiated field. The measured results also show that horizontal polarized LCXs show better performance in terms of radiated field, than the vertically polarized LCXs.


## 3.1. Horizontal Polarization

In this experiment, we considered the horizontally polarized radio waves radiated from the leaky coaxial cable along thez-axis and evaluated its effect on the receiving antenna which was horizontally polarized and it was located at minimum distance of 2 m away from the LCX along the x-axis. We extracted the LOS path from the total radiated path using the Ricean K-factor method [20]. This estimated moment method provides a satisfactory resemblance with the actual experimental data. To save space, mathematical formulas for the moment method are not covered here. Further details can be determined in [20]. We only give final results here; that is,(13)K=V2σ2,where(14)V2=Ga2-Gv21/2,σ2=Ga-Ga2-Gv21/2.Here|V|2 and σ2 give LOS and NLOS received powers, respectively. Further, Ga represents the first moment of received power gain and Gv is the real value of the second moment which is the root mean square (rms) variation of the corresponding power gain around Ga. First path contains only the LOS path which is illustrated as Path 1, while the second part (Path 2) consists of the NLOS paths containing reflection from roof, wall, and floor as illustrated in Figure 4. Transmitted power and resistance (R) along LCX were considered, respectively, as 23 dBm and 50 ohm. The height of the LCX was 2.7 m from floor and the height of receiving antenna was 1.6 m. We divided the concern area into three different regions of same length. We further compared these theoretical results with the experimental data which was conducted in the Nantong subway-like tunnel. First comparison consists of the LOS path components extracted from the real time data evaluation of the Nantong tunnel and simulated results (MATLAB results based on theory), while second comparison consists of both the LOS and NLOS components of simulations and Nantong tunnel experimental data as illustrated in Figure 6(a). Results show good agreement between the simulated and real time calculated data. From Figure 6(a), it is evident that in Region 1 when period of slots is 0.6 m and length of cable is 50 m then Ey variations of vertically slotted LCX are stable. Same procedure was repeated for Region 2 and Region 3 as given in Figures 6(b) and 6(c), respectively, and the results show similarity with the former experiments of Region 1.Figure 6
The distribution ofEy of horizontally polarized LCX for the LOS and NLOS paths and its comparison with the Nantong Tunnel different measuring locations such as in (a) Region 1, (b) Region 2, and (c) Region 3, respectively.
(a)
(b)
(c)


## 3.2. Vertical Polarization

In order to further investigate the effect of radiated electric field, we considered the vertically polarized LCX of 0.6 m of period of slots and 50 m alongz-axis, locating a receiving antenna of vertically polarized radio waves at 2 m distance from the LCX along x-axis following Path 1 and Path 2 as clarified in previous experiment. Then the overall radiated field can be achieved by accumulating the effect of all the slots on LCX using (12). The theory and measurement data are compared for both the LOS and NLOS paths and it proves resemblance in behavior as given in Figure 7. In Region 1, Region 2, and Region 3, Ey shows variations as the distance of reference points of respective regions increase along z-axis as specified in Figures 7(a), 7(b), and 7(c).Figure 7
The distribution ofEy of vertically polarized LCX for the LOS and NLOS paths and its comparison with the Nantong Tunnel different measuring locations such as in (a) Region 1, (b) Region 2, and (c) Region 3, respectively.
(a)
(b)
(c)From Figures6 and 7, it is evident that the period of slots, length of cable, and the separation between antennas have a significant impact on the magnitude of radiated field. By proper selection of slots period, stable Ey can be achieved which is essential for radio communication. It is also clear that, in Region 2, we have a strong radiated field as compared to Region 1 and Region 3 in both horizontally polarized and vertically polarized cases, whereas Region 1 has lowest radiated field. The measured results also show that horizontal polarized LCXs show better performance in terms of radiated field, than the vertically polarized LCXs.


## 4. Conclusions

In this paper, the study on the distribution of the radiated field of LCX for both the LOS and NLOS paths in a confined area by using Ray-Tracing Method as well as radiated theory of slots at 1.8 GHz was carried out. In summary this study concludes as follows:(i)
Minimizing the period of slots in LCX yields a better radiated field performance.(ii)
The selection of the appropriate period of slots in LCX and its orientation with respect to the receiving antenna reduces the fluctuation of the electric field.(iii)
The horizontally polarized LCX provides a better performance as compared to vertically polarized LCX.(iv)
In particular, this study reveals a better radiated field in Region 2 in comparison to Region 1 and Region 3.The reported study is useful to devise an optimum system design. Thus this paper conveys a potential direction for the LTE system design based on the LCX deployment in tunnel.



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