Simulations and Measurements of Electric Fields Emitted from a LTE Base Station in an Urban Area

Radiation patterns emitted from a long-term evolution (LTE) base station antenna were first simulated by the finite-difference time domain (FDTD) method. The validity of simulation results of radiation patterns was further checked by measurement data. After validating the accuracy of the FDTD method, electric fields at 123 test sites around a LTE base station in an urban area of Taipei City were simulated. Simulated electric fields were also validated by comparison with measured data obtained by a high frequency selective radiation meter with an isotropic E-field probe. Simulated and measured electric fields are in the range of 0.104–1.182 and 0.098–1.179V/m at 1795MHz, respectively. From obtained electric field strengths, it is ensured that the urban area is a good signal environment. The maximum power density emitted from the LTE base station is about 1.853 × 10−4 mW/cm and is thus far below the safety standard value of 1.197mW/cm for human exposure to RF radiation at 1795MHz.


Introduction
Mobile broadband networks are becoming insufficient as operators offer widespread broadband multimedia access to meet the increased demand.Fortunately, the long-term evolution (LTE), known as the fourth generation wireless communication system, promises to meet the requirements of real time applications, advanced games and video downloading, and other ultrafast broadband services for mobile phones and data terminals.LTE is a technical specification used to enhance and to optimize the third Generation Partnership Project radio access architecture [1].It is based on the global system for mobile communications (GSM) and the universal mobile telecommunications system (UMTS) network technologies to increase capacity and speed using a different radio interface together with core network improvements [2,3].Its spectrum includes LTE 700, GSM 850, GSM 900, DCS 1800, PCS 1900, WCDMA 2100, LTE B7 (2.5-2.69GHz), LTE B38 (2.57-2.62GHz), and LTE B40 (2.3-2.4GHz).Taiwan's National Communications Commission (NCC) decided to issue 6 LTE licenses on October 31st, 2013.The spectrum offered by the NCC was in the 700, 900, and 1800 MHz frequency bands.
To meet the demand for LTE communication with extended coverage, high cell capacity, and high data rates, the number of LTE base stations will also increase sharply.With the increased number of LTE base stations, the possible health hazards are a matter of concern for people in Taiwan due to exposure to electromagnetic (EM) radiation from LTE base stations.In recent years, some residents near cellular phone base stations have reported feeling several unspecific symptoms including fatigue, sleep disturbance, dizziness, loss of mental attention, and headaches.However, there is no convincing scientific evidence that the EM fields emitted from cellular phone base stations cause adverse health effects.
On the other hand, EM field intensities at users' locations should be guaranteed above a threshold level in order to meet the best RF (radio frequency) condition where it is free from interference.However, EM field intensities drop rapidly as the distance increases from a LTE base station because of the attenuation of power with the square of distance.Consequently, it is an important trade-off issue for RF engineers to determine the safety distance for EM radiation from a LTE base station and also to keep EM field intensity above a threshold level.Some advisory authorities have recommended safety guidelines for human exposure International Journal of Antennas and Propagation to EM energy.These authorities include the Institute of Electrical and Electronics Engineers and American National Standards Institute (IEEE/ANSI) [4], the International Commissions on Non-Ionizing Radiation Protection (ICNIRP) [5], and the National Council on Radiation Protection and Measurements (NCRP) [6].For example, for human exposure in uncontrolled environments to EM energy at radio frequencies from 300 MHz to 15 GHz, the ANSI/IEEE safety standard is expressed by f /1500 mW/cm 2 , where frequency  is in MHz.Measurements of RF electric and magnetic fields around cellular phone base stations may be available in the literature [7][8][9].There are only a few reports regarding theoretical studies on electric field strengths near cellular phone base stations [10].In this paper, the finite-difference time-domain (FDTD) method [11] and the near zone to far zone transformation technique [12] were used to calculate electric fields emitted from a LTE base station constructed on the roof-floor of a building with a height of 29 meters in an urban area of Taipei City.The validity of the FDTD method and the near zone to far zone transformation technique was checked by comparing numerical results of radiation patterns of a LTE base station antenna with those obtained by the measuring method in Yuan Ze anechoic chamber.Simulated electric fields at 123 test sites around the LTE base station in the urban area were also compared with measurement data and safety standard levels recommended by the IEEE/ANSI.

Brief Description of FDTD
The FDTD method was first presented by Yee [11] for solving Maxwell's curl equations directly in the time domain on a spatial grid in 1966 and later developed by many researchers for antenna analysis, electromagnetic interference (EMI), EM wave propagation and scattering problems, design of microwave and optical circuits, EM biological effects, defense applications, and many electromagnetic problems.In the FDTD solution procedure, six components of EM fields  and  are each positioned in discrete half spatial step intervals around a unit cell and the coupled Maxwell equations in differential form are solved for various points of the target as well as the surrounding in a time-stepping manner until converged solutions are obtained.Following Yee's notation and using centered difference approximation on both of the time and space first-order partial differentiations, six coupled scalar finite-difference equations for six unique field components within a unit cell are obtained.In these six coupled scalar finite-difference equations, electric fields are assigned to half-integer ( + (1/2)) time steps and magnetic fields are assigned to integer () time steps for the temporal discretization of fields.Two of the six coupled scalar finitedifference equations are shown in where  0 is the permittivity of free space,  0 is the permeability of free-space,  rx is the relative permeability,   is the permittivity, and   is the conductivity of the media at respective locations.The normalized electric field in (1) is defined by Ẽ = ( 0 / 0 ) 1/2 .The time step   is set to /(2  ) [13], where  and   are the cell size and the speed of light, respectively, to ensure numerical stability.An important issue encountered in the FDTD method is the absorbing boundary conditions (ABC).They are applied to truncate the computational domain when modeling an open region problem.Several ABC techniques have been proposed in the FDTD method such as second-order Mur [14], and Liao [15] and perfectly matched layer (PML) [16].Liao ABC and PML require a lot of memory.Second-order Mur absorbing boundary conditions are the most commonly used grid truncation techniques.In our formulation, the second-order Mur absorbing boundary conditions are used for the near-field emission problems.The second-order Mur absorbing boundaries are employed because they do not require much memory and have a reasonable accuracy.For near-field applications, the FDTD computation space has only one region; that is, there is no scattering region, as shown in Figure 1(a).In order to reduce the FDTD model space, it is desirable to bring the absorbing boundaries as close to the region of interest as possible.In general, the external absorbing boundaries are placed at a distances of 5-8 on all sides of the scattering object.In this study, the external absorbing boundaries are placed at a distance of 8 on all sides of the scattering target as shown in Figure 1, where  is the cell size.

EM Fields Emitted from Antenna Radome
Applying the field equivalence principle [17][18][19][20], electromagnetic fields in space due to equivalent sources at the emitting surface  can be obtained from electric and magnetic surface currents flowing on , where electric and magnetic surface currents are equivalent to tangential magnetic and electric fields at the emitting surface , respectively.Based on the equivalence principle, if the tangential electric and magnetic fields are completely known over the LTE antenna radome surface, the electric and magnetic fields in the source-free region can be determined.
As the electric and magnetic fields in the radome are determined by the FDTD method, the electric and magnetic current densities on the surface of the radome can be obtained from boundary conditions expressed by where The   ,   ,   , and   can be obtained by where  and  are the polar and azimuthal angles defined in a spherical coordinate system.Consider

Scattered Fields of the Ground and Building
The induced electric fields in the ground and buildings can be obtained by using the computation procedure described in Section 3 and boundary conditions.From boundary conditions, the tangential component of an electric field is continuous and the normal component of an electric flux is discontinuous across an interface.However, the normal component of an electric flux is enforced tobe continuous since the surface charge density on the ground and buildings is negligible.As the induced electric fields in the ground and buildings are obtained, the equivalent current density ⃗  eq [21] in the ground and buildings can be computed by where  ⇀ (  ) is the electric field in the ground and buildings,  is the angular frequency,   and  denote the relative dielectric constants and conductivities of the ground and buildings, respectively.The first term of ( 8) is the conduction current and the second term represents the polarization current.
Therefore, the electric field  ⇀   scattered from the ground or buildings can be obtained from the equivalent current density expressed as [22] where In the above equations, ← →  is the identity tensor,  0 = 8.854 × 10 −12 F/m is the permittivity of free space,  0 = 4×10 −7 H/m is the permeability of free space,  0 is the wave propagation constant of free space, and  ⇀  (, , ) and  ⇀   (  ,   ,   ) are field position vector and source position vector, respectively.
For far-field approximation,  0  ≫ 1,  ⇀  ≫  ⇀   , and  ⇀  //  ⇀   , a simpler formula for the integral equation ( 9) can be obtained by where  and  are the polar and azimuthal angles defined in a The scattered far-field components   and   can easily be found by calculating the far-field radiated from currents distributed in the ground and buildings as presented in [20] where  0 is the wave impedance,  0 is the wave propagation constant, ⃗  is the field position point, ⃗   is the source position point, and   ( ⃗   ),   ( ⃗   ), and   ( ⃗   ) are the current densities flowing in the -, -, and -axis inside the ground and buildings, respectively.Since EM waves can quickly decay in lossy materials, the integral equation ( 13) only takes into account a depth of 20 cm from the ground and the building surfaces as the volume space for calculations of scatter fields.In addition, only primary scattered fields from the ground and buildings are considered as contributing to the receiving fields at test sites.[23].The maximum radome depth is 70 mm.The 32 radiators are equally divided into two groups that are fed by two identical feeding lines with different excitation phases of +45 ∘ and −45 ∘ as shown in Figure 1(c).The LTE base station antenna has three frequency bands of 1710∼1880, 1850∼1990, and 1920∼2170 MHz.Each feeding line has an impedance of 50 ohms operating at frequencies of 1710∼2170 MHz.The LTE base station antenna is designed to have a radiation power of 1∼300 watts.Due to the NCC regulation, a maximum radiation power of 20 watts is permissible for the LTE base station antenna to operate in urban areas.The metallic case of the LTE base station antenna and the mounting kit are DC grounded.Base station antennas with vertical down-tilting have some impact on the antenna performance such as gain, capacity, coverage, and interference [24][25][26][27][28][29][30].In this study, the down-tilting angle of the LTE base station antenna is 8 degrees with respect to the vertical plane.

Simulation and Measurement
For FDTD simulations, the metallic material used for the LTE base station antenna is assumed to be nonmagnetic (  = 1.0).The tangential components of electric and magnetic fields in the conducting case are enforced to zero.The LTE base station antenna is constructed with 16,944,580 cubic cells of 1.0 mm on each side.The maximum excitation source voltage  of 31.625 volts at the input port of each radiator emitting a power of 0.625 watts at frequencies of 1710∼ 1880, 1850-1990, and 1920-2170 MHz is adopted for FDTD simulations.The excitation source voltage is then transferred into a sinusoidally modulated Gaussian pulse wave [31] over International Journal of Antennas and Propagation  the gap between the two arms of each radiator by  =  0 exp(−[( −  0 )/] 2 ) sin 2 0 ( −  0 ), where  0 = (/) is the amplitude of the excited electric field,  0 = 3 is the center of the pulse,  denotes the pulse width at its 1/ characteristics decay point which is in terms of frequency bandwidth (BW) expressed by BW(GHz) = 1000/(ps),  0 is the center frequency (modulation frequency),  = 3 is the distance of the gap between the two arms of each transmitter, and  = 1 mm is the cell size used in the FDTD. Figure 3 shows a sinusoidally modulated Gaussian pulse with pulse width  = 5.88 × 10 −9 s and center frequency  0 = 1795 MHz.The relative dielectric constants and electrical conductivities of conducting cases (iron), transmitters, and radome are adopted to be (  = 1.0,  = 1.0 × 10 7 S/m), (  = 1.0,  = 5.8 × 10 7 S/m), and (  = 2.5,  = 7.01 × 10 −4 S/m) [32], respectively.As the electric fields in the radome are calculated by the FDTD method, the scattered electric fields radiated from the ground and buildings can be obtained by using the computation procedures described in Sections 3 and 4. Finally, the electric fields at 123 test sites in an urban area of Taipei City can be obtained by adding the electric fields radiated directly from the LTE base station antenna and the scattered electric fields radiated from the ground and buildings.
The measurements of radiation patterns were performed in an anechoic chamber as shown in Figure 4 using an Anritsu 37369C Vector Network Analyzer and an Anritsu MS2687B spectrum analyzer.The distance between the LTE base station antenna and the receiving antenna was set at 6.5 meters for vertical and horizontal polarizations.Figures 5, 6, and 7 show measurement data and FDTD results of radiation patterns under the far-field condition for vertical and horizontal polarizations at frequencies of 1795, 1920, and 2060 MHz, respectively.From Figures 5-7, it is clear that the measurement data make a good agreement with simulation results.It is also found that the LTE base station antenna has an averaged beam width of about 120 degrees with −10 dB drop in the horizontal plane and about 7.5 degrees with −3 dB drop in the vertical plane for frequencies operating at 1795, 1920, and 2060 MHz, respectively.The LTE antenna has a narrow beam pattern in the vertical plane but quite wide beam pattern in the horizontal plane.
A model of an urban area of Taipei City having 123 test sites adopted for measuring electric fields emitted from a LTE base station is shown in Figure 8.The LTE base station antenna system employs a sector arrangement, with three sets of directional transmitting and receiving antennas oriented 120 degrees apart and aiming at the horizon.The International Journal of Antennas and Propagation  down-tilting angle of each LTE base station antenna is 8 degrees with respect to the vertical plane.These 123 test sites were on a horizontal plane with a height of 1 meter above the ground plane.The LTE base station antenna tower located at the center of the urban area marked with a red sign having a height of 29 meters from the ground plane was constructed on the roof-floor of an eight-storey building.The relative dielectric constants, conductivities, and relative permeabilities at 1795 MHz used for modeling the ground and building are adopted to be (  = 2.55,  = 2.64 × 10 −3 S/m, International Journal of Antennas and Propagation    = 1.0) and (  = 3.25,  = 1.147 × 10 −3 S/m,   = 50) [32][33][34], respectively.Measurements of the field strengths were obtained by using a Narda Model NBM-3006 high frequency selective radiation meter [35] as shown in Figure 9.The Model NBM-3006 with an isotropic E-field probe is designed to measure RF fields over the frequency range from 420 MHz to 6.0 GHz.Comparison of simulated and measured electric fields is shown in Figure 10.The simulation result of electric field distribution for the LTE base station antenna with a down-tilting angle of 8 degrees has a good agreement with the measurement data.The measured and simulated electric field strengths on a horizontal plane with a height of 1 meter above the ground are in the range of 0.098-1.179and 0.104-1.182V/m, respectively.Since the basic sensitivity requirement for a mobile terminal is about −100 dBm, the minimum power density of about −20 dBm obtained inside the coverage area of the LTE base station means a good signal will be picked up in the urban area.According to ANSI/IEEE standards for public exposure in uncontrolled environments, the maximum permissible exposure at 1795 MHz should be below 1.197 mW/cm 2 .It is clear that the maximum power density emitted from the LTE base station is about 1.853 × 10 −4 mW/cm 2 which is far below the ANSI/IEEE standard for public exposure.

Conclusions
In this study, we first used the FDTD method and the near zone to far zone transformation technique to simulate radiation patterns of a LTE base station antenna on vertical and horizontal planes at frequencies of 1795, 1920, and 2060 MHz, respectively.The validity of simulation results of radiation patterns was further checked by measurement data.The FDTD method and the near zone to far zone transformation technique, of which the accuracy had been validated, as well as boundary conditions were used to calculate electric fields at 123 test sites around a LTE base station in an urban area of Taipei City at 1795 MHz.Simulated electric fields were compared with measured data obtained by a Narda Model SRM-3006 high frequency selective radiation meter with an isotropic E-field probe.It is found that an excellent agreement between simulated and measured data is achieved.Simulated and measured electric fields in the urban area are in the range of 0.104-1.182and 0.098-1.179V/m at 1795 MHz, respectively.From obtained electric field strengths, it is clear that a good signal inside the coverage area of the LTE base station in the urban area is ensured.Corresponding to the maximum electric field strength of 1.182 V/m in the urban area, the maximum power density emitted from the LTE base station is 1.853 × 10 −4 mW/cm 2 and is thus far below the ANSI/IEEE standard for maximum permissible exposure of 1.197 mW/cm 2 .This research work provides a time efficient and cost-effective solution to calculate electric fields emitted from LTE base stations in an urban area without measurements and to check the safety distance for public exposure to LTE base stations.
An overview of a LTE base station antenna is shown in Figure 2. The LTE base station antenna dimension is about 155 × 70 × 1143 mm 3 as shown in Figure 2(b).It is manufactured with an aluminum reflector screen and 32 tin-plated zinc radiators protected by a flat fiberglass radome as shown in Figure 1(b)

Figure 4 :
Figure 4: Measurements of radiation patterns in an anechoic chamber.

Figure 5 :
Figure 5: Comparison of radiation patterns at 1795 MHz on the horizontal and vertical planes obtained by FDTD method and measurement.(a) Horizontal plane ().(b) Vertical plane ().

Figure 6 :
Figure 6: Comparison of radiation patterns at 1920 MHz on the horizontal and vertical planes obtained by FDTD method and measurement.(a) Horizontal plane ().(b) Vertical plane ().

Figure 7 :
Figure 7: Comparison of radiation patterns at 2060 MHz on the horizontal and vertical planes obtained by FDTD method and measurement.(a) Horizontal plane ().(b) Vertical plane ().

Figure 8 :
Figure 8: An urban area of Taipei City with 123 test sites numbered from 1 to 123.The LTE base station is located at the center of the urban area marked with a red sign A.

Figure 9 :Figure 10 :
Figure 9: The Narda Model SRM-3006 high frequency selective radiation meter with an isotropic E-field probe.(a) The Narda Model SRM-3006 E-field meter.(b) Isotropic E-field probe with three axis antennas.