2.1 Electromagnetic radiation

Electromagnetic radiation consists of waves of electric and magnetic energy oscillating through space at the speed of light (OET, 1999). The electromagnetic spectrum is an arrangement of various electromagnetic energy in the forms of particles and waves. These form of energy are characterized by frequency and wavelength. The wavelength is the distance per seconds covered by an electromagnetic wave, while the frequency, the number of oscillation of electromagnetic waves for one second. Figure 2.0.1 bellow shows an electromagnetic spectrum.

Figure 2.0.1. Electromagnetic spectrum

The electromagnetic spectrum shows the arrangement of electromagnetic sources based on their frequency and wavelength. Below is Table 2.0.1 which describes the radiofrequency sources and their allocated bands and frequency ranges.

Table 2.0.1. Characteristics and frequency bands of radiofrequency field sources

The most important application of electromagnetic energy is in the use of radio broadcasting, mobile telephony, microwave application and satellite communication as reported by Kelly (2011). Others include magnetic resonance imaging (MRI), Microwave ovens, radar, industrial heaters and sealing (Kelly, 2011).

2.2 Radio waves

Radio-frequency (RF) is a part of the arrangement of electromagnetic energies in terms of their frequencies from 3 kilohertz (3 kHz) to 300 gigahertzes (300 GHz) (Kelly, 2011). Radio-transmitters are devices that serve as transducers for converting electrical current into electromagnetic waves. The knowledge of the presence of electromagnetic field was first discovered as far back as 1887 when a Physicist proved experimentally that electromagnetic fields can be produced and detected in space. This phenomenon was predicted three years earlier by Clarke Maxwell (1831-1879). A radio transmitter communicates with a receiver via radio waves when electric charges moves up and down the transmitter’s antenna and are detected when the electric charge oscillate up and down a receiver’s antenna. In the process, when the charges moves, they produce magnetic fields. The resulting changing electric-magnetic fields (electromagnetic waves) are able to travel long distances through an empty space (Vacuum). The ability of a transmitter to send signal to a receiver or another transmitter nearby depends on the oscillation of the charges up and down its antenna at a particular resonant frequency.

2.3 Characteristics of radiofrequency (RF) antenna

There are a number of physical parameters and principles that define the type of wave and intensity of the radio waves generated and broadcasted into the environment. These parameters are relevant in understanding the behavior of the antennas. These are the antenna element, element array, gain or directivity, radiation pattern, radiation intensity, beam-width and power density.

2.3.1 Antenna Elements

The antenna element is a basic unit of the antenna. They may exist as individuals or as a group of elements. There are three most common types: dipole, monopoles and loop. A dipole antenna is most commonly a linear metallic wire or rod with a feed point at the center. It has two symmetrical radiating arms. A monopole antenna on the other hand has a single radiating arm. A number of authors have performed calculation and measurements on the pattern generated by these field on mobile handset in air and also against the head (Jensen & Rahmat-Samii, 1995) ; (Okoniewski & Stuchly, 1996) and (Lazzi, 1998). Other works on wireless devices such as cellular telephones using monopole antenna has also being reported in literature (Luebbers, 1992). An interesting application of loops is the wireless telemetry for medical devices and used for the first pacemaker (Greatbatch & Holmes, 1991).

2.3.2 Antenna Arrays

To yield a highly directive patterns, multiple antennas or elements can be arranged in space, in various geometrical configurations to yield a pattern (Stutzman & Thiele, 1998); (Bucci, Ella, Mazzarella, & Panariello, 1994) ; (Balanis, 2005); (Elliott, 2003) and (Mailloux, 1994). This antenna configuration are called arrays. The field from an array can add constructively or destructively in others. When well-engineered, the array can be used to control the beam by changing the phase of the excited currents of the individual elements (Elliott, 2003) ; (Dolph, 1946) ; (Safaai-Jazi, 1994) and (Shpak & Antoniou, 1992). By so doing, an optimum radiation beam can be generated. The geometry of the arrangement of the element also affects the performance. Other factors are distance between the elements, amplitude of the excited currents, phase excitation and radiation pattern.

2.3.3 Directivity and Gain

Another parameter used to describe the directional properties of an antenna is the directivity or gain. The directivity of an antenna, is a figure of merit that quantifies the antenna directive properties by comparing them with those of a hypothetical isotropic antenna that radiates the same total power as the antenna being characterized. Antenna such as dipoles and loops generates omnidirectional pattern, (McDonald, 1978) and (Pozar, 1993) derived a formula for such. The gain of an antenna is a measure that takes into account the efficiency of the antenna as well as its directional capabilities. The total antenna efficiency accounts for losses at the input terminals and the structure of the antenna due to reflection, conduction and dielectric losses.

2.3.4 Radiation Pattern    

Besides the parameters described above, the radiation pattern is the property used to describe the resulting shape of the beam generated. Radiation or an antenna pattern is a mathematical function of the antenna that describe the space coordinates (Balanis, 2005). The main beam is the region where the radiation is strongest and the other directions forms the side-lobes. The half-power beam width is the measure of the direction of maximum radiation. The beam width or Half-Power Beam width (HPBW) is the width of the power pattern at the location where the beam is 3 dB below its maximum value (half-power points) or the location where the field is 1/š2 of its peak. It is often used as a trade-off between it and the side lobe level (The ratio of the radiation intensity of the largest side-lobe to the maximum radiation intensity). The HPBW varies inversely as the side lobe level. The most common resolution criterion states that the resolution capability of an antenna to distinguish between two sources is equal to half the first-null beam width (FNBW/2), which is usually used to approximate the half-power beam width (HPBW) (Kraus, 1996) and (Kraus & Marhefka, Antennas, 2002).

2.3.5 Polarization

Furthermore, the generated wave can oscillate up and down, left and right or characteristic between these. These behavior describe the kind of polarization the wave exhibits. Polarization of a radiated wave is defined as that property of a wave in a time-varying direction and relative magnitude of the electric field vector. In general, however, when the shape of the electric field appears in the form of an ellipse, the polarization is described as elliptical. When the shape appear linear or circular, the polarization is described as such. The polarized radiated wave by the antenna can also be represented on the Poincare’s sphere (Balanis C. A., 1989) ; (Poincar´e, 1892) ; (Deschamps, 1951) and (Bolinder, 1967).

2.3.6 Radiation Intensity

Another important property of the antenna is the radiation intensity. The radiation intensity is the power radiated per unit solid angle subtended by the antenna. It is the property of the far field. The radiation intensity is obtained by multiplying the density by the square of the distance. The power pattern is also a measure of radiation intensity. To be able to obtain the total power density, one need to integrate the radiation intensity.

2.3.7 Power Density

Finally, the radiation power density describes the power associated with an electromagnetic wave. The power density is the total power crossing a closed surface by integrating the normal component of the Poynting vector over the entire surface.

2.4 Electromagnetic field around an antenna

An electromagnetic field is the region created around a source of electromagnetic radiation. An antenna is a device which changes electrical charges or current into electromagnetic waves into space. The distribution of RF energy from an antenna was found from literature to obey a directional pattern and varies with distance from the antenna. The fields created around an antenna can be grouped into two:

2.4.1 Near Field

The near field is the region around an antenna such that; the electric and magnetic fields are decoupled, quasi-static and are not uniform. And the impedance which is the resistance in air and the power associated with the field varies with distance.

2.4.2 Far Field

The far field on the other hand have plane fronts which do not depend on the shape of the source but rather unchanging. The radiated power decreases inversely with distance from the antenna theoretically. The electric and magnetic fields are uniquely defined by approximately a constant impedance of the medium. Figure 2.0.2 below illustrate the field regions around an antenna.

Figure 2.0.2. Electromagnetic field regions around a typical antenna

2.5 Advances in field modeling

A modeling is a good approximation of a problem to a real world solution. There are various mathematical modeling methods available in literature to date (Sarkar, Ji, Kim, Medouri, & Salazar-Palma, 2003) ; (COST-231, 1999) and (Correia, 2001). Extensive theoretical and experimental research on electromagnetic field Levels has been carried out and reported in literature (Lin, 2002) ; (Cicchetti, 2004) and (Nicolas, Lautru, Jacquin, Wong, & Wiart, 2001). Currently, the studies in electromagnetic fields can be grouped into two dominant channel modelling approaches: theoretical and empirical (Rappaport, 2002). While theoretical models depend on the knowledge of the physical laws of the wireless channel, such as the electrical properties of the ground, empirical models are based on actual radio frequency (RF) measurements of wireless channels. Furthermore, one can regroup it into Monte Carlo, Empirical and Physical models (Rappaport, 2002). Monte Carlo method are statistical in nature and make use of statistical and distribution functions such as channel characteristics of radio-transmitters and ray-optics. (Okumura, Ohmori, Kawano, & Fukuda, 1968) Found out from measurement that for a situation where one cannot have a line of sight with the transmitter, the fading (attenuation) of the received voltage approximates relay distribution. Okumura also developed a correction factor to be used together with the data to correct for the field strength. When Okumura’s measured results were averaged, the results showed properties of a lognormal distribution. (Okumura, Ohmori, Kawano, & Fukuda, 1968) And (Mogensen, Eggers, Jensen, & Andersen, 1991). The style of settlement and nature of buildings also affect the propagation of the radio waves when traveling from a source into the environment. Also random variation of building also contributed to loss of propagation of the waves. Some earlier work suggested that radio waves propagates over buildings and are diffracted down to street levels (Parsons, 1992). To be able to obtain reliable statistics, a lot more of measured data was required. Diffraction is when the path of the beam is obstructed by surface of irregular shape edges. Diffraction methods were developed and used to account for diffractions at rooftop (Ikegami, Yoshida, Takeuchi, & Umehira, 1984). Variations in building height contributed to the shadow loss of propagation over low buildings. The most general approach uses numerical integration of physical optics integrals (Walfisch & Bertoni, 1988) and (Bertoni, 2000). Measurement has shown that Monte Carlo methods need to consider the effect of trees (Mogensen, Eggers, Jensen, & Andersen, 1991), (Rizk, Mawira, Wagen, & Gardiol, 1996), (Vogel & Goldhirsh, 1986) and (LaGrone, 1977). Trees are able to attenuate the signal to the order of 10 dB (Vogel & Goldhirsh, 1986). The Monte Carlo methods even though are good when adequate measured data is used, suffers from modifications to the buildings and terrains and are very expensive to carry out.

Empirical methods make use of information gathering on the basis of systematic experimentation instead of making use of logic or mathematics. The empirical model uses extensive measured data and analysis tools to formulate relationship between parameters of interest. Measurements have shown that a simple two-ray model consisting of the direct and the ground-reflected ray was sufficient to predict the path gain (loss) for propagation over a flat earth (Rustako, Jr., Owens, & Roman, 1991) and (Xia, Bertoni, Maciel, Lindsay-Stewart, & Rowe, 1993). Reflection occurs when the wave from a source hit an object whose dimension is large as compared to the wavelength of the wave. The path loss represents the signal attenuation in decibel (dB). The path loss is the difference between effective transmitter and receiver power. Most published work concerning outdoor propagation depends on free space and two-ray models (Pande, Choudhari, & Pathak, 2012), (Willis & Kikkert, 2007), (Neto, Neto, Yang, & Glover, 2010). The free space model assumes that both transmitter and receiver, use line-of-sight communication with no obstruction or reflection of any form. The free space model obeys the relation:

(2. 1)

Where f is the frequency in MHz and d is the separation distance between the transmitting and receiving antennas in meters. The receiver power has been found to falls off as the square of the transmitter-receiver separation distance. The receiver power decays at the rate of 20dB per decade. When the effect of ground ray reflection is considered, a Plane Earth model was used. The model is given as:

(2. 2)

Where d is the distance as above and and are the elevations of the transmitter and receiver heights in meters respectively. The separation distance (d) in this model is assumed to be much larger than and .In our real environment today, there are obstruction everywhere and the propagation of the electromagnetic waves are affected by it (Mao, Anderson, & Fidan, 2007). The radio signals in our environment are attenuated by reflection, diffraction and scattering. Scattering occurs when an object in a medium are smaller as compared to the wavelength of the incoming wave. To be able to account for location characteristics and the impact of vegetation, it was found in literature that the average signal power decreases logarithmically with distance (Rappaport, 2002). To be able to estimate the path loss due to real world approximation, a log-distance model was developed. The average path loss for a typical distance between a transmitter and a receiver can be represented as an expression of distance by using the exponent n. The path loss is given as (Liao & Sarabandi, 2005):

(2. 3)

Where is the path loss in dB at a reference distance and n is the path loss exponent that represent the rate of the path loss decrease as a function of distance. The value n also characterizes the propagation environment. Table 2.0.2 below summarizes the characteristic of the exponent n in the environment.

Table 2.0.2. Characteristics of typical propagation environments

The reference distances from research was taken to be between 100 m to 1 km depending on the height of the transmitter. The International Telecommunication Union (ITU) recommended that in a situation where majority of the signal propagates through trees or vegetation, the ITU-R model can be used (Rappaport T. S., 1996).

(2. 4)

Where the frequency used was between 200 MHz and 95 GHz. One of the most important fully empirical prediction method was conducted by (Okumura, Ohmori, Kawano, & Fukuda, 1968). Okumura’s method was based entirely on an extensive measurement in Tokyo city. Okumura developed a set of curves given the median attenuation relatively to free space in the urban area over a quasi-smooth terrain. From these curves, Okumura deduce from the graphs a simple power law which was a function of the environment and it characteristics. The model was applicable to frequency range between 200 MHz and 2 GHz and covers a distance of 100 km. Okumura’s data was further modified by (Hata, 1980) who made it into a series of graphs. However, other methods disagree with the predictions of the Okumura’s methods. Others have also tried to improve the method by applying building density (Kozono & Watanabe, 1977) but was rejected by the scientific community. The Okumura-Hata model, together with related corrections was found to be one of the most common and single model used in designing real systems. Lee in 1982 came out with a power law model which was based on measurement and takes into account the variation in terrain (Lee, 1982). The model was environment specific because it was based on the assumption of the characteristics of the environment. It will be very difficult to tell which environment characteristics one need to use since the environment varies from one country to the other. Even though empirical method was easy to implement and their ability to include all environment-related factors that affect the propagation of radio waves in practice (Rappaport T. , 2002), they suffer from parameter ranges; the environment must be classified which may vary from one place to the other .the method also do not provides insight into propagation mechanism and analytical explanations.

The Physical model method attempt to produce deterministic field strength at specified points. (Ikegami, F.; Takeuchi, T.; Yoshida, S., 1991). The model makes use of characteristics of the environments, physical optics and other theories to account for the intended parameter of interest. A careful assessment of the exposure of urban populations to electromagnetic fields requires the use of deterministic models that take into account the interferences caused by the buildings in the propagation of the field. Deterministic models were developed to account for terrain in the absence of buildings based on geometric theory of diffraction (Bullington, 1977), (Luebbers R. J., 1984) and (Lampard & Vu-Dinh, 1993). Other methods such as parabolic equation method (Janaswamy & Andersen, 1998) and (Levy, 1990) takes the detail terrain profile into account. The method uses detail map of an area taking into consideration building configurations and using a ray optics to trace the waves. There are 3-D (three dimensional) ray tracing models that are able to accurately estimate site-specific propagation situations (Catedra, Perez, Saez de Adana, & Guiterrez, 1998). Although it accounts reasonable well for close in variation of field strength, it suffers from unrealistic assumptions, theories and underestimate in some cases (Saunders, 1999). Other works also uses numerical methods such as method of moments (MOM) to analyze the electromagnetic field of antennas (Johnson, Shin, & Eidson, 1997), (Wanzheng, Yan, & Anmin, 2000), (Povinelli & D’Angelo, 1991), (Lou & Jin, 2005) and (Tofani, d’Amore, & Fiandino, 1995). However, these Methods require higher mathematical and programming skills such as large sparse matrix solution as well as more computer resources such as larger memory and multiple CPUs than the analytical method (Johnson, Shin, & Eidson, 1997). A semi-analytical treatment has been carried out for cases where the horizontal separation between the base station and first row of buildings is knownand all the buildings are of the same height (Xia, Bertoni, Maciel, Lindsay-Stewart, & Rowe, 1993), (. Bertoni & Maciel, 1992). From the above analysis, it was evident from literature to date that there is no one method which will be able to predict accurately well and also help us understand and make meaning of the physics involved in the process of study. This research work focuses on the need for a hybrid model (Semi-Empirical) which will achieve a good level of accuracy and also help us understand the physical interaction of the parameters involved and also serve as an advancement on this field.

2.6 Advances in measurements

The natural electromagnetic energy comes from terrestrial and extra-terrestrial sources such as electrical discharges during thunder storms in the atmosphere and radiation from sun and space. It is of interest to note that the blackbody radiation from a person in the RF-band is approximately 3 mW/m². The man-made source originates from mainly telecommunication and broadcasting services in the environment. There are several methods developed to assess the electromagnetic fields (EMF) exposure level in literature. One of them was the use of a personal exposure measurement methods (Viel, Cardis, Moissonnier, Seze, & Hours, 2009), (Urbinello, Joseph, & Huss, 2014), (Bolte & Eikelboom, 2012), (Urbinello, Huss, Beekhuizen, Vermeulen, & Röösli, 2014), (Radon, Spegel, & Meyer, 2006) and (Frei, Mohler, & Bürgi, 2009). Another method is the used of stationary measurement approach (Bürgi, Frei, & Theis, 2010), (Calin, Ursachi, & Helerea, 2013), (Pachón-García, Fernández-Ortiz, & . Paniagua-Sánchez, 2015), (Ozen, Helhel, & Colak, 2007), (Korpinen & Pääkkönen, 2015) and (Verloock, Joseph, & Goeminne, 2014) where measurement is made at a define period of time such as 6 minutes averaging. The 6-minute averaging time comes from the time constant for the thermoregulation of the body (ICNIRP, 1998) to occur. FM and TV broadcast transmitters, GSM and UMTS base stations are important sources of RF EMF in terms of exposure level in the environment. In general, FM and TV broadcast transmitters were installed in places far off distance from the city center in the past but in today’s world, they are installed within our communities. In 1980, Tell and Mantiply published a study of RF fields measured at 486 sites across 15 major metropolitan areas in the USA which at that time, accounted for nearly 20 % of the nation’s population of 226.5 million people (Tell & Mantiply, 1980). The measurements covered the low VHF TV (54-88 MHz), FM radio (88-108 MHz), high VHF TV (174-216 MHz) and UHF TV (470-806 MHz) bands. They reported a median wideband time-averaged field level of 0.005 mWcm-², with an estimated 1 % of the population exposed to fields with power densities of 1 mW cm-². In addition, the fields from FM radio broadcasts were clearly dominant over the fields from the other three bands. Typically for High-power broadcast transmitters, the effective radiated power (ERP) was 250 kW per channel for FM radio and 500 kW per channel for television. The antennas were mounted towards the top of a 300 m mast. For medium-power broadcast and telecommunications transmitters, the transmitted powers were in the region of 100-200 W per channel. The exposure to the general public was very small relatively to people living in the immediate neighborhood of medium and short-wave stations (Jokela, Puranen, & Gandhi, 1994). People working in FM and TV towers which are near to high power FM or TV broadcast antennas were exposed to high levels in the range of 50 to 800 MHz (Jokela & Puranen, Occupational RF exposures, 1999) and (Hansson-Mild, 1981). Other studies have been carried out in the domains of exposure field measurement by (Viel, et al., 2009a), (Viel J. , Cardis, Moissonnier, R., & Hours, 2009b) and possible consequences of human exposure to such fields(Hossmann & Hermann, 2003). A study of ambient RF fields conductedmostly outdoors in Gothenburg, Sweden reportedan average wideband power densities of between 0.04and 0.05 mW cm-² (Ahlbom, Feychting, Hamnerius, & Hillert, 2012).European studies reported generally, in the five-country analysis, the totalexposures were lowest in the urban residential environment(range of means 8.5E-03 to 1.45E-02 µW cm-²). The results for a set of African countries was qualitatively and quantitatively similar to the results of RF measurement surveys conducted in the Americas, Europe and Asia (Rowley & Joyner, 2012) where the global weighted average was 0.073 mW cm-². The mean for the selected South African data set was 0.016 mW cm-². Some of the conclusion drawn was that the signal strengths for the cellular bands was unchanging in both time and across countries. Even though introduction of 3G and 4 G services are on the increase, the field levels are log-normally distributed and more data points makes the FM signal strengths relatively constant. In addition to these findings, several studies have reported that residential (and outdoor) fields from broadcast and cell downlink sources are lower in rural areas compared with fields in urban and suburban areas (Breckenkamp, et al., 2012), (Viel, et al., 2009a) and (Joseph, Vermeeren, Verloock, Heredia, & Martens, 2008). Cancer has been the primary concern among populations in the immediate vicinity of broadcast transmitters. Scientific evidences point toward heating effect from high levels of exposure, and most safety limits are based on it. Among these are the exposure limits proposed by the International Commission for Non-Ionizing Radiation Protection (ICNIRP) (ICNIRP, 1998) or Institute of Electrical and Electronics Engineers (IEEE) (IEEE, 2005) to prevent such effects (WHO, 2006).There is little scientific evidence on the risks associated with long-term exposure to low levels of RF EMF (ICNIRP, 1996). In 2012, the International Agency for Research on Cancer classified RF EMF as ‘possibly’ carcinogenic (Group 2B), based on studies on mobile phone usage (IARC, 2012). Mobile phone usage has increased tremendously, with about 6.8 billion subscriptions by the end of 2013 (ITU, 2013) and nearly 7 billion cell phone subscribers in 2014 (ITU). Statistics show that as at May 2008, the number of mobile phone users in Ghana was well over 8 million but as at the end of January 2016, the number of mobile phone users in Ghana rose to 26.09 million, according to the latest figures from the National Communications Authority (NCA). Urban areas are mostly affected by the over population of Base Station Transceivers (BTSs). Their closeness to homes and schools are raising concern about some health risks that might be associated with them (Khurana, et al., 2010). Numerous studies have demonstrated that a very significant part of the human exposure in the radiofrequency (RF) band is due to mobile communications radiation (Bornkessel, Schubert, Wuschek, & Schmidt, 2007), (Genc, Bayrak, & Yaldiz, 2010), (Joseph, Verloock, Goeminne, Vermeeren, & Martens, 2010), (Kim & . Park, 2010), (Rufo, Paniagua, Jimenez, & Antolín, 2011), (Joseph, W.; Verloock, L.; Goeminne, F.; . Vermeeren, G; Martens, L., 2012a), (Joseph, W.; Verloock, L.; Goeminne, F.; Vermeeren, G.; Martens, L., 2012b), (Rowley & . Joyner, 2012). The maximum output powers of a radio channel used in GSM and UMTS networks are 10-40W and 20-60 W, respectively (Koprivica, Neskovic, Neskovic, & Paunovic, 2014).It has been shown t