# Path Loss Prediction In Forest Biology Essay

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Abstract - The aim of this research presented in this report is to study the effects of radio waves propagating through vegetation and to develop a semi-empirical model of signal attenuation in the forest. This was achieved through a combination of theoretical studies and deterministic modelling to prove that the proposed model is sufficient for propagation prediction in forest. The main approach in this analysis is the demonstration of coupled lossy transmission line with nonlinear loads for the study of radio propagation in forest. An attempt is done on the transmission line analysis in order to study the losses in the forest by an empirical approach. To develop the model, major losses occurred in transmission line are taken in account. By using the predominant characteristic of the lumped elements in the transmission line, the loss factors are derived in order to fit into the loss equation of the forest model. The final model will consists of lumped elements equivalent circuit with the desired parameters. By using this circuit, an analytical result is shown for the transmission line parameters that fixed into the forest model. Nevertheless, only the effect of attenuation characteristic respect to the propagation constant is taken into account. This effect has become the determining factors for the performance of the forest model owing to the high frequency transmission through the foliage. An important feature of this paper is to prove that these analytical results may be presented in terms of transmission line parameters with less complicated calculation while getting acceptable results for radio losses in a forest environment. It is instead constitute a simple solution rather than the complicated calculation.

## INTRODUCTION

In nowadays technology, information can be transmitted in several ways. Nevertheless, the use of electromagnetic energy for this purpose is indeed attractive because physical connections are not necessarily required. This brings up the wireless technology which commonly used for radio transmission in early 20th century. The connectionless feature of electromagnetic propagation is utilized in many engineering systems such as long distance point to point communications, radar, radio and television broadcasting, navigational aids and so on. The same considerations also make electromagnetic energy useful in sensors systems in which the information is obtain from and to which the energy is directed. Electromagnetic sensors usually used for measuring the electron concentrations in the Earth's upper atmosphere, the wave-state of the sea, the moisture content of the lower atmosphere, the moisture in soils and vegetation, the size distributions of particles in smoke and many other parameters. Radio propagation research mostly focuses on the interaction between radio waves and the transmission media. This is the scientific concept behind the functionality of wireless phones as well as countless other wireless communications technologies. Over the past two decades, the demand for and dependency on such wireless products, services and networks have grown rapidly. As traffic load in wireless networks increases, there is a need to improve the radio spectrum which is used by these technologies.

In the development of electromagnetic theory, we were understood that the invention of wireless signalling by radio and the development of electromagnetic antennas is needed to transmit and receive the signals with high efficiency. The idea that electromagnetic signals might propagate over considerable distances with the velocity of light was first proposed in 1865 by James Clerk Maxwell. He added the displacement current term to the set of equations governing electromagnetic events, called Maxwell's equations. He deduced that among their possible solutions rectilinear wave motion would be included. Thus, an electromagnetic disturbance should be capable of being propagated over substantial distances. Therefore, the very possibility of wireless communications is founded on Maxwell's research. Today, Maxwell's equations form the basis of computational electromagnetics. This prediction was verified experimentally by Heinrich Hertz in a series of experiments conducted in the late 1880s. Most of his experiments utilized high frequency currents to produce the first wireless waves, thus validating the theory of Maxwell. He used the waves of approximately one meter wavelength which also termed as the ultra-high frequency (UHF) range and transmission distances were generally on the order of a few feet in obtaining the desired result.

## PROPOSE FOREST MODEL DESCRIPTION

In a lossy transmission line, the attenuation constant can be broken into at least four components involving the metal loss, dielectric loss due to loss tangent, due to conductivity of the dielectric and due to stray radiation [1]. The parameters contribute to the losses are resistance per unit length, conductance per unit length, inductance per unit length as well as capacitance per unit length. Different loss mechanisms will have different behaviors over conductivity value and frequency range [2]. These different behaviors are found useful in determining the forest attenuation loss under certain condition. In this study, a coaxial line type transmission line will be used to develop the appropriate model for the forest. This is due to the circular symmetry of the line which best used to represent a line of trees in a forest. Besides, coaxial line also less susceptible to complicated loss effects such as proximity effect and radiation loss which involved difficult calculation to observed the loss.

A transmission line model is chosen to develop the forest model as its parameter is comparable to the forest characteristic. For instance, in a long lossy transmission line, the frequency of the signal and the wavelength components are taken into account while deriving the transmission line equation. Similar to the forest model, frequency component act as an important parameter in determining the attenuation happened in the forest.

To match the characteristic of transmission line with characteristic of forest, the loss factor of transmission need to define first since forest act as obstacle which cause attenuation. Coaxial cable is optimal for carrying radio waves ranging in frequency from 3Hz to 3000GHz. Coaxial cable is comprised of an inner conductor of wound copper surround by a polyethylene dielectric. On the top of insulating polyethylene layer, there is an outer conductor of braided copper and then followed by PVC jacket.

The inner conductor of copper wire and the outer copper is very important because it defined the characteristics impedance, Zo from the capacitance and inductance per unit length of the cable. In a lossy transmission line, there are at least four components which affect the signal quality. The components are metal loss, dielectric loss, conductivity of dielectric and stray radiation. The fundamental electrical parameters which contribute to losses are shunt capacitance per unit length, series inductance per unit length, series resistance per unit length and shunt conductance per unit length. The resistance per unit length is just the resistance of inner conductor and the shield at low frequencies. Once the frequencies get higher, skin effect will increases the effective resistance by confining the conduction to a thin layer of each conductor. The shunt conductance is usually very small because insulators with good dielectric properties are used. At high frequencies, a dielectric can have a significant resistive loss.

Figure 2.1: Coaxial Cable

In the proposed model, the transmission line characteristic is matched to the forest characteristic with some slight adjustment to derive the loss factor. It is necessary to model the forest environment before develop the model to ensure that forest characteristic can be matched to the transmission line characteristic. Several considerations and assumptions on the forest density, antennas separation distance and the antennas height are taken into account in developing the forest model. In modeling the forest profile, the first assumption made is the location of forest on a flat terrain with almost equal size of trees. The tree age, height and diameter of trunk is also the considerable parameters where all of them are assumed to be equal and the forest consisting of the same types of trees. The density of the forest is measured based on the trunk layer which mean that the canopy is having the same density as the tree trunk and it is taken as a whole unit instead of considered separately. Since the present study will only concentrated on the characteristic of the forest elements, therefore, all others randomness such as the temperature of the forest, parasitic elements and moving objects in the forest will be fixed.

From all the assumption made above, a forest model is developed as shown in Figure 2.1. Besides, the trees separation is assumed to be very close to each other and its value is much smaller than the distance between the transmitter and receiver. The interface between the canopy-trunk and canopy-air is assumed to be flat. The forest model is built as shown below with both transmitting and receiving antenna situated inside the vegetation. The trees act as obstacles in the radio path causing both absorption and scatter of radio signals.

Figure 2.2: Basic Forest model

Relationship of Forest Density and Attenuation Loss

Kent Chambelin [12] has proven that forest density contributes the major loss upon radio propagation in forest. His research is followed up by Tamir [3] who denotes that a denser forest will experience more loss due to the poor conductivity. This relationship is closely related to the transmission line model which expressed the dominant loss due to attenuation in metal conductivity. The attenuation loss is modeled by the resistance per unit length component in transmission line model and mainly cause by skin effect. An important parameter in this derivation is the conductivity of the material due to current flow.

A forest model built to examine the relationship of forest density to the loss factor is shown in Figure 2.2. The trees are separated with a distance much smaller than the antenna separation. The transmitting and receiving antenna are located with certain height inside the vegetation. However, since the present study only account for the density of the forest, the transmitting and receiving antennas will be set into a fixed value in this analysis.

According to theory of transmission line, the resistance per unit length can be derived as:

The forest density contributes the major loss when radio wave passes through the forest. This can be related to the resistance per unit length component in transmission line model which cause attenuation due to skin effect. When the frequency is higher, skin effect increases the effective resistance by confining the conduction to a thin layer of each conductor. In figure 4.1, a and b is the antennas height with trees separation, d much smaller than distance of transmitting and receiving antenna. This antenna is located inside the forest. For coaxial line, the resistance per unit length is given by:

(4.1)

Where

a = radius of inner conductor

b = radius of outer conducting cylinder

= skin depth of the conductor

= electrical conductivity

The skin depth can be written as below:

(4.2)

The equations in (4.1) and (4.2) can be matched with forest density which contributes the propagation loss in the forest model. In this case, parameter "a" which denotes the inner conductor radius can be replaced with transmitting antenna height while b as receiving antenna height. In general, non-ferromagnetic substances have permeability almost equal to, which is 1.0. From the above equations can be derives that conductivity and loss per unit length as:

(4.3)

By replacing the equation (4.1) into (4.3), the relationship between forest density and attenuation can be derived as:

[Nepers/m] (4.4)

By expressing it in dB/m, the equation as below:

[dB/m] (4.5)

In equation (4.5), the parameter Zo acts as correcting factor in determining the forest total loss due to other vegetation factor such as conductivity and permittivity of different types of trees, parasite effect and temperature aspect of the forest. This parameter will determine the different forest characteristic when studies are done on different types of forest.

Relationship of antenna height gain factor and attenuation loss in forest

Tamir stated the height gain effect in his slab model. Tamir's model yields a simple explanation between the height of antennas and attenuation loss in forest. He expressed the dependence of field intensity, EL on the antenna height by exponential of - is given at (4.6).

(4.6)

and,

(4.7)

Where

is the exponential attenuation factor produced by presence of vegetation

S is the antenna elevation

is the distance variation of radio wave

n is the complex refractive index

In transmission line model, the inductance per unit length can be derived from magnetic flux as below.

(4.8)

B is the field itself. Which can denoted as:

(4.9)

Where I is the current flowing through the inner conductor out, the area element will be rectangle and perpendicular to the two conductors, thus dA becomes 1.dr. By substituting (4.9) into (4.8), the equation of inductance per unit length can be yield as follow:

(4.10)

a and b denoted as transmitting and receiving antenna height. When high frequency wave is transmitted, skin effect, proximity effect and radiation loss effect will cause a reduction in inductance per unit length.

From (4.10), it can be derive the gain factor equation as (4.11). When the antenna height is increased, the gain will increase also.

(4.11)

Hence the antenna height gain is related to attenuation loss:

(4.12)

Same as section 4.5, a and b are the transmitting and receiving antenna height. By substituting (4.10) into (4.12), the final attenuation loss can be denoted as:

(4.13)

By expressed it in the unit of dB per meter, the equation becomes:

[dB/m] (4.14)

Relationship of Antenna Separation Distance and Attenuation Loss in Forest Environment

In Burrow's model, he mentioned the received field is inversely proportional to the square of antenna distance. Therefore, the attenuation in forest is closely related to antenna separation. Referring to Tamir's analysis, he stated the variation of the lateral wave with distance is in the form where p denotes as antenna distance and EL is the dependence field intensity. Such a distance dependence produces a path loss which is greater than that of a geometric-optical variation of , but the larger loss is expected since the lateral wave is essentially a diffracted field.

In coaxial line, the parameter of capacitance per unit length can be matched with the characteristic of distance loss in the forest environment. Since a coaxial cable has two separate conductors, the capacitance per unit length equation can be yields from the difference in potential between the two conductors.

(4.15)

The equation of electric field (E) can be written as:

(4.16)

By replace (4.16) into (4.15), the capacitance per unit length can be expressed as below, since capacitance is equal to total charge over voltage.

[F/m] (4.17)

where

Permittivity of conductors

outer radius of coaxial line

inner radius of coaxial line

In this paper, the permittivity of value is taken from dry wood which is equal to 1.5. Besides that, Tamir [1] also setting the range of permittivity with minimum value equals to 1.01 and maximum equals to 1.5. Capacitance per unit length depends primarily on dielectric constant of the insulating medium and conductor geometry. In equation (4.17), when the radius of outer conductor increases, the capacitance per unit length will decrease. Since the radius of inner conductor is much smaller than radius of outer conductor, an assumption is made to match with forest characteristic that antennas separation is much larger than trees separation. The relationship between loss factor due to antennas distance and capacitance per unit length can be expressed as:

(4.18)

Substituting the equation (4.17) to (4.18), the final equation is:

(4.19)

[dB/m] (4.20)

Relationship of Antenna Location and Attenuation Loss in Forest Environment

In a four layered anisotropic forest, the electric fields excited by an inclined electric dipole embedded inside the forest are obtained at the receiving points located either inside the forest or outside the vegetation. In the paper, we will focus in the antennas are placed inside the forest only. A radio wave propagating within the forest may consist of three components, quasi-direct wave, multiply reflected wave and lateral wave. Lateral wave which propagate along the trunk-canopy or ground-trunk interfaces do not contribute much to the total electric field because the forest layers are lossy media. Since the antennas are placed inside the forest model, lateral wave which propagate along the upper side of the air-canopy interface plays an important role in contributing to the overall waves as the distance becomes large.

In coaxial cable, conductance per unit length is given as below:

[S/m] (4.21)

The shunt conductance is usually very small because insulators with good dielectric properties are used. At high frequencies, a dielectric can have a significant resistive loss. Dielectric loss effect is the dielectric losses result from leakage currents through the dielectric material. This causes an increase in the shunt conductance per unit length and produces signal attenuation. The relationship of conductance and resistance is related by:

(4.22)

Equation (4.3) shows the relationship between conductivity and the resistance loss per unit length. Since the equation in (4.22) is inversely proportional, it can be concluding that:

(4.23)

The final attenuation loss equation is expressed as:

(4.24)

[dB/m] (4.25)

Final Equation of Forest Model

Coaxial cable is used as a transmission line for radio frequency signals, in applications such as connecting radio transmitters and receivers with their antennas, computer network connections and distributing cable television signals. However, resistance per unit length, inductance per unit length, capacitance per unit length and conductance per unit length, these four components contributes the major losses when a signal is go through coaxial cable. In this paper, it is shown that characteristic of coaxial cable can be match with characteristic of forest environment to find the losses in an easier way by eliminating the complicated mathematical calculations. The total loss equation is the summing of propagation loss on forest due to factors of forest density, antenna height-gain effect, antennas separation and antennas location.

(4.26)

Where

= loss factor due to forest density

= loss factor due to antenna height-gain effect

= loss factor due to antenna distance

= loss factor due to antenna location

## RESULT AND DISCUSSION

Comparison between Propose model and Simulated data by Tamir's Model, ITU- R+Plane Earth

In this section, in order to verify the propose model that able to compute the path loss prediction data accurately within 200MHz, there is needed to make comparison between 2 other forest path loss prediction model which are Li et al's model and FITU-R+Plane Earth model[3]. When 1967, Tamir [3] proposed a half-space model to deal with radio wave (1-100 MHz) propagation in the forest and explained the associated phenomenon dominated by a lateral wave mode of propagation. Furthermore, he [4] continued his study on the propagation in forested environment to the dissipative dielectric slab model to account for the ground effect on radio wave (2-200 MHz) propagation. Besides, Li et al. [5], [4] performed an extensive study of the four-layered model with the lateral wave mode of propagation in anisotropic forests using dyadic Green's functions.

Figure3.1. Comparison between Propose model and

simulated data by Li et al, FITU-R+Plane Earth

The experimental data is no enough in the deep forest which over 1000m of depth of foliage, therefore the propose model is force to compared with the analytical results that reported by Li et al. [6] using the numerical simulation method. Besides, FITU-R+Plane Earth is the upgrade model of ITU-R [3] which is derived from a set of data measured up to 20GHz in uniformly distributed plantations where the trees are equally spaced and with very little or no undergrowth. The propose model have assume transmit antenna height a (Htx) equal to 5m and receive antenna height b (Hrx) equal to 10m respectively, while the depth of foliage is fixed to be 5km. Then the propose model followed the simulated data and presented as Fig. 3.1.

The Fig. 3.1 shows that Simulated by Li el al. have slightly lower path losses compare with proposed model and FITU-R-Earth plane, while proposed model is better than the FITU-R-Earth plane. Besides, it can be observed that propose model is close to the numerically simulated results by Liet al. This because the simulation has taken into consideration the lateral wave contributions, especially when at larger foliage depth when both the transmitter and the receiver where placed inside the forest. The lateral wave travels mostly in the lossless air region and becomes dominant at relatively large foliage depth. Thus FITU-R model show poor prediction accuracy is caused by without consider lateral wave contribution.

The propose model is found to be good model for the prediction of foliage loss over a large foliage depth which up to 5km at UHF band for the ground forested readio wave propagation. It can be verified for the frequencires from 250MHz to 1000MHz. Moreover, it can be assumed that as the equation computation point, propose model is highly simplified compare to this 2 models, thus this show good pontential for expertise to cut down the time computation when predict the path loss in forest.

Comparison Between Dyadic Green's Function and Proposed Model

From Fig 3.2, there is some improvement from the Fig3.1. The FITU-R model is limited to the lower frequencies which only can up to 1000MHz. In order to prove that the propose model is able to predict the losses up to UHF band frequency which up to 2000MHz, there is needed to compare it with Dyadic Green's Funtions by Li [6].

By adding the four components, resistance per unit length, inductance per unit length, capacitance per unit length and conductance per unit length, the total loss for propose model are computed. The forest is considered to be with a height of 30m, and canopy and trunk to be 10 and 15 m high, respectively. Transmit and receive antenna heights, Htx and Hrx used in both model are 5m and 10m respectively. Beside the depth of foliage is assumed to be 1000m, it because to ansured the prediction accuracy from Li's model [6].The relative permeability is taken at = 1 and the density would be 0.6. The conductivity is the inverse of density, which is equal to 1.7.

Figure3.2. Comparison between Dyadic Green's Function and Proposed Model

The graph can be observed that the propose model is presented closely to the Dyadic Green's Funtions by Li. Thus it is proved that the proposed model able to predict the losses at depth of foliage 10km at UHF band which from 1MHz up to 2000MHz. Although the propose model showed quite high path loss at 1500MHz to 2000MHz, it is still considered at acceptable stage in the forest environment. It can be assumed that as the communication point approaches the treetop level, the accuracy will decline, because there will be more contribution by the lateral wave as reported in [6].

In a transmission line model, it has been proven theoretically that at higher frequency the achievement of loss factor in transmission line due to resistance per unit length inductance per unit length, capacitance per unit length and conductance per unit length, all will become higher. Thus the propose model and Dydic Green's Function are presented overall accurate prediction of path loss, especially from 1MHz to 1500MHZ.

However, the most crucial point here is the way of the propose model presented good pontential and can be used easily by users who doing research of path loss prediction in forest.

Loss Dependence on Antenna Distance

Relationship between path loss constant and antenna distance

The basic transmission loss in forest often involved the parameter of antenna separation. For the same forest environment, the relationship between the path loss and the antenna separation are investigated.

Figure3.3. Relationship between path loss constant and antenna distance

Figure 3.3 shows the effect of antenna separation to the path loss constant. It can be observed that the attenuation loss in forest medium is directly proportional to the antenna separation in meter. This relationship is verified by Tamir in the study of variation of radio wave with distance [3]. The antenna range is consider from 1 meter up to 10000 meters as those evaluated by Tamir in the entire frequency range of 1 to 100MHz. However, from the measurement report submit by Jansky and Bailey [8], the geometric loss was obtained up to 32 kilometers even though the terrain was very irregular.

Comparison between Proposed Model, ITU-R,FITU-R and Cost235 Models at 2000MHz

In this section, in order to proved the propose model is useable with the prediction of loss dependance of antenna distance, it is necessary to compare the propose model with other models.

The Cost235 model [3] and FITU-R model [5], there are only the in-leaf foliage models are used, because the tropical plantation under consideration is an evergreen [6]. Experimental data collected from the ITU-R models, since FITU-R model and Cost235 model are modified from the ITU-R, thus it is more convenient to be the experimental data and the accuracy will be ensured. The frequency to be used is 2GHz, since COST234 model is optimized from the measured data at milimeter waves (up to 57.6GHz), which results in a higher predicted path loss at UHF [5]. Besides, ITU-R and FITU-R are both derived from measured data taken at frequencies (up to 20GHz) [5]. Thus there are suitable to be choosing as the model to be compared.

Figure3.4. Comparison between Proposed Model, ITU-R, FITU-R and Cost235 Models

From Fig 3.4, it can be observed when the foliage depth increases, the ability to predict the path loss by the Cost235 model and ITU-R model become poor. Contrary, the propose model shows very good predict ablility if compare to other 3 models since it is the closest model to the experimental data. Besides, the Cost235 shows high attenuation from 100m to 10km, while the propose model provide average low attenuation if compare to other 3 models. This again proved that propose model is more accurately. When the foliage depth < 400m, ITU-R model, FITU-R model and propose model are located at the very stable stage if compare to Cost235 model. There are shows approximately equal to each other, thus this ensure that the propose data is accurate in the small depth stage.

Loss Dependence on Antenna Height Gain Factor

In this section, the loss dependece on antenna height gain factor is examined. Using the same forest environment profiles, the receiving antenna height, Hrx is adjusted in this analysis to verify its relationship to the forest loss. Furthermore, there is no direct comparison data found in the Dyadic Green's function. The loss dependence on antenna height gain factor is examined between proposed data and the FITU-R-Earth Plane [5] [9]. The frequency 2000MHz is used to propagate through the forest model. In present study, the height gain factor is found related to inductance per unit length parameter in the coaxial line.

Figure3.5. Comparison between Proposed Model and FITU-R+Plane Earth

Figure 3.5 show the relationship of receiver height and attenuation loss. In the proposed model, only receiver height will be change and the transmitter height will be fixed as mentioned earlier. From the data, low attenuation can be achieved by keep the antenna same height or higher than the tree when propagate in the forest. This attenuation loss due to receiver height was first analyzed by Tewari [10], who performed an in-depth empirical modeling of antenna height-gain on the path loss in the forest. The final result proven that the attenuation loss is indeed dependent on the receiving antenna height. The larger height value will gives smaller attenuation loss when wave propagates through the forest.

Loss Dependence on Antenna Location

In this section, the Li et al. [6] experiment data is used, since it able to support UHF which up to 2000MHz. The second experimental data is use from the propose model which same with the ITU-R model [5] that used at Fig 3.4, the frequency is 500MHz.

Figure3.6. Comparison between Proposed Model and FITU-R Model with

Li et al. Experimental data.

From Fig. 3.6, it can be observed that the propose model shows good prediction accuracy as compared to LITU-R with perfect plane earth that proved from the comparisons and analysis made from [11]. Besides, if compared to the predicted results by ITU-R model with perfect plan earth model, the accuracy of the propose model is significantly good and increasingly at large foliage depths. Obviously, the experimental with 500MHz shows less attenuation if compare to the experimental data with 2000MHz, it is due to the frequency proportional to the path loss (attenuation), which mean that if the larger frequency, the larger path loss to be occurred.

## CONCLUSION

As conclusion, a path loss prediction in forest model is developed to predict the path losses during the radio wave propagation in forest environment. The propose model is builted based on the transmission line model with lumped elements including of resistance per unit length, inductance per unit length and capacitance per unit length. Besides, the frequency ranges able to support the model is from 1MHz up to 2000MHz.

Every parameter from the lumped elements can be representing for different forest parameters. The resistance per unit length parameter is used to predict the attenuation loss due to forest density, while inductance per unit length is used to predict the attenuation loss due to antenna height gain effect and capacitance per unit length is used to predict the attenuation loss due to antenna distance. At the end, the final model sum up the total loss contributes by those lumped elements and the losses equation for the forest model is presented.

From the result proven, the propose model is found to be good model for the prediction of foliage loss over a large foliage depth which up to 5km at UHF band for the ground forested radio wave propagation. It can be verified from Fig 3.1. Moreover, it can be assumed that as the equation computation point, propose model is highly simplified, thus it have very good pontential for expertise to cut down the time computation when predict the path loss in forest. Besides, the Fig 3.2 proved that the propose model presented closely result as compare to the famous Dydic Green's Function by Li's model. On top of that, the Fig 3.3 shows that the attenuation loss in forest medium is directly proportional to the antenna separation in meter thus prove that the equation of capacitance per unit length from lump elements is verified.

From the results, all are proven that the transimission line parameters can be direct derived and fit to the forest chracteristic. Thus the propose model can be consider as one of the new path loss model that help to inverstigating the radio propagation in forest environment.