Path Loss Models For Vegetational Areas Biology Essay

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This essay has been submitted by a student. This is not an example of the work written by our professional essay writers.

This is to certify that the main-project upon which this report is based was carried out by AKINYEMI, LATEEF ADESOLA of the department of Electrical and Electronic Engineering, Faculty of Engineering, under the supervision of Dr. O.D OSUNDE for the award of Masters of Science (M.Sc.) in Electrical and Electronic Engineering (Communication Option)

This thesis presents the path loss models for vegetational areas in Lagos Environs, Nigeria and the effects of weather on communication systems.

The data analysis is done using Statistical Package for Social Scientists (SPSS).Also, path loss models for macro cells such as Plane earth, Early ITU models are equally reviewed and their results compared.

The simulation of the data obtained is done using path loss software which when applied effectively shows the true topographic nature of the investigated areas in question. At any point in time, two points are considered and parameters such as EIRP, FSL, Rx signal, TX signal and so on will be depicted.

It was observed that as the distance of measurement increases, path loss increases. Hence, the model developed can also help in planning and improving better network for rural and suburban areas in Nigeria in as much as the investigated areas have the same characteristics.

LIST OF ABREVATIONS

SR received power at the Antenna

ST signal transmitted or transmitted power at the antenna

GT transmitted antenna gain

GR received antenna gain

radiated wavelength

d distance between transmitting and receiving point

AT transmitting antenna area

T antenna efficiency parameter for transmitter

AR Receiving antenna area

R antenna efficiency parameter for receiver

Ld path loss

BS Base station

BSC Base Switching Center

BTS Base Transmitting Station

dB Decibel

DL Down link

EMC Electromagnetic compatibility

EMI Electromagnetic Interference

FDMA Frequency division Multiple Access

FMT Fade mitigation technique

FUL Frequency of up-link

GSM Global system of mobile telecommunication

MS Mobile station

MSC Mobile Switching Center

MTSO Mobile telephone switching office

PSTN Public switched telephone networks

RF Radio Frequency

UL Uplink

CHAPTER ONE

INTRODUCTION

1.0 Background of study

Radio wave propagation path loss or attenuation generally is the reduction in power density of an electromagnetic wave as it propagates through space. Hence, radio wave propagation path loss model is regarded as a vital tool that is widely used for communication applications such as the quality of mobile communications effective radio coverage and network optimization. The term path loss model is also a major factor in the analysis and design of the link budget of any telecommunication system. Therefore, it does predict to a high level of accuracy, the actual signal strength reliability and performance of the network and the quality of antenna coverage in any location. Finally, path loss occurs when the received signal becomes weaker and weaker due to increasing distance between mobile station (MS) and base stations (BS), even if there are no obstacles between the transmitting (TX) and receiving (RX) antenna. The path loss problem usually leads to dropped calls because before the problem becomes complex and complicated, a new transmission path is established and setup via another BTS.

More so, weather is a physical atmosphere phenomenon that is associated with air masses and their corresponding interactions with the environment. It also includes the state, factor and motion of the masses, including the pressure, winds, temperature, clouds and precipitations produced by them. The condition of the air or atmosphere with respect to heat or cold, wetness or dryness, cloudiness or clearness, storm or calm and any other metrological phenomena. In addition, the average weather conditions of a region over time are normally used to define and describe a region's climate.

Many types of weather have been used in Nigeria for the purpose of improving and modifying the quality of services provided by the operators of these transmitters and receivers called base stations. Nigeria's weather basically features a tropical type of climate where most of the seasons are very humid and slightly wet. There are mainly two seasons that are common in Nigeria, namely the dry and the wet seasons (rain and harmattan as the case may be). Therefore, Nigeria's weather is not eco-friendly throughout the year although there some variations in the climate in some particular regions within the country.

For instance, the southern part of Nigeria is relatively wet and humid than the northern part of the country. In the southern parts of Nigeria, the dry season begins from the month of November and does last till the month of March. For the northern regions, it is much drier in nature when compared to the southern parts. The dry season starts from the month of October and lasts till the month of April.

In addition, Nigeria's weather is highly influenced by the south-western winds and the north-eastern winds. The south-eastern winds are full of moisture and blusters from the Atlantic Ocean whereas the northern easterlies are dry and dirt-laden winds that basically blow from the deserts of Sahara. The rainy seasons come into existence due to the movement of winds into the northern region of Nigeria. The south-west winds bring about rainfall in the extreme southern areas of Nigeria. The average rainfall in southern coastal areas of Nigeria is almost 400mm and the northern eastern side is 500mm.

Furthermore, vegetative areas are places where communication transmitters are situated (radio propagation antenna). Communication receiving gadgets such as our mobile phones receive signal and make use of this antenna to communicate with one another using that type of transmitter.

1.2 Statement of problem

Owning to daily increase in number of subscribers in telecommunications world, the use of antenna is arithmetically increasing while there is geometric decrease in number of call drops usually experienced by most Nigerians (customers) in recent times. This now justifies the effort geared towards the path loss models for vegetational areas of Lagos Environs, southwest, Nigeria.

1.3 Aim

The aim of this project is to determine the pathloss for a particular location and the effect of pathloss as well as weather conditions affecting communication signals. Thus, a very crucial factor in mobile cellular network project is the ability to make an accurate prediction model which will help largely in the planning, designing and more so implementation process of mobile cellular network project in Nigeria. It is pertinent to note that the path loss model developed as an empirical model is used in this research work to determine losses in signal strength.

1.4 Objectives/methodology

The methodology to be adopted in this study is as follows.

To obtain the mean receive power distribution, EIRP,TX power, RX power distribution at specified receiver distances from the respective GSM station.

To know the effect of path loss and foliage on communications gadgets.

Measurements would be likening in some spots in parts of Lagos, south-west, Nigeria.

To conduct site verification using Sony Ericson K800i mobile station and a piece of compass.

To compare the obtained values from field measurements and then compared with those obtained analytically.

Finally, to investigate the degree of coherence or variation between path loss values obtained at different locations within the State.

1.5 Scope of Study

To use the existing path loss model in vegetative areas in Lagos State. This is carried out to obtain the loss in signal strength. The investigation is limited to some parts of Lagos State.

1.6 Relevance of the study

The results of the study would enhance the performance of the base stations thereby reducing the call drops in telecommunication industry which normally result in loss of signal. More so, this study will look at how effectively it can cater for weather in other to prevent poor quality of services in our global satellites for medium communication in Nigeria. More importantly, it will predict the short coming of weather and how it could improve communication and contribute to the income of Nigeria.

1.7 Application of Study

This study is to apply the existing path loss models for vegetation areas of Lagos State and the effect of path loss on communication gadgets and the rate at which the communication signals get lost or dropped. Propagation models such as path loss models, Plane earth model, Early ITU-R model and free space model in Nigeria environment will be reviewed. However, if the path loss distribution is proposed by these existing models are in consonance with the measurements taken, then, these models will be regarded as appropriate for use in the design and planning for Nigerian states.

1.8 Presentation of Thesis

This thesis is arranged in the following order;

Chapter one contains the introduction of this study. Chapter two contains the literature review, where previous studies relating to the present research are discussed. The methodology for this study is discussed in chapter three. A detailed discussion, analysis and results as well as graphical representations will be discussed in chapter four. Chapter five finally talks about conclusion and recommendation of the study.

CHAPTER TWO

LITERATURE REVIEW AND THEORETICAL FRAME WORK

2.1 Literature Review

Most of the studies on path loss models for both cellular mobile and wireless communications and sometimes related to the prediction and measurement for village, town, state or country as the case may be. It can also be for sub-urban and urban areas.

In recent times, efforts were made by notable researchers to model for sub-urban and urban areas. Among them is S.Phaiboon (2004) that worked on prediction for path loss for correct location of base station in cellular mobile communication systems using fuzzy logic approach. S.Paibon equally developed a model for urban environment using four different terrains as a case study and striking results were achieved by this model.

Moreso, S.Paibon, P.Phokharatkul and S.Somkuarnpanit (1999) also worked on propagation path losses characterization for a 800 MHz cellular communication in far area Bangkok. There were about 52 locations used as studied areas at /mile finding out that the path loss (Lo) is 72.7dB and the slope of the path loss Y is 36.0dB/ decade using regression analysis having antenna heights of transmitter and receiver 30 and 3 meters with associated gains of 6dBd and OdBd respectively.

In addition, Shalangwa, D.A and Singh, S.K (2010) equally researched on measurement and modeling of path loss for GSM 900 in sub-urban environment over irregular terrain. The model developed showed that the investigated areas should have a minimum and maximum path losses ranging between 257dB and the mean square errors were found to be less than 0.25 Db (<0.25 Db).

According to Ayyappan, K and Dananjayan,P(2006) who carried out research on propagation model for high in mobile communication system between Pondicherry-Villupuran in India with coverage area of 40km.A comparative analysis with real time measurement obtained from Bharat Sanchar Nigam Limited(BSNL) a GSM based wireless network for Pondicherry, India. At the end, the results obtained show that Sub-urban model for highway using HATA-Okumura and COST 231 is nearer and closer to the observed received signal strength and predicted to be suitable model for highway received signal strength calculation.

Additionally, Greg, D, Theodore, S.A and Hao, X (1998) and worked on measurements and models for radio path loss and penetration loss in and around Homes and Trees at 5.85GHz.In the paper,270 local area path loss measurements and over 276,000 power measurements were used. The outdoor transmitters at a height of 5.5cm were placed at distances between 30 and 210m from the homes. The model developed was based on measurement path loss models for the prediction of the propagation in and around residential communication system for wireless internet access, wireless cable distribution and wireless local loops.

Moreso, Mohammed, S.Al-Bashir, Raed M.Shubair, and Sami M.Sharif (2006) carried out research on investigation of excess attenuation of radio signal at 2.1GHz through Date palm trees in North of Abu Dhabi City, United Arab Emirates (UAE) using vegetation attenuation models, exponential decay and maximum attenuation model. The results obtained were compared with the ITU-R model parameter values which yield an RMS (root mean square) of 10.60dB, 4.37dB and 3.59dB for Brasil, France and UAE respectively with the RMS error associated with exponent decay of 5.97dB.

Importantly, Themistoklis Sofos and Philip Constantinou (1999) researched on the propagation model for vegetation effects in terrestrial and satellite mobile systems. Measurements were taken and results obtained can be used for prediction models and ray-tracing algorithm for mobile and land mobile satellite system application.

Also, Adebayo,T.L and Edeko,F.O(2006) worked on characterization of propagation path loss at 1.8 GHz: A case study of Benin city, Nigeria and striking results were able to achieve.

However, this research will focus on the path loss models for vegetational areas of Lagos Environs, South-West, Nigeria to determine the effect of path loss on communication signals.

2.2 RADIO FREQUENCY SPECTRUM

Table 2.1: Radio Frequencies and their Primary Mode of Propagation

Band

Frequency

Propagation via

VLF

Very Low Frequency

3-30kHz

100-10km

Guided between the earth and the oinosphere

LF

Low Frequency

30-300 kHz

10-1 km

Guided between the earth and the D layer of the ionosphere

MF

Medium Frequency

300-3000 KHz

1000-100 m

E, F layer ionospheric refraction at night, when D layer absorption weakness

HF

High Frequency (Short Wave)

3-30MHz

100-10 m

E layer ionospheric refraction

F1, F2 layer ionospheric refraction

VHF

Very High Frequency

30-300 MHz

10 - 1m

Infrequent E ionospheric refraction. Extremely rate F1, F2 layer ionospheric refraction during high sunspot activity up to 80 MHz. Generally direct wave. Sometimes tropospheric ducting

UHF

Ultra High Frequency

300-3000 MHz

100-10 cm

Direct wave. Sometimes tropospheric ducting

SHF

Super High Frequency

3 - 30 GHz

10 - 1 cm

Direct wave

EHF

Extremely High Frequency

30 - 300 GHz

10 - 1 mm

Direct wave limited by absorption

2.3 MODES OF RADIO WAVE PROPAGATION

2.3.1 Surface modes

Lower frequencies (between 30 and 3,000 kHz) have the property of following the curvature of the earth via ground wave propagation in the majority of occurrences. In this mode, the radio wave propagates by interacting with the semi-conductive surface of the earth. The wave "clings" to the surface and thus follows the curvature of the earth. Vertical polarization is used to alleviate short circuiting the electric field through the conductivity of the ground. Since the ground is not a perfect electrical conductor, ground waves are attenuated rapidly as they follow the earth's surface. Attenuation is proportional to the frequency making this mode mainly useful for LF and VLP frequencies.

Today LF and VLF are mostly used for time signals, and for military communications, especially with ships and submarines. Early commercial and professional radio services relied exclusively on long wave, low frequencies and ground-wave propagation. To prevent interference with these services, amateur and experimental transmitters were restricted to the higher (I-IF) frequencies, felt to be useless since their ground-wave range was limited. Upon discovery of the other propagation modes possible at medium wave and short wave frequencies, the advantages of HF for commercial and military purposes became apparent. Amateur experimentation was then confined only to authorized frequency segments in the range.

2.3.2 Ionospheric Modes (Sky wave)

Sky wave propagation, also referred to as skip, is any of the modes that rely on refraction of radio waves in the ionosphere, which is made up of one or more ionized layers in the upper

atmosphere. F2-layer is the most important ionospheric layer for HF propagation, though Fl, E, and D-layers also play some role. These layers arc directly affected by the sun on a daily cycle, the seasons and the 11-year sunspot cycle determines the utility of these modes. During solar maxima, the whole HF range up to 30 MHz can be used and F2 propagation up to 50 MHz arc observed frequently depending upon daily solar flux values. During solar minima, propagation of higher frequencies arc generally worse.

Forecasting of sky wave modes is of considerable interest to amateur radio operators and commercial marine and aircraft communications, and also to shortwave broadcasters.

2.3.3 Direct Modes (line-Of-Sight)

Line-of-sight is the direct propagation of radio waves between antennas that are visible to each other. This is probably the most common of the radio propagation modes at VHF and higher frequencies. Because radio signals can travel through many non-metallic objects, radio can be picked up through walls. This is still line-of-sight propagation. Examples would include propagation between a satellite and a ground antenna or reception of television signals from a local TV transmitter.

Ground plane reflection effects are an important factor in VI-IF line of sight propagation. The interference between the direct beam line-of-sight and the ground reflected beam often leads to an effective inverse-fourth-power law for ground-plane limited radiation. [Need reference to inverse-fourth-rower law ± ground plane. Drawings may clarity].

2.4 Tropospheric Modes

2.4.1 Tropospheric scattering

At VHF and higher frequencies, small variation (turbulence) in the density of the atmosphere at a height of around 6 miles (10 km) can scatter some of the normally line-of-sight beam of radio frequency energy back toward the ground, allowing over-the-horizon communication between stations as far as 500 miles (800 km) apart. The military developed the White Alice communications system covering all of Alaska, on these principles.

Tropospheric ducting and enhancement or refraction via inversion layer sudden changes in the atmosphere's vertical moisture content and temperature profiles can on random occasions make microwave and UHF & VHF signals propagate hundreds of kilometers up to about 2,000 kilometers (1,300 mi) - and for ducting mode even farther -beyond the normal radio-horizon. The inversion layer is mostly observed over high pressure regions, hut there arc several tropospheric weather conditions which create these randomly occurring propagation modes. Inversion layer's altitude for non-ducting is typically found between 100 meters (300 fi) to about 1 kilometer (3,000 Ii) and for ducting about 500 meters to 3 kilometers (1,600 to 10,000 ft), and the duration of the events are typically from several hours up to several days.

Higher frequencies experience the most dramatic increase of signal strengths, while on low-VHF and HF the effect is negligible. Propagation path attenuation may be below free-space loss. Some of the lesser inversion types related to warm ground and cooler air moisture content occur regularly at certain times of the year and time of day.

2.4.2 Rain scattering

Rain scattering is purely a microwave propagation mode and is best observed around 10 GHz, but extends down to a few gigahcrtzes - the limit being the size of the scattering particle size vs. wavelength. This mode scatters signals mostly forwards and backwards when using horizontal polarization and side-scattering with vertical polarization. Forward-scattering typically yields propagation ranges of 800 km. scattering from snowflakes and ice pellets also occurs, but scattering from ice without watery surface is less effective. The most common application for this phenomenon is microwave rain radar, but rain scatter propagation can he a nuisance causing unwanted signals to intermittently propagate where they are not anticipated or desired.

Similar reflections may also occur from insects though at lower altitudes and shorter range. Rain also causes attenuation of point-to-point and satellite microwave links. Attenuation values up to 30 dB have been observed on 30 GHz during heavy tropical rain.

2.4.3 Aeroplane scattering

Aeroplane scattering (or most often reflection) is observed on VHF through microwaves and besides back-scattering, yields momentary propagation up to 500 km even in a mountain-type terrain. The most common hack-scatter application is air-traffic radar and bistatic forward-scatter guided-missile and aeroplane detecting trip-wire radar and the US space radar.

2.4.4 Lightning scattering

Lightning scattering has sometimes been observed on VHF and UHF over distance of about 500 km. The hot lightning channel scatters radio waves for a fraction of a second. The RF noise burst from the lightning makes the initial part of the open channel unusable and the ionization disappears soon because of combination at low altitude high atmospheric pressure. This mode has no practical use.

2.4.5 Diffraction

Knife-Edge diffraction is the propagation mode where radio waves are bent around sharp edges. For example, this mode is used to send radio signals over a mountain range when a line-of-sight path is not available. However, the angle cannot be too sharp or the signal will not diffract. The diffraction mode requires increased signal strength, so higher power or better antennas will be needed than for an equivalent line-of-sight path. Diffraction depends on the relationship between the wavelength and the size of the obstacle. In other words, the size of the obstacle in wavelengths.

Lower frequencies diffract around large smooth obstacles such as hills more easily. For example, in many cases where Vi IF (or higher frequency) communication is not possible due to shadowing by a hill, one lnds that it is still possible to communicate using the upper part of the

HF band where the surface wave is of little use. Diffraction phenomena by small obstacles are also important at high Frequencies. Signals for urban cellular telephony tend to be dominated by ground-plane effects as they travel over the rooftops of the urban environment. They then diffract over roof edges into the street, where multipath propagation, absorption and diffraction phenomena dominate.

2.4.6 Absorption

Low-frequency radio waves travel easily through brick and stone and VLF even penetrates seawater. As the frequency rises, absorption effects become more important. At microwave or higher frequencies, absorption by molecular resonance in the atmosphere (mostly water, H2O and oxygen, O2) is a major factor in radio propagation. For example, in the 58 - 60 GHz band, there is a major absorption peak which makes this band useless for long distance use.

This phenomenon was first discovered during radar research during World War II. Beyond around 400 GHz, the Earth's atmosphere blocks some segments of spectra while still passes some - this is true up to UV light, which is blocked by ozone, hut visible light and some of the NIR is transmitted.

CHAPTER THREE

(MODELLING AND MATHEMATICAL ANALYSIS)

(1) METHODOLOGY

This research involves obtaining the various transmitter and receiver parameters such as EIRP (effective isotropically radiated power), transmit power, received power, free space loss (fsl) at specified distances from the respective test GSM station in Lagos State, Nigeria. This research work is carried out using the existing path loss models suitable for vegetational areas in some parts of Lagos State. This work presents measurements taken at different spots in the investigated areas of Lagos State and the effect of pathloss on communication systems.

Hence, a site verification exercise was done using Sony Ericson K800 mobile station and a piece of compass. This is to ensure that the Base Transceiver Station (BTS) considered at different locations were performing optimally and does meet up with all stated parameters.

(2) STUDY AREA/INVESTIGATION AREA

Lagos falls within the western part of Nigeria vegetation zone. This investigation was carried out in different locations within Lagos State, southwest of Nigeria. Lagos State is 60 35'N and 30 45'E on the chart with total distance of 3,475.1km2 and population of 18 million and above. A goggle map of these areas was taking along with BTS mast antenna.

(3) THE TEST MOBILE STATION

The test mobile phone connects to the personal computer and it's used to initiate calls during the data collection.

(4) EXPERIMENTAL EQUIPMENT SET-UP

The experiment is set-up usually using a set of equipment as connected below in a moving vehicle.

Power Supply Unit

PC GPS

Test Mobile Phone

Figure 3.1: Experimental Equipment Set-Up

(5) Global Positioning Satellite (GPS)

The global positioning system (GPS) operates with global positioning satellite to provide the location tracking for the system during data collection. It enables the system to determine its position on a global map which has been installed on the personal computer (PC).

(6) Data Collection

In this work, a lot of GSM Base Stations (BS) planted in the town in different locations of the same GSM network operator although only some few ones were considered in this work.

In the investigated area where the measurements were taken, the highest foliage is about 100m, the small trees and buildings are sparsely located around the town and village. In order to generate measurements of signal strength level for the uplink and downlink at the investigated point for a particular area all using Terminal Equipment Mobile Station (TEMS) software. This is very useful when carrying out a drive test around the investigated areas.

(7) Theoretical Propagation Mode/Large-Scale Propagation Mechanism

This work introduces the basic theoretical propagation models which are initially put into consideration and are now being classified into free space model, smooth plane earth propagation, Cost - 231, Hata, Okumura - Hata Model, Exponential decay model, the ITU-R (maximum alternation) model.

(a) Free Space Propagation Model Analysis

Free space transmission is the primary consideration in all wireless communication system. In other words, every communication system takes into consideration free space loss. The propagation model in free space begins when a wave is not reflected or absorbed through the normal propagation. It connotes that equal radiation of signals in all directions from the radiating source and propagate to an infinite distance with no reduction of signal strength. Hence, free space attenuation or loss increases as the frequency of propagation increases. For a particular unit of distance, this happens in the sense that higher frequencies definitely have smaller wavelengths in order to cover a specific distance.

ANALYSIS OF THE FREE SPACE MODEL

Consider the figure below in which the radiated power at a some distance from a transmitting antenna is inversely proportional to the square of the distance from the transmitting antenna

antenna is inversely proportional to the square of the distance from the transmitting antenna.

Radiator

Receiver

Area of sphere = 4r2

Rx (GR1 PR

d

Tx (Gy, Py

Figure 3.2: Free Space Model Diagram

Therefore, the power density at the receiver in watt/m2 is given as

Power density (3.1)

Where the surface area is tangent to the measurement point with the antenna at the centre. Mathematically, it can be expressed as

(3.2)

Then, the effective power density Power density * gain

(3.3)

The antenna gain ( (3.4)

Where is transmitting antenna and is antenna efficiency

The receiver would also be of the same type as the transmitter so that the receiver's and the receiver's efficiency diminish the receiver's power by the factor.

Thus, (3.5)

= (3.6)

Noting that the receiver gain is also given as ;

4Ï€ ( 3.7)

= ( 3.8)

Substitute equation (3.8) into equation (3.6)

* ( 3.9)

(3.10)

Equation (3.10) can equally be expressed in decibel (dB) as follows

10 (3.1 1)

Equation (3.11) is called Transmitter- Receiver Formula.

Therefore, in an isotropic medium, antenna transmits signals evenly and equally in all directions. Hence, for basic transmission free space path loss denoted as L, is defined as the reciprocal of equation (3.10) which is the ratio of transmitted power to the received power usually expressed in decibel. For transmission between isotropic antennas, the gain of the receiver and transmitter assumes the value of unity(1).

L = / = 2 (3.12)

Expressing equation (3.12) in decibel (dB)

L(dB) = = ( 3.13)

Note: A path loss is a gain that is viewed as a loss.

(b)Plane Earth Loss:

The free space propagation model consideration in the previous paragraph does not take into account the effects of propagation over ground. If we now consider the effect of the earth surface, the expression of the received signal becomes more complicated. The figure below depicts a typical diagram for plane earth loss model where by R and d are heights of transmitter and receiver and distance between the transmitter and receiver.

hy

Transmitter

Receiver

hR

d

Figure 3.3: Plane Earth Loss

For (theoretical) isotropic antenna above a plane earth, the received electric field strength is given as

(1 + + (1- )F. +…) (3.14)

Where is the reflection and is the field strength for propagation in free space. This expression can be interpreted as the complex sum of a direct line of sight wave, a ground reflected wave and a surface wave.

For a horizontally polarized wave incident on the surface of a perfectly smooth earth, the reflection coefficient is given as

Where is the reflection dielectric constant of the earth,φ is the angle of incidence(between the radio ray and the earth surface) and X is given as

X = ( 3.15)

With s being the conductivity of the ground and is the dielectric constant of the vacuum.

For vertical polarization, is given as

= (3.16)

Therefore, the relative amplitude F(.) of the surface wave is very small for most cases of mobile UHF communication (F(.) ).Its contribution is relevant only a few wavelength above the ground.

Analysis of Plane Earth Loss

Referring to the figure 3.1 above, the phase difference () between the direct and the ground- reflected wave can be found from two-ray approximation considering only a line of sight and a ground reflection. By denoting the transmit and receive antenna Heights as respectively, the phase difference can be expressed as

= ( 3.17)

For d, one finds using the expression below

1+ (3.18)

= * (3.19)

For large d (d ), the reflection coefficient tends to so the received signal( is given

= (3.20)

For propagation distance substantially beyond the turn over point i.e. d= this tends to the fourth power distance law written as

= ( 3.21)

Hence, the plane earth path loss is given as

= 40 -20-20 (3.22)

Experiments confirm that in macro-cellular links over smooth, plane terrain, the received signal power(expressed in dB) decreases with" 40".

In contrast to the theoretical plane earth loss, Egli measured a significant increase of the path loss with the carrier frequency ().He further proposed the semi- empirical model to be

= ( 3.23)

In addition, Egli introduced a frequency dependent empirical correction for ranges 1 and carrier frequencies 30MHz 1GHz.

Propagation model Types

The path loss propagation can usually be modelled in three different ways namely empirical model approach, deterministic model approach and stochastic model approach.

The empirical models are usually based on observation and measurements taken alone in the site which are normally used to forecast the path loss. Deterministic model uses a form of law governing the electromagnetic wave propagation to compute the receive signal power at a particular location .While stochastic model requires a complete and comprehensive details usually in 3-D map form of the propagation environment.

The deterministic and stochastic models are often used with least accuracy but require the least information pertaining to the environment.

However, for the determination of path loss at each distance, empirical method was chosen because of its applicability with the investigated environment and it has merits over the other models such as high level of accuracy, simplicity and clarity. The aforediscussed theoretical propagation models above such as free space, plane earth loss may require critical details of the site location, dimension, and constitutive parameters of every foliage. This is complex and tedious.But, there are many forms of empirical prediction among few are Okumura-Hata model, COST-231 model, Weissberger model, Early ITU model and Updated ITU-R model. All these models may actually proffers solution to the poor quality of network service by telecommunications outfits and as well may address the problem drop calls experienced by GSM subscribers in Lagos State but Weissberger model and Updated ITU-R model are suitable for this research work because of the features the investigated environment posseses.Therefore,in this work,Weissberger model is chosen.

(a)Early ITU-R Vegetation Model

Although, it has been superceded by another ITU model but it's still useful to compute the path loss where the frequency of propagation is in Megahertz.Mathematically,it can be expressed as

L(dB) = 0.2 (3.24)

Hence, the performance of the above model can be investigated against the measured data obtained on site.

(b) Updated ITU Model

This model is fairly specific and does not cover all possible scenarios. One key element of this model is that the total losses obtained by the foliage or vegetation are limited. The reason why it's preferable is that it assumes there is always a diffraction path as depicted in the figure below.

Word land

Diffraction path

Figure 3.4: Updated ITU - Model

There are two approached to this kind of model.

Case One

The first scenario is when the first terminal (antenna) is at wildlife in the forest (thick bushes). The figure below shows this.

d

Antenna B

Antenna A

Figure 3.5: Updated ITU - Model When one of the Antennas is Outside the Foliage

The attenuation due to particular vegetation specifically is given as

= ( 3.25)

Where Am = maximum attenuation for one terminal between a specific type and depth of vegetation.

Aer = Attenuation due specifically to a particular vegetation.

d = distance

y = specific attenuation for very short vegetation path.

Case Two

The second approach is when a single type of vegetation of obstruction where foliage or vegetation is between the two antennas.

Foliage in between two antennas

Figure 3.6: Updated ITU - Model the Foliage is in between Two Antennas

When the frequency of propagation is at or less than 3GHz, the vegetation loss model is simplified as Aer = dy where d and y have the same interpretations as the first approach.

It should be noted that d is the length of path within trees in meters, y is the specific attenuation for very short vegetation paths in decibel per metre. Am is the maximum attenuation for one terminal within a specific type and depth of vegetation in decibel. It depends on the types and density of the vegetation, plus the antenna pattern of the terminal within the vegetation and the vertical distance between the antenna and the top of the vegetation.

A frequency dependence of Am (dB) is of the form given below.

Am = A1 f (3.26)

Where f is the frequency, A and  are the constants.

In addition, the path loss (net) for this kind of foliage is computed as

L = Lfs (dB) + Lwm(dB) (3.27)

Where Lfs = free space path loss

Lwm = Weissberger model attenuation loss

(c) Weissberger Model:

This is one of the models used in a vegetation area in which losses are due to foliage where the signals fall exponentially. In a point to point communication link, a lot do happen. For instance, a scenario can be created in which both transmitter and are fixed. In cellular telecommunication system, the cells are fixed but subscribers change position. A good example of this is a moving car and a fixed base station .Moreso, both can be moving e.g. a mobile NTA station trying to broadcast from a street. Mathematically, Weissberger model equation can be expressed as;

14m≤ (3.28)

(3.29)

Where F is frequency in GHz, is depth of the foliage along the line of sight(LOS).This model is used when the propagation path is blocked, by a dense, dry and leafy trees. The frequency ranges from 230MHz to 95GHz.

Path loss Computations

In the path loss cases consider, various frequencies ranging from 7,700MHz to 19GHz were used for the computation. The respective distances of transmitter to the foliage were varied from 20m to 100m while their corresponding path losses were calculated.

PARAMETERS MEASURED FOR DIFFERENT CASES

Case I VE 1034 - LAG 419A (ELEKO)

EIRP(dBm)=46.6,TX Power(watts)=0.05,TX Power(dBm)=17.00,RX Threshold level(dBm)=-83.00,Maximum received signal(dBm)=-20.00.

Case II LAG 127A - LAG 441C (OPEBI AXIS)

EIRP(dBm) =55.7,TX Power(watts)=0.16,TX Power(dBm)=22.00,RX Threshold level(dBm)=-85.00,Maximum received signal(dBm)=-15.00.

Case III LAG 804B - LAG 412C (AGBOWA IKOSI - IMOTA, IKORODU, LAGOS)

EIRP(dBm) =54.3,TX Power(watts)=0.16,TX Power(dBm)=22.00,RX Threshold level(dBm)=-90.00,Maximum received signal(dBm)=-15.00.

Case IV LAG 757B - LAG 814A (CHEVRON - ALPHA BEACH)

EIRP(dBm) =48.6,TX Power(watts)=0.0501,TX Power(dBm)=17.00,RX Threshold level(dBm)=-88.00,Maximum received signal(dBm)=-20.00.

Case V LAG 135A - LAG 294 (BADAGR AXIS)

EIRP(dBm) =41.7,TX Power(watts)=0.0501,TX Power(dBm)=17.00,RX Threshold level(dBm)=-88.00,Maximum received signal(dBm)=-20.00.

Case VI ( LAG 960A - LAG901A)

EIRP(dBm) =45.6,TX Power(watts)=0.0501,TX Power(dBm)=17.00,RX Threshold level(dBm)=-86.00,Maximum received signal(dBm)=-20.00.

Case VII (VE1033A - VE1003A)

EIRP(dBm)=47.3,TX Power(watts)=0.16,TX Power(dBm)=22.00,RX Threshold level(dBm)=-91.00,Maximum received signal(dBm)=-15.00.

Case VIII (VE10330 - LAG 403F) BADORE, LAGOS

EIRP(dBm) =54.30,TX Power(watts)=0.16,TX Power(dBm)=22.00,RX Threshold level(dBm)=-90.00,Maximum received signal(dBm)=-15.00.

Case 1: VE1034 -LAG 419A( ELEKO,LAGOS)

Path length=3122m,F=18GHz, =20m

Using Weissberger model of eqn (3.28)

=17.59 dB

=

= 127.43 dB

The total path loss =+ =127.43+17.59

=145.02 dB

When =40m, F= 18GHz

=26.45 dB

The total path loss =+ =127.43+26.45

=153.88 dB

When =60m, F= 18GHz

=33.57 dB

The total path loss =+ =127.43+33.57

=160.10 dB

When =80m, F= 18GHz

=39.75 dB

The total path loss =+ =127.43+39.75

=167.18 dB

When =100m, F= 18GHz

=45.33 dB

The total path loss =+ =127.43+45.33

=172.76 dB

Case 2 LAG441C -LAG 127A (OPEBI AREA)

F= 19 GHz, path length =3820m

=17.87 dB

=

= 129.66 dB

The total path loss =+ =129.66+17.87

=147.53 dB

When =40m, F= 19GHz

=26.86 dB

The total path loss =+ =129.66+26.86

=156.52 dB

When =60m, F= 19GHz

=34.09 dB

The total path loss =+ =129.66+34.09

=163.75 dB

When =80m, F= 19GHz

=40.37 dB

The total path loss =+ =129.66+40.37

=170.03dB

When =100m, F= 19GHz

=46.03 dB

The total path loss =+ =129.66+46.03

=175.69 dB

Case 3 LAG804B -LAG 412C (AGBOWA IKOSI-IMOTA)

Path length=5020m, F=18GHz, =20

=17.59 dB

=

= 131.56 dB

The total path loss =+ =131.56+17.59

=149.15 dB

When =40m, F= 18GHz

=26.45 dB

The total path loss =+ =131.56+26.45

=158.01 dB

When =60m, F= 18GHz

=33.57 dB

The total path loss =+ =131.56+33.57

=165.13 dB

When =80m, F= 18GHz

=39.75 dB

The total path loss =+ =131.56+39.75

=171.31dB

When =100m, F= 18GHz

=45.33 dB

The total path loss =+ =131.56+45.33

=176.89dB

Case 4: LAG757B -LAG 814A (CHEVRON-ALPHA BEACH)

Path length=2800m, F=7.7GHz, =20m

Using Weissberger model of eqn (3.28)

=13.82 dB

=

= 119.11 dB

The total path loss =+ =119.11+13.82

=132.93 dB

When =40m, F= 7.7GHz

=20.78 dB

The total path loss =+ =119.11+20.78

=139.89dB

When =60m, F= 7.7GHz

=26.37 dB

The total path loss =+ =119.11+26.37

=145.48 dB

When =80m,Ff= 7.7GHz

=31.23 dB

The total path loss =+ =119.11+31.23

=150.34 dB

When =100m,F= 7.7GHz

=35.61 dB

The total path loss =+ =119.11+35.61

=154.72 dB

Case 5 : LAG135A -LAG 294( BADAGRY AXIS)

Path length=5020m,F=13GHz, =20m

Using Weissberger model of eqn(3.28)

=16.04 dB

=

= 128.73 dB

The total path loss =+ =128.73+16.04

=144.77 dB

When =40m,f= 13GHz

=24.11 dB

The total path loss =+ =128.73+24.11

=152.84 dB

When =60m,f= 13GHz

=30.60 dB

The total path loss =+ =128.73+30.60

=159.33 dB

When =80m,f= 13GHz

=36.24 dB

The total path loss =+ =128.73+36.24

=164.97 dB

When =100m,f= 13GHz

=41.32 dB

The total path loss =+ =128.73+41.32

=170.05 dB

Case 6: LAG980A -LAG 901A( IKEJA)

F= 19 GHz, path length =2710m

=17.87 dB

=

= 126.67 dB

The total path loss =+ =126.67+17.87

=144.55 dB

When =40m,f= 19GHz

=26.86 dB

The total path loss =+ =126.67+26.86

=153.53 dB

When =60m,f= 19GHz

=34.09 dB

The total path loss =+ =126.67+34.09

=160.76 dB

When =80m,f= 19GHz

=40.37 dB

The total path loss =+ =126.67+40.37

=167.04dB

When =100m,f= 19GHz

=46.03 dB

The total path loss =+ =126.67+46.03

=172.70 dB

Case 7: VE1033A-VE1003A

Path length=760m,F=18GHz, =20m

Using Weissberger model of eqn(3.28)

=17.59 dB

=

= 115.16 dB

The total path loss =+ =115.16+17.59

=132.75 dB

When =40m,f= 18GHz

=26.45 dB

The total path loss =+ =115.16+26.45

=141.61 dB

When =60m,f= 18GHz

=33.57 dB

The total path loss =+ =115.16+33.57

=148.73 dB

When =80m,f= 18GHz

=39.75 dB

The total path loss =+ =115.16+39.75

=154.91 dB

When =100m,f= 18GHz

=45.33 dB

The total path loss =+ =115.16+45.33

=160.49 dB

Case 8: VE1030 -LAG 403F( BADORE,LAGOS)

Path length=2670m,F=18GHz, =20m

Using Weissberger model of eqn(3.28)

=17.59 dB

=

= 126.08 dB

The total path loss =+ =126.08+17.59

=143.67 dB

When =40m,f= 18GHz

=26.45 dB

The total path loss =+ =126.08+26.45

=152.53 dB

When =60m,f= 18GHz

=33.57 dB

The total path loss =+ =126.08+33.57

=159.65 dB

When =80m,f= 18GHz

=39.75 dB

The total path loss =+ =126.08+39.75

=165.83 dB

When =100m,f= 18GHz

=45.33 dB

The total path loss =+ =126.08+45.33

=171.41 dB

From the mathematical analysis done in this chapter, it can be inferred that the various path losses obtained varied from one location to another due to the fact different path length and frequencies were used.

CHAPTER FOUR

RESULTS AND DISCUSSION

4.0. RESULTS.

The vegetation path loss in Weissberger model will be analyzed after the computation in the previous chapter. The Weissberger model was used in various frequencies ranging from 7,700MHz to 19,000MHz (different locations within Lagos State) with the respective foliage distances (df) from the transmitting antenna varying from 20m to 100m and their corresponding Weissberger loss and total path loss were computed assuming that the transmitting and receiving antennas have a gain of OdB.

After the above computations were anatically and carefully done,the following were obtained

Case I VE 1034 - LAG 419A (ELEKO)

Table 4.1 Results at 18GHz for df ranging from 20m to 100m for d = 3122m

Elevation(m)

df (m)

path length(km)

Path loss (dB)

Total path loss (dB)

1

5

28

0.624

17.59

145.02

2

10

40

1.249

26.45

153.88

3

15

60

1.249

33.57

160.10

4

20

80

1.250

39.75

167.18

5

25

100

3.120

45.33

172.76

CASE 1

Foliage dist

Measured Ploss

Calculated Ploss

20

16.87

17.59

40

24.53

26.45

60

31.75

33.57

80

35.6

39.75

100

43.2

45.33

Case II LAG 127A - LAG 441C (OPEBI AXIS)

Table 4.2 Results at 19GHz for df ranging from 20m to 100m for d = 3820m

Elevation(m)

df (m)

path length(km)

Path loss (dB)

Total path loss (dB)

1

10

20

0.764

17.87

147.53

2

20

40

1.528

26.86

156.52

3

30

60

2.292

34.09

163.75

4

40

80

3.056

40.37

170.63

5

50

100

3.82

46.03

175.69

CASE II

Foliage dist

Measured Ploss

Calculated Ploss

20

17.03

17.87

40

25.73

26.86

60

32.37

34.09

80

39.23

40.37

100

44.86

46.03

Case III LAG 804B - LAG 412C (AGBOWA IKOSI - IMOTA, IKORODU, LAGOS)

Table 4.3 Results at 18GHz for df ranging from 20m to 100m for d = 5020m

Elevation(m)

df (m)

path length(km)

Path loss (dB)

Total path loss (dB)

1

10

20

1.004

17.59

149.15

2

20

40

2.008

26.45

158.01

3

30

60

3.012

33.57

165.13

4

40

80

4.016

39.75

171.31

5

50

100

5.20

45.33

176.89

CASE III

Foliage dist

Measured Ploss

Calculated Ploss

20

16.95

17.59

40

25.03

26.45

60

32.45

33.57

80

38.06

39.75

100

44.75

45.33

Case IV LAG 757B - LAG 814A (CHEVRON - ALPHA BEACH)

Table 4.4 Results at 7.7GHz for df ranging from 20m to 100m for d = 3122m

Elevation(m)

df (m)

path length (km)

Path loss (dB)

Total path loss (dB)

1

2

20

0.560

13.82

132.93

2

4

40

1.120

20.78

139.89

3

6

60

1.680

26.37

145.48

4

8

80

2.240

31.23

150.34

5

10

100

2.80

35.61

154.72

CASE IV

Foliage dist

Measured Ploss

Calculated Ploss

20

12.75

13.82

40

19.14

20.78

60

25.27

26.37

80

30.45

31.23

100

34.07

35.61

Case V LAG 135A - LAG 294 (BADAGR AXIS) d = 5.002km

Table 4.5 Results at 13GHz for df ranging from 20m to 100m for d = 5020m

Elevation(m)

df (m)

path length (km)

Path loss (dB)

Total path loss (dB)

1

6

20

1.004

16.04

144.77

2

12

40

2.008

24.11

152.84

3

18

60

3.012

30.60

159.33

4

24

80

4.016

36.24

164.97

5

30

100

5.020

41.32

170.05

CASE V

Foliage dist

Measured Ploss

Calculated Ploss

20

15.75

16.04

40

23.28

24.11

60

29.13

30.60

80

34.75

36.24

100

40.52

41.32

Case VI LAG 960A - LAG901A

Table 4.6 Results at 19GHz for df ranging from 20m to 100m for d = 2710m

Elevation(m)

df (m)

path length (km)

Path loss (dB)

Total path loss (dB)

1

9

20

0.542

17.87

144.55

2

18

40

1.084

26.86

153.53

3

27

60

1.626

34.09

160.76

4

36

80

2.168

40.37

167.04

5

45

100

2.710

46.03

172.70

CASE VI

Foliage dist

Measured Ploss

Calculated Ploss

20

17.03

17.87

40

25.73

26.86

60

32.37

34.09

80

39.23

40.37

100

44.86

46.03

Case VII (a) L=760m (VE1033A - VE1003A)

Table 4.7 Results at 18GHz for df ranging from 20m to 100m for p = 760m

Elevation(m)

df (m)

path length (km)

Path loss (dB)

Total path loss (dB)

1

10

20

0.152

17.59

132.75

2

20

40

0.304

26.45

142.61

3

30

60

0.456

33.57

148.73

4

40

80

0.608

39.75

154.91

5

50

100

0.760

45.33

160,49

CASE VII

Foliage dist

Measured Ploss

Calculated Ploss

20

16.95

17.59

40

25.03

26.45

60

32.45

33.57

80

38.06

39.75

100

44.75

45.33

Case VIII L=2670m (VE10330 - LAG 403F) BADORE, LAGOS

Table 4.8 Results at 18GHz for df ranging from 20m to 100m for d = 2670m

Elevation(m)

df (m)

path length (km)

Path loss (dB)

Total path loss (dB)

1

4

20

0.534

17.59

143.67

2

8

40

1.068

26.45

152.53

3

12

60

1.602

33.57

159.65

4

16

80

2.136

39.75

165.83

5

20

100

2.670

45.33

171.41

CASEVIII

Foliage dist

Measured Ploss

Calculated Ploss

20

16.95

17.59

40

25.03

26.45

60

32.45

33.57

80

38.06

39.75

100

44.75

45.33

ANALYSIS OF RESULTS

The analysis of the tables above is presented as follows

Table 4.9 Analysis of table 4.8 showing different parameters

Elevation (m)

df

Path Lenght

Pathloss (dB)

Total Pathloss (dB)

N

Valid

5

5

5

5

5

Missing

0

0

0

0

0

Mean

30.00

60.00

.45600

32.5380

147.6980

Std. Error of Mean

7.071

14.142

.107480

4.88477

4.88477

Median

30.00

60.00

.45600

33.5700

148.7300

Std. Deviation

15.811

31.623

.240333

10.92268

10.92268

Variance

250.000

1000.000

.058

119.305

119.305

Table 4.10 Analysis of table 4.7 showing different parameters

Total Pathloss (dB)

Path Lenght

Pathloss (dB)

N

Valid

5

5

5

Missing

0

0

0

Mean

158.6180

1.60200

32.5380

Std. Error of Mean

4.88477

.377595

4.88477

Median

159.6500

1.60200

33.5700

Std. Deviation

10.92268

.844328

10.92268

Variance

119.305

.713

119.305

Table 4.11 Analysis of table 4.6 showing different parameters

Elevation (m)

df

Path Lenght

Pathloss (dB)

Total Pathloss (dB)

N

Valid

5

5

5

5

5

Missing

0

0

0

0

0

Mean

27.00

60.00

1.62600

33.0440

159.7160

Median

27.00

60.00

1.62600

34.0900

160.7600

Std. Deviation

14.230

31.623

.856977

11.08933

11.08591

Variance

202.500

1000.000

.734

122.973

122.897

Table 4.12 Analysis of table 4.5 showing different parameters

Elevation (m)

df

Path Lenght

Pathloss (dB)

Total Pathloss (dB)

N

Valid

5

5

5

5

5

Missing

0

0

0

0

0

Mean

18.00

60.00

3.01200

29.6620

158.3920

Median

18.00

60.00

3.01200

30.6000

159.3300

Std. Deviation

9.487

31.623

1.587463

9.95543

9.95543

Variance

90.000

1000.000

2.520

99.111

99.111

Table 4.13 Analysis of table 4.4 showing different parameters

Elevation (m)

df

Path Length

Pathloss (dB)

Total Pathloss (dB)

N

Valid

5

5

5

5

5

Missing

0

0

0

0

0

Mean

6.00

60.00

1.68000

25.5620

144.6700

Median

6.00

60.00

1.68000

26.3700

145.4800

Std. Deviation

3.162

31.623

.885438

8.58026

8.58368

Variance

10.000

1000.000

.784

73.621

73.680

Table 4.14 Analysis of table 4.3 showing different parameters

Elevation (m)

df

Path Lenght

Pathloss (dB)

Total Pathloss (dB)

N

Valid

5

5

5

5

5

Missing

0

0

0

0

0

Mean

30.00

60.00

3.01200

32.5380

164.0980

Median

30.00

60.00

3.01200

33.5700

165.1300

Std. Deviation

15.811

31.623

1.587463

10.92268

10.92268

Variance

250.000

1000.000

2.520

119.305

119.305

Table 4.15 Analysis of table 4.2 showing different parameters

Elevation (m)

df

Path Lenght

Pathloss (dB)

Total Pathloss (dB)

N

Valid

5

5

5

5

5

Missing

0

0

0

0

0

Mean

30.00

60.00

2.29200

33.0440

162.7040

Median

30.00

60.00

2.29200

34.0900

163.7500

Std. Deviation

15.811

31.623

1.207990

11.08933

11.08933

Variance

250.000

1000.000

1.459

122.973

122.973

Table 4.16 Analysis of table 4.1 showing different parameters

Elevation (m)

df

Path Lenght

Pathloss (dB)

Total Pathloss (dB)

N

Valid

5

5

5

5

5

Missing

0

0

0

0

0

Mean

15.00

60.00

1.49840

32.5380

159.7880

Median

15.00

60.00

1.24900

33.5700

160.1000

Std. Deviation

7.906

31.623

.946079

10.92268

10.90883

Variance

62.500

1000.000

.895

119.305

119.003

The two dimensional graphs of the analysis of results of the different cases considered are shownbelow;

Figure a.The graph of measured and calculated pathloss Vs Foliage distance(CaseI).

Figure b.The graph of measured and calculated pathloss Vs Foliage distance(CaseII).

Figure C.The graph of measured and calculated pathloss Vs Foliage distance(CaseIII).

Figure d.The graph of measured and calculated pathloss Vs Foliage distance(CaseIV).

Figure e.The graph of measured and calculated pathloss Vs Foliage distance(CaseV).

Figure f.The graph of measured and calculated pathloss Vs Foliage distance(CaseVI).

Figure g.The graph of measured and calculated pathloss Vs Foliage distance(CaseVII).

Figure h.The graph of measured and calculated pathloss Vs Foliage distance(CaseVIII).

Fig 4.1:Frequency versus Elevation for case VIII

Fig 4.2 Frequency: versus path length for case VIII

Fig 4.3: Frequency versus foliage distance (df) for case VIII

Fig 4.4: Frequency versus path loss for case VIII

Fig 4.5: Frequency versus Total path loss for case VIII

Fig 4.6: Frequency versus Total path loss with standard deviation for case VII

Fig 4.7: Frequency versus path length with mean for case VII

Fig 4.8: Frequency versus path loss for case VII

Fig 4.9: Frequency versus Elevation for case VII

Fig 4.10: Frequency versus foliage distance ranging from 20m to 100m for case VII

Fig 4.11:Frequency versus path length for case VI

Fig 4.12:Frequency versus path loss for case VI

Fig 4.13:Frequency versus Total path loss for case VI

Fig 4.14:Frequency versus Elevation for case VI

Fig 4.15:Frequency versus Foliage distance ranging from 20m to 100m for case VI

Fig 4.16:Frequency versus Foliage distance ranging from 20m to 100m for case V

Fig 4.17:Frequency versus path length for case V

Fig 4.18:Frequency versus path loss for case V

Fig 4.19:Frequency versus Total path loss for case V

Fig 4.20:Frequency versus Elevation for case V

Fig 4.21: Frequency versus Foliage distance ranging from 20m to 100m for case IV

Fig 4.22:Frequency versus path length for case IV

Fig 4.23:Frequency versus path loss for case IV

Fig 4.24:Frequency versus Total path loss for case IV

Fig 4.25:Frequency versus Elevation for case IV

Fig 4.26: Frequency versus Foliage distance ranging from 20m to 100m for case III

Fig 4.27:Frequency versus path length for case III

Fig 4.28:Frequency versus path loss for case III

Fig 4.29:Frequency versus Total path loss for case III

Fig 4.30:Frequency versus Elevati

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