M.N.Jayaram, Dept. of E&C, SJCE, Mysore - 06 88

CHAPTER 4

Indoor and Outdoor Propagation Models

Introduction

A radio propagation model, also known as the radio frequency propagation

model, is an empirical mathematical formulation for the characterization of radio

wave propagation as a function of frequency, distance and other conditions .A single

model is usually developed to predict the behavior of propagation for all similar links

under similar constraints. Created with the goal of formalizing the way radio waves

are propagated from one place to another, such models typically predict the path loss

along a link or the effective coverage area of a transmitter.

4.1 Channel Models

There are different types of channel models in underground communication.

These models vary from one situation to other based on number of parameters .

Modeling is different for tunnels as compared to mines . Some of the important

models used in underground communication are :

4.1(a) The Geometrical Optical (GO) Model

In recent years, the computational and visualization capabilities of computers

have accelerated rapidly. Predicting radio signal coverage involve the use of Site

Specific ( SISP ) propagation models and Graphical Information System ( GIS )

databases .SISP models support ray tracing as a means of deterministically modeling

any indoor or outdoor propagation environment . Through the use of terrain databases,

which may be drawn or digitized using standard graphical software packages, wireless

system designers are able to include accurate representation of terrain features. Hence

GO model uses geometrical optics, which traces all the paths from the transmitter to

the receiver. The ray path includes LOS path, multi path reflections etc [75].

M.N.Jayaram, Dept. of E&C, SJCE, Mysore - 06 89

4.1b The Waveguide Model

This is mainly used in modeling the tunnel channels. Here we consider the

underground wireless channel as an oversized wave guide with imperfect loss walls.

Due to lossy dielectric characteristic of walls, ceilings electromagnetic wave gets

strongly attenuated. Also vehicles inside the tunnel act as obstructing units for the

signal (Fig 4.1).

Fig 4.1 - Tunnel with obstructions.

Using Geometrical Optical (GO) Model, EM distribution for the excitation

plane is determined. Multiple waveguide modes propagating inside the guide is based

on excitation and under goes different levels of attenuation. The effective field

distribution will be the algebraic sum of all the modes as shown in Fig 4.2.

Fig 4.2 - Effective field distribution

Once the mode intensity is determined in the excitation plane, the propagation

of each mode is mostly governed by the tunnel itself. Hence the EM field of the rest

of the tunnel can be accurately predicted by summing the EM field of each mode.

Position of antenna determines mode intensity. Mode attenuation is determined by

tunnel size and operating frequency .Material of tunnel, humidity, pressure and

temperature determine signal propagation. In practical tunnel traffic produces

additional signal loss of a guided mode.

M.N.Jayaram, Dept. of E&C, SJCE, Mysore - 06 90

4.1(c) Room-and-Pillar Model

This is used in underground mines, where there are number of paths to a given

entrance. Mine is considered as a big room with number of pillars. Structure of

mining area is important. By characterizing the room and pillars with the help of

dielectric constants modeling is done.

4.1(d) The Full Wave Model

This utilizes numerical solutions to solve the temporal and spatial Maxwell's

equations with approximate boundary conditions to model the signal propagation in

underground mines.

Some of the important limitations of above models are:

• These models are not general but are site limited or applicable to a

particular situation .eg: Mine/tunnel with a particular geometry or terrain, at a

particular frequency.

• They don’t consider all the signal losses for modeling .Consider only

penetration & Multipath fading losses.

• Geometrical optical model & full wave models don’t consider

frequency as a parameter for modeling. Frequency is important because depth of

penetration, bending of wireless signals and most of the losses depends on frequency.

• In optical modeling ray path tracing is difficult.

• In wave guide modeling all the times they consider the geometry as

rectangular. This is not true in mines with circular and other types of complex

geometry.

In Maxwell’s equation modeling several approximations regarding boundary

conditions like smooth surface, infinite conductivity etc are assumed. This is not true

because soil conductivity changes with moisture, Mine terrain is not smooth.

M.N.Jayaram, Dept. of E&C, SJCE, Mysore - 06 91

Hence we have considered a different type of modeling where we can consider

all losses, overcome some of the problems faced by the above models.

4.2 Path Loss

Path loss (or path attenuation) is the reduction in power density of an

electromagnetic wave as it propagates through space or underground. This term is

commonly used in wireless communications and signal propagation. Path loss may be

due to many effects, such as free-space loss, refraction, diffraction, reflection,

aperture-medium coupling loss, and absorption. Path loss is also influenced by terrain

contours, environment, propagation medium (dry or moist air), the distance between

the transmitter and the receiver and the height and location of antennas.

4.2(a) Causes for path loss

Path loss normally includes propagation losses caused by the natural

expansion of the radio wave front in free space (which usually takes the shape of an

ever-increasing sphere), absorption losses (sometimes called penetration losses), when

the signal passes through media not transparent to electromagnetic waves, diffraction

losses when part of the radio wave front is obstructed by an opaque obstacle, and

losses caused by other phenomena.

The signal radiated by a transmitter may also travel along many and different

paths to a receiver simultaneously; this effect is called multipath. Multipath can either

increase or decrease received signal strength, depending on whether the individual

multipath wave fronts interfere constructively or destructively. The total power of

interfering waves in a Rayleigh fading scenario vary quickly as a function of space

(which is known as small scale fading), resulting in fast fades which are very sensitive

to receiver position.

4.2(b) Prediction of path loss

Calculation of the path loss is usually called prediction. Exact prediction is

possible only for simpler cases, such as the above-mentioned free space propagation

M.N.Jayaram, Dept. of E&C, SJCE, Mysore - 06 92

or the flat-earth model. For practical cases the path loss is calculated using a variety of

approximations.

Statistical methods (also called stochastic or empirical) are based on measured

and averaged losses along typical classes of radio links. Among the most commonly

used such methods are Okumura-Hata, the COST-Hata model etc. These are also

known as radio wave propagation models. For wireless communications in the VHF

and UHF frequency band, one of the most commonly used methods is that of

Okumura-Hata as refined by the COST231 project. For FM radio and TV

broadcasting the path loss is most commonly predicted using the ITU model.

Deterministic methods based on the physical laws of wave propagation are

also used; ray tracing is one such method. These methods are expected to produce

more accurate and reliable predictions of the path loss than the empirical methods;

however, they are significantly more expensive in computational effort. For these

reasons they are used predominantly for short propagation paths. Among the most

commonly used methods in the design of radio equipment such as antennas and feeds

is the finite-difference time-domain method.

The path loss in other frequency bands (MW, SW, and Microwave) is

predicted with similar methods, though the concrete algorithms and formulas may be

very different from those for VHF/UHF. Reliable prediction of the path loss in the

SW/HF band is particularly difficult, and its accuracy is comparable to weather

predictions.

Easy approximations for calculating the path loss over distances significantly

shorter than the distance to the radio horizon:

In free space the path loss increases with 20 dB per decade (one decade

is when the distance between the transmitter and the receiver increases ten times) or 6

dB per octave (one octave is when the distance between the transmitter and the

receiver doubles). This can be used as a very rough first-order approximation for SHF

(microwave) communication links.

For signals in the UHF/VHF band propagating over the surface of the

Earth the path loss increases with roughly 35 to 40 dB per decade (10 to 12 dB per

octave). This can be used in cellular networks as a first guess.

M.N.Jayaram, Dept. of E&C, SJCE, Mysore - 06 93

Some of the important models are

4.3 Longley –Rice Model

It is applicable to point to point communication system in frequency range

40MHz to 100GHz. The median transmission loss is predicted using the path

geometry of the terrain profile and the refractivity of the troposphere, geometric

optics techniques is used to predict the signal strength. The demerit of this model is

that it doesn’t provide a way to determine correction due to environmental factors,

further multipath is not considered.

4.4 Durkin’s Model

It provides a perspective in to the nature of propagation over irregular terrain

and the losses caused by obstacles in a radio path.

The demerit of this model is it cannot predict propagation effects due to

foliage, buildings, and other manmade structures and doesn’t support multi path

communication.

4.5 Young’s Model

Young model is a Radio propagation model that was builds on the data

collected on New York City. It typically models the behavior of cellular

communication systems in large cities. It was built on the data at New York City in

1952. This model is ideal for modeling the behavior of the cellular communications in

large cities with tall structures. The coverage for this model is 150 MHz to 3700 MHz

The mathematical formulation for Young Model is:

L= GBGM . β ……….(4.1)

Where:

L = The Path loss. Unit: Decibel (dB)

GB = Gain of Base transmitter. Unit: Decibel (dB)

GM = Gain of Mobile transmitter. Unit: Decibel (dB)

Hb = Height of Base station antenna. Unit: Meter (m)

M.N.Jayaram, Dept. of E&C, SJCE, Mysore - 06 94

Hm = Height of Mobile station antenna. Unit: Meter (m)

d = Link distance. Unit: Kilo Meter (km)

β = Clutter factor

4.6 Okumura Model

One of the most widely used models for signal prediction. Operational

frequency range from 150 MHz- 1920MHz. But it can be extended up to 3000MHz.

Distances range from 1km-100km and antenna height range from 30-1000m. It is the

simplest and best in terms of accuracy.

Major demerit is its slow response to rapid changes in terrain.

Formula for Okumura Model is expressed as:

Lm (dB) = LF (d) + Amu(f,d) – G (hM) – G(hB) – GAREA ….(4.2)

Where;

Lm = (i.e., median) of path loss

LF (d) = free space propagation path loss.

Amu (f, d) = median attenuation relative to free space

G (hB) = base station antenna height gain factor

G (hM) = mobile antenna height gain factor

G (hB) = 20log (hB/200) 1000m > hB > 30m

G (hM) = 10log (hM/3) hM<= 3m

G (hM) = 20log (hM/3) 10m > hM > 3m

GAREA: gain due to type of environment given in suburban, urban or open area

This Okumura Model probably remains the most widely quoted of the

available models. It has come to be used as a standard by which to compare others

since it is intended for use over a wide variety of radio paths encompassing not only

urban areas but also different types of terrain.

M.N.Jayaram, Dept. of E&C, SJCE, Mysore - 06 95

4.7 Hata Model

It is an empirical formulation of graphical path loss data provided by

Okumura and is valid from 150MHz-1500MHz. Hata established empirical

mathematical relationships to describe the graphical information given by Okumura.

Hata’s formulation is limited to certain ranges of input parameters and is applicable

only over quasi-smooth terrain.

The mathematical expression and their ranges of applicability are as follows:

L (db) = 69.55 + 26.16fc - 13.82loghte - a (hre) + (44.96.55loghte) log10d …(4.3)

Carrierfrequency: 150MHz≤ fc ≤1500MHz

Base station antenna height (hte): 30m ≤ hb ≤ 200m

Mobile unit antenna height (hre): 1m ≤ hm ≤ 10m

Transmission distance (d):1km≤ d ≤ 20 km

These expressions have considerably enhanced the practical value of the

Okumura method, although Hata’s formulations do not include any of the path

specific corrections available in the original model.

4.8 Cost 231 Model

COST (COperation européenne dans le domaine de la recherche Scientifique

et Technique) is a European Union Forum for cooperative scientific research which

has developed this model accordingly to various experiments and researches. Also

called the Hata Model PCS Extension, it is a radio propagation model that extends the

Hata Model (which in turn is based on the Okumura Model) to cover a more

elaborated range of frequencies

Most future PCS systems are expected to operate in 1800-2000 MHz

frequency band. It has been shown that path loss can be more dramatic at these

frequencies than those in the 900 MHz range. Some studies have suggested that the

M.N.Jayaram, Dept. of E&C, SJCE, Mysore - 06 96

path loss experienced at 1845 MHz is approximately 10 dB larger than those

experienced at 955 MHz, all other parameters being kept constant.

The COST231-Hata model extends Hata's model for use in 1500-2000 MHz

frequency range, where it is known to underestimate path loss.

The model is expressed in terms of the following parameters:

Carrier Frequency fc: 1500-2000 MHz

BS Antenna Height hb: 30-200 m

MS Antenna Height hm : 1-10 m

Transmission Distance d: 1-20 km

The path loss according to the COST231-Hata model is expressed as:

Lp(db)=A+Blog10(d)+C ……………(4.4)

Where, A = 46.3 + 33.9 log10(fc) -13.28 log10(hb) - a(hm)

B = 44.9 – 6.55 log10(hb)

C = 0 for medium-city and suburban areas(moderate tree density) and

3 for metropolitan areas

While both the Hata and COST231 are designed for use with base station

antenna heights greater than 30 meters, they may be used with shorter antennas

provided that surrounding buildings are well below this height. Neither model should

be used to predict path loss in an urban canyon. Lastly, the model should not be used

for prediction with transmission distances below 1 km, as path losses become highly

dependent on local topography below this range.

4.9 Cost 231 Walfisch-Ikegami Model

This model (Fig4.3) is proposed of a combination of the Walfisch-Bertoni

method and Ikegami model to improve path loss estimation through the inclusion of

more data. Four factors are included which are heights of building, width of roads,

building separation and road orientation with respect to the LOS path.

M.N.Jayaram, Dept. of E&C, SJCE, Mysore - 06 97

This model is restricted to the following range of parameters:

fc = 800 to 2000 MHz

hb = 4 to 50 m

hm = 1 to 3 m

d = 0.02 to 5 km

This model distinguishes between LOS and non-LOS paths as follows.

For LOS paths the equation is given as:

L = 42.6 + 26log10d + 20log10f for d ≥ 0.020 km …… (4.5)

Where,

L = L0 + Lrts + Lmsd

L =32.4 + 20log10d + 20log10f

Lrts = rooftop-to-street diffraction and scatter- loss.

Lrts = -16.9 - 10log10w + 10log10f + 20log10 (hb - hr) + Lori for hb > hr

Lmsd = The multiscreen diffraction loss.

Lmsd= Lbsh+ ka+ kdlog10d + kflog10f - 9log10b

Fig4.3. Parameters used in Walfisch-Ikegami model

This model gives predictions which agree quite well with measurements when

the base station antenna is above rooftop height, producing mean errors of about 3db

with standard deviations in the range 4-8 db. However the performance deteriorates as

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hb approaches hr and is quite poor when hb<<hr. The model produces large errors in

the microcellular situation.

4.10 Lee Model

Named after W.C.Y. Lee, this empirically derived path loss model is

parameterized by Pro, the power at the 1-mile point of interception, and γ, an

experimentally determined path loss slope. It is indicated for use with flat terrain and

is specified as follows:

Pr = 10log10 Pro α0 dBm ………..(4.6)

Where:

Pr = field strength of the received signal at a distance r from the transmitter

Pro = received power at 1 mile (1.6 km)

r = distance between MS and BS antennas

r0 = 1 mile (1.6 km)

f = actual carrier frequency

f0 = nominal carrier frequency, (= 900 MHz)

n = empirically derived exponent. Depends on geographical locations and

operating frequency ranges 2 ≤ n ≤3.

n=2 is recommended for a suburban or open area with f < 450 MHz

Use n=3 for an urban area with f > 450 MHz

α0=correction factor accounts for antenna heights, transmit power and antenna

gains which differ from nominal values.

The limitations for this model are:

Carrier frequency = 900 MHz

Base Station antenna height = 30.48m

Base Station transmit power = 10 watts

M.N.Jayaram, Dept. of E&C, SJCE, Mysore - 06 99

Base Station antenna gain = 6db above dipole gain

Mobile station antenna height = 3m

Correction Factor (α0)

Note that the actual frequency of the transmitted signal does not explicitly

appear in the formulae specifying α0. The formula is a general one which is valid for

all frequencies greater than 30 MHz

The path loss formula is express as :

Lp = Pt - Pr (all in dBm) …………………(4.7)

Where, Pt is the transmit power.

4.11 ITU Model

It estimates the path loss inside a room or a closed area inside a building

delimited by walls of any form and is restricted to following range of parameters:

Frequency: 900 MHz to 5.2 GHz

Proposed model for path loss:

L = 20logf +N log d+ Pf (n) – 28 …… (4.8)

Where,

L = the total path loss. Unit: (dB).

f = Frequency of transmission. Unit: (MHz).

d = Distance. Unit: meter (m).

N = The distance power loss coefficient.

n = Number of floors between the transmitter and receiver.

pf (n) = the floor loss penetration factor.

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4.11(a) Environmental Effects

There are differences between the two most popular models, ITU terrestrial

model and Crane model. These models produce slightly different estimates of the long

term mean fade probability. Crane models tend to produce higher attenuation than the

ITU model. But the uncertainty of either of these models or alternatively the short-

term expectation of fade is quite large. Uncertainty stems from variations from year-

to-year and location-to- location.

4.11(b) ITU Rain Attenuation Model

This is one of the examples of environmental effects. Rain attenuation is a

major constraint in microwave radio link design above 10 GHz. Several empirical and

no empirical rain attenuation prediction models that have been developed are based on

the measured data obtained from temperate regions. Most of these existing rain

attenuation prediction models do not appear to perform well in high rainfall regions.

Cumulative distribution empirical evidence shows that the ITU-R model

underestimates the measured rain attenuation cumulative distribution when applied to

tropical regions, leading to a poor prediction. Other impairments are due to gaseous

absorption, cloud, troposphere refractive effects, scintillation, wet antenna etc.

4.11(c) Crane Model

Crane determined that the distribution of deviations was lognormal and

presents a model for variability in terms of risk. Standard deviation of the natural

logarithm of rain-rate, Sm, was obtained as follows:

Year-to-year, Sm = 0.21

Location-to-location, Sm = 0.17

Combined year-to-year and location-to-location, Sm = 0.28

The year-to-year standard deviation corresponds to 23% in dB and the

Combined standard deviation corresponds to 32% in dB.

M.N.Jayaram, Dept. of E&C, SJCE, Mysore - 06 101

A risk model is presented by Crane to estimate the attenuation for any year

over a selected number of years using the variability standard deviation.

4.12 Log-distance Path Loss Model

The Log-distance path loss model is a radio propagation model that predicts

the path loss a signal encounters inside a building or densely populated areas over

distance.

Log-distance path loss model is formally expressed as:

….(4.9)

Where,

PL is the total path loss measured in Decibel (dB)

Is the transmitted power in dBm, where PTx

is the transmitted power in Watt.

Is the received power in dBm, where PRx is

the received power in Watt.

PL0 is the path loss at the reference distance d0 (in dB) given by Friis’s formula

as,

PL0=20log10 (4πd/λ) …………………………………………………(4.10)

d is the length of the path

d0 is the reference distance; usually 1 km (or 1 mile) is the path loss exponent.

Xg is a normal (or Gaussian) random variable with zero mean, reflecting the

attenuation (in decibel) caused by at fading. In case of no fading, this variable is 0.

[75],[78],[79],[80],[81],[83],[84],[86]

In our thesis we have considered only Okumura, Hata, ITU and COST231

models.

M.N.Jayaram, Dept. of E&C, SJCE, Mysore - 06 102

4.13 Correction factors for the Models

From the above discussion it is clear that different models vary differently

with respect to frequency and distance, which are the basic parameters in all the

models. To make them uniform frequency and distance correction factors must be

added. Earlier we have stated that these models are designed for terrestrial

communication. To apply these models to underground communication we need to

add correction factors to these models based on the various losses discussed earlier.

Beam Forming For Signal Estimation

1. Standard Deviation: The standard deviation of a signal x, denoted by the

symbol x serves as a measure of how much deviation from the mean the signal

demonstrates. For instance, if the standard deviation is small, most values of x are

close to the mean. If the standard deviation is large, the values are more spread out.

2. Mean Square Error: Beam forming is a classical method of processing

tem-poral sensor array measurements for signal estimation, interference cancellation,

source direction, and spectrum estimation. In estimation context, where our goal is to

design a beam former in order to obtain an estimate of the signal amplitude that is

close to its true value. We derive beam formers for estimating a signal in the presence

of interference and noise using the mean-squared error (MSE) as the performance

criterion

4.13(a) Methods for curve fitting: Curve fitting is nothing but fitting empirical

equations to the data. There are number of methods of curve fitting namely:

4.13(a.1) Data Linearization Method for y = CeAx

Suppose that we are given the points (x1, y1), (x2, y2). . . (xN, yN ) and want to fit

an exponential curve of the form

y = CeAx …… (4.11)

Taking the logarithm on both sides gives

ln(y) = Ax + ln(C) ………(4.12)

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Then introducing the change of variables, we have

Y = ln(y), X = x, and B = ln(C)……….………………(4.13)

This results in a linear relation between the new variables X and Y as:

Y = AX + B………………..……………………………….(4.14)

The original points (xk, yk) in the xy-plane are transformed into the points (xk ,

yk) = (xk , ln(yk )) in the XY-plane. This process is called data linearization. Then the

least squares line given in eq (4.14) fits to the points {( xk , yk)}.

After A and B has been found, the parameter C in equation (4.11) is computed

as,

C = eB ……………………………………………….(4.15)

4.13(a.2) Polynomial Fit

Polynomial models are a great tool for determining which input factors drive

responses and in what direction we use polynomial models to estimate and predict the

shape of response values over a range of input parameter values. Polynomial models

are a great tool for determining which input factors drive responses and in what

direction. These are also the most common models used for analysis of designed

experiments. A quadratic (second-order) polynomial model for two explanatory

variables has the form of the equation below. The single x-terms are called the main

effects. The squared terms are called the quadratic effects and are used to model

curvature in the response surface. The cross-product terms are used to model

interactions between the explanatory variables.

The polynomial fit model is given by

…(4.16)

Equation (4.16) can be expressed in matrix form in terms of a design matrix ,

a response vector , a parameter vector , and a vector ε of random errors. The ith row

of and will contain the x and y value for the ith data sample. Then the model can be

written as a system of linear equations:

M.N.Jayaram, Dept. of E&C, SJCE, Mysore - 06 104

…(4.17 )

Using pure matrix notation above equation can be written as,

……………………….(4.18)

The vector of estimated polynomial regression coefficients (using ordinary

least squares estimation) is

……………………….(4.19)

This is the unique least squares solution as long as has linearly independent

columns. Since is a Vander monde matrix, this is guaranteed to hold provided that

at least m + 1 of the x i are distinct (for which m < n is a necessary condition).

4.13(a.3) Method Of Least Squares

The method of least squares is a standard approach to the approximate

solution of over determined systems, i.e., sets of equations in which there are more

equations than unknowns. "Least squares" means that the overall solution minimizes

the sum of the squares of the errors made in solving every single equation. The most

important application is in data fitting. The best fit in the least-squares sense

minimizes the sum of squared residuals, a residual being the difference between an

observed value and the fitted value provided by a model. When the problem has

substantial uncertainties in the independent variable (the 'x' variable), then simple

regression and least squares methods have problems; in such cases, the methodo logy

required for fitting errors- in-variables models may be considered instead of that for

least squares.

…………………………………(4.20 )

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A residual is defined as the difference between the actual value of the

dependent variable and the value predicted by the model.

……………………………….(4.21)

4.13(a.4) Regression Method

The regression methods deal with finding the relation-ship between one

outcome (dependent) variable and one predictor (independent) variable, or finding the

relationship between two variables where the designation of dependent and

independent variables is irrelevant.[87],[88]

We have followed two methods of modeling namely, Two parameter

modeling and Composite or Hybrid modeling.

4.14 Two Parameter Modeling

Steps followed in this modeling are

1. For the above models we calculate path loss( predicted or theoretical )

from the available empirical equations based on the practical specifica tions like

frequency, distance, base station and mobile antenna heights and other related

parameters .

2. We plot both predicted (called theoretical) and practical path losses.

3. A proper model is selected out of these based on minimum deviation

between practical and predicted values (Later it will be shown that COST231 model is

the best model).

4. For the selected model we add correction factors based on two parameters

(losses). Here we assume two parameters as variable and others as constants for a

given modulation format. E.g.: Penetration loss and bending losses as variable

keeping other losses as fixed .Superposition method is used in adding the correction

factors.

5. Corrected model is again plotted and curve fitting is done based on

regression methods .MATLAB tool is used for plotting the curves.

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6. Resulting curves are compared with the practical values. This process is

repeated for other modulation formats.

7. Finally the model with best modulation format is selected based on

minimum deviation.

4.15 Composite Modeling

Here all the loss parameters are together considered.

Steps followed for obtaining the correction factors:

• Code was written for obtaining different values of losses at different

frequencies and distances within specified range.(we have chosen MATLAB because

of the convenience of plotting tools).

• In each case specific loss was varied keeping other losses constant(

evaluated at UHF)

• Curve fitting of the values obtained was done with respect to log of

frequency and distance.

• It was compared with the measured values curve and the deviation was

obtained.

• Polynomial corresponding to the deviation was calculated using curve

fitting which is the correction factor is pertaining to that loss.

• All the correction factors so obtained were subtracted from the COST-231

model and finally hybrid correction factor to be added was obtained owing to the

deviation of the measured plot and the corrected COST 231 plot.

• The final hybrid COST-231 model fits the measured values given and thus

can be used in underground conditions at ease.

• The procedure was implemented for 2 modulation formats BFSK and 0.3

GMSK.

• All the correction factors we obtained are with respect to frequency. They

can even be modelled with respect to distance and other parameters which affect the

signal strength. The method used for obtaining these correction factors is Linear and

quadratic regression.

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Several predictions methods have been described in his Chapter. They all aim

to predict the median signal strength either at a specified receiving point or in a small

area. Receiving point methods are needed for point-to-point links whereas small area

methods are useful for base-to-mobile paths where the precise location of the receiver

is not known. All of these methods have been available for many years and have stood

the test possibly with modification and updating. They differ widely in approach,

complexity and accuracy. But sometimes, when it comes to accuracy, no one method

outperforms all others in all conditions.

Statistical methods are based on measured and average losses along typical

classes of radio links. Among the most commonly used such methods are COST 231,

Okumura-Hata, Lee model and others. Deterministic methods based on the physical

laws of wave propagation are also used. Ray Tracing is such one method. These

methods are expected to produce more accurate and reliable predictions of the path

loss than the empirical methods. However they are significantly more expensive in

computational effort and depend on the detailed and accurate description of all objects

in the propagation space such as buildings, roofs, windows, doors and walls. For these

reasons they are used predominantly for short propagation paths. Every propagation

models has its own advantage and disadvantage. Choosing a method appropriate to

the specific problem under consideration is a vital step in reaching a valid prediction.