tonal Bureau of Stanaaras

library, »•«• »148

OCT 2 i 1965

^ecknlcciL v2ote ^o. 3JZ*

INTERFERENCE PREDICTIONS FOR THE

INSTRUMENT LANDING SYSTEM

By

G. D. GIERHART AND M. E. JOHNSON

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

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* Located at Boulder, Colorado 80301. ** Located at 5285 Port Royal Road, Springfield, Virginia 22171.
NATIONAL BUREAU OF STANDARDS

technical ^ote. 324

ISSUED September, 1965

INTERFERENCE PREDICTIONS FOR THE

INSTRUMENT LANDING SYSTEM

By

G. D. Gierhart and M. E. Johnson

Central Radio Propagation Laboratory

National Bureau of Standards

Boulder, Colorado

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U. S. Government Printing Office Washington, D.C. 20402

Price: 30*
NOTICE

This report has been prepared by the National Bureau

of Standards for the Systems Research and Development

Service, Federal Aviation Agency, under Contract No.

FA-64-WAI-69, and has been published as a SRDS

contractor report numbered RD-65-39- The contents

of this report reflect the views of NBS, which is responsible for the facts and the accuracy of the data presented

herein, and do not necessarily reflect the official views

or policy of the FAA. This report does not constitute a standard, specification, or regulation.
TABLE OF CONTENTS

Page No,

ABSTRACT

1. INTRODUCTION 1

2. SYSTEM PARAMETERS 3

3. TRANSMISSION LOSS CALCULATIONS 7

4. INTERFERENCE BETWEEN TWO STATIONS .... 12

5. RESULTS OF THE STUDY 14

5.1 Service Limitations Due to Co -Channel

Interference 14

5. 2 Service Limitations Due to AdjacentChannel Interference 19

APPENDIX A. PROPAGATION MODELS 24

A.l Desired Station ILS Model 31

A. 2 Unde sired Station ILS Model 32

A. 3 Undesired Station VOR Model 33

APPENDIX B. COMPUTATION TECHNIQUES ... 35

B.l Interference Prediction Program 35

REFERENCES v 41

1X1
LIST OF FIGURES

Figure No. Title Page No, :a.

1 8-Loop Array Antenna Pattern 4

2 V-Ring Array Antenna Pattern 5

3 Cumulative Distributions of Aircraft Antenna

Gain Ratios 8

4 Sketch Showing Relative Positions of Aircraft

and of Navigational Aids over a Smooth Earth 9

5 Co-Channel ILS Interference; 6, 250 feet 15

6 Co-Channel ILS Interference; 12,000 feet 16

7 Co-Channel ILS Interference; 18,000 feet 17

8 Adjacent-Channel ILS Interference; 1, 000 feet 20

9 Adjacent-Channel ILS Interference; 6, 250 feet 21

10 Adjacent-Channel ILS Interference; 12,000 feet 22

11 Geometry for Ray Interference within the

Radio Horizon 26

12 Flow Diagram for Interference Prediction

Program 36-37

LIST OF TABLES

Table No. Title Page No,

1 Characteristics of ILS Localizers 3

2 VOR System Parameters 6

3 Co -Channel Station Combination Factor, C 18

4 Adjacent-Channel Station Combination Factor, C 19

iv
ABSTRACT

Co-channel and adjacent-channel interference predictions for the

Instrument Landing System are presented in this report. Information

on the various types of ground facilities involved is given first. Propagation mechanisms applicable to the 108 to 112 Mc/s frequency range

are "discussed second together with the calculation of transmission loss

and its variability. Third, the statistical treatment of interference

problems is explained. Finally; the results of the study are presented

as curves of normalized desired-to-undesired signal strength ratios

versus distance from the desired station. Aircraft altitudes of 1, 000,

6, 250, 12, 000, and 18, 000 feet along with station separations ranging

from 20 to 330 nautical miles were considered.

Detailed procedures, mathematical formulas, and computer

programs used are discussed in the Appendices.

KEY WORDS

Instrument Landing System

Interference Predictions

Propagation

INTERFERENCE PREDICTIONS FOR THE

INSTRUMENT LANDING SYSTEM

by

G. D. Gierhart and M. E. Johnson

1. Introduction

Increasing air traffic density together with fast, high-flying jets

have made the use of reliable air navigation aids more important than

ever before. In expanding the present complex of navigation aids to meet future demands, consideration must be given to potential interference between facilities operating on the same or on adjacent channels.

The amount of interference is a function of the desired-to-unde sired

signal ratio at the aircraft antenna terminals; as both signals vary with

time and aircraft location, the ratio varies as well, and the interference

becomes dependent on time and location. Because of the nature of radio

wave propagation in the frequency ranges used, the variations of the

received signals and of the interference ratios are best described

statistically. The large number of possible conditions dictates the use

of a digital computer with programs that take into account all variables

as well as the fixed equipment parameters.

The air navigation aid treated in this report is the Instrument

Landing System (ILS). This system includes a runway localizer, a

glide path, and marker beacons. However, in this study only the localizer is considered, since it is most susceptible to co-channel and

adjacent-channel interference. The ILS localizer operates in the 108 to

112 Mc/s frequency range and shares this range with the VHF Omnirange
(VOR) in such a way that VOR facilities have to be considered as the

source of adjacent-channel interference.

At very high frequencies in the 30-300 Mc/s range (VHF), propagation of radio frequency energy is affected by the lower atmosphere

(the troposphere), specifically by variations in the refractive index of

the atmosphere. The terrain along and in the vicinity of the great circle

path between transmitter and receiver also plays an important part.

Within the last decade a number of methods and procedures have

been developed to calculate field strength and its variability at VHF.

In the work discussed here procedures were followed which have been

used by the Central Radio Propagation Laboratory to predict in a

statistical manner the effect of terrain and atmosphere on the variability

of field strength and on the performance of radio systems [Rice, Longley,

Norton, and Barsis, 196 5 J . It is also convenient to use the concept of

transmission loss [Norton, 1953 and 1959] , which is the ratio of power

radiated to the power that would be available at the receiving antenna

terminals if there were no circuit losses other than those associated

with the radiation resistance of the receiving antenna. It is used under

the assumption that losses in the antenna circuits can be neglected, and

it is usually expressed in decibels. Methods used for its calculation as

a function of path length, terminal heights, and carrier frequency are

discussed in Section 3. Computation techniques are discussed in

Appendix B.

After some initial calculations, parameters for the ILS localizer

and the VOR were assembled into a. computer program which yields

normalized signal-to-interference ratios for given probability-ofservice values as a function of aircraft location in relation to the desired

and the unde sired ground stations. The normalization involves the

assumptioii that both the power and antenna gain associated with the

desired and unde sired station are the same.
Results in the form of curves showing these ratios for both cochannel and adjacent-channel cases were obtained. Section 5 contains

the information required to interpret the normalized curves in terms of

parameters associated with three types of ILS ground equipment.

2. System Parameters

System parameters are based on several types of ILS ground

equipment, a standard VOR ground installation, and passenger -jet

aircraft antennas. Characteristics of three ILS localizers are listed

in Table 1. Other equipment exists, but consideration of these three

is sufficient for practical purposes.

TABLE 1 Characteristics of ILS Localizers

Standard Directional Low Cost

Carrier Power* + 20 dBW + 20 dBW + 10 dBW

Array Type 8 -Loop V-Ring V-Ring

Antenna Gain* + 4 dB + 12 dB +12 dB

Array Height 5. 5 ft 7.5 ft 7. 5 ft

In Table 1 carrier power refers to the carrier power delivered to

the terminals of the carrier antenna, and antenna gain refers to the

main lobe free space gain of the carrier antenna with reference to an

isotropic radiator. Figures 1 and 2 show relative gain as a function of

azimuth angle for the carrier portion of the 8 -Loop [Civil Aeronautics

Administration, 1957] and V-Ring arrays, respectively.

*See text.
FREE SPACE GAIN FOR THE LOCALIZER CARRIER ANTENNA IN THE AZIMUTH

PLANE IS PLOTTED IN DECIBELS RELATIVE TO THE MAIN LOBE MAXIMUM.

THE GAIN OF THE MAIN LOBE MAXIMUM RELATIVE TO AN

ISOTROPIC RADIATOR IS 4 DECIBELS.

270°

Figure 1. 8-Loop Array Antenna Pattern
FREE SPACE GAIN FOR THE LOCALIZER CARRIER ANTENNA IN THE AZIMUTH PLANE

IS PLOTTED IN DECIBELS RELATIVE TO THE MAIN LOBE MAXIMUM.

THE GAIN OF THE MAIN LOBE MAXIMUM RELATIVE TO

AN ISOTROPIC RADIATOR IS 12 DECIBELS.

VALUES PLOTTED ARE FOR A V- RING ARRAY (TYPE FA-5549X) WITH

A TYPE m ELEMENT SPACING AND CURRENT DISTRIBUTION.

270c

Figure 2 V -Ring Array Antenna Pattern
Both the ILS localizer and the VOR use horizontally polarized

antennas and were assumed to be operating at 110 Mc/s. Other parameters used for the VOR are listed in Table 2.

TABLE 2

VOR System Parameters

Carrier Power Delivered to Antenna 20 dBW

Ground Antenna Type 4-Loop Array (located

above counterpoise)

Maximum Antenna Gain Relative to

Isotropic Antenna 2. 15 dB

Free Space Horizontal Pattern Approximately Circular

Free Space Vertical Pattern Approximately Like Dipole

Counterpoise Diameter 52 feet

Antenna Height Above Counterpoise 4 feet

Counterpoise Height Above Ground 12 feet

Transmission line loss associated with the airborne terminal was

considered to affect both the desired and the undesired signals equally

and was neglected.

Aircraft antenna gain statistics were obtained from modeling

study data based on an E -cavity type VOR antenna in the vertical stabilizer of passenger type jet aircraft [Convair, 1959; Commercial Jetstar,

1959] . Only the forward ± 20 ° of azimuth were considered in obtaining

statistics for gain toward the desired station, but two sets of statistics

were developed for gain in the direction of the undesired station. One

set considered only the rear ± 20° of azimuth and the other considered

all azimuth angles as equally likely. From these statistics a single

distribution was established for the ratio of antenna power gain in the

direction of desired station to that in the direction of the undesired
station. This ratio, expressed in decibels, is denoted by the symbol

R and the cumulative distribution, R (p) , used to account for aircraft antenna gain is shown in figure 3. Also shown in figure 3 are two

additional cumulative distributions of R . that resulted from the above A

mentioned analysis and were used as a guide to establish the R distribution used in the calculations.

3. Transmission Loss Calculations

Figure 4 shows a typical configuration of an aircraft (representing

the receiving terminal), a desired navigational transmitting facility,

and an unde sired navigational transmitting facility. All three are

aligned along a great circle path, and for simplicity assumed to be

above a smooth surface. In the example drawn, the aircraft is within

the radio horizon of the desired facility, but beyond the radio horizon of

the interfering station. The distances along the great circle path from

a point vertically below the aircraft to the desired and the unde sired

station are denoted by d and d , respectively. The aircraft is at

a height h above the terrain. The angle 6 between the horizon rays

from the aircraft and the interfering station is an important parameter

in the calculation of transmission loss for beyond -the -horizon paths

[Norton, Rice, and Vogler, 1955]. For the assumption of a smooth

spherical earth, 9 is also the distance between radio horizons expressed

in angular measure, and it is therefore called the "angular distance, "

as indicated on figure 4. As is customary in the analysis of tropospheric propagation paths, first order allowance for the refractive

effects of the atmosphere was made by assuming an earth radius 4/3

times the actual radius. This permits radio rays to be drawn as

straight lines, and simplifies the determination of geometric parameters.

Transmission loss calculations were accomplished by (a) calculating a reference value of basic transmission loss, (b) calculating a
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cumulative distribution for long-term variations, (c) calculating a cumulative distribution for short-term variations, and (d) calculating

the cumulative distribution of transmission loss by combining the

results of previous calculations. More detail on these four steps

follows:

(a) A reference value of basic transmission loss was calculated

in accordance with methods given by Rice, et al. [1965] . This reference value, as explained by Norton, et al. [1955] ,

is the median of all hourly medians within "Time Block 2, "

representing the hours 1:00 p.m. to 6:00 p.m., November

through April. In calculating "basic transmission loss" the

antennas are considered to be isotropic with unity power or voltage gain in all directions. Actual antenna characteristics

are brought in later on when converting from basic transmission loss to transmission loss. Within the radio horizon,

basic transmission loss was calculated using geometric optics

methods, including interference between the direct and the

ground-reflected ray. For the desired ILS localizer and VOR

propagation models, specular reflection was assumed with

reflection coefficients equal to -0.9. Because of the irregular

nature of the terrain (buildings, etc. included) surrounding

the unde sired ILS stations, specular reflection was considered

less dominating, and a combination of specular and diffused

reflection was assumed. The primary effect of this assumption was to lower transmission loss values associated with the

undesired ILS relative to comparable values for the desired

ILS. This is discussed further in Appendix A. Beyond the

radio horizon, basic transmission loss was calculated using

smooth-earth diffraction or forward scatter models, depending

10
on the path distance involved. Calculations for both models,

and the method of properly combining diffraction and scatter

fields if they are of comparable magnitude, were based on

procedures contained in a Technical Note by Rice, et al. [1965].

(b) Long-term variations in basic transmission loss were estimated

for a continental temperate climate by means of the time variability function V(p,d). This empirical function was calculated

in accordance with methods given by Rice, et al. [1965] . It was used to determine the cumulative distribution with time of

hourly median basic transmission loss values relative to the

reference values calculated under (a) above for all hourly

median basic transmission loss values during the year as functions of path length, angular distance, terminal height, and

carrier frequency.

(c) In addition to the distributions of hourly medians representing

long-term variations, short-term (usually within -the -hour)

distributions of the received signal levels had to be estimated.

Short-term variations in this particular application are principally due to two causes. One is the inherent short-term fluctuation of the tropospheric signal ascribed to phase interference

of rays reflected from small layers or scattered from refractive

index discontinuities, or to reflections from ground irregularities. The other is the pattern of the aircraft antenna: numerous

small lobes cause gain changes with varying bearings which can

be represented by a cumulative distribution of antenna gain with

time as the aircraft moves through space. However, it was

more efficient to neglect the effect of the aircraft antenna gain

in the initial transmission loss calculations and include it in

later calculations as the R.(p) distribution discussed in

11
Section 2. Short-term fading was described by a cumulative

distribution function V (p, 0) which is based on fading range

data given by Janes [1955] .

(d) To obtain the cumulative distribution of transmission loss the

functions discussed in a, b, and c above were combined. The

mechanics of combining cumulative distributions is discussed

in more detail in Appendix B.

The prediction of interference conditions requires a knowledge of

the time distribution of transmission loss or field strength at many

points in space; therefore, time variability calculations have to be

performed for these points with distance from the desired and unde sired

station, aircraft height, spacing of desired and undesired ground facilities, carrier frequency, and antenna patterns as parameters.

It should be noted here that the one -hour period taken as the

dividing line between long-term and short-term variations is somewhat

arbitrary. It is convenient in view of the available empirical time

variability functions.

4. Interference Between Two Stations

As shown by figure 4, both the desired and the undesired signals

arrive at the aircraft over propagation paths characterized by the

distances d and d , respectively, and by the aircraft height. The

distances are measured along the great circle path. Both signals vary

with time, and the distributions of signal levels were calculated in

accordance with the procedures outlined in the preceding section. Then

the ratio of desired to undesired signal exceeded for given percentage

of-time values at a particular aircraft location was determined.

The ratio of desired-to-undesired signal can be expressed as the

decibel difference of desired and undesired signal levels and was

12
obtained from calculated transmission loss values and other system

parameters. The distribution of this ratio will be denoted D/U(p),

where p is that percentage of time during which a given value of D/U

is exceeded. By virtue of the aircraft being in motion, time variations

also include variations in space. As the actual time distribution of

D/U may vary from installation to installation because of terrain

characteristics and other factors not taken into account in this analysis,

the time availability p may be interpreted as an expression of relia-.

bility for a typical installation. The concepts of "prediction uncertainty" and "service probability" in the sense defined by Barsis, et al.

[1962] were not used explicitly. It should, however, be understood

that there is an uncertainty associated with the D/U predictions of this

study and that this uncertainty will increase under conditions where the

assumed propagation models become less valid.

As an example, D/U(95) = 10 dB means that for a typical

installation the ratio of the desired-to-undesired signal is equal to or greater than 10 dB during 95% of the time. Values of D/U(95) are

associated with the variables used in the calculations. These include:

(1) interference type (co- or adjacent-channel), (2) aircraft altitude,

(3) station separation, and (4) aircraft distance from the desired

station.

To obtain the time availability of the desired-to-undesired ratio

at any point in space it was necessary to properly combine the cumulative distributions of (a) transmission loss from the desired station,

(b) transmission loss from the undesired station, and (c) the antenna

power gain ratios, R A

(p). Actually these calculations resulted in a cumulative distribution of a normalized D/U. The process for converting normalized D/U to actual D/U values is discussed in

Section 5.

13
5. Results of the Study

The results of this study are in the form of normalized prediction

curves. These curves may be used to estimate the service limitations

imposed on ILS installations by co-channel and adjacent-channel interference. Other limitations to service such as thermal or man-made

noise at the receiver and self interference caused by reflections from

airport structures or other aircraft were not considered in this study.

In particular, an "acceptable" desired-to-undesired signal ratio does

not imply that the desired signal is strong enough for operational use.

In this section and in Appendix B values of normalized D/U(95)

will be denoted by the symbol N{D/U(95)}. These normalized values

were calculated for the condition when the two ground stations and the

aircraft were aligned over the same great circle arc. This was mentioned previously in Section 3 and is implied by the inset in figures 5

through 10. However, N{D/U(95)} values can also be obtained for

cases v/here the assumed alignment is not valid by properly interpreting

the station separation shown on the curves. Regardless of the shortest

distance between the ground stations, the station separation, S, shown

on the curves should always be regarded as the algebraic sum of the

distance from the aircraft to the desired station, d , and the distance

from the aircraft to the undesired station, d ; i.e., S = d + d .

5.1. Service Limitations Due to Co -Channel Interference

N{D/U(95)} curves for aircraft altitudes of 6,250, 12,000, and

18,000 feet are shown in figures 5, 6, and 7, respectively. Desired

values of D/U(95) may be converted to values of N{D/U(95)} which

can be read from the curves by the following procedure.

(a) Determine the value of co -channel station combination factor,

C, from Table 3, on page 18.

14
FREQUENCY 110 Mc/s

ALTITUDE 6,250 FEET

STATION SEPARATION ,S, AS LABELED

95% RELIABILITY

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V 150

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-10

-20

-7rt 20 30 40 50 60 70 80 DISTANCE, d D

, FROM DESIRED STATI ON IN NAUTICAL MILES

90 100

Figure 5. Co-Channel IL.S Interference; 6, 250 feet

15
FREQUENCY 110 Mc/S

ALTITUDE 12,000 FEET

STATION SEPARATION ,S, AS LABELED

95% RELIABILITY

1 u

Q- H j-H

DESIREC

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->'" b ^y-UNDESIRED

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310

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270

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-20 \70

-in

20 30 40 50 60 70 80

DISTANCE , d D

, FROM DESIRED STATION IN NAUTICAL MILES

90 100

Figure 6. Co-Channel ILS Interference; 12, 000 feet

16
FREQUENCY 110 Mc/s

ALTITUDE 18,000 FEET

STATION SEPARATION ,S, AS LABELED

95 % RELIABILITY

Q

Q

UJN

o

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DESIREC

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, FROM DESIRED STATION IN NAUTICAL MILES

90 100

Figure 7. Co-Channel ILS Interference; 18, 000 feet

17
(b) Determine the azimuth angle, a, between main lobe maximum

of localizer carrier antenna at the unde sired station and the

aircraft.

(c) Using a and the antenna pattern (figure 1 or 2) appropriate for

the unde sired station type, determine the gain factor, G, of the

unde sired localizer carrier antenna in the direction of the

aircraft.

(d) Calculate N {D/U(95) } using

N{D/U(95)} = D/U(95) - C + G (1)

TABLE 3

Co -Channel Station Combination Factor, C

Desired Station Type

Undesired Station Type

Standard Directional Low Cost

Standard

Directional

Low Cost

dB

10. 5 dB

0. 5 dB

-10. 5 dB

dB

-10 dB

0. 5 dB

+ 10 dB

dB

The values of C in Table 3 were calculated from information

given in Table 1 by using the following equation:

C = PD- P

U

+AD- A

U

+HD- H

U

(2)

where P = desired station carrier power in dBW,

P = undesired station carrier power in dBW,

A = free space antenna gain referred to an isotropic

radiator for the main lobe of the desired station

localizer carrier antenna,

18
A = antenna gain similar to A , but for unde sired station,

H = height gain factor for desired station,

H = dB for array height of 5. 5 feet (8-Loop).

H = 2. 5 dB for array height of 7. 5 feet (V-Ring).

H = height gain factor similar to H , but for unde sired

station (H = dB for adjacent-channel calculations).

Values of G read from figures 1 or 2 represent the gain of the

unde sired localizer carrier antenna in the direction of the aircraft

relative to the gain of the same antenna in the direction of the main

lobe maximum. Because of this, values of G are always negative

and D/U(95) will have its worst (lowest) values for a particular pattern

when G is 0.

5. 2. Service Limitations Due to Adjacent-Channel Interference

Adjacent-channel N{D/U(95)} curves for aircraft altitudes of

1, 000, 6, 250, and 12, 000 feet are shown in figures 8, 9, and 10, respectively. Values of D/U(95) maybe converted to values of N{D/U(95)}

which can be read from the curves by the following procedure:

(a) Determine the value of the adjacent-channel station combination

factor, C, from Table 4.

(b) Calculate N{D/U(95)} using

N{D/U(95)} - D/U(95) -C (3)

TABLE 4

Adjacent-Channel Station Combination Factor, C

Desired Station Type

Standard Directional Low Cost

1.85 dB 12. 35 dB 2. 35 dB

19
FREQUENCY 110 Mc/S

ALTITUDE 1,000 FEET

STATION SEPARATION ,S, AS LABELED

95% RELIABILITY

IV

^50

[ \

-10 \ \iO

\20

±\ . S=i9onm

IT \ 1

20 LZY

V \--l70

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viso^ \ 130 »

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40 L 90-

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70 -

50

60

DESIRED

o- uq^Uu

70

-. h S - ^UNDESIRED

T

Jh Jo *'" du

80

.on 20 30 40 50 60 70 80

DISTANCE , d D , FROM DESIRED STATION IN NAUTICAL MILES

90 100

Figure 8. Adjacent-Channel IL.S Interference; 1, 000 feet

20
FREQUENCY 110 Mc/S

ALTITUDE 6,250 FEET

STATION SEPARATION ,S, AS LABELED

95% RELIABILITY

UJ

CD

<3

LUQ

Q

Q

UJN

HU

S=d D +d u DESIRED-^" s 'I^UNDtSIHtD

30 t T1 d D H- dy 1

20

10

170

VpO N-. 13°

-10 \ V

\ \ 110 \

>V 30 \

\

^90

20 zt

\

\20 ^-70- ^,

30

i

40

50

en

20 30 40 50 60 70 80 DISTANCE, d D

, FROM DESIRED STATION IN NAUTICAL MILES

90 100

Figure 9. Adjacent-Channel ILS Interference; 6, 250 feet

21
FREQUENCY 110 Mc/S

ALTITUDE 12,000 FEET

STATION SEPARATION ,S, AS LABELED

95% RELIABILITY

—

bJQ

3

Q

Q

UJN

O

4U

C- <H -t-A

DESIREC

^ ^D W U

30 _> s - ^--UNDESIRED T

I— T

] D " JU

20

10

V s = 190 nm

50

-10 ,30 VI50 ^N

\20 130

'V

-20 Sr no

-30 70

-40

-50

_cn

20 30 40 50 60 70 80 DISTANCE , d D , FROM DESIRED STATION IN NAUTICAL MILES

90 100

Figure 10. Adjacent-Channel LLS Interference; 12, 000 feet

22
The values of C in Table 4 were calculated from information

given in Tables 1 and 2 by using the equation given in Section 5. 1. (H =0 dB for VOR. ) In the adjacent-channel case the calculation of D/U(95) is somewhat simpler than in the co -channel case. This is because the adjacentchannel unde sired station is always a VOR and the VOR has an omnidirectional radiation pattern in the horizontal plane; thus no gain factor

is required.

23
APPENDIX A

Propagation Models

A smooth, spherical earth model was used to calculate transmission loss for the ILS and VOR system at 110 Mc/s. A linear

gradient atmosphere was assumed for the initial calculations, so that

for a first approximation, radio rays could be considered to be

straight lines above an earth having an effective radius k times its

actual value. In conformance with usual practice, the effective earth

radius factor, k, was assumed to be 4/3 for the "standard" atmosphere.

Calculation methods are based on material contained in a Technical

Note by Rice, et al. [1965].

It was found convenient to include only the gain of the transmitting

antenna in the definition of transmission loss as used in these calculations. Usually, the term "transmission loss" includes the antenna

gains at both path terminals, whereas the term "basic transmission

loss" excludes all antenna gains [Norton, 1953 and 1959] . In this study,

an hourly median transmission loss, L , is defined to include the free- m

space gain of the transmitting antenna as a function of the elevation

angle as well as the effect of reflections from the counterpoise (VOR

only) and from the ground.

Within the radio horizon, values of the hourly median transmission

loss, L , were calculated using geometrical optics methods [ Kirby, m

Herbstreit, and Norton, 1952] . These methods take into account the

interference between the direct and the ground-reflected ray. Figure 11 shows the geometry for this ray interference problem, and defines

many of the symbols used in the analysis. Using this geometry, curves

of L versus distance were calculated for each assumed aircraft m

altitude. The following constants and relationships were used, with

24
distances and angles measured in statute miles and radians, respectively:

a . 5280 statute miles = 4/3 times the actual radius of

the earth

h . . . . height of the transmitting antenna above the reflecting

surface

h ... aircraft altitude above the reflecting surface

|R I . . . magnitude of the reflection coefficient

c . phase angle of the reflection coefficient relative to TT, and assumed to be zero

D . divergence factor

d . distance along the great circle path to a point on the

reflecting surface below the aircraft

r . length of the direct ray path

o

r + r . length of the reflected ray path

d . . . . distance from transmitting antenna to reflection point

d ... distance from aircraft to reflection point

La

i|» . grazing angle at reflection point

The first step was the determination of the grazing angle ijj. For a given value of d the following equations were used:

d = d

1 + d

2

(4)

V

=h

i ~ di

2

/ 2a (5)

V

- h 2" d

2

2

/ 2a {6)

taniJJ =h

1

, /d

1 =h

2

'/d

2

. (?)

Equations (5), (6), and (7) are approximate relations. In order to

utilize the electronic computer in solving the above expressions for

25
Figure 11. Geometry for Ray Interference within the Radio Horizon

26
grazing angle, ijj, an iteration method was used, assuming for each d

different values of d until the equations were satisfied within the

desired limits of accuracy, which was ±10 miles. Final values for

\\i for each assumed total distance d were then used in calculating

various auxiliary angles and quantities to be used in ray-tracing and in

the final calculation of the transmission loss L. m

Using the previously calculated value of ijj other geometrical

parameters shown in figure 11 were calculated as follows:

sin (j> = (a cos ijj)/(a + h ) (8)

sin cj> = (a cos 4»)/(a + h ) (9)

> x = tt/2 - iji- ^

(10)

2

= n/2 - i|i- ct> 2

(11)

r

2

= (a sin Qj/ (sin <J> 2

) (12)

9 = 9

1 + 92 W

- / (h

x - h2

) 2 + 4(a + h

1)(a + h2

)[sin (0

Q /2)]

2

(14)

dn (3 = [r

2

sin ( tt - 2i|>)] /r

Q

(15)

Y

01

= P- +-0 (16)

V rl

= -(++ B

x

) (17)

27
The divergence factor D was calculated using

D = (18)

1 + 2d

l d2 a d tan ip

Voltage gains g and g of the ground antenna relative to that

of an isotropic radiator were calculated by:

g

Q1

= 1. 28 cos v

Q1

(19)

and

g - 1. 28 cos v

rl rl

(20)

The phase angle A, in radians, between the direct and reflected

rays due only to the difference in ray length was calculated using

2.42 f h' h ' A - Mc 1 2 (21)

where f , , = 110 Mc/s. Mc

Then L was calculated from the following formula: m

L = 36. 58 + 20 log., f . m °10 Mc (22)

+ 20 1og

10 r -10 1og1() |g01 + D |R| g

rl ]

2

- 2 g01 sr i D l R l cos A

}

In the above equations distances and heights are measured in

statute miles and angles measured in radians. The distance d was

converted to nautical miles after L was calculated. m

28
For large distances and low angles the linear gradient atmosphere

predicts too much bending [Bean and Thayer, 1959] . To correct for

this, a ray leaving the ground station antenna at the same angle, y , as the direct ray (calculated using a linear gradient atmosphere) was

traced through an exponential atmosphere until it reached the aircraft

altitude. The great circle distance below the ray was then used in the

final calculations instead of the distance d first assumed. The exponential atmosphere used corresponds to the reference atmosphere

given by Rice, et al. [1965] with a surface refractivity of N = 301.

Calculations of transmission loss beyond the radio horizon were

made by combining smooth-earth diffraction with tropospheric scatter.

The short-cut method of Vogler [1961] was used for diffraction computations. Scatter computations and methods of combining the two mechanisms follow the work by Rice, et al. [1965] . Calculations for the beyond-the -horizon case are based on the

same exponential atmosphere used for within-the -horizon computations.

The electrical constants of the ground assumed for calculations of the

diffracted wave were a dielectric constant, c = 15, and a conductivity

value, cr = 5 millimhos per meter. At the carrier frequency used,

however, the effect of ground constants is small.

Finally, from a large number of computations both within and

beyond the radio horizon, a set of curves was drawn for discrete aircraft altitudes showing the expected median transmission loss as a function of the great circle distance, d, (assuming the antenna gain of

the ground station to correspond to a half -wave dipole). The construction of these curves involved a certain amount of blending in the vicinity

of the radio horizon [Kerr, 1964] . Long-term variability, short-term fading, and the effective gain

variations of the airborne antenna were treated statistically. Longterm variability was described by the time availability function V(p,d).

29
Equations and curves given by Rice, et al. [1965] were used to calculate the V(p, d) applicable to all hours of the year, for a continental

temperate climate.

Short-term fading was described by a cumulative distribution

function V (p, 9) which includes the summing of a constant vector and F

a Rayleigh-distributed vector. The angular distance, 9, is defined to

be the angle between horizon rays from the transmitter and receiver

[Norton, Rice, and Vogler, 1955] , and is defined on figure 4 of the

main body of this report. An auxiliary distribution function V (p, 9) F

was developed using, 1) fading range data for 199 Mc/s from a paper by

Janes [1955] to express fading range as a function of 9, and 2) figure 6

and Table 1 from Norton, Vogler, Mansfield, and Short [1955] to specify a cumulative distribution, V (p, 9), for the fading range given by F

a particular value of 9. The distribution functions V (p, 9) and F

V (p, 9) are related by F

V

F

(p, 9) = V' F

(p, 9) - V' F

(50,9). (23)

It was unnecessary to consider a different aircraft antenna gain

for the direct and reflected rays because their arrival angles are

nearly equal as would be more apparent if figure 11 was drawn to scale.

This made calculations considerably simpler since the effect of aircraft

antenna gain on N{D/U(95)} could be considered in transmission loss

calculations without including the above mentioned gain. The method

involved is outlined in Appendix B and uses the distribution R A

(p)

shown in figure 3. Distributions of transmission loss values were calculated using

the following equation:

L(p,d) = L - [V(p,d)*V_(p, 9)] . (24) m x

39
In this equation all terms except L are cumulative distributions, so m

that the calculation of L(p, d) required the use of a convolution process

which is indicated by the operational symbol * , and will be further

discussed in Appendix B. As previously implied, in calculating L(p, d)

an isotropic aircraft antenna was assumed. When the fading range was

zero the effect of V (p, 9) could be neglected and V (p, 9) was F F

dropped from equation (24).

In general the above discussion applies to all propagation models

used in this study. However, more information is required to make the

description of each model reasonably complete. Information relevant

to particular models is contained in the remaining parts of this appendix.

A.l Desired Station ILS Model

The propagation model used for the desired ILS localizer carrier

system is described accurately, but not completely in the first part of

this appendix.

In the calculations, the ground antenna was assumed to be a single

Alford loop 5. 5 feet above ground. The total gain of the carrier antenna

and the carrier power were not considered in the calculation of

N{D/U(95) }. These can be taken into account by the procedure given in

Section 6 for converting N{D/U(95)} to D/U(95).

For this model the fading range values on which V (p, 9) was F

based were approximated by

for 9 <

1 + 12.49 dB for 9 <9 <1°

13.4 dB for 9 > 1° .

31
A. 2 Undesired Station ILS Model

The propagation model used for the unde sired ILS localizer

carrier system was the same as that used for the desired ILS station

with respect to assumptions made about the ground antenna and the

methods used to calculate L beyond the radio horizon. It differed m

in the method used to calculate L within the radio horizon and the m

approximation used to describe fading range.

The within-the -horizon L curves for the unde sired ILS were m

developed by utilizing the L curve used for the desired ILS along m

with a similar curve developed by essentially neglecting the ground

reflections. Both curves were plotted on the same sheet with loss

measured along the ordinate by a scale linear in decibels and distance

from the station measured along the abscissa by a scale linear in

nautical miles. The unde sired ILS L curve was then obtained by m

interpolating a smooth curve between the curves previously drawn such

that the new curve merged with the desired ILS L curve in the vicin- m

ity of the radio horizon and merged with the "free space" loss curve at

about 10 nautical miles from the station. This procedure was used in

order to estimate the effect of terrain roughness around the undesired

ILS and to avoid making quantitative assumptions about the effect of

terrain roughness on the specular reflection coefficient. It assumes

that the specular reflection coefficient is -0. 9 at maximum within-the - horizon range (low grazing angle) and that as the range is decreased

with fixed altitude (higher grazing angle) the effect of terrain roughness

serves to reduce the absolute value of the specular reflection coefficient.

A random reflection coefficient of 0. 3 [McGavin and Maloney, 1959]

was assumed to be associated with the rough terrain surrounding an

undesired ILS. The effect of this reflection was accounted for by the

short-term fading function V (p,9). For this model the fading range

32
values on which V (p, 9) was based, were F

4. 7 dB for 9 < 9°

1 + 12. 49 dB for < 9 < 1°

13. 4 dB for 9 > 1°.

A. 3 Unde sired Station VOR Model

The propagation model used for the undesired VOR localizer follows the description given at the beginning of this appendix except in

the region where reflection from the counterpoise was considered.

Remarks made concerning antenna assumptions in the discussion of

the desired ILS model are applicable to the VOR model except for the

specific value of antenna height. The fading range values used in the

desired ILS model to determine V (p, 9) were also used in the VOR F

model.

Two L -versus -distance curves were calculated for each air- m

craft altitude within the horizon. One curve was used for reflections

from the counterpoise, where applicable, and the other for reflections

from the ground. Both curves were blended in the region where the

reflection point was close to the edge of the counterpoise. In order to

facilitate this blending, the curves were calculated so that they extended

beyond their region of validity.

For reflections from the counterpoise, calculated for elevation

angles greater than 5 degrees, the effective earth radius was increased

by the height of the counterpoise above ground so that a sphere through

the level of the counterpoise became the reflecting surface with a reflection coefficient of -9.9 and the antenna was assumed to be an Alford

loop 4 feet above this surface. The aircraft altitude was also adjusted

to compensate for the counterpoise height. In these calculations d

33
was very much smaller than d and the following two approximations

were used to simplify the calculations:

Pj S h^sin i|i (25)

) = (r cos ljj )/a . (Z6)

Beyond the region where reflection from the counterpoise was

important L was calculated using the methods outlined at the beginning of this section. The antenna was assumed to be an Alford loop

located 16 feet above the ground.

34
APPENDIX B

Computation Techniques

Calculations necessary to produce all desired distributions of

transmission loss values or power levels as well as the processes involving the combination of various distributions were so numerous and

complex that the use of a large electronic computer was mandatory.

The calculation of transmission loss values, L , was accom- m

plished by modifying existing programs to include the effect of the

transmitting antenna only as a function of distance and aircraft height.

The resulting propagation curves were reduced to a set of tables for

each aircraft altitude that included L information for each of the m

three propagation models discussed in Appendix A. Additional tables

for distribution functions of short-term variability and aircraft antenna

power gain ratios were developed. This information was then used in

the Interference Prediction Program to generate tables of interference

ratios for various values of time availability as a function of interference type, station separation and aircraft location. Values of normalized D/U(95) plotted in Section 5 were extracted from these tables.

B. 1 Interference Prediction Program

The Interference Prediction Program consisted primarily of a series of loops by which the calculations are sequenced and systematic

changes of parameters achieved. Figure 12 is a flow diagram of the

program showing the series of loops and the computational sequence.

The primary loop considers different aircraft altitudes. At the

start of each pass around the loop a set of L tables (as explained

above) for a particular height is read in. This loop continues until the

supply of tables is exhausted. Altitudes of 1,000, 6, 250, 12,000, and

18, 000 feet were used.

35
C START "*)

Read transmission

loss table for height

Set

I Do loop for \

\dp

- 5to3ZS/

<

Do loop for two ndesired system

Call VPD

for V(p, dv

)

No If we use

Yes

\

r Call FALTG to convolute Vp-(p, 9) and V(p, dy)

Calculate L(p, dxj) = Lm

- V(p, du )

I SetS = 30]

I <Do loop for \

S = 30 to 330/

dD

= S - dU

I

O

<D

<s)

36
G>

Yes

Yes

Call VPD

for V(p. d D)

No

Call FALTG to convolute VF(p, 9) and V(p,dD

) 3:

Calculate L(p, d )

/ Do loop for two \

Aundesired systems /

Call FALTG to calculate N{D/U(p)} = L(p. d u

) * [- L(p.dD

)] * RA

(p)

Punch S, d , dy, N{D/U(p)}

No

©"

©

Figure 12, Flow Diagram for Interference Prediction Program

37
A secondary loop considers the distance along the great circle

path on the ground from the unde sired station to the aircraft, d . An

initial value of 5 nautical miles is used and this is incremented by 5

miles until 325 nautical miles is reached.

For a given unde sired distance an inner loop is used to calculate

the time distributions of transmission loss for the two unde sired

systems. The expression for the cumulative distribution of transmission

loss as previously given is

L(p.d) = Lm

- [V(p,d)i* V

F

(p,9)], (27)

Here the term V(p, d) is the cumulative distribution representing

long-term variability of hourly medians. V (p, 9) represents the shortterm (within-the -hour) variability.

The symbol * in (27) denotes the statistical convolution of cumu-*

lative distributions. Basically, if two variables x and y are statistically independent and given by their cumulative distributions, their

statistical convolution is the cumulative distribution of either the variable z = x + y, or the variable z' = x - y, depending on the application

of the result, and determined in the machine program by an appropriate

input code. The cumulative distribution of z is obtained most simply

by selecting n equally spaced percentage values from the individual

distributions of both x and y, calculating all possible sums z, = x. + y., k l j and forming the cumulative distribution of all values of z obtained in

this manner. Similarly, the cumulative distribution of z' is obtained

by forming all possible differences z ' = x. - y.. k i

7 j Successive convolutions are handled by first convoluting two distributions and then using this intermediate result in a convolution with

the third individual distribution. The convolution process is cumulative;

i.e. , the order in which the individual distributions are used does not

matter.

38
The distributions for the two unde sired systems are stored and a new secondary loop which considers the station separation, S, is now

entered. The initial separation is 30 nautical miles and is incremented

by 20 nautical miles until a separation of 330 nautical miles is reached.

For a given station separation the desired distance d is now defined

as d_ = S - dTT and the time distribution of transmission loss for the

D U

desired ILS is determined in the same manner as the undesired systems

using the median transmission loss value from the appropriate table.

The resultant distribution, L(p,d ), is then used in conjunction

with the L(p,d ) distributions previously stored to calculate N{D/U(p)}

for the two desired -unde sired station combinations by using the following

equation:

N{D/U(p)} = L(p,d

u

) * [- L(p,dD

)] *RA(p) (28)

where R.(p), as explained earlier, represents the variability introduced

by the aircraft antenna. From these final distributions a number of

percentage values between p = 1% and p = 99% are selected and

punched out.

The calculations are primarily handled by three subroutines:

FALTG, VPD, and INTERP. This technique enables the program to be

more easily changed for other combinations of systems not being considered in this study.

The convolution of distributions is handled by the subroutine

FALTG.

The subroutine VPD calculates the predicted long-term variability

(or power fading) as a function of the effective distance using the

methods developed for a continental climate and presented by Rice, et

al. [1965] . With the extensive use of tables, the need to interpolate arises

often, and linear interpolation will not always suffice. Therefore, a

39
subroutine INTERP was included in the program which calculates the

n Lagrangian approximation [Lance, I960] , where n < m - 1 with

m being the number of entries in the table. The special case n = 1 results in linear interpolation. Asa practical matter, n is usuallyrequired to be less than five. This is necessitated by the fact that

Lagrangian interpolation may exhibit large oscillations between tabular

entries whenever they do not lie on rather smooth analytic functions.

It should be realized that this discussion is abbreviated, and that

the calculation procedure was more involved than indicated. In particular, the method used to extend calculations to a station separation of

20 nautical miles was not discussed.

40
REFERENCES

Barsis, A. P., K. A. Norton, and P. L. Rice (1962), Predicting the

performance of tropospheric communication links, singly and in

tandem, IRE Trans, on Comm. Systems, CS-10, No. 1, 2-22.

Bean, B. R. , and G. D. Thayer (1959), Models of the atmospheric

radio refractive index, Proc. IRE 47, No. 5, 740.

Civil Aeronautics Administration (1957), Description and theory of the

Instrument Landing System, Federal Airways Manual of

Operations, IV-B-1-4, 4.

Commercial Jetstar Antenna Installation (1959), Report No. ER-3938

(Company Confidential).

Convair 880 Jet-Liner Antennas (1959), Report No. ZN-22-006.

Janes, H. B. (1955), An analysis of within -the -hour fading in 100- to 1,000-Mc transmissions, J. Res. NBS 54, No. 4, 231-250.

Kerr, D. E. (1964), Propagation of short radio waves, MIT Radiation

Laboratory Series 13, 125-130 (Boston Technical Publishers, Inc. , Lexington, Mass.).

Kirby, R. S. , J. W. Herbstreit, and K. A. Norton (1952), Service

range for air-to-ground and air-to-air communications at

frequencies above 50 Mc, Proc. IRE 40, No. 5, 525-536.

Lance, G. N. (I960), Numerical methods for high speed computers,

142-144 (Iliffe, London).

McGavin, R. E. , and L. J. Maloney (1959), Study at 1,046 megacycles

per second of the reflection coefficient of irregular terrain at

grazing angles, J. Res. NBS 63D (Radio Prop.), No. 2, 235-248.

Norton, K. A. (1953), Transmission loss in radio propagation, Proc.

IRE 41, No. 1, 146-152.

Norton, K. A. (1959), System loss in radio-wave propagation, Proc.

IRE 47, No. 9, 1661.

41
Norton, K. A., P. L. Rice, and L. E. Vogler (1955), The use of

angular distance in estimating transmission loss and fading

range for propagation through a turbulent atmosphere over

irregular terrain, Proc. IRE 43, No. 10, 1488-1526.

Norton, K. A., L. E. Vogler, W. V. Mansfield, and P. J. Short (1955),

The probability distribution of the amplitude of a constant vector

plus a Rayleigh-distributed vector, Proc. IRE 43, No. 10, 1354-

1361.

Rice, P. L. , A. G. Longley, K. A. Norton, and A. P. Barsis (1965),

Transmission loss predictions for tropospheric communication

circuits, NBS Technical Note 101.

Vogler, L. E. (1961), Smooth earth diffraction calculations for horizontal polarization, J. Res. NBS 65D (Radio Prop.), No. 4,

397-399.

42

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