The primary experimental objective of Project Echo was the transmission of radio communications between points on the earth by reflection from the balloon satellite. This paper describes system calculations made in preparation for the experiment and their adaptation to the problem of interpreting the results. The calculations include path loss computations, expected audio signal-to-noise ratios, and received signal strength based on orbital parameters

Jakes, William C., Jr.

Ruthroff, Clyde L.

English

NASA Technical Reports Server

ZZ
TECHNICAL
D-II28
NASA TN D-1128
NOTE
PROJECT ECHO -
SYSTEM CALCULATIONS
Clyde L. Ruthroff and William C. Jakes, Jr.
Bell Telephone Laboratories
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
WASHINGTON November 1961
https://ntrs.nasa.gov/search.jsp?R=19980227738 2020-06-15T22:50:42+00:00Z

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PROJECT ECHO-
SYSTEM CALCULATIONS
by
Clyde L. Ruthroff and William C. Jakes, Jr.
Bell Telephone Laboratories
SUMMARY
The primary experimental objective of Project Echo
was the transmission of radio communications between points
on the earth by reflection from the balloon satellite. This
paper describes system calculations made in preparation for
the experiment and their adaptation to the problem of inter-
preting the results. The calculations include path loss compu-
tations, expected audio signal-to-noise ratios, and received
signal strength based on orbital parameters.
PREFACE
The Project Echocommunications_xperimentwasa
joint operationby theGoddardSpaceF1LghtCenterof the
NationalAeronauticsandSpaceAdministration(NASA),the
Jet PropulsionLaboratory (JPL), theNavalResearchLab-
oratory (NRL),andthe Bell TelephoneLaboratories(BTL).
Theequipmentdescribedherein,althougl;designedby BTL
aspart of its ownresearchanddevelopmentprogram,was
operatedin connectionwith Project Echounder contract
NASW-110for NASA.Overalltechnicalm_nagementofProj-
ect Echowasthe responsibilityof NASA'sGoddardSpace
Flight Center.
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CONTENTS
Summary ................................
Preface .................................
INTRODUCTION ............................
FREE-SPACE PATH LOSS FORMULA AND
COMPUTATIONS ..........................
EXPECTED SIGNAL-TO-NOISE RATIOS IN VOICE
CIRCUITS ..............................
RECEIVED SIGNAL STRENGTH USING ORBITAL
PARAMETERS ...........................
References ...............................
Appendix A - Free-Space Path Loss as a Function of
Satellite Position .................
Appendix B - Error Incurred by Assuming Round-
Trip Path Loss from Either Terminal . . .
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PROJECT ECHO-
SYSTEM CALCULATIONS*
by
Clyde L. Ruthroff and William C. Jakes,
Be/! Telephone L.ahoratories
Jr,
INTRODUCTION
A satellite communication system such as that of tile Project Echo experiment is in-
fhlenced by many factors such as power output, frequency, antenna gain, free-space path
loss, receiver noise temperature, and method of modulation -- factors which are also
common to poin(-Io-point microwave systems. Three other factors must be considered in
the design of satellite communication systems; all three are functions of satellite position
in the region of mutual visibility. They are:
1. Variations in free-space path loss
2. Variations in sky noise temperature
3. Loss in the earth's atmosphere.
This report shows how these system parameters are used to predict the performance
of the voice circuits that constitute the Echo conlnmnications experiment. This discussion
assumes normal propagation conditions and does not take into account statistical occur-
rences such as attenuation due to rainfall or nmltipath fading, which are beyond the scope
of this paper.
FREE-SPACE PATH LOSS FORMULA AND COMPUTATIONS
Assume a transmitting antemm with actual gain G1, radiating a power of Pr watts.
The power density % at a distance ,1_
"1
will then be
G1 P'[ .
4.'<11 2
'::The substance of this paper was published in the I_¢1[ System Technical Journal, V_I. Xl,,
No. 4, July 19(_1. It is republished here, with minor revisiol_s, 1oy permission of l%el[
'Pelcphone I,_l)oratories.
The amount of power intercepted by an object of projec ed area _ will then be
P1 = ¢1 _ "
A sphere, in effect, radiates this energy isotropically; hence the power density ¢2 at a dis-
tance d2 from the sphere will be
P1
¢2 =
4_d2 2
!
The amount of power PR received by an antenna with ef!ective aperture area A2 in this
field is
K2 G2
PR : ¢2A2 = _2 4_
where K is the wavelength and
After suitable substitutions the received power is
£2_P T
: (i)
PR G1G2 (477)3 dl 2 d22
Rearranging Equation 1 gives the free-space path loss I :
L - PT _ ( 4w)3 d12d2 2 (2)
PR GIG2A2_
This expression serves to calculate the expected free-s:mce path loss, provided that the
various parameters can be determined to sufficient acc_ racy. The presence of d12d2
in Equation 2 shows that the expected free-space path loss L is a function of the satellite
position.
In order to compute the free-space path loss, anten:la gains and frequencies of operation
are required. These constants are given in Table 1.
Table1
AntennaGainsandFrequenciesof Operation
for ComputingFree-SpacePathLoss
C_q
Antenna Gain (db) Line Loss (db) Net Gain (db)
BTL 2390 Mc horn
BTL 960 Mc dish
BTL 961 Mc dish
JPL 2390 Mc dish
JPL 960 Mc dish
NRL 2390 Mc dish
43.3 + 0.16
43.1 ± 0.1
32.6 ± 0.2
53.7*
45.8 ± 0.6
50.2*
0
0.5
0
0.4
0.2
1.6"
43.3 ± 0.16
42.6 + 0.1
32.6 + 0.2
53.3
45.6 + 0.6
48.6
*Estimated values, not measured.
The free-space path loss has been computed from Equation 2 for the Echo I satellite
balloon as a function of position for the two-way path between the Jet Propulsion Labora-
tory (JPL) facility at Goldstone Lake, California and the Bell Telephone Laboratories
(BTL) station at Holmdel, New Jersey. The results are given in Figures 1 and 2.
The balloon scattering cross section _ was assumed to be that of a 100-foot-diameter
sphere, perfectly conducting and many wavelengths in diameter, so that
_(100)2
c_ : 7854 ft 2 .4
The frequency in the east-west direction was 960 Mc; in the west-east direction it was
2390 Mc. Figure 1 is a plot of the free-space path loss versus satellite altitude when the
balloon was midway between these terminals.
Figure 2 shows contours of constant free-space path loss relative to the loss at mid-
path for a satellite height of 1000 statute miles, with the radius of the earth taken to be
3950 miles. The contours, in steps of 1 db, are plotted on a stereographic projection. The
orbital inclination of Echo I is 47.27 degrees, which limits the northern extent of mutual
visibility. The equations necessary for these computations are derived in Appendix A.
Because the Naval Research Laboratory (NRL) facility at Stump Neck, Maryland is
only 200 miles from Holmdel, New Jersey, the free-space path loss from Stump Neck to
Holmdel can be computed as the round-trip loss from either of these two locations to the
satellite. The error in this assumption is less than 0.6 db (Appendix B) for any position
in the area of mutual visibility. Figure 3 shows the contours of constant free-space path
loss for this case. The free-space path loss is 178.7 db at 2390 Mc for a satellite altitude
of i000 miles.
41500
1400
1300
LLI 1200------
.--I
II00
1000
"5 900
_J
_ 800
....... i[
70o /
6OO
500 /
178 179
---m! i
I
/
• = __
/
180 181 182 183 184 185 186
FREE-SPACEPATHLOSS(di_,
Figure I - Free-space path loss versus satellite altitude tar Echo I midway between
Holmdel, New Jersey and Goldstone Lake, California (east-west direction; for west-
east, subtract 0.5 db, owing to the difference in frequency _nd antenna gain)
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30
..t_ECHO I INCLINATION
)=
20'
10 o
RELATIVE LONGITUDE
I Y
0 ° 0 o
N
//
/7
-_ _O°
40°
__ 30 °
20 °
10 °
0 o
I .... I .... I .... [ .... t .... I .... t .... I .... I .... IL_,,I
0.5 0.4 0.3, 0.2 0.1 0
RELATIVE DISTANCE
Figure 2 - Contours of constant free-space path loss relatiw_ to the loss at midpath be-
tween Holmdel, New Jersey and Goldstone Lake, California for a satellite height of
1000 miles, with the earth's radius assumed to be 3950 miles
710 °
30 °
20 °
10 °
RELATIVE LONGITUDE
I,h_,l,LJ _L,,,*I,,,,I_,LJI JL_+I''_LI+''*I'''+I''''I
0,5 0.4 0.3 0.2 0,I 0
RELATIVE DISTANCE
20 °
Figure 3 - Contours of constant free-space path loss relative to the loss at midpath
between Stump Neck, Maryland and Holmdel, New Jersey
It can be noted from Figures 2 and 3 that the difference between maximum and
minimum free-space path loss on the JPL-BTL path is about 10 db, while for the NRL-BTL
path this difference is 19 db. It should be also noted that between NRL and BTL this maxi-
mum difference is encountered twice on every pass, while the maximum difference almost
never occurs on the JPL-BTL path.
6EXPECTED SIGNAL-TO-NOISE RATIOS IN VOICE CIRCUITS
The signal-to-noise power ratios (S/N) to be expected depend on the type of modulation
technique employed, as well as upon the received carrier-to-noise power ratio (C/N). The
first step is to compute the C/N at the receiver for suit:tble conditions, and then to discuss
the modulation methods and voice band signal-to-noise terformance. This has been done
for the two-way voice path between JPL and BTL, and tb.e results are given in Table 2.
The satellite is assumed to be midway between the terminals.
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Table 2
Communication Parameters for Echo I Midway Between Goldstone Lake,
California and Holmdel, New Jersey
Parameter East- to-West West-to-East
Transmitted power: +70 dbm (10 kw) +70 dbm (10 kw)
Frequency: 960.05 Mc 2390 Mc
Transmitting antenna net gain: 42.6 db 53.3 db
Receiving antenna: net gain: 45.6 db 43.3 db
Free-space path loss:
Loss through atmosphere:
Received carrier power:
Receiver system noise temperature:
Receiver noise power in 6-kc band:
Carrier-to-noise ratio at receiver:
183.1 db
0 d_
-113.1 dbm
350 °_:_
-135.4 dbm
22.3 db
182.6 db
0 db
-112.6 dbm
25°K
-146.8 dbm
34.2 db
For other positions of the Echo I balloon in the region of mutual visibility, the C/N
ratio is modified by three effects:
1. Variations in free-space path loss
2. Variations in sky noise temperature
3. Loss in the earth's atmosphere.
The first effect has been discussed earlier and the corr ._ction for position can be made
from Figure 2 for any satellite position. The remaining: two effects have been discussed
by Hogg 1 and by DeGrasse, Hogg, Ohm, and Scovil. 2 For example, the sky noise tempera-
ture and atmospheric loss can be calculated when the antennas are pointed at the horizon.
The loss through the atmosphere and system noise temperature are then 3.2 db and 435°K
for the east-west path, and 4.2 db and ll0°K for the west-east path; this would be the worst
case. For elevation angles above 10degrees, however, these effects are essentially negligible.
The audio S/N depends to a considerable extent on the modulation technique. Three
techniques are considered here: single-sideband (SSB), FM, and FM with feedback (FMFB).
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The transmitters are assumed to be peak-power-limited and the audio signal to be
the maximum rms sine wave obtainable. The audio bandwidth is 3 kc, and the noise band-
width is assumed to be 6 kc.
The maximum transmitted rms sine wave power is 3 db less than the transmitter
peak c. However, for the SSB technique, the noise bandwidth may be reduced to 3 kc, re-
sulting in an audio S/N which is equal to C/N:
(S/N) = (C/N).
The audio S/N for the case of frequency modulation is given by the standard FM for-
mula, which applies when the receiver input is above the threshold:
(S/N) = 3M 2 (C/N) ,
where ._,Iis the index of modulation. This index for the Echo experiment was 10, so when
the receiver was operated above the threshold the S/N is 25 db better than that for SSB.
However, the threshold for this receiver occurs at a C/N of approximately 22 db, because
the noise bandwidth required to accommodate this signal is about 66 kc.
The audio S/N for the FM receiver with feedback (FMFB) is the same as that for FM
when the C/N is above the threshold. However, this receiver 3 has a threshold near
C/N = 13 db. At any C/N equal to or greater than 13 db, the audio S/N exceeds that for
SSB by 25 db.
Based on the foregoing, the expected audio S/N ratios for the satellite when it is mid-
way between JPL and BTL are as shown in Table 3.
Table 3
Expected Audio Signal-to-Noise Ratios for the Three Modulation Techniques
When the Satellite is Midway Between the Terminals (Overhead in the Case of NRL-BTL)
Path of Transmission
BTL-JPL (E-W)
JPL-BTL (W-E)
NRL-BTL
SSB
22.3
34.2
38.6
Expected Audio S/N
(db)
FM or FMFB
47.3
59.2 (57 db measured*)
63.6 (> 57 db measured*)
:::The maximum S/N obtainable in this receiver is limited by the audio amplifier noise.
This begins to be significant at a S/N of about 50 db and accounts for the difference
between the computed and measured S/N ratios.
The discussion above has been for the JPL-BTL circuit; however, the same general com-
ments would apply to the NRL-BTL circuit with the path loss modified according to tile
free-space path loss differences shown in Fig-ure 3 and t._e difference in free-space path
loss when the satellite is directly above the terminals. The expected audio S/N when the
satellite is directly over the terminals is included in Table 3.
RECEIVED SIGNAL STRENGTH USING ORBITAL PARAMETERS
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The foregoing material was based on the assumptior that the satellite orbit was circular
and the altitude was 1000 miles. After the experiment was underway it was necessary to
compute the loss for the known position of the satellite in order to compare the measured
mid theoretical received signal amplitudes. For this purpose a program was written for
the IBM 7090 computer to calculate a path loss paramet_ r L for two given stations using
Echo I at the same time:
L(t) : 10 lOgl 0 I(47r)3 dl2(t)-- (22(t) 1A2_
where t refers to time. The inputs to this program are the orbital elements, station co-
ordinates, frequency, and balloon cross section. The re,:eived power, in decibels, is then
(PR) : 10 Io_10(G1G2PT) - L:t) .
To save computer time, L(t) was calculated for only one frequency, 2390 Mc, since
the values only differed by a constant from those of anot]ter frequency. Calling this value
L0(t), and using the antenna gains from Table 2, the e_pressions given in Table 4 for
received power in dbm were derived.
Table 4
Received Power for a Transmitted Power of 10 kw
Path Frequency (Me) Received Power PR (dbm)
BTL-JPL
JPL-BTL
NRL-BTL
BTL-BTL
960
2390
2390
961
166.1 - L0 ± 0.7
166.6 - L 0
162.9 - L 0
-122.0 - 40 loglod
(d = slant range in km)
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REFERENCES
1. Hogg, D. C., "Effective Antenna Temperatures Due to Oxygen and Water Vapor in the
Atmosphere," J. Appl. Phys. 30(9):1417-1419, September 1959
2. DeGrasse, R. W., Hogg, D. C., Ohm, E. A., and Seovil, H. E. D., "Ultra-Low-Noise
Antenna and Receiver Combination for Satellite or Space Communications," Proc. Nat.
Elect. Conf. 15:370-379, 1959
3. Ruthroff, C. L., "FM Demodulators with Negative Feedback," Bell System Tech. J.
40(4):1149-1156, July 1961; also NASA Technical Note D-1134, 1961
10
APPENDIX A
Free-Space Path Loss as a Function of Satellite Position
The variation in free-space path loss as a function of the position of the satellite in
the region of mutual visibility can be understood by exan_Aning the behavior of dl2d 2 in
Equation 2 of this report. The geometry is shown in Figure A1. The distances from the
satellite to terminals H and G are d I and d2 respectively. The path loss is proportional
to d12 d2 2 . From the law of cosines,
d12 = R 2 + (R + h) 2 - 2R(R + h) cos a : A - B cos a,_
(A1)
d22 = R 2 + (R + h) 2 - 2R(R + h) cos y = A - B cos y,
where
Now let M
cos 7 = cos ¢ sin a sin _ + cos _ cos _5 .
= B/A and normalize to A:
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b_
d12 d 2
A2 -(1- Mcos a_(1 - Mcos q_sin asinfl - Mcos acos fl). (A2)
(b)
Figure A1 - Satellite geometryfor path-loss calculations
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Solving for cos ¢
with
results in
cos ¢ = (1 -
M(1 - M cos a) (sin a sin £)
11
(A3)
2R(R + h)
M =
R 2 + (R + h) 2
= central angle between terminals H, G,
d12 d 2
A 2
- normalized path-loss parameters.
We are interested only in points which do not fall below the horizon. Thus, a has a
maximum determined by
R (A4)COS ama x = R + h
The normalized path-loss parameter when the satellite is midway between the terminals
is found by noting that ¢ = 0 and _ = 7 = /3/2. Thus
(d12d22/ = l1 - Mcos_-_/2 (AS)\ A2 /0
The maximum value of this parameter occurs when the satellite appears on the horizon to
both terminals. For this case, 7 = am_x and
ld? d}/ (A6)
When the satellite is at midpath for an altitude of 1000 miles, the values of these para-
meters are:
R = 3950 miles
= /_/2 = 16.89degrees
A = 4.01 x l0 T miles 2
B = 3.91 × l0 T miles 2
M = 0.975
d12d22 = 7.2 x 1012 miles 4.
12
A programhasbeenpreparedfor theIBM 704computeremployingEquationsA3=A6,
andthepath-losscontoursof Figures2 and3 of this report wereplottedfrom thesedata.
Negativesignsindicateincreasingloss.
Thepointsof minimumpathloss are foundby settir_g¢ = 0 in Equation A2 and dif-
ferentiating with respect to _:
da \-A2_J = M sin a - M cos (/3 - a - - M cos M sin (_ - a) . (AT)
The desired points will be solutions of the equation obta:ined by setting Equation A7 equal
to zero; _ = /3/2 is a solution, but it is not necessaril; a point of minimum loss. By the
usual tests we have the following: the midpath point is a maximum loss point if cos (fl/2)-M
is negative. Conversely, if cos (/3/2)-M is positive, the midpath is a minimum loss point.
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APPENDIX B
Error Incurred by Assuming Round-Trip
Path Loss from Either Terminal
When the terminals are close together, as are Stump Neck and Holmdel, their central
angle _ is small, and the path-loss computations are simplified, because d12a22 = d14. It
is important to derive the maximum error incurred by using this approximation. From
Equation A1 of Appendix A,
where
d22 = dl 2 + _(R + h)(cos _ - cos :_) , (B1)
cos Y = cos ¢ sin a sin fi + cos a cos /5 .
Substituting for cos _ results in
d22 = d12 + 2R(R + h)[cos a (1-cos /3)-cos 4_sina sin /_].
If _ << 77/2, this reduces to
d22 = d12 - 2R(R + h)_ sin ct cos ¢ .
The ratio of the two sides of the approximation is
d12d22 = d22 = 1 - 2/?R(R + h) cos ¢ sin a
dl 4 d12 R2 + (R + h) 2 - 2R(R + h) cos ct
(B2)
(B3)
(B4)
The path-loss error in decibels is given by 10 loglo [Equation B4]. The error will be
maximum when cos¢ = _+1 and = = _max • Assuming that R = 3950 miles, h = 1000
miles, and cos _ = -1, then area x -- 37.1 degrees, and
d2 2
: 1 + 2.65_, _ << 17/2. (B5)
d12
For the NRL-BTL path, # = 200/3950 = 0.0506 radian, and d22/di 2 = 1.134. The maxi-
mum error is 10 log10 1.134 = 0.546 db.
NASA-Langley, 1961



Project Echo: System Calculations

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