Similarities between experimentally measured power spectral density curves of landing radar signal returned from rough surface and computer simulated curves for sinusoidal surface

Chambers, D. E.

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https://ntrs.nasa.gov/search.jsp?R=19690007630 2020-03-12T07:19:23+00:00Z
11176-HO77-RO-00
APOLLO SPACECRAFT SYSTEMS ANALYSIS PROGRAM
TECHNICAL REPORT
TASK E-34D
	
NAS9-8166	 26 November 1968
A COMPARISON OF THE COMPUTED LR RECEIVED SIGNAL SPECTRUM
AND THE 1967 PEARL DATA
Prepared For
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
MANNED SPACECRAFT CENTER
HOUSTON, TEXAS
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11176-HO77-RO-00
APOLLO SPACECRAFT SYSTEMS ANALYSIS PROGRAM
A COMPARISON OF THE COMPUTED LR RECFIVED SIGNAL SPECTRUM
AND THE 1967 PEARL DATA
TASK E-34D
26 NOVEMBER 1968
Prepared by:
_OdAl
Da l e E. Chambers
Approved by:
C. E. Blakely, Task Manager
Approved by: _.(}
/9'. DeVillier, Manager
ommuni cati on and Sensor Systems
'Department
TRW.
SYMMS GROUP
L 12, A R Y C 0 P y
DEC 1 0 1968
MANNED SPAGEOI~AFT CEN , i:.a,
HOUSTON, TEXAS
TABLE OF CONTENTS
1.0	 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . .	 1
2.0	 DISCUSSION. . . . . . . . . . . . . . . . . . . . . . . . r . . . 	 2
3.0	 SUMAARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	 14
REFERENCES . .
	
. . . . . . . . . . . . . . . . . . . . . . . 	 . . .	 15
APPENDIX. . . .	 . . . . . . . . . . . . . . . . . . . . . . . . . . .	 16
i
R
i
LIST OF ILLUSTRATIONS
Figure Page
1 Upper and Lower Envelopes of a WSMR Summer 1967 Landing
Radar PSD for the Lavic Site(545 foot altitude).
	
.	 .	 .	 .	 . 3
2 Computed Power Spectral
	
Density Plot	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 . 4
3 Computed Power Spectral
	
Density Plot
	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 . 5
4 Upper and Lower Envelopes of a WSMR Summer 1967 Landing
Radar PSD for the AFSWC Site(547 foot altitude).
	 .	 .	 .	 .	 . 6
5 Computed Power Spectral
	
Density Plot	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 . 7
6 Upper and Lower Envelopes of a WSMR Summer 1967 Landing
Radar PSD for the AFSWC Site(228 foot altitude). 	 .	 .	 .	 .	 . 8
7 Computed Power Spectral
	
Density Plot	 .	 .	 .	 .	 .	 .	 .	 .	 .	 .	 . 9
8 Competed	 PSD Plot for a	 Pbr;e :,,'^face.
	
.	 .	 .	 .	 .	 .	 .	 .	 .	 . 11
9 Effects of Surface Amplitude on Computed PSD Curves.	 .	 .	 . 12
10 Effects of Surface Wavelength on Computed PSD Curves . 	 .	 . 13
11 Geometrical Quantities Associated with the Computer
Comparison PSD Curves:	 :	 .	 .	 .	 .	 .	 .	 .	 .	 .	 . 17
11.0 INTRODUCTION
Ail
The purpose of this report is to exhibit similarities  between experi-
mentally measured power spectral density (PSD) curves of the signal returned
from a rough scattering surface and the curves obtained from a computer
program for a sinusoidal surface, The report also shows how the shape of
the computed PSD curves is affected by varying the geometrical parameters
of the surface.
The PSD of the signal returned from the lunar surface is a quantity
needed to evaluate the performance of the Landing Radar. Reference [1]
formulates a numerical algorithm which could be used to compute the PSD
whenever a detailed specification of the surface geometry is known. The
specific surface considered in Reference [1] is a sinusoidal surface of
limited extent. A computer program TEORR, (Terrain Effects on Radar
Return), was developed as a tool to expedite this numerical algorithm and
was used to generate the data for the PSD curves in this report.
The number of computed and measured cases compared in this report were
limited because of the range of parameters available and the amount of
computer time required for each .omparison. Further comparisons will be
made as additional data become available.
i
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2.0 DISCUSSION
Power spectral density plots from the 1967 summer test program at WSMR
of the Landing Radar were obtained from LEC (see Figures 1, 4, and 6) and
were used to show similarities between the measured and the computed PSD
curves. The geometri cal inputs to the computer model are discussed in the
Appendix and were constructed to simulate the configuration used in the
actual test program.
All the PSD's in this report are for vel ocity sensor beam 3. Figure 1
shows the approximate upper and lower envelopes of an experimentally measured
PSU plut for the WSMR LAVIC site. The large difference between the upper
and lower envelopes is attributed to the signal-to-noise  rati o of the data
reduction system. Figures 2 and 3 are PSD curves from the computer program
for the s ame velocity and altitude as given in Figure 1 but for a sinusoidal
surface of 35 foot surface wavelength and an amplitude of 2 feet and 10 feet
respectively. They have the same general shape as the experimental curve
but differ in fine structure. The si del obes occurring at approximately
700 and 1700 Hz are due to the antenna pattern employed in the calculations.
This pattern is of the sin p/p 'type, hence the first pair of sidelobes is
26 db below the main lobe.
Figure 4 and Figure 6 are the approximate upper and lower envelopes
of experimentally measured PSD plots for the WSMR AFSWC site for different
altitudes and velocities. Figuire 5 is a computed PSD curve for comparison
with Figure 4. Figure 7 is a similar curve to compare with Figure 6. Both
of these computed curves compare less favorably with the experimentally
measured curve with respect to the mean frequency and shape. The computer
program was used to show that a small change in the vehicle attitude re-
sulted in a large change in the mean frequency of the main lobe. For
example, a three degree shift in the vehicle attitude could shift the main
lobe as much as 175 Hz. Since no attitude data was given on the WSMR PSD
plots the mean frequency shift (as shown in Figures 5 and 7) can be attributed
to a possible difference in the ('^Ittitude data input to the computer program
and the actual vehicle attitude.
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The effects of varying the geometrical parameters of the sinusoidal
surface on the shape of the computed PSD curves is illustrated in Figures 8,
9 and 10. All three of these figures were for the physical conditions used
in Figure 1. The PSD return from a planar surface with small scale scatter-
ing properties is shown in Figure 8. It is mainly a function of the two-way
antenna pattern and is a smooth curve. It can be thought of as a sinusoidal
surface of zero amplitude. As the amplitude increases, small undulations
start appearing in the vicinity of the main lobe. These are caused by the
surface terrain since for a sinusoidal surface of constant wavelength vari-
ations in the wave amplitude causes the undulations to vary in magnitude
but to remain in approximately the same location. Figure 9 shows these
undulations for amplitudes of 5, 7.5 and 10 feet. Figure 2 is the same
curve for an amplitude of 2 feet and is a much smoother curve. The surface
wavelength is 35 feet on Figures 2 and 9.
The wavelength of the sinusoidal surface can also affect the shape of
the PSD curves as is shown in Figure 10. The amplitude is 10 feet and wave-
--	
lengths of 35, 70 and 100 feet are shown. Figure 10 shows that as the wave-
ieO gth gets larger the PSD curves get smoother as could be expected.
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3.0 SUMMARY
It has been shown that the antenna pattern is the primary factor
in determining the shape of the power density spectrum for low altitude
flights. The specific geometry of the terrain can perturb the shape of
the spectrum only slightly around the envelope of the antenna pattern.
Undulations in the vicinity of the main lobe caused by the sinusoidal
surface could be smoothed by allowing the transmitter-receiver to move
over several positions, calculating the PSD data for each position and
averaging the data for each frequency. A curve so obtained would be more
similar to an actual measured curve since in the actual case the vehicle
is in motion and the measurement takes place over a finite time.
Since the antenna used during the data collection was an early
prototype model, information concerning the antenna sidelobe structure
is not available. For this reason no attempt was made to compare the
computed to measured curves in the sidelobe region.
It was shown with the
	 es computer program that small attitude changeP	  g	 g
(3 deg) resulted in a large shift of the mean frequency (175 Hz). That is
a possible explanation for the difference in the mean frequency between
the measured and computed PSD curves in some cases. Otherwise, the general
shape of the measured PSD curves can be predicted by the computer program
using a sinusoidal surface to simulate the actual experimental site.
14
t
REFERENCES
1. W. B. Warren and L. Armijo, A Technique for ComputinTerrain Effects
on Radar Return, TRW Project Technical Report, Task f 
	
G=^i
05952-HSO340-4-0, 14 May 1968.
2. R. Mireles and L. Armijo, Geometric Transformations Associated with
Pct PEARL, TRW Project Technical Report. Task 34B, 595 -H26 -RO-00,
14 July 19670
3, R, Mireles and J. Wilson, LM Landing Radar Evaluation Program (LRTRWI),
TRW Project Technical Report, Task 34B, 05952-H211 RO-00, 1 June 1967
4, E. T. Dickerson, Interim LR Reflectivity Model, TRW Project Technical
Report, Task E-30,	 -H0 8-TO-00, 9 August 1968.
APPENDIX
GEOMETRICAL AND PHYSICAL PARAMETERS USED IN THE COMPUTER PROGRAM
The sinusoidal surface used in the computer program is given by
2"Zs
Xs - Asin
	 ^
s
where A is the amplitude and As is the surface wavelength. The first
quadrant of the surface is illustrated  i n Figure 11. The extent of the
sinusoidal surface is limited in the Zs direction to
(h-A) as
(zs1max _ 2^"
for analytical expediency. Beyond 1Zs1max the surface is a plane. A and
Xs were chosen for these runs so that the sinusoidal surface extended far
beyond the intersection of beam 3 with the surface.
The surface coordinate system (X s ,Y s ,Zs ) has origin on the surface
plane and is oriented so that Xs i s; vertical and goes through the trans-
mitter-receiver which is at an altitude h above the surface. It was
assumed that the antenna coordinate system ( XAt YAs zA ) with origin at the
transmitter-receiver was oriented so that except for translation it was
coincident with the surface coordinate system. The velocity sensor beam
3 was modeled with e l = 24.460018 deg and ^, = 34.379734 deg according to
p. 27 of Reference [2] and the wavelength of the transmitted signal was
0.09358 feet (10.51 GHz). The vehicle velocity was assumed to be along
the positive Zs direction.
4J _
16
„_
tier-Receiver
V
S
Velocity Sensor Seam 3
YA
(l
Y
s /
Zs
XA
0'`
4_
Figure 11. Geometrical Quantities Associated with the
Computer Comparison PSD Curves
17
 
'P I-IMAqw- P.
A sin p/p type function was used to compute the two-way normalized
antenna beam pattern. The constants 4 of the function were adjusted to give
major and minor beamwidths of 6.3 deg and 3.7 deg, respectively, which
were obtained from the August 1968 revision of the training manual for the
LM-3.
The reflectivity was computed using the Beckmann-Smith theoretical
reflectivity function. For these runs an initial reflectivity for Os = 0
deg was chosen to be •8 db in accordance with Reference [4].
t
c
18


Apollo spacecraft systems analysis program. A comparison of the computed LR received signal spectrum and the 1967 PEARL data

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