Design considerations for beamwaveguide in the NASA Deep Space Network
Post on 26Mar2017
213 views
DESCRIPTION
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 36, NO. 12, DECEMBER 1988 1779 Design Considerations for Beamwaveguide in the NASA Deep Space Network THAVATH VERUTTIPONG,…TRANSCRIPT
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 36, NO. 12, DECEMBER 1988 1779
Design Considerations for Beamwaveguide in the
NASA Deep Space Network
THAVATH VERUTTIPONG, MEMBER, IEEE, JAMES R. WITHINGTON, VICTOR GALINDOISRAEL, FELLOW, IEEE,
WILLIAM A. IMBNALE, MEMBER, IEEE, AND DAN A. BATHKER, SENIOR MEMBER, IEEE
AbstractRetrofitting an antenna that was originally designed without
a beamwaveguide (BWG) introduces special difficulties because it is
desirable to minimize alteration of the original mechanical truss work and
to image the actual feed without distortion at the focal point of the dual
shaped reflector. To obtain an acceptable image, certain geometrical
optics (GO) design criteria are followed as closely as possible. The
problems associated with applying these design criteria to a 34m dual
shaped Deep Space Network (DSN) antenna are discussed. The use of
various diffraction analysis techniques in the design process is also
discussed. The geometrical theory of diffraction (GTD) and fast Fourier
transform (FFT) algorithms are particularly necessary at the higher
frequencies, while physical optics (PO) and spherical wave expansions
(SWE) proved necessary at the lower frequencies.
I. INTRODUCTION
PRIMARY requirement of the NASA Deep Space A Network (DSN) is to provide for optimal reception of
very low signal levels. This requirement necessitates optimiz
ing the antenna gain to the total system operating noise level
quotient. Low overall system noise levels of 1620 K are
achieved by using cryogenically cooled preamplifiers closely
coupled with an appropriately balanced antenna gain/spillover
design. Additionally, highpower transmitters (up to 400kW
continuous wave (CW)) are required for spacecraft emergency
command and planetary radar experiments. The frequency
bands allocated for deep space telemetry are narrow bands
near 2.1 and 2.3 GHz (S band), 7.1 and 8.4 GHz ( X band),
and 32 and 34.5 GHz (KO band). In addition, planned
operations for the Search for Extraterrestrial Intelligence
(SETI) program require continuous lownoise receive cover
age over the 110GHz band. To summarize, DSN antennas
must operate efficiently with low noise and highpower uplink
over the 135GHz band.
Feeding a large lownoise groundbased antenna via a
beamwaveguide (BWG) system has several advantages over
directly placing the feed at the focal point of a dualshaped
antenna. For example, significant simplifications are possible
in the design of highpower watercooled transmitters and low
noise cryogenic amplifiers, since these systems do not have to
rotate as in a normally fed dual reflector. Furthermore, these
systems and other components can be placed in a more
accessible location, leading to improved service and availabil
Manuscript received August 14, 1987; revised November 13, 1987. This
work was supported by the National Aeronautics and Space Administration.
The authors are with the Jet Propulsion Laboratory, California Insitute of
Technology, 4800 Oak Grove Drive, Pasadena, CA 91109.
IEEE Log Number 8823645.
ity. Also, the losses associated with rain on the feedhorn
radome are eliminated because the feedhorn can be sheltered
from weather.
Many existing beamwaveguide systems use a quasioptical
design, based on Gaussian wave principles, which optimizes
performance over an intended operating frequency range.
These designs can be made to work well with relatively small
reflectors (a very few tens of wavelengths) and may be viewed
as âbandpass,â since performance suffers as the wavelength
becomes very short as well as very long. The long wavelength
end is naturally limited by the approaching small D/X of the
individual beam reflectors used; the short wavelength end does
not produce the proper focusing needed to image the feed at
the dualreflector focus. In contrast, a purely geometrical
optics (GO) design has no upper frequency limit, but
performance suffers at long wavelengths. These designs may
be viewed as âhighpass.â Considering the need for practically
sized beam reflectors and the high DSN frequency and
performance requirements, the GO design is favored in this
application.
Retrofitting an antenna that was originally designed without
a beamwaveguide introduces special difficulties because it is
desirable to minimize alteration of the original structure. This
may preclude accessing the center region of the reflector
(typically used in conventional beamwaveguide designs) and
may require bypassing the center region. A discussion of the
mechanical tradeoffs and constraints is given herein, along
with a performance analysis of some typical designs. In the
retrofit design, it is also desirable to image the original feed
without distortion at the focal point of the dualshaped
reflector. This will minimize gain loss, reflector redesign, and
feed changes.
To obtain an acceptable image, certain design criteria are
followed as closely as possible. In 1973, Mizusawa and
Kitsuregawa [ 11 introduced certain GO criteria which guaran
tee a perfect image from a reflector pair (cell). If more than
one cell is used (where each cell may or may not satisfy
Mizusawaâs criteria), application of other GO symmetry
conditions can also guarantee a perfect image. The problems
and opportunities associated with applying these conditions to
a 34m dualshaped antenna are discussed.
The use of various diffraction analysis techniques in the
design process is also discussed. Gaussian (Goubau) modes
provide important insight to the wave propagation characteris
tics, but geometrical theory of diffraction (GTD), fast Fourier
transform (FFT), spherical wave expansion (SWE), and
OO18926X/88/12OO1779$01 .OO O 1988 IEEE
1780 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 36, NO. 12, DECEMBER 1988
oc
t
/ I \
E
\
Y
m
(a) (b) (C)
Fig. 1 . Examples of twocurved reflector beamwaveguide configurations; E = ellipsoid, H = hyperboloid, P = paraboloid, F =
flat plate.
CELL 1 CELL 2 physical optics (PO) have proven faster and more accurate.
GTD and FFT algorithms are particularly necessary at the
higher frequencies. PO and SWE have been necessary at the
lower frequencies.
11. DESIGN CONSIDERATIONS
FIRSTPAIR
A . Highpass Design Feed Imaging
For a 2.4m (8ft) reflector beamwaveguide operated over
135 GHz with near prefect imaging at X band and Ka band
and acceptable performance degradation at L band (1 GHz)
and S band, a highpass type beamwaveguide should be used.
This type of design is based upon GO and Mizusawaâs criteria.
Mizusawaâs criteria can be briefly stated as follows. For a
circularly symmetric input beam, the conditions on a conic
reflector pair necessary to produce an identical output beam
are:
1) the four loci (two of which may be coincident) associated
with the two curved reflectors must be arranged on a
straight line; and
2) the eccentricity of the second reflector must be equal to
the eccentricity or the reciprocal of the eccentricity of
the first reflector.
Figs. l(a)l(c) show some of the orientations of the curved
reflector pair that satisfy Mizusawaâs criteria. We term a
curved reflector pair as one cell.
For the case of two cells where at least one cell does not
satisfy Mizusawaâs criteria, a perfect image may still be
achieved by imposing some additional conditions, described
below. Let SI, S2, S3 , and S4 be curved surfaces of two cells as
shown in Fig. 2. Each surface can be an ellipsoid, hyperbo
loid, or paraboloid. Keeping the same sequence order, the
surfaces are divided into two pairs (first pair ( S 2 , S,) satisfies
Mizusawaâs criteria; second pair (S, , S,) satisfies Mizusawaâs
criteria after eliminating the first pair).
Note that the first pair can be eliminated because the input is
identical to the output. Also, this concept can be applied to
cases with more than two cells. An example of an extension of
Mizusawaâs criteria for a multiplereflector beamwaveguide is
given in Fig. 3.
SECOND PAIR
Fig. 2. Multiple curved reflector beamwaveguide system; S, = ellipsoid,
hyperboloid, or paraboloid.
Fig. 3. Demonstrating extension of Mitzusawaâs criteria for a multiple
reflector beamwaveguide (ellipsoids/hyperboloids).
VERUTTIFQNG et al.: BEAMWAVEGUIDE IN NASA DEEP SPACE NETWORK 1781
25 0 25
0. deg
(e)
Fig. 4. Geometrical optics field reflected from each surface of beamwaveguide system consisting of four consecutive offset
paraboloids S , , S2 , S3 , and S,.
Fig. 4 shows a geometrical optics field reflected from each
reflector of a beamwaveguide system consisting of four
consecutive offset paraboloids. It is clear from Fig. 4 that the
distorted pattern from the first cell is completely compensated
for by the second cell and yields an output pattern identical to
the input pattern.
B. Bandpass Design Feeding Imaging
For many systems, a singlefrequency or bandpass design
can be advantageously employed. The design considerations
can best be described with reference to Fig. 5, where the
center frequency is given as f o and L2 is the spacing between
two curved surfaces. A bandpass beamwaveguide system is
usually composed of two nonconfocal (shallow) ellipsoids
(eccentricity close to one). Again from Fig. 5 , FAl and FA2 are
the GO foci of ellipsoid A , while FAA and FAB are the best fit
phase centers of the scattered field from surface A (evaluated
at frequency = fo by using physical optics technique) in the
neighborhood of surfaces A and B , respectively. The distances
from FA2, FAA, and FAB to surface A are normally large
compared to L1 and Lz. Similarly, FBI, Fm, FBB and FBA are
for ellipsoid B. The locations of FAA, FAB, FBB and FBA
depend on frequency as well as surface curvatures and Lz. For
example, with a 2.4m, reflector with eccentricity = 0.97 at
I
A / \ E
(b)
Fig. 5 . Bandpass feed imaging configuration.
f = 2 . 3 GHz and L2 = 8 m (26 ft), FAB is about 120 m (400
ft) to the left of ellipsoid A (while FAA is about the same
distance as FAB but to the right), as shown in Fig. 5(a). In the
GO limit, FAA and FAB are at the same location, to the right of
ellipsoid A .
For a good bandpass system, FAA and FBs should be at the
1782 IEEE TRANSAC'I 'IONS ON ANTENNAS AND PROPAGATION, VOL. 36, NO. 12, DECEMBER 1988
ic T TWO IDENTICAL ELLIPSOIDS
1 D = 2 8 M ( 1 1 0 1 n )
L1 = 3 9 M (155 In I
L 2 = 7 9 M ( 3 1 0 m )
e = 09703
25 t 1
m
6
D
U
120 t
60 I r IN PUT
120 
INPUT
I
a
60 
+*+ I 0 
60
120 I 17 17 1
180 I I l l I I I 1 I I l l I
30 25 20 15 10 5 0 5 10 15 20 25 30
8. deg
Fig. 6. Comparison between input feed pattern and feed image from
bandpass beamwaveguide at center frequency = 2.3 GHz.
same locations as F B A and F A B , respectively. It is also
desirable to have two identical surfaces for low cross
polarization and a symmetrical system. Trial and error is
needed to determine surface parameters for the desired
operating frequency and bandwidth within specified losses.
Fig. 6 shows the input and output patterns from a bandpass
beamwaveguide system where F A A and F B ~ are chosen to be at
the same locations as F B A and F A B , respectively. The two
identical ellipsoids are designed atfo = 2.3 GHz. The results
show good agreement between the input feed and the imaged
feed. Bandpass beamwaveguide systems appear useful when a
limited band coverage is required, using modestly sized (D =
20 to 30 A) reflectors. However, these systems do not perform
well as the wavelength approaches either zero or infinity. In
contrast, a highpass (GO) design focuses perfectly at zero
wavelength and focuses very well down to D  40X. The
performance then decreases monotonically as D becomes
smaller in wavelengths.
111. APPLICATION CONS~DERATIONS FOR THE DSN
The DSN presently operates three 34m highefficiency
dualshaped reflector antennas with a dualband (2.318.4
GHz) feed having a farfield gain of +22.4 dBi that is
conventionally located at the dualshaped focal point. The
structures were designed prior to beamwaveguide require
34 METERS
150 IN. DIA
L
I
 +1174 IN.
~ ELEV AXlX 630 IN.
F = FLAT MIRROR
P = PARABOLOID
E = ELLIPSOID
TOP OF TRACK
DATUM 0.0
Fig. 7. Preliminary possible configuration of 34m bypass beamwaveguide.
34 METERS
+lo26 IN.
VERTEX +767 IN.
ELEV AXlX +630 IN.
F = FIAT MIRROR
P = PARABOLOID
TOP OF TRACK
DATUM 0.0 IN.
Fig. 8. 34m centerline beamwaveguide.
ments and feature a continuous elevation axle and carefully
designed elevation wheel substructure. The elevation wheel
substructure, shown in Fig. 7, plays a key role in preserving
main reflector contour integrity as the antenna rotates in
elevation. Retrofitting an antenna that was originally designed
without a beamwaveguide introduces some difficulties in
maintaining contour integrity at 8 GHz and above (for good
RF performances) as well as keeping low retrofit costs. Fig. 8
shows a conventional beamwaveguide approach that is a
compact and straightforward RF design and also suitable for a
brand new antenna. However, the conventional beamwave
guide may not be suitable to retrofit into existing DSN
antennas because it severely impacts retrofit costs and the
contour integrity of the main reflector. Fig. 8 shows one of the
possible arrangements of an unconventional approach (bypass
mode) attempted to reduce structure impacts and retrofit costs.
Although several detailed options are possible, most options
use two cells (four curved reflectors) with two flat reflectors.
30
8. deg
Nearfield one ellipse diffraction patterns (RCPpol, S band, offset plane) Fig. 9.
l l l l l l l l I l l I I I I I I
Some of the options make use of the flexibility afforded by
allowing each cell to be distorting (of itself), but then
compensated for by the second cell as described in Figs. 3 and
4.
Our goal is therefore to image perfectly a feed located
perhaps 4050 ft below the main reflector to a dualshaped
focus. This goal applies over the 135GHz frequency range,
using a beamwaveguide housing limited to about 2.4 m (8 ft)
in diameter. The image should be a 1 : 1 beamwidth transfor
mation of the original feed, permitting reuse of that feed and
no changes to the subreflector or main reflector contour.
IV. ANALYTICAL TECHNIQUES FOR DESIGN AND ANALYSIS
The software requirements for the study and design of
beamwaveguides are extensive. These include the capability
for GO synthesis, Gaussian wave analysis, and high and low
frequency diffraction analysis. These requirements are dis
cussed below.
A . Geometrical Optics Synthesis Capability
This capability includes software that synthesizes as well as
analyzes reflectors satisfying the MizusawaKitsuregawa con
ditions [ I] for minimum cross polarization and best imaging.
In the highfrequency domain (835 GHz for the designs
considered herein), the focused system shown in Fig. 1 is
desired. Of course, two paraboloids or mixtures of various
conicsection reflectors (as shown in Fig. 1) can be synthe
sized. Optimization at lower frequency bands generally is
accomplished by appropriate defocusing of the BWG system.
B. Gaussian Wave Analysis Capability
The required defocusing for the lower bands can be
determined by using various beam imaging techniques [2]
which are based on Gaussian beam analysis methods first
develoned bv Goubau and Schwering 131. While Gaussian
mode analysis is useful at high as well as low frequencies for
ââconceptualâ â designing, conventional diffraction analysis
methods are found to be more suitable.
One consideration is that Gaussian mode analysis does not
supply spillover losses directly with as great an accuracy as
conventional diffraction analysis methods. The Gaussian
modes supply the discrete spectrum, whereas the spillover
losses are directly related to the continuous spectrum [4].
Spillover for Gaussian modes is computed by a method more
suitable in terms of computational efficiency for a great
number of reflection (refraction) elements [3]. The antenna
systems considered here rarely contain more than four curved
reflectors. Futher, spillover losses must be reliably known to
less than the tenth of a decibel for highperformance systems.
C. LowFrequency Diffraction Analysis Capability
Because of the large bandwidth of operation (135 GHz), no
single diffraction analysis method will be both accurate and
efficient over the entire band. Efficiency, in the sense of speed
of computation, is critical, since in a constrained design many
different configurations may be analyzed before an optimum
beamwaveguide configuration is selected.
In the region of 2.3 GHz (for the 34m antenna considered
herein), the reflector diameters are generally about 20X. Since
a very low edge taper illumination, at least 20 dB, is used
to reduce spillover loss, the âeffectiveâ reflector diameters
are very small in this frequency range.
A comparison between three diffraction algorithms: PO,
GTD, and JacobiBessel (JB) [5] leads to the conclusion that:
1) GTD is not sufficiently accurate at the low frequencies;
2) JB is very slowly convergent in many cases and gives
only the farfield in any case (we must determine near
field patterns);
3) PO is both accurate and sufficiently fast below 3 GHz.
The above results are illustrated in Figs. 9 and 10 when an
1784 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 36. NO. 12, DECEMBER 1988
40 30 20 1 0 0 10 20 30 40
8. deg
Fig. 10. Farfield one ellipse diffraction patterns (RCPpol, S band, offset plane).
actual + 22.4 dBi corrugated feedhorn is used. It can be seen
from Fig. 10 that PO and JB agree perfectly to  t 20â, GO
beamwidth to reflector edge = t 13â. The indices ( 5 , 9, 9)
and (3, 6, 6) refer to the (P, N, M) indices in [ 5 ] . They are the
number of modes ( P x N x M ) required for convergence in
application of the JB analysis.
There are two general PO computer algorithms useful at the
low frequencies. One is a straightforward PO algorithm,
which subdivides the reflectors into small triangular facets.
This is essentially a trapezoidal integration of the nearfield
radiation integral and is a very flexible algorithm.
A second algorithm is based on a spherical wave expansion
[6] and is also a PO technique. It has two useful characteris
tics: 1) when a high degree of circular symmetry exists in the
scattered fields, then the twodimensional radiation integral is
reduced to a small number of onedimensional integrals with a
resultant marked decrease of computational time; and 2) an (r)
interpolation of the scattered field (at different radial distances
from the coordinate origin ) is done very accurately.
The PO (directtrapezoid) and SWE algorithms are useful
for crosschecking results. Nearfield and farfield computa
tions and comparisons in both amplitude and phase are shown
in Figs. 11 and 12. Fig. 11 contains nearfield PO and SWE
results for scattering from one paraboloid reflector. Fig. 12
contains the nearfield scattering for two paraboloid reflectors
and a comparison of the âimagingâ with the feed pattern. At
higher frequencies ( > 8 GHz), the feed pattern will be
virtually perfectly imaged over an angle of t 15â.
D. HighFrequency Diffraction Analysis Capability
For reflector diameters of 70 or more wavelengths ( > 8
GHz), including a 24 dB edge taper, PO analysis methods
25 
20 
15 12 9 6 3 4 3 6 9 12 15
e,
( a )
1501 , I 1 I 1 1 l I , I
e, d.a
(b)
2 . 3 GHz. (a) Amplitude. @) Phase.
Fig. I I . PO and SWE nearfield scattering from single 2.4m paraboloid at
become too expensive and time consuming. (The SWE may
still be useful if a high degree of rotational symmetry exists.)
An alternative approach is to use GTD analysis. The GTD
computation time does not increase with increasing reflector
diameters, but the accuracy of the analysis does increase.
VERUTTIPONG et U / . : BEAMWAVEGUIDE IN NASA DEEP SPACE NETWORK 1785
n. do
120
180
350 IN. 
280 IN. 280 IN.

r = 280 IN.

I l l l l l l l l l
8. deg
Fig. 13. Nearfield one 2.4m ellipse diffraction patterns (RCP, 8.4 GHz, offset and I plane cuts)
To test the acuracy of GTD at 8 GHz, comparisons were
made between GTD and PO. Results for the diffraction of a
single ellipsoid are shown in Fig. 13. The results for the phase
of the scattered field were almost as good. GTD was
determined to be accurate at 8 GHz and higher.
Analysis of two or more reflectors by GTD involves some
manipulation of the fields scattered between any two reflec
tors. The fields scattered from one reflector must be placed in
format suitable for GTD scattering from the next reflector.
This is accomplished by computing the vectorscattered field
in the vicinity of the next reflector and then interpolating as
follows:
1) use of an FFT for +variable interpolation;
2 ) use of a secondorder Lagrangian local interpolation for
8 interpolation (for a z axis along the axis of the
reflector, 4 and 8 are spherical coordinates);
3) for the r (of [r, 8 41 spherical coordinates) interpolation,
an approximation consistent with the GTD approxima
tion was to assume a l lr variation in amplitude and a kr
variation in phase. This approximate interpolation
should be checked against exact computations of the near
fields.
By the method described above, mutiple reflector computa
tions, even with a large number of reflectors, can be calculated
with both great speed and accuracy at frequencies above  8
GHz for reflectors of > 70A in diameter.
A typical result is shown in Fig. 14 for a pair of deep
ellipsoids which satisfy the MizusawaKitsuregawa criteria.
The object is to perfectly image the input feed over about
k20". This is accomplished with good accuracy and small
distortions in amplitude and phase at X band frequencies and
higher. However, significant phase distortion is observed at S
band. Nearfield scatter patterns for a pair of 2.2 m parabo
loids at S , X , and Ku bands are shown in Figs. 15, 16, and 17,
respectively. It is seen from these figures that image patterns
and input feed at X and Ka bands are in good agreement within
1786
"? Y "? 2 45 ,4 4 5  ,, 0
\ 90 I
\ , 135
/' '\  90 / I
135 #
I 1 I I I I
1
1m 180
E E E TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 36, NO. 12, DECEMBER 1988

 

I I I I , 1
 INPUT FEED
 IMAGE FEED
1 80
45 0 45
8. deg
Fig. 14. GTD scattering for two 2.4m ellipses, RCP at 8.4 GHz.
101 I , I I I I I
15 10 I 5 0 5 1 IO 15
 ern 9, DEGREE e rn
I
5
I
0
e, DEGREE
INWT FEED
IMAGE FEED '.
IO 15
ern
5 
the useful range (  Om to +Om). Patterns at S band are in
reasonably good agreement.
V. CONCLUSION
A generalized solution has been achieved for retrofitting a
large dualshaped reflector antenna for a beamwaveguide. The
design is termed a bypass beamwaveguide. Several detailed
options within the bypass category remain to be studied and
work continues.
With the analysis capability available, we are gaining some
valuable views of the RF performance behavior of some of the
many options. It appears fairly clear for the 135GHz
requirement that highpass (pure GO) designs are necessary in
contrast to a bandpass (nonconfocal ellipsoids) approach. It
appears that a pair of deep confocal ellipsoids or paraboloids
satisfying the Mizusawa criteria operate (focus) well with
reflector diameters of about 70 X and larger. However, a pair
of paraboloids give a better image for diameters of about 20 X
and smaller.
As a part of this activity, an important extension of the
MizusawaKitsuregawa criteria has been revealed. The princi
ple revealed shows how a tworeflector cell, although in itself
VERUTTIPONG el al.: BEAMWAVEGUIDE IN NASA DEEP SPACE NETWORK 1787
 INPUT FEED
 IMGE FEED \ âââid
James R. Withington was born in Honolulu, HI, in
1948. He graduated from the U.S. Navyâs Elec
tronic Class A School at Treasure Island, San
Francisco, CA, in 1967, and received the B.S.
degree from the University of California, Los
Angeles in 1977.
He was stationed at Cape Canaveral, FL, during
the Apollo years (19681970), where he worked
with reflector antenna and microwave electronics.
The launching of missiles from submerged subma
rines and the tracking of Polaris and Poseidon 
5 missiles occupied his time up until 1972, at which time he was honorably
10 I , I 1 I I discharged. He is now a Senior Engineer and a technical staff member in the
15 10 I 5 0 5 I IO 15 Antenna and Microwave Development Group of the Radio Frequency and
 8, e, DEGREE  ern Microwave Subsystem Section at the Jet Propulsion Laboratory. He was
instrumental in the design and implementation of a feed system to track the
joint French/Soviet Vega Mission (19851986) to Venus and Halleyâs Comet.
He is currently involved in the design of a new beamwaveguide fed 34m
reflector antenna for NASAâs Deep Space Network, and has just completed a
test facility to measure BWG component performances from 2 to 105 GHz.
Mr. Withington was a member of the Technical Program Committee for the
Antennas and Propagation Society in the 198 1 International IEEEIAntennas
and Propagation Society Symposium held in Los Angeles. In 1986, he
mission.
= 45
Y received a NASA Group Achievement Award for his work on the Vega
135 1
I . I I I I
15 10 I 5 4 5 â 10 I5 Victor GalindoIsrael (Sâ52Mâ57SMâ75Fâ77), for a photograph and id â
e rn biography please see page 755 of the July 1987 issue of this TRANSACTIONS. e, DEGREES  ern
Fig. 17. GTD scattering for two 2.2m paraboloids at 32 GHz (comparison
with feed pattern).
William A. Imbriale (Sâ64Mâ70), for a photograph and biography please
see page 755 of the July 1987 issue of this TRANSACTIONS. distorting, may be combined with a second Cell which
compensates for the first and delivers an output beam which is
a good image of the input beam.
REFERENCES
[l] M. Mizusawa and T. Kitsuregawa, âA beamwaveguide feed having a
symmetric beam for Cassegrain antennas,â IEEE Trans. Antennas
Propagat., vol. AP21, pp. 844886, Nov., 1973.
[2] T. S . Chu, âAn imaging beam waveguide feed,â ZEEE Trans.
Antennas Propagat., vol. AP31, pp. 614619, July 1983.
[3] G. Goubau and F. Schwering, âOn the guided propagation of
electromagnetic wave beams,â IEEE Trans. Antennas Propagat.,
vol. AP9, pp. 248256, May 1961.
R. E. Collin, Field Theory of Guided Wave. New York: McGraw
Hill, 1960, pp. 474475.
V. GalindoIsrael and R. Mittra, âA new series representation for the
radiation integral with application to reflector antennas,âIEEE Trans.
Antennas Propagat.,vol. AP25, pp. 631641, Sept. 1977.
A. C. Ludwig, âCalculation of scattered patterns from asymmetrical
reflectors,â Jet Propulsion Lab., Pasadena, CA, Tech Rep. 321430,
Feb. 15, 1970.
[4]
[5]
[6]
Thavath Veruttipong (Sâ77Mâ78), for a photograph and biography please
see page 755 of the July 1987 issue of this TRANSACTIONS.
Dan A. Bathker (Sâ59Mâ62SMâ75) was born in
Minnesota in 1938 He received the B.S. degree in
electronic engineering from California State Poly
technic College, San Luis Obispo, in 1961.
While a student, he became interested in the (then
new) wideband antennas and completed an investi
gation and constructiodtest project of a VHF log
periodic antenna. Since joining the Jet Propulsion
Laboratory Telecommunications Division in 1963,
he has worked to further the rmcrowave antenna
capabilities of the NASA/JPL Deep Space Network.
This work has included ultrahigh CW power transrmssion with lownoise
reception, high accuracy radio flux calibrations and reliable antenna stand
ards, high performance multifeed and simultaneous multiband feeds, correla
tion of mcrowave with large reflector structural performance, and planning
and designing new deep space communications capabilities He is Supervisor
of the Antenna and Microwave Development Group
Mr Bathker is a member of IEEE PGAP and PGMTT He received a
NASA exceptional engineering achievement medal in 1984 âfor sustained
contributions and leadership in application of high performance ground
microwave technology resulting in manyfold increases in data return from
deep space mssions.â
I788 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 36, NO. 12, DECEMBER 1988
A Theoretical Model of UHF Propagation in Urban
Environments
AbstractUrban communications systems in the UHF band, such as
cellular mobile radio, depend on propagation between an elevated
antenna and antennas located at street level. While extensive measure
ments of path loss have been reported, no theoretical model has been
developed that explains the effect of buildings on the propagation. The
development of such a model is given in which the rows or blocks of
buildings are viewed as diffracting cylinders lying on the earth. Represent
ing the buildings as absorbing screens, the propagation process reduces to
multiple forward diffraction past a series of screens. Numerical computa
tion of the diffraction effect yields a power law dependence for the field
that is within the measured range. Accounting for diffraction down to
street level from the rooftops gives an overall path loss whose absolute
value is in good agreement with average measured path loss.
I . INTRODUCTION
HE introduction of cellular mobile telephones and other T radio communications systems in the UHF band (300
MHz3GHz) has imposed the need to predict radio path loss in
urban environments between an elevated antenna and mobiles
at street level. Response to this need has generally been the
development of empirical prediction models based on col
lected measurements of received signal strength. Measure
ments are typically reduced to give average signal strength
versus range from the transmitter, assuming certain antenna
height, etc., as well as to give statistical properties of
variations about the average. Extensive measurements have
shown that in flat terrain, average signal strength has power
law dependence l / R M on range R from a fixed antenna, with
M between 3 and 4 [ 11[7]. The influence of parameters such
as building height, street width, terrain roughness, and slope
are poorly understood and are currently accounted for by a
series of ad hoc correction factors [ l ] , [2], [8].
So far no overall theoretical model has been put forward to
explain the measurements. In this study we present a physical
model of the propagation process that takes place in urban
environments outside the highrise urban core. The model
describes the influence of buildings in neighborhoods com
posed of residential, commercial, and light industrial buildings
which take up the majority of urban land area. The elevated
fixed (base station) antenna is viewed as radiating fields that
propagate over the roof tops by a process of multiple
diffraction past rows of buildings that act as cylindrical
Manuscript received September 17, 1986; revised June 26, 1988. This
work was supported in part by a Contract from GTE Laboratories, Inc., and in
part by a Grant from the New York State Science and Technology Foundation.
This paper is based on a dissertation submitted by J. Walfisch to the
Polytechnic University in partial fulfillment of the requirements for the Ph.D.
degree.
J . Walfisch is with Rafael Institute, Ministry of Defense, Haifa, Israel.
H. L. Bertoni is with the Center for Advanced Technology in Telecommu
IEEE Log Number 8823640.
nications, Polytechnic University, 333 Jay Street, Brooklyn, NY 11201.
a
F
L
H
L R L d J hm
Fig. 1 . Various ray paths for UHF propagation in presence of buildings.
obstacles, as suggested by path 1 in Fig. 1. This process is
found to give range dependence l / R 3 . s for low transmitting
antennas, which is in good agreement with measurements.
A portion of the field diffracted by each row of buildings
reaches street level where it can be detected by the mobile.
Diffraction down to the mobile from the rooftops of neighbor
ing buildings has previously been proposed as the final stage in
the propagation process [9], [lo]. Coupling this final stage
with the computed range dependence, an overall propagation
model is obtained that agrees with observed values of average
signal strength to within a few dB.
11. MODELING ASSUMFTIONS FOR URBAN PROPAGATION
Many cities consist of a core containing highrise buildings
surrounded by a much larger area having buildings of
relatively uniform height spread over regions comprising
many square blocks, except for isolated clusters of highrise
buildings. In this surrounding urban area the buildings lining
one side of a street are adjacent to each other or have
passageways between them that are narrower than the width of
the buildings. The street grid organizes the buildings into rows
that are nearly parallel.
At street level the fields emanating from an elevated fixed
transmitting antenna are shadowed by the buildings. Except
along occasional streets aligned with the transmitter, or at very
close ranges, the transmitting antenna is not visible from street
level. Thus propagation must take place through the buildings,
between them, or over the rooftops with the field diffracted at
the roofs down to street level.
Propagation through buildings is accompanied by loss due
to reflection, attenuation, and scattering by exterior and
interior walls. While the fields penetrating the row of
buildings immediately in front of the mobile may be signifi
cant, as suggested by the path marked 3 in Fig. 1 , the majority
of the propagation path cannot lie through the buildings. When
passageways do exist between buildings, they are seldom
aligned from row to row and aligned with the transmitting
source. As a result, the majority of the paths cannot be
associated with propagation between the buildings.
OO18926X/88/12001788$01 .OO 0 1988 IEEE
WALFISCH AND BERTONI: MODEL OF UHF PROPAGATION IN URBAN ENVIRONMENTS 1789
We conclude that the primary propagation path lies over the
tops of the buildings, as indicated by path 1 in Fig. 1. The field
reaching street level results from diffraction of the fields
incident on the rooftops in the vicinity of the mobile [9], [ 10).
While the process by which the fields at the rooftops reach
ground level may be more complicated than that suggested in
Fig. 1, the process is still expected to take place in the
immediate vicinity of the mobile.
Because the rows of buildings have the form of cylindrical
obstacles lying on the ground, as seen in cross section in Fig.
1, propagation over the rooftops involves diffraction past a
series of parallel cylinders with dimensions large compared to
wavelength. At each cylinder a portion of the field will diffract
toward the ground. These fields can rejoin those above the
buildings only after a series of multiple reflections and
diffractions as suggested by the rays labeled 4 in Fig. 1.
Because the diffractions are through large angles and/or the
fields must be reflected two or more times between the
buildings, these fields will have small amplitude and are
neglected. Note that while fields reflected between two rows
of buildings contribute to the multipath interference between
those two rows, they do not contribute to multipath interfer
ence between any other two rows.
The field incident on the top of each row of buildings is
backward diffracted as well as forward diffracted. Fields that
are back diffracted twice will propagate in the direction of the
primary field. These twice back diffracted fields are neglected
for two reasons. First, unless the buildings act as perfect
reflectors with the shadow boundary of the reflected fields
horizontal, the back diffracted field at rooftop level will be
smaller than the forward diffracted field. The second reason
has to do with irregularities in the roofs of the buildings, which
are on the order of a halfwavelength or greater at UHF. For
low glancing angles (Y these irregularities do not affect the
phase of the forward diffracted field. However, they will
strongly influence the phase of the back diffracted field. A
second back diffraction increases the phase variation so that
when averaged along the rows these back diffracted fields tend
to cancel.
Since diffraction past many cylinders must be taken into
account for low glancing angles, several simplifying assump
tions are made. To find the range dependence of the average
field, we assume that all of the rows are of the same height. A
further simplification for an elevated fixed antenna is achieved
by using the local planewave approximation to find the
influence of the buildings on the sphericalwave radiation by
the elevated antenna. We first determine the amplitude Q(a)
of the field at the roof tops due to a plane wave of unit
amplitude incident at the glancing angle a on an array of
building rows. The roof top fields due to the spherical wave
are then the product of Q(a), with (Y as shown in Fig. 1, and
the spherical wave amplitude, which is inversely proportional
to the range R in Fig. 1. This planewave approximation is
similar to that used when finding the field above a homogene
ous earth, where the spherical wave amplitude is multiplied by
the factor [ l k r ( a ) ] , and r (a) is the planewave reflection
coefficient.
To find Q(cY), we consider the problem of planewave
diffraction past a semiinfinite sequence of rows labeled n =
0 , 1, 2 , * * . . For n large enough the rooftop field is found to
settle to a constant value that is taken to be Q(a). The rows of
buildings are replaced by opaque absorbing screens of
vanishing thickness. This simplifying assumption is made
since the shape of actual roofs varies from region to region and
from building to building so that no one choice is always
correct. Moreover, for diffraction through small angles the
fields are not strongly dependent on the cross section of the
diffracting obstacle. Because reflections from the ground are
neglected, the screens are assumed to be semiinfinite when
finding Q(a). Finally, the analysis assumes propagation
perpendicular to the rows of buildings and magnetic field
polarized parallel to the ground.
111. NUMERICAL INTEGRATION FOR MULTIPLE DIFFRACTION
In the previous section it was argued that the propagation
model for the average field reduces to an analysis of plane
wave forward diffraction by a series of absorbing halfscreens
of uniform height, as indicated in Fig. 2. A plane wave
propagating at an angle a to the horizontal falls on a series of
halfscreens separated by a distance d. Here d represents the
centertocenter spacing of the rows of buildings and is in the
range of 3060 m. For frequencies in the UHF band (300
MHz3 GHz), d / X ranges from 30 to 600.
In studying diffraction over hills the forward diffraction
approximation has been employed [ 1 11, [ 121. Most studies are
limited to one or two halfscreens, although an approximate
method has been suggested for more than two screens [13].
Vogler [14] has developed a method for treating diffraction by
a series of halfscreens, starting with an approximate solution
that may be obtained by repeated application of the Kirchhoff
integral to the plane of each screen. He further approximates
this solution into a double infinite summation of terms
containing the repeated integral of the complementary error
function whose arguments are complex. Besides being difficult
to work with, the approximation was developed for incidence
from below the horizon, rather than from above as in Fig. 2 ,
and its applicability to the latter case is questionable.
A method based on direct numerical evaluation of the
KirchhoffHuygens integral is adopted here to evaluate the
fields diffracted past a series of halfscreens. The field in the
aperture of the n = 0 halfscreen is used to compute the field
in the aperture of the n = 1 halfscreen, and so on. We assume
that the incident plane wave has unit amplitude magnetic
intensity H, polarized along z in Fig. 2, acd time dependence
exp ( j u t ) .
When there is no variation along z , the field H , + l ( y )
incident on the plant of the n + 1 halfscreen due to the field
H,( y â ) above the nth halfscreen is given by [ 151
e J * / 4 m e  ikr
H,,+,(y)= 1 H,(yâ) ~ (cos &+cos a ) dyâ (1)
2 4 i O &
where
r = Jd * + ( y  y
cos 6 = d / r .
Recommended
View more >