Design considerations for beamwaveguide in the NASA Deep Space Network

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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,…


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 GALINDO-ISRAEL, FELLOW, IEEE, WILLIAM A. IMBNALE, MEMBER, IEEE, AND DAN A. BATHKER, SENIOR MEMBER, IEEE Abstract-Retrofitting 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 34-m 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 16-20 K are achieved by using cryogenically cooled preamplifiers closely coupled with an appropriately balanced antenna gain/spillover design. Additionally, high-power transmitters (up to 400-kW 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 low-noise receive cover- age over the 1-10-GHz band. To summarize, DSN antennas must operate efficiently with low noise and high-power uplink over the 1-35-GHz band. Feeding a large low-noise ground-based antenna via a beamwaveguide (BWG) system has several advantages over directly placing the feed at the focal point of a dual-shaped antenna. For example, significant simplifications are possible in the design of high-power water-cooled 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 quasi-optical 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 dual-reflector 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 trade-offs 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 dual-shaped 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 34-m dual-shaped 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 OO18-926X/88/12OO-1779$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 two-curved 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 2.4-m (8-ft) reflector beamwaveguide operated over 1-35 GHz with near prefect imaging at X band and Ka band and acceptable performance degradation at L band (1 GHz) and S band, a high-pass 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 multiple-reflector 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 single-frequency 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 2.4-m, 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 34-m high-efficiency dual-shaped reflector antennas with a dual-band (2.318.4- GHz) feed having a far-field gain of +22.4 dBi that is conventionally located at the dual-shaped 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 34-m 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. 34-m 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 Near-field one ellipse diffraction patterns (RCP-pol, 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 40-50 ft below the main reflector to a dual-shaped focus. This goal applies over the 1-35-GHz 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 Mizusawa-Kitsuregawa con- ditions [ I] for minimum cross polarization and best imaging. In the high-frequency domain (8-35 GHz for the designs considered herein), the focused system shown in Fig. 1 is desired. Of course, two paraboloids or mixtures of various conic-section 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 high-performance systems. C. Low-Frequency Diffraction Analysis Capability Because of the large bandwidth of operation (1-35 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 34-m 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 Jacobi-Bessel (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 far-field 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. Far-field one ellipse diffraction patterns (RCP-pol, 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 near-field 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 two-dimensional radiation integral is reduced to a small number of one-dimensional 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 (direct-trapezoid) and SWE algorithms are useful for cross-checking results. Near-field and far-field computa- tions and comparisons in both amplitude and phase are shown in Figs. 11 and 12. Fig. 11 contains near-field PO and SWE results for scattering from one paraboloid reflector. Fig. 12 contains the near-field 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. High-Frequency 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 near-field scattering from single 2.4-m 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. Near-field one 2.4-m 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 vector-scattered 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 second-order 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 Mizusawa-Kitsuregawa 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. Near-field 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 2.4-m 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 dual-shaped 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 1-35-GHz requirement that high-pass (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 Mizusawa-Kitsuregawa criteria has been revealed. The princi- ple revealed shows how a two-reflector 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 (1968-1970), 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 (1985-1986) to Venus and Halleyâs Comet. He is currently involved in the design of a new beamwaveguide fed 34-m 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 Galindo-Israel (Sâ52-Mâ57-SMâ75-Fâ77), 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 2.2-m paraboloids at 32 GHz (comparison with feed pattern). William A. Imbriale (Sâ64-Mâ70), 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. AP-21, pp. 844-886, Nov., 1973. [2] T. S . Chu, âAn imaging beam waveguide feed,â ZEEE Trans. Antennas Propagat., vol. AP-31, pp. 614-619, July 1983. [3] G. Goubau and F. Schwering, âOn the guided propagation of electromagnetic wave beams,â IEEE Trans. Antennas Propagat., vol. AP-9, pp. 248-256, May 1961. R. E. Collin, Field Theory of Guided Wave. New York: McGraw- Hill, 1960, pp. 474-475. V. Galindo-Israel and R. Mittra, âA new series representation for the radiation integral with application to reflector antennas,âIEEE Trans. Antennas Propagat.,vol. AP-25, pp. 631-641, Sept. 1977. A. C. Ludwig, âCalculation of scattered patterns from asymmetrical reflectors,â Jet Propulsion Lab., Pasadena, CA, Tech Rep. 32-1430, Feb. 15, 1970. [4] [5] [6] Thavath Veruttipong (Sâ77-Mâ78), for a photograph and biography please see page 755 of the July 1987 issue of this TRANSACTIONS. Dan A. Bathker (Sâ59-Mâ62-SMâ75) 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) wide-band 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 ultra-high CW power transrmssion with low-noise 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 PG-AP and PG-MTT 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 many-fold 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 Abstract-Urban 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 MHz-3GHz) 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 high-rise 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 high-rise 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 high-rise 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. OO18-926X/88/1200-1788$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 half-wavelength 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 plane-wave approximation to find the influence of the buildings on the spherical-wave 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 plane-wave 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 plane-wave reflection coefficient. To find Q(cY), we consider the problem of plane-wave diffraction past a semi-infinite 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 semi-infinite 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 half-screens of uniform height, as indicated in Fig. 2. A plane wave propagating at an angle a to the horizontal falls on a series of half-screens separated by a distance d. Here d represents the center-to-center spacing of the rows of buildings and is in the range of 30-60 m. For frequencies in the UHF band (300 MHz-3 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 half-screens, 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 half-screens, 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 Kirchhoff-Huygens integral is adopted here to evaluate the fields diffracted past a series of half-screens. The field in the aperture of the n = 0 half-screen is used to compute the field in the aperture of the n = 1 half-screen, 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 half-screen due to the field H,( y â ) above the nth half-screen 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 .