1、 Rep. ITU-R SA.2098 1 REPORT ITU-R SA.2098 Mathematical gain models of large-aperture space research service earth station antennas for compatibility analysis involving a large number of distributed interference sources (2007) 1 Introduction Compatibility studies between space research service (SRS)
2、 earth stations and high-density fixed systems are being conducted in the 31.8-32.3 GHz and 37-38 GHz bands. One of the key parameters that needs to be defined to determine the level of interference that may occur at SRS earth stations is the antenna pattern to be used in the calculations. A peak en
3、velope radiation pattern for fixed wireless systems is provided in Recommendation ITU-R F.699 and a radiation pattern representing average side-lobe levels for line-of-sight point-to-point radio-relay systems is provided in Recommendation ITU-R F.1245. The Recommendation ITU-R F.699 pattern, when ap
4、plied only to polar angles larger than 1, is the same as the pattern in Recommendation ITU-R SA.509. Peak envelope radiation patterns for Earth stations operating in the fixed-satellite service (FSS) are given in Recommendations ITU-R S.580 and ITU-R S.465 and a radiation pattern representing averag
5、e side-lobe levels of fixed-satellite service earth stations is provided in Recommendation ITU-R S.1428. This Report compares the performance of these patterns and introduces a new model. Actual and realistic patterns involve many factors, too complicated and diverse to be exactly accounted for in a
6、 simple theoretical computation. For example, the position of nulls and peaks in the side-lobe regions vary as a function of antenna gravitational loading, winds, etc., and are best represented by an envelope. Over the years many pattern models have been suggested for large reflector antennas, (see
7、e.g. Recommendation ITU-R F.1245-1 Mathematical model of average and related radiation patterns for line-of-sight point-to-point radio-relay system antennas for use in certain coordination studies and interference assessment in the frequency range from 1 GHz to about 70 GHz. Recommendation ITU-R SA.
8、509-2 Space research earth station and radio astronomy reference antenna radiation pattern for use in interference calculations, including coordination procedures. Recommendation ITU-R SA.1345 Methods for predicting radiation patterns of large antennas used for space research and radio astronomy and
9、 Jamnejad, 2003. A simple but effective method of characterizing an actual antenna pattern is to use a model which is based on many theoretical and experimental results and provide an upper- and/or lower-bound or envelope for the antenna which can be easily applied to many situations. Ideally, as di
10、scussed in Recommendation ITU-R F.1245, following the definition of directivity of an antenna, the gain model G given in dB should obey the equation for the average gain ratio, ga: =2001)sin(),(41ddgga2 Rep. ITU-R SA.2098 in which is the polar angle from boresight and is the azimuth angle, as shown
11、in the following figure: For a circularly symmetric pattern, the equation reduces to: =01)sin()(21dggaTypically gain models are given in dB as parameter G, which is related to the gain ratio g by: 10),(10),(or),(log(10),(=GggGIn the models which are usually proposed in the literature, since an upper
12、 limit envelope or some other approximation is used instead of the actual pattern, the average gain values, as calculated from the integrals above, are much larger than unity (or larger than 0 in dB). However they can be used as a validity check for evaluating the general accuracy of the model compa
13、red to an actual antenna pattern. Typically a value of less than or around 2 (less than 3 dB) would provide a reasonable approximation. Here, we evaluate the left-hand side involving the integral numerically for a number of circularly symmetric gain models and provide plots for variation of its valu
14、e as a function of antenna parameters, such as frequency and aperture diameter. Rep. ITU-R SA.2098 3 2 Gain models In all the models given below, gain values are specified in dB, angles are specified in degrees, and: D: diameter of the main aperture of the antenna (m) (m)h wavelengt,3.0GHzffc= We ar
15、e only considering large apertures with D/ 100 in this paper. a) The Recommendation ITU-R F.699-7 model Recommendation ITU-R F.699-7 proposes the following radiation pattern (maximum envelope) for the frequency range of 1-70 GHz: 23105.2)(=DGGmaxfor 0 100 b) The Recommendation ITU-R RA.1631 model Fr
16、ance has proposed to use the model given in Recommendation ITU-R RA.1631. It is not a peak envelope but an average pattern defined by: 23105.2)(=DGGmaxfor 0 m1)( GG = for m r)(log2529)(10=G for r 10 4 Rep. ITU-R SA.2098 )(log3034)(10=G for 10 34.1 12)( =G for 34.1 80 7)( =G for 80 120 12)( =G for 12
17、0 180 with: =DGmaxlog20 +=DG101log151 1120=DGGmaxmdegrees 6.085.15=Drdegrees, or kkrDk6.028.1 08.0210=degrees 6.085.15=Drdegrees, for k = 1 c) The Recommendation ITU-R F.1245-1 model Recommendation ITU-R F.1245-1 proposes the following average radiation pattern for the frequency range of 1-40 GHz an
18、d provisionally for the range of 40-70 GHz: 23105.2)(=DGGmaxfor 0 m1)( GG = for m r)(log2529)(10=G for r 48 13)( =G for 48 180 with: Gmax: peak gain +=DG101log152 1120=DGGmaxm6.002.12=DrRep. ITU-R SA.2098 5 d) The Jp model (peak envelope) This is a new model providing peak envelope for all frequency
19、 ranges of interest. It is similar to Recommendation ITU-R F.699 with some modifications. The modifications involve the following areas: i) The main beamwidth of the pattern can vary somewhat, based on various parameters of the antenna such as aperture illumination, blockage, surface errors, etc. Th
20、e one-sided half-power beamwidth is defined as hp= 0.5Chp/(D/), in which the constant Chphas an approximate value between 65 and 71. For a more accurate modelling, this parameter can be varied according to the type and quality of the antenna used. Here, a value of Chp= 69 is selected for compatibili
21、ty with Recommendation ITU-R F.699. ii) The flat shoulder area of the pattern is set to a more realistic value. This value is normally not dependent on the antenna dimensions or wavelength, but is a rather complicated function of aperture illumination and blockage. A value of 17 dB is used which can
22、 be adjusted if necessary. iii) The pattern efficiency is taken into account in determining the peak as well as the slope of the model pattern. This is in contrast to other models which consider a fixed slope. The pattern efficiency is a combination of aperture illumination efficiency, blockage effi
23、ciency, spillover efficiency, and efficiency due to surface errors. We separate the efficiency into a surface tolerance component which is directly dependent on the frequency and lump all the others into a separate component which is more or less independent of the frequency. iv) A 5 dB raised platf
24、orm area in the flat far-side lobe region of the pattern, in the 80 to 120 range, is introduced to account for possible main reflector spillover effects whose exact height and location varies with F/D (focal length to diameter ratio) and other design parameters of the reflector antenna. In rare occa
25、sions this platform is subject to the provisions of Note 2 given below. Thus, the model pattern in given by: ()203=hpGG for 0 110)( GGG = for 1 2=210210log)( GGGG for 2 33)( GG = for 3 80 5)(3+= GG for 80 120 3)( GG = for 120 180 in which: 221004343.4log10 =rmsahDG 171=G6 Rep. ITU-R SA.2098 +=rmsahG
26、 60log)(log102710102103=G 69) valuenominal ,7065()/(5.0 =hphphpCDC311Ghp= 36102221GGGhp= 23101023GGGG = The avalue refers to the pattern-related (aperture illumination, spillover, blockage, etc.) antenna efficiency excluding that associated with surface tolerance. Note that in this model the gain at
27、 boresight decreases with a, but the gain slope, G2, in angle range between 2and 3increases with a. This reflects the physical reality that a decrease in peak gain has to be accompanied with increases in the side-lobe regions. This feature is not incorporated in other models. NOTE 1 The gain loss du
28、e to the surface tolerance is separately included as a function of hrms, the surface tolerance, which also affects the slope of the pattern model. The valid range of surface tolerance for use in the above formulae is: 151601rmshAny value of hrms/ above 1/15 must be replaced by 1/15; any value below
29、1/60 must be replaced by 1/60. Thus one can use the value 1/60 for a very good antenna, 1/30 for a moderately good antenna and 1/15 for a poor antenna. NOTE 2 In rare cases, for large surface errors, 3might exceed 80, and an overlap of the sloped side-lobe region with the flat bump at 80-120 region
30、occurs. In such cases, the maximum value of the two at each angle must be selected. e) The Ja model (average) In addition to the peak envelope, an average envelope for the gain at any given angle in the side-lobe region can be defined, which is meaningful in the following sense. Let us assume a numb
31、er of antennas and a fixed given angle from boresight. Since the antennas are not identical, they might have their side lobes shifted such that for one antenna the peak of a lobe falls at the given direction while a different antenna might have a null in that direction and yet a third antenna might
32、have a value between the peak and the null, etc. So, one presumably can use an average value for the gain at the given direction which is an average of all these values from null to peak. It turns out that for a given lobe with very sharp null, this average is close to 3 dB below the peak of the lob
33、e (usually less if the nulls are not sharp and are to some extent filled in). Now, if one assumes that the peak envelope model touches all the peak points of the lobes, then an average envelope is parallel to this envelope but below it by about 3 dB. Rep. ITU-R SA.2098 7 Accordingly, a model for an
34、“average” envelope is obtained by a simple modification of the above model by increasing the G1value by 3 dB, reducing the G3 value by 3 dB, and modifying the 2value accordingly. Caution should be used in the application of this model to particular situations of interest. It is given as: ()203=hpGG
35、for 0 1 10)( GGG = for 1 2=210210log)( GGGG for 2 33)( GG = for 3 80 5)(3+= GG for 80 120 3)( GG = for 120 180 in which: 221004343.4log10=rmsahDG 201=G ()+=rmsahG 60loglog102710102133=G 69) valuenominal ,7065()/(5.0 =hphphpCDC311Ghp= 361022231GGGhp= 23101023GGGG = All the notes for the Jp model appl
36、y equally to the Ja model. 3 Numerical analysis and results In order to calculate and plot and compare various gain models and their “averaged” gain, a few MATLAB programs have been written. These programs are very easy to use and provide a simple way to add new models for analysis and plotting. The
37、 following results have been obtained by these programs. 8 Rep. ITU-R SA.2098 Each plot in Figs. 1-6 (a, b, c) shows several patterns for comparison. These include Recommendation ITU-R F.699-7 peak envelope (which for angles above 1 is the same as the model given in Recommendation ITU-R SA.509), the
38、 average envelope model in Recommendation ITU-R F.1245-1, the average envelope model in Recommendation ITU-R RA.1631, and finally a newly proposed peak envelope model “Jp” derived from the model contained in Recommendation ITU-R F.699. Comparison at D/ = 1 000 (e.g. 34 m antenna operating near 8.4 G
39、Hz) Figures 1-3 are plotted for a 1 000-wavelength diameter antenna, corresponding to an aperture of 34 metre diameter operating near the 8.4 GHz band extensively used in deep space research. Patterns according to model Jp and Ja are given for the “poor”, “average” and “good” quality antennas, corre
40、sponding to the root-mean-square (rms) surface tolerance of 1/15, 1/30, and 1/60 of wavelength, respectively. Cases a), b), and c) refer to linear, expanded linear and log representation of angle variable on the horizontal axis. Comparison at D/ = 4 000 (e.g. 34 m antenna operating near the 32 and 3
41、7 GHz bands) Figures 4-6 are the corresponding cases for a 4 000 wavelength diameter antenna, corresponding to antennas with 34 m diameter operating near the 32 and 37 GHz bands where sharing between deep space research and HDFS is at issue. Performance depending on surface tolerance As can be seen
42、for the proposed models Jp and Ja, the gain performances of the main beam and side-lobe regions change with the variation in surface tolerance. In models Jp and Ja, an initial aperture efficiency value of a= 0.8 is assumed, not including the surface tolerance effects. This is a typical value for the
43、 combination of aperture and spillover efficiency for a nominal 10-11 dB edge taper. This initial value is multiplied by a surface tolerance factor to arrive at the net aperture efficiency for the antenna. The surface tolerance factor are built in the formulas, and for the “poor”, “average” and “goo
44、d” cases are 0.5, 0.9 and 1.0 respectively. The net aperture efficiency for the three cases is therefore 0.4, 0.7 and 0.8 respectively. Note that this aperture efficiency is to be multiplied by other loss factors, such as the loss in the feed horn, to arrive at the overall efficiency of the antenna.
45、 In the case of other models the surface tolerance is not explicitly considered. An aperture efficiency of 0.7 is assumed for these models in all cases. Among the large aperture antennas used in for deep space research in the NASA Deep Space Network, for example, surface tolerance of the 34 m antenn
46、as can be characterized as “good” at 8.4 GHz and 2.3 GHz, “average” to “good” at the 32 GHz, and potentially “average” at the 37 GHz when implemented. The surface tolerance of the 70 m antennas can be characterized as “good” at 8.4 GHz and 2.3 GHz, and potentially “poor” at 32 GHz if implemented. Ga
47、in averaged over all angles Figures 7-9 (a, b) show a comparison of the gain averaged over all angles according to equations given above for the various models discussed, using the “poor”, “average”, and “good” quality antenna models for the Jp and Ja cases. Cases a) and b) provide the averaged gain
48、 in dB and linear scale, respectively. As can be seen the Jp and Ja models are consistent across the range of D/ (antenna diameter to wavelength) ratio. At higher D/ ratio near 4 000, the “average” case shows a lower average gain and the “good” cases a much lower average gain, than other models. Figure 10 (a, b) shows a similar set of plots for the case of the 34 m antenna (w
