Mathematical gain models of large-aperture space research service earth station antennas for compatibility analysis involving a large number of distributed interference sources
Introduction Compatibility studies between space research service (SRS) 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 envelope 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 applied 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 average 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 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 e.g. Recommendation ITU-R F.1245-1 ?C 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.509-2 ?C Space research earth station and radio astronomy reference antenna radiation pattern for use in interference calculations@ including coordination procedures. Recommendation ITU-R SA.1345 ?C Methods for predicting radiation patterns of large antennas used for space research and radio astronomy and [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 discussed in Recommendation ITU-R F.1245@ In the models which are usually proposed in the literature@ since an upper 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 compared 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 value as a function of antenna parameters@ such as frequency and aperture diameter.