**Suggested Citation:**"Appendix H Use of 0 dBi for Sidelobe Gain in Calculations of Interference in Radio Astronomy Bands." National Research Council. 2007.

*Handbook of Frequency Allocations and Spectrum Protection for Scientific Uses*. Washington, DC: The National Academies Press. doi: 10.17226/11719.

### Appendix H

Use of 0 dBi for Sidelobe Gain in Calculations of Interference in Radio Astronomy Bands

The use of 0 dBi for the gain of the sidelobes of a radio astronomy antenna, in the computation of levels of detrimental interference, originated in the analysis in International Radio Consultative Committee (CCIR) Report 224.^{1} Report 224 evolved into Recommendation ITU-R RA.769 when the CCIR was replaced by the International Telecommunication Union’s Radiocommunication Sector (ITU-R). As stated in Report 224: “To estimate typical values of the harmful interference level, we may approximate our real antenna by an isotropic antenna, except in the direction of the main lobe and near side lobes.”

The isotropic model represents the average gain of any low-loss antenna, independent of the details of its design. In practice, it is less than the gain of the main beam and near sidelobes of a radio astronomy antenna and a little higher than the gain of the sidelobes that are more than about 20° from the boresight (the center of the main beam). The use of a single reference value for the gain of the radio astronomy antenna in calculations of detrimental thresholds of interference is intended to provide approximate numbers that are independent of the detailed type of antenna and its pointing direction. This single reference value facilitates the assessment of any interference situation. It frees the transmitter engineer from a consideration of the detailed radio telescope design and pointing angles. Also, the calculations are much simplified when gain and pointing direction are removed as variables.

In some specific cases, however, this simple gain model is not adequate—in particular, in the case of interference from non-geosynchronous satellites. A more detailed antenna pattern and coordination algorithm are then used, as described in Recommendations ITU-R S.1586 and M.1583. The resulting analysis sets a value of the detrimental threshold such that the fraction of time that the interference level exceeds the threshold is equal to the maximum tolerable value of 2 percent for any one network, as specified in Recommendation ITU-R RA.1513. Generally, however, it is found that this threshold is within a very few decibels of that derived using the simpler isotropic-sidelobe model.

**Suggested Citation:**"Appendix H Use of 0 dBi for Sidelobe Gain in Calculations of Interference in Radio Astronomy Bands." National Research Council. 2007.

*Handbook of Frequency Allocations and Spectrum Protection for Scientific Uses*. Washington, DC: The National Academies Press. doi: 10.17226/11719.

TABLE H.1 Characteristics of Antenna Sidelobe Models

ITU-R Recommendation |
Φ |
Ω/2π |

SA.509 (32-25 log Φ) |
19.05° |
5.5% |

S.580 (29-25 log Φ) |
14.45° |
3.2% |

RA.1631 and S.1428 (34-30 log Φ) |
13.59° |
2.85% |

An examination of the choice of 0 dBi, rather than some other constant gain figure, can be made with the aid of the more detailed reference models of sidelobe levels that have subsequently been developed. An early reference model for a large antenna is found in Recommendation ITU-R RS.509. The sidelobe gain as a function of boresight angle Φ is equal to (32-25 log Φ) dBi for 1°<Φ<48°, and is a constant value of −10 dBi for Φ >48°. With this model the 0 dBi sidelobe level occurs at a boresight angle of Φ_{0} = 19°. However, radio astronomy antennas are commonly used over a range of elevation angles down to ~10° when tracking a source under study across the sky. As a result, sidelobes of a level several decibels greater that 0 dBi are sometimes presented toward the horizon, which is the direction of incidence for signals from terrestrial transmitters. Hence, for sidelobes represented by Recommendation ITU-R RS.509, the 0 dBi figure does not guarantee freedom from interference.

The average percentage of data loss when the detrimental threshold is determined using the 0 dBi figure can be estimated using the models for antenna sidelobe levels, as follows. Included here are more recent models based on improved antenna design, which are found in Recommendations ITU-R S.580, S.1248, and RA.1631. For each of the models, the boresight angle Φ_{0} for which the gain is 0 dBi is given in column 2 of Table H.1. The solid angle of the antenna response for which the gain exceeds 0 dBi is Ω = 2π (1-cos Φ_{0}) steradian. This is given for each model in column 3 of the table, expressed as a fraction of the hemisphere (from the horizon to the zenith) from which interference can arrive. Thus, if it is assumed that the angles of pointing of the radio astronomy antenna are uniformly distributed over the sky (which is only approximately the case) and that one interfering transmitter is active, the values in column 3 provide an estimate of the fraction of time that the interference received exceeds the detrimental level.^{2} For the more recent sidelobe models in the table these values are ~3 percent, and to reduce this result to 2 percent (the maximum tolerable value, as noted above), one would need to use a detrimental threshold based on a sidelobe gain slightly higher than 0 dBi. However, the 0 dBi value has the advantage of simplicity, and within the uncertainties of the pointing distribution, it results in detrimental thresholds in reasonable accord with the acceptable loss of observing time.

**Suggested Citation:**"Appendix H Use of 0 dBi for Sidelobe Gain in Calculations of Interference in Radio Astronomy Bands." National Research Council. 2007.

*Handbook of Frequency Allocations and Spectrum Protection for Scientific Uses*. Washington, DC: The National Academies Press. doi: 10.17226/11719.

**Suggested Citation:**"Appendix H Use of 0 dBi for Sidelobe Gain in Calculations of Interference in Radio Astronomy Bands." National Research Council. 2007.

*Handbook of Frequency Allocations and Spectrum Protection for Scientific Uses*. Washington, DC: The National Academies Press. doi: 10.17226/11719.