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and the topocentric angle .
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Interference
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and the equatorial arc subtended by this angle is about 314 km. In interference calculations, therefore, the earth stations will be assumed to be situated on the 3-dB contours of the satellite footprints, in which case the satellite antennas do not provide any gain discrimination between the wanted and the interfering carriers on either transmit or receive.
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13.2.1 Downlink
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Equation (12.13) may be used to calculate the wanted and interfering downlink carrier powers received by an earth station. The carrier power [C] in dBW received at station B is [C] [EIRP]1 3 [GB] [FSL] (13.1)
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Here, [EIRP]1 is the equivalent isotropic radiated power in dBW from satellite 1, the 3 dB accounts for the 3-dB contour of the satellite transmit antenna, GB is the boresight (on-axis) receiving antenna gain at B, and [FSL] is the free-space loss in decibels. A similar equation may be used for the interfering carrier [I], except an additional term [Y]D dB, allowing for polarization discrimination, must be included. Also, the receiving antenna gain at B is determined by the off-axis angle , giving [I ] [EIRP]2 3 [GB ( )] [FSL] [Y ]D (13.2)
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It is assumed that the free-space loss is the same for both paths. These two equations may be combined to give [C ] [I ] [EIRP]1 [EIRP]2 [GB] [GB ( )] [Y ]D
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or c C d I D [E] [GB] [GB( )] [Y]D (13.3)
The subscript D is used to denote downlink, and [E] is the difference in dB between the [EIRP]s of the two satellites.
Example 13.1
The desired carrier [EIRP] from a satellite is 34 dBW, and the ground station receiving antenna gain is 44 dB in the desired direction and 24.47 dB toward the interfering satellite. The interfering satellite also radiates an [EIRP] of 34 dBW. The polarization discrimination is 4 dB. Determine the carrierto-interference ratio at the ground receiving antenna. From Eq. (13.3) c C I d
Solution
23.3 dB
13.2.2 Uplink
A result similar to Eq. (13.3) can be derived for the uplink. In this situation, however, it is desirable to work with the radiated powers and the antenna transmit gains rather than the EIRPs of the two earth stations. Equation (12.3) may be used to substitute power and gain for EIRP. Also, for the uplink, GB and GB ( ) are replaced by the satellite receive antenna gains, both of which are assumed to be given by the 3-dB contour. Denoting by [P] the difference in dB between wanted and interfering transmit powers, [GA] the boresight transmit antenna gain at A, and [GC( )] the off-axis transmit gain at C, it is left as an exercise for the reader to show that Eq. (13.3) is modified to c C d I U [P] [GA] [GC( )] [Y]U (13.4)
Example 13.2 Station A transmits at 24 dBW with an antenna gain of 54 dB, and
station C transmits at 30 dBW. The off-axis gain in the S1 direction is 24.47 dB, and the polarization discrimination is 4 dB. Calculate the [C/I] ratio on the uplink.
Solution
Equation (13.4) gives c C I d
27.53 dB
Interference
13.2.3 Combined [C/I ] due to interference on both uplink and downlink
Interference may be considered as a form of noise, and assuming that the interference sources are statistically independent, the interference powers may be added directly to give the total interference at receiver B. The uplink and the downlink ratios are combined in exactly the same manner described in Sec. 12.10 for noise, resulting in I a b C ant I a b C U I a b C D (13.5)
Here, power ratios must be used, not decibels, and the subscript ant denotes the combined ratio at the output of station B receiving antenna.
Example 13.3 Using the uplink and downlink values of [C/I] determined in Examples 13.1 and 13.2, find the overall ratio [C/I]ant.
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