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Calculation of antenna azimuths and elevations (Interfering Transmitter - Victim Receiver path)

As far as the Interfering Transmitter (IT) - Victim Receiver (VR) path is concerned, mutual angles and subsequent antenna discrimination angles/azimuths in horizontal plane are pre-determined by calculations already performed:

• relative azimuths on the victim (WT-VR) and interferer (IT-WR) paths;
• relative positioning of the VR and IT.

At the same time, the vertical angles (tilt) of the antennas in the vertical plane are similarly assumed to be pre-determined during the antenna gain calculations for WT-VR and IT-WR paths.

For all angle calculations:

• The azimuth reference is the IT-VR path
• The elevation reference is the horizontal plane

The antenna azimuth (bearing, or discrimination angle) in the horizontal plane from the VR in the direction of the IT is derived from:

• - direction of the victim link (i.e. the relative angle between VR and WT),
• - direction of the VR-IT path. This direction may also be defined by Xvr, Yvr, Xit, Yit, absolute coordinates of the VR and IT, and
• - azimuth of the VR antenna in the direction of the WT,

through the following relationship:

Similarly, the azimuth (in the horizontal plane) from the IT in the direction of the VR is derived from:

• - direction of the interfering link (i.e. the relative angle between IT and WR),
• - direction of the VR-IT path. This direction may also be defined by Xvr, Yvr, Xit, Yit, absolute coordinates of the VR and IT,
• - azimuth of the IT antenna in the direction of the WR,

through the following relationship:

The elevation of the VR antenna in the direction of the IT antenna is then derived from both the tilt and the azimuth angles as follows:

where:

• φ is the angle of the VR antenna as seen from the IT antenna:

• The corrected tilt function α is defined as the tilt of the VR antenna as seen from the IT antenna:

The elevation angle of the IT antenna in the direction of the VR antenna is then derived from both the tilt and azimuth angles as follows:

where:

• φ is the angle of the WR antenna as seen from the IT antenna:

• The corrected tilt function α is defined as the tilt of the VR antenna as seen from the IT antenna: