Computing Antenna Gain

This below step-by-step process is used to determine the antenna gain when utilizing antenna profiles. It should be noted that antenna gains are computed as part of the OTA receive packet processing.

The following steps 1 through 12 define the process of determining the \(rxAntennaGain\) when the receiving node is configured to use antenna profiles. Steps 2 through 12 would be required to compute the \(txAntennaGain\) if the transmitter was also configured to use antenna profiles.

1. Transform the positions from WGS84 (lat/long/alt) to ECEF (Earth Centered Earth Fixed)

   1. Define the WGS84 ellipsoid constants

       semi_major=6378137
       semi_minor=6356752.3142
       f=1/298.257223563
       e2 = 2*f - f^2
      

   2. Compute the prime vertical radius of curvature

       N = semi_major/sqrt(1-e2*sin(latitude)^2)
      

   3. Perform the following coordinate transformation

       X = (N + altitude) * cos(latitude) * cos(longitude)
       Y = (N + altitude) * cos(latitude) * sin(longitude)
       U = (N*(1-e2) + altitude) * sin(latitude)
      

   4. Perform above transformation for both the transmitter and receiver

       [Xt, Yt, Ut] = Transmitter Position ECEF
       [Xr, Yr, Ur] = Receiver Position ECEF
      

   5. Compute the ECEF vector between receiver and transmitter

        X = Xt-Xr
        Y = Yt-Yr
        Z = Ut-Ur
      

2. Transform ECEF to NEU (North, East Up) in receiving NEM’s frame

    N1 = -X*sin(latitude)*cos(longitude) - Y*sin(latitude)*sin(longitude) + Z*cos(latitude)
    E1 = -X*sin(longitude) + Y*cos(longitude)
    U1 = X*cos(latitude)*cos(longitude) + Y*cos(latitude)*sin(longitude) + Z*sin(latitude)
   

3. Adjust yaw and pitch angles to account for velocity vector

    yaw = yaw + V_azimuth
    pitch = pitch + V_elevation
   

4. Perform the following transformation to account for yaw, pitch and roll

   1. Define the transformation matrix

       a11 = cos(pitch)cos(yaw)  
       a12 = cos(pitch)sin(yaw)  
       a13 = sin(pitch)  
       a21 = sin(pitch)cos(yaw)sin(roll) - cos(roll)sin(yaw)  
       a22 = cos(roll)cos(yaw) + sin(pitch)sin(roll)sin(yaw)  
       a23 = -cos(pitch)sin(roll)  
       a31 = -cos(yaw)sin(pitch)cos(roll) - sin(yaw)sin(roll)  
       a32 = -sin(yaw)sin(pitch)cos(roll) + sin(roll)cos(yaw)  
       a33 = cos(pitch)cos(roll)  
      

       | a11 a12 a13 |
       | a21 a22 a23 | = A
       | a31 a32 a33 |
      

   2. Perform the transformation

       N = N1 * a11 + E1 * a12 + U1 * a13
       E = N1 * a21 + E1 * a22 + U1 * a23
       U = N1 * a31 + E1 * a32 + U1 * a33
      

5. Update NEU to include receiving node’s location on the platform

    N = N + north
    E = E + east
    U = U + up
   

   Where, north/east/up are obtained from the antenna profile manifest for the receiving node.

6. Rotate transmitter’s antenna placement into receiver’s coordinate frame using the same transformation defined in Step 4 above replacing N1, E1 and U1 with the transmitter’s antenna placement values obtained from the antenna profile manifest.

    N = N + north(transformed)
    E = E + east(transformed)
    U = U + up(transformed)
   

7. Compute range from receiver to transmitter

    range = sqrt(N^2 + E^2 + U^2)
   

8. Compute bearing and elevation from receiver to transmitter

    bearing = atan(E/N)
    elevation = asin(U/range)
   

9. Look up the blockage value for the receiver (if provided) based on the blockage pattern associated with the receiver’s antenna profile Id and the bearing and elevation values from Step 8.

10. Adjust bearing and elevation to account for receiving NEM’s antenna pointing (if provided)

    bearing = bearing - AzPointing
    elevation = elevation - ElPointing
    

11. Look up antenna gain value for the receiver based on the antenna pattern associated with the receiver’s antenna profile Id and the bearing and elevation values from Step 10.

12. Compute rxAntennaGain

    rxAntennGain = antennaGain + blockage