Airborne antenna pointing and projection
A method and computer for pointing a beam of a directional antenna located above ground is disclosed. A method includes receiving a beam width 2ϕ, and determining an angle ψ max where ψ max +θ is an angle for a projection of maximum signal strength on the ground. ψ max is based on the beam width 2ϕ and tilt angle θ. The method also includes determining an effective ground beam width defined by a total relative gain of the directional antenna and the above the ground to ground range being at half the maximum signal strength on the ground at angles above and below ψ max . The method further includes determining a ground footprint of the beam based at least on part on the determined effective ground beam width, and causing the antenna to be pointed based at least in part on the determined ground footprint of the beam.
1. A method for pointing a beam of a directional antenna located above ground, the beam being projected downward toward the ground, the method comprising:
receiving a beam width 2ϕ;
determining an angle ψ max such that ψ max +θ is an angle for a projection of maximum signal strength on the ground, ψ max being based on the beam width 2ϕ and tilt angle θ;
determining an effective ground beam width defined by a total relative gain of the directional antenna and the above the ground to ground range being at half the maximum signal strength on the ground at angles above and below ψ max ;
determining a ground footprint of the beam of the directional antenna based at least on part on the determined effective ground beam width; and
causing the antenna to be pointed based at least in part on the determined ground footprint of the beam of the directional antenna.
2. The method of claim 1 , wherein ψ max is determined from an arctangent of a root of a quadratic equation in terms of the tilt angle θ and a value N that is based on the beam width 2ϕ according to the equation, N=Log (0.5)/Log (cos ϕ).
3. The method of claim 1 , wherein the maximum signal strength is determined based at least in part on a derivative of a relative total gain equation.
4. The method of claim 1 , further comprising determining the tilt angle to be an angle for which a maximum signal strength is directed toward a selected point.
5. The method of claim 4 , wherein the tilt angle is determined from a look up table.
6. The method of claim 5 , wherein values in the lookup table are determined as follows:
θ′=ρ−ATAN[2/( N tan ρ)],
where ρ is a pointing angle to the selected point.
7. The method of claim 1 , wherein −3 dB near and far projection angles of the beam are determined by a linear function of one half the beam width 2ϕ and the tilt angle θ.
8. A computer for pointing a beam of a directional antenna located above ground, the beam being projected downward toward the ground, the computer including processing circuitry configured to:
receive a beam width 2ϕ;
determine an angle ψ max such that ψ max +θ is an angle for a projection of maximum signal strength on the ground, ψ max being based on the beam width 2ϕ and tilt angle θ;
determine an effective ground beam width defined by a total relative gain of the directional antenna and the above the ground to ground range being at half the maximum signal strength on the ground at angles above and below ψ max ;
determining a ground footprint of the beam of the directional antenna based at least in part on the determined effective ground beam width; and
cause the antenna to be pointed based at least in part on the determined ground footprint of the beam of the directional antenna.
9. The computer of claim 8 , wherein ψ max is determined from an arctangent of a root of a quadratic equation in terms of the tilt angle θ and a value N that is based on the beam width 2ϕ according to the equation, N=Log (0.5)/Log (cos ϕ).
10. The computer of claim 8 , wherein the maximum signal strength is determined based on a derivative of a relative total gain equation.
11. The computer of claim 8 , wherein the processing circuitry is further configured to determine the tilt angle to be an angle for which a maximum signal strength is directed toward a selected point.
12. The computer of claim 11 , wherein the tilt angle is determined from a look up table.
13. The computer of claim 12 , wherein values in the lookup table are determined as follows:
θ=ρ−ATAN[2/( N tan ρ)],
where ρ is a pointing angle to the selected point.
14. The computer of claim 8 , wherein −3 dB near and far projection angles of the beam are determined by a linear function of one half the beam width 2ϕ and the tilt angle θ.
15. A method for pointing a beam of a directional antenna located above ground, the beam being directed downward toward the ground, the method comprising:
determining a tilt angle θ, the tilt angle θ being determined to be an angle for which a maximum signal strength on the ground is directed toward a selected point;
receiving a beam width 2ϕ;
determining an angle ψ max such that ψ max +θ is an angle for a projection of maximum signal strength on the ground, ψ max being based on the beam width 2ϕ and the tilt angle θ; and
determining an effective ground beam width defined by a total relative gain of the directional antenna and the above the ground to ground range being at half the maximum signal strength on the ground at angles above and below ψ max ;
determining a ground footprint of the beam of the directional antenna based on the determined effective ground beam width; and
causing the antenna to be pointed based at least in part on the determined ground footprint of the beam of the directional antenna.
16. The method of claim 15 , wherein ψ max is determined from an arctangent of a root of a quadratic equation in terms of the tilt angle θ and a value N that is based on the beam width 2ϕ according to the equation, N=Log (0.5)/Log (cos ϕ).
17. The method of claim 16 , wherein ψ max is determined as:
ψmax
=
ATAN
(
N
+
2
)
tan
θ
-
(
2
+
N
)
2
tan
2
θ
+
8
N
-
2
N
18. The method of claim 17 , wherein the tilt angle θ is determined as:
θ=ρ−ATAN[2/( N tan ρ)]
where ρ is a pointing angle to the selected point.
19. The method of claim 15 , wherein the maximum signal strength is determined based on a derivative of a relative total gain equation.
20. The method of claim 15 , wherein the tilt angle is an angle for which a maximum signal strength is directed toward a selected point.