Appl. Sci. 2023, 13, 1872 
550N' 
50" 
| 
30 
Do 
ja 
za | 
© 20 
„| 
a 40 
& 
5 
10 
195er 
cn‘ 
1 
Rglei- - 
a 
72 
40° 
50f17 
55°N 
50’ 
40’ 
30’ 
> 20° 
10 
AuSTO 
54°N! 
m 
0.16 
12°E 
20° 40 = 13°E 
Longitude [deg] 
07 
Ta 
0.32 0.48 0.64 
S LL FAN 
9.80 0.96 1.12 1.28 
AGDPF in [rad] 
44 
Ay 
AM 
<5a°N 
1.60 
Figure 2. Groß Mohrdorf AGDF calculated for the southern Baltic Sea in radians. 
In a simplified scenario, we can assume a one-ray reflection model, where the sky- 
wave sum-up to the ground-wave signal at the receiver side. By neglecting the influence of 
*he noise, we can define the real value ground-wave signal, as follows 
Scw = Acw(t) cos(27 ft + 9cw) (2) 
where Acw is the signal amplitude, f is the frequency of a particular CW and 9cw is the 
phase shift due to the propagation path. Similarly, the sky-wave can be given as follows 
SSW = Asw(t) cos(27x ft + sw) (3) 
where now Asw represents the sky-wave amplitude, and 9sw is the phase shift due to the 
sky-wave propagation path, which clearly differs from the ground-wave one. The sum of 
‘he two signals can be expressed as follows 
SSUM = Scw + ssw = Asım(t) cos(2x ft + Osym) 
(4) 
wi. re 
ASUM = A/ Akaırr + Ad + 2AcwAsw cos(9cw Pf Osw) 
(5) 
_ Acw sin(9cw) + Asw sin(9sw) 
tan(9sumMm) — AA I 
AGw cos(8cw) + Asw cos (8sw) 
The derivation of Equations (4)-(6) is given in the Appendix A. 
We attempt to explain the impact of a sky-wave on the phase error and amplitude 
ın a simulated scenario. We assume Acw = 1, 9cw = 0 for simplicity and we define the 
ground-wave to the sky-wave amplitude ratio (GSAR) as follows 
ic 
GSAR = Acw 
Asw 
(7) 
With these assumptions, Equation (6) becomes