# Experimental Study of a Signal Modulation Method to Improve eLORAN Data Channel Communications
## 3 Results  
### Signal Transmission Characteristics  
The carrier frequency of the eLORAN signal is 100 kHz, and it is mainly transmitted through two paths to reach the receiving terminal: one is a ground wave signal that is transmitted along the surface of the earth to the receiving terminal; the other is a sky wave signal that is reflected by the ionosphere and reaches the receiving terminal. Among them, because the eLORAN ground wave signal propagates along the surface, the signal energy attenuates as the transmission distance increases, and the transmission delay increases accordingly. The speed of the signal attenuation and the transmission delay are mainly related to the transmission distance and path, the ground conductivity, relative permittivity, ground curvature, and atmospheric refractive index are related; the eLORAN sky wave signal is reflected and propagated through the ionosphere, and its arrival at the receiving terminal must lag behind the ground wave signal.  
According to the \"minimum performance standards for marine eLORAN receiving equipment\" issued by Radio Technical Commission for Maritime Services (RTCM), the delay variation range of Loran-C's sky-wave signal relative to its ground-wave signal is greater than 37.5 \(\mathrm{\SIUnitSymbolMicro s}\). The eLORAN receiver equipment will be capable of acquiring signals with field strength above 40 dB\(\mathrm{\SIUnitSymbolMicro m}\).  
eLORAN ground wave signals are affected by the vertical component of ground wave field strength and ground wave propagation delay during transmission. Among them, the eLORAN ground wave field strength determines the range of the system, the sensitivity of the receiving terminal, and the design of the dynamic range, which is an important technical indicator of the eLORAN system; the propagation delay of the ground wave determines the path transmission between the eLORAN transmitting system and the receiver Delay accuracy.  
eLORAN ground wave signals usually use the \"Millington\" semi-empirical method to calculate the signal field strength [20]:  
\[\mathrm{E(dB\SIUnitSymbolMicro V/m)=109.54+101 lgP_{\Sigma}+20-20 lg}d \tag{6}\]  
\(\mathrm{P_{\Sigma}}\)--radiation power of transmitting antenna, \(\mathrm{kW}\);  
\(\mathrm{W_{g}}\)--ground wave attenuation factor;  
d--great circle distance between transmitting and receiving antennas, \(\mathrm{km}\);  
The propagation delay of eLORAN ground wave signal can be expressed as:  
\[\begin{array}{ll}\mathrm{t_{g}}(\omega)&=t_{0}+\mathrm{t_{w}}(\omega)\\ &=\frac{\mathrm{d}}{\mathrm{c}}\mathrm{n_{s}}\times 10^{6}+\left(\mathrm{argW_{g}} /\omega\right)\times 10^{6}\end{array} \tag{7}\]  
\(t_{0}\)--basic delay;  
\(\mathrm{t_{w}}(\omega)\)--secondary phase factor;c--speed of light in free space, km/s;  
d--the great circle distance between the transmitting and receiving antennas, km;  
n\({}_{\rm s}\)--ground atmospheric refractive index;  
W\({}_{\rm g}\)--ground wave attenuation factor;  
\(\omega\)--angular frequency, rad/s.  
\[{\rm W_{g}=F(q)+j\frac{1}{k\rm d}-\left(\frac{1}{k\rm d}\right)^{2}} \tag{8}\]  
\[{\rm q=j\left(\frac{Ka_{e}}{2}\right)^{1/3}\frac{\sqrt{\varepsilon-1+j60\lambda \sigma}}{\varepsilon+j60\lambda\sigma}} \tag{9}\]  
K--wave number in the air, \(K=2\pi/\lambda\);  
\(a_{e}\)--equivalent earth diameter, km;  
\(\varepsilon\)--the relative dielectric constant of the ground;  
\(\sigma\)--equivalent ground conductivity, S/m;  
\(\lambda\)--the signal wavelength in vacuum, m.