BLoS Loss

Algorithm Overview & Step-by-Step Description

The BLoS Loss link budget calculator performs a forward-link and return-link satellite budget estimation based on typical physical models tailored for Ku-Band Geostationary (GEO) satellite communications. Below is the step-by-step mathematical reasoning employed by the application.

Step 1: Geometry Calculation

To calculate the distance to the satellite and the elevation angle, we assume a spherical Earth (radius \( R_{E} = 6371 \) km) and a geostationary orbit radius of \( R_{G} = 42157 \) km (approx 35786 km altitude). Given the ground station latitude (\( \theta \)) and relative longitude (\( \Delta\lambda \)):

• Central Angle (\( \gamma \)): cos(γ) = cos(θ) × cos(Δλ)
• Slant Distance (\( d \)): Using the Law of Cosines, d = √(RE² + RG² - 2·RE·RG·cos(γ))
• Elevation Angle (\( \alpha \)): sin(α) = (RG·cos(γ) - RE) / d

Step 2: Free Space Path Loss (FSPL)

The FSPL accounts for the geometric spreading of the radio frequency wave.

Where \( d \) is in km and \( f \) is in GHz.

The 92.45 constant: This number arises from the base FSPL derivation \( \left( \frac{4\pi d f}{c} \right)^2 \). Taking \( 20 \log_{10} \left( \frac{4\pi}{c} \right) \), where \( c \) is the speed of light in m/s, yields \( -147.55 \) dB. When substituting distance \( d \) from meters to kilometers (\( +60 \) dB) and frequency \( f \) from Hertz to Gigahertz (\( +180 \) dB), the combined unit offsets produce: \( -147.55 + 60 + 180 = \mathbf{92.45} \).

Step 3: Antenna Gain & EIRP

The parabolic antenna gain depends on its diameter (\( D \)), frequency (\( f \)), and efficiency (\( \eta \approx 0.65 \)).

The Effective Isotropic Radiated Power (EIRP) for the transmitting earth station is the sum of the Transmit Power (in dBW) and the Transmit Antenna Gain (in dBi). Line losses are assumed negligible or pre-factored into transmit power for simplicity.

Step 4: Atmospheric and Rain Attenuation

At Ku-band (12-14 GHz), atmospheric gases and rain cause significant signal attenuation.

• Clear Sky Attenuation: mode is approximated using a cosecant law with a base zenith loss: Latmos = Lzenith / sin(α)
• Rain Fade: Approximated using a simplified ITU-R P.618 / P.838 model. Specific attenuation is calculated as γR = k · Rα (with k and α interpolated for Ku-band). This is integrated over the effective rain height, corrected for the elevation angle and spatial variance.

Step 5: Carrier-to-Noise Density Ratio (C/N₀)

The budget uses Boltzmann's constant (\( k = -228.6 \) dBW/K/Hz) to find the noise floor.

Uplink: C/N0 = EIRPearth - Lossesup + (G/T)sat - k

Downlink: C/N0 = EIRPsat - Lossesdown + (G/T)earth - k

Step 6: Overall Link Performance

The total Carrier-to-Noise Density ratio is the reciprocal sum of linear C/N₀ values for uplink and downlink (bent-pipe transponder).

Finally, the Carrier-to-Noise Ratio (C/N or SNR) is calculated by subtracting the required noise bandwidth from the total C/N₀: