Calculation of the main characteristics and parameters of the radio system
This code demonstrates the calculation of the main characteristics and parameters of a radio system, including the range of radio communication, the level of signal attenuation, the signal-to-noise ratio, and the probability of detecting a radio signal. The influence of various factors such as antenna parameters, atmospheric attenuation, and spectral noise density is considered.
The key steps and principles of the calculation include the following steps.
- Calculation of antenna heights, direct radio visibility range and inclined range between transmitter and receiver.
- Calculation of attenuation of radio waves in free space and atmosphere.
- SNR determination based on the transmitter power, antenna gain and noise level.
# Determining the source data
Rз = 6371.0 # Radius of the Earth, km
RЭ = 8500.0 # Equivalent radius of the Earth, km
f = 49.0 # Frequency, MHz
P = 100.0 # Power, W
Δfc = 0.025 # Frequency band width, MHz
φN = 0.965167 # Latitude N, rad
λN = 1.448623 # Longitude N, rad
ΔhN0 = 0.162 # Altitude above sea level N, km
hN = 0.016 # Height of the antenna of the transmitter, km
Gφ = -2.0 # Gain of the transmitter antenna, dB
ha = 42000.0 # Apogee height, km
hp = 32000.0 # Perigee height, km
i = 0.17453 # The inclination of the orbit, rad
φM = 0.0 # Latitude M, rad
λM = 1.666789 # Longitude M, rad
ΔhM = 0.0 # Altitude above sea level M, km
N0 = -201.0 # Spectral noise power density of the receiver, dB
Gp1 = 22.0 # Antenna gain at frequency f1
Gp2 = 35.0 # Antenna gain at frequency f2
pfa = 1e-5 # The probability of a false alarm
ν = 1 # Number of frequency parameters
println("Initialization is completed")
The distance between the PRD and the PRM on the surface of the Earth
θ0 = 0.981489 # Geocentric angle, rad
D = Rз * θ0 # Distance between PRD and PRM on the Earth's surface, km
println("Дальность между ПРД и ПРМ: $D км")
The height of the detector above sea level
hM = 36423.578 # Height M above Ground, km
hM0 = ΔhM + hM # Altitude above sea level
println("Высота обнаружителя над уровнем моря: $hM0 км")
The height of the antenna of the transmitter above sea level
hN0 = ΔhN0 + hN # The height of the antenna of the transmitter above sea level
println("Высота антенны передатчика над уровнем моря: $hN0 км")
Total range of direct radio visibility
DM0 = 9187.426 # The range of direct radio visibility for the detector, km
DN0 = 55.009 # Range of direct radio visibility for PRD, km
D0 = DM0 + DN0 # Total range of direct radio visibility, km
println("Общая дальность прямой радиовидимости: $D0 км")
Attenuation of radio waves in free space
Dн = 39609.292 # Inclined range, km
Z0 = -32.45 - 20 * log10(Dн * f) # Attenuation in free space, dB
println("Ослабление радиоволн в свободном пространстве: $Z0 дБ")
Attenuation of the radio signal in the atmosphere and during meteorological phenomena
Va = -0.02 # Attenuation in the atmosphere, dB
Vг = 0.0 # Attenuation in hydrometeorological formations, dB
V2 = Va + Vг # Total attenuation
println("Общее затухание в атмосфере и гидрометеообразованиях: $V2 дБ")
Signal attenuation on the space track
Z = Z0 + V2 # Complete signal attenuation
println("Полное ослабление сигнала: $Z дБ")
# 1.24.2 Atmospheric noise level
Nш = -177.2 - 20 * log10(f) + 47.2 * (2.34 + 0.78 * log10(f))^(-2/3) + Gp1 # Atmospheric noise, dB
println("Уровень атмосферных шумов: $Nш дБ")
Signal-to-noise ratio at the output of the detector receiver
PВт = 100.0 # The power of the transmitter in watts
Gp = 22.0 # Antenna gain on the main lobe
Z = Z0 + V2 # Complete signal attenuation
# Calculation of the signal-to-noise ratio
SNR = 10 * log10(PВт) + Gp - Z - N0 # Signal-to-noise ratio, dB
println("Отношение сигнал/шум на выходе приемного устройства: $SNR дБ")
Normalized threshold level
Qф = sqrt(2 * log(1 / pfa)) # The probability of a false alarm pfa
println("Нормированный пороговый уровень: $Qф")
Function parameter X
X = SNR - Qф # Functional parameter
println("Функциональный параметр X: $X")
The probability of registering a radio signal based on the counts. We use an approximation for the probability function if X < 0.
if X < 0
Y = (0.707 * abs(X))^2
Pн = exp(-Y) # Probability of registration
println("Вероятность регистрации радиосигнала по отсчетам: $Pн")
else
# If X >= 0, another formula must be used (you can add it if necessary)
println("The functional parameter X >= 0, requires a different approximation")
end
# If we perform the calculation for the frequency f = 50 MHz
f2 = 50.0 # New frequency
Nш2 = -177.2 - 20 * log10(f2) + 47.2 * (2.34 + 0.78 * log10(f2))^(-2/3) + Gp1 # Noise level at 50 MHz
SNR2 = 10 * log10(PВт) + Gp - Z - N0 # Updated signal-to-noise ratio for f = 50 MHz
X2 = SNR2 - Qф
if X2 >= 0
println("At a frequency of 50 MHz, the probability of registration is 1.0")
else
Y2 = (0.707 * abs(X2))^2
Pн2 = exp(-Y2)
println("На частоте 50 МГц вероятность регистрации радиосигнала: $Pн2")
end
Conclusion
The calculation results show that:
-
The signal in the system is stable. The signal-to-noise ratio SNR=111 dB at attenuation Z=-211.4 dB provides the condition X>0.
-
Attenuation and noise are minimal. Atmospheric attenuation (-0.02 dB) and noise level provide favorable conditions for signal transmission.
Practical significance:
the high level of reliability of the system confirms its suitability for operation in difficult conditions, which is especially important for remote detection systems and satellite communications.