Evaluation of the characteristics of the ultrashort wave radio channel model
The purpose of this demonstration is to evaluate the characteristics of a VHF radio channel model in the frequency range from 30 to 80 MHz.
First, let's declare the input values for our channel. These are the following indicators:
- Lifting height of the transmitter antenna,
- Receiver antenna lifting height,
- The gain of the transmitter antenna,
- Receiver antenna gain,
- the power of the transmitted signal,
- Receiver sensitivity,
- The distance between the transmitter and receiver,
- frequencies from 30 to 80 MHz in 5 MHz increments,
- Height of the forest area.
using Printf
# Исходные параметры
h_tx = 16.0 # Высота подъема антенны передатчика, м
h_rx = 16.0 # Высота подъема антенны приемника, м
G_tx = 1.64 # Коэффициент усиления антенны передатчика
G_rx = 1.64 # Коэффициент усиления антенны приемника
P_tx = 400.0 # Мощность передаваемого сигнала, Вт
sensitivity = 4e-6 # Чувствительность приемника, В
R = 1000.0 # Расстояние между передатчиком и приемником, м
frequencies = 30e6:5e6:80e6 # Частоты от 30 до 80 МГц с шагом 5 МГц
c = 3e8 # Скорость света, м/с
# Условия распространения
forest_height = 30.0; # Высота лесного массива, м
The received_power function calculates the received signal power based on a model
of radio wave propagation in free space. It takes as input the power
of the P_tx transmitter, the gain coefficients of the antennas of the G_tx transmitter and the G_rx receiver,
the wavelength of the signal λ and the distance between the transmitter and receiver R. The formula
used in the function is based on the Friis equation, which describes
signal attenuation under ideal conditions: the received signal power is proportional
to the product of the transmitter power, antenna gain coefficients and the square
of the wavelength, and is inversely proportional to the square of the distance and the square of the wavelength.,
multiplied by
(4π)^2. This model is useful for estimating signal strength in conditions where
there are no obstacles and additional sources of attenuation.
# Функция для расчета мощности принимаемого сигнала
received_power(P_tx, G_tx, G_rx, λ, R) = P_tx * G_tx * G_rx * λ^2 / ((4 * π)^2 * R^2)
The results are calculated for direct visibility without taking into account attenuation in the forest.
println("Моделирование радиоканала в зоне радиотени\n")
# Таблица результатов
@printf("%10s %15s %15s\n", "Частота (МГц)", "Длина волны (м)", "P_prm (Вт)")
@printf("%s\n", "-" ^ 45)
for f in frequencies
λ = c / f # Длина волны
P_prm = received_power(P_tx, G_tx, G_rx, λ, R)
@printf("%10.2f %15.4f %15.6e\n", f / 1e6, λ, P_prm)
end
Summarizing the table without taking into account the height of the forest, the following conclusions can be drawn.
- The received signal power (P_prm) decreases with increasing frequency.
This is because the wavelength (λ) decreases, and the signal power is inversely
proportional to the square of the wavelength. - At a frequency of 30 MHz, the received signal power is about
6.81×10^-4 watts, and at a frequency of 80 MHz it decreases to 9.58×10^-5 watts.
This behavior corresponds to the classical model of radio wave propagation in
free space, where signal attenuation depends on distance and frequency.
Let's perform calculations for the woodlands. To do this, we will add a previously implemented function.
- The new function calculates the attenuation of the signal depending on the frequency and height of the forest relative to the height of the antennas.
If the antennas are below the height of the forest, the attenuation is greater.
If the antennas are higher than the forest, the attenuation is less.
The attenuation is expressed in decibels (dB), and then converted to times to multiply by the signal power. - The received P_prm signal power is multiplied by attenuation_factor attenuation factor to account for the forest effect.
- The results table now displays the received signal power, taking into account the attenuation in the forest.
This code allows you to more realistically simulate a radio channel in conditions when the signal passes through a forest area.
# Функция для расчета затухания в лесу
function forest_attenuation(f, forest_height, h_tx, h_rx)
# Упрощенная модель затухания в лесу
# Затухание зависит от частоты и высоты леса относительно высоты антенн
if h_tx < forest_height || h_rx < forest_height
# Если антенны находятся ниже высоты леса, затухание больше
attenuation = 0.1 * (forest_height - min(h_tx, h_rx)) * (f / 1e6) # Затухание в дБ
else
# Если антенны выше леса, затухание меньше
attenuation = 0.01 * (f / 1e6) # Затухание в дБ
end
return 10^(-attenuation / 10) # Преобразование из дБ в разы
end
println("Моделирование радиоканала в зоне радиотени с учетом высоты леса\n")
# Таблица результатов
@printf("%10s %15s %15s\n", "Частота (МГц)", "Длина волны (м)", "P_prm (Вт)")
@printf("%s\n", "-" ^ 45)
for f in frequencies
λ = c / f # Длина волны
P_prm = received_power(P_tx, G_tx, G_rx, λ, R)
# Учет затухания в лесу
attenuation_factor = forest_attenuation(f, forest_height, h_tx, h_rx)
P_prm_forest = P_prm * attenuation_factor
@printf("%10.2f %15.4f %15.6e\n", f / 1e6, λ, P_prm_forest)
end
Summarizing the data from the table, taking into account the height of the forest, the following conclusions can be drawn.
- The introduction of a correction for signal attenuation in the forest significantly reduces
the received signal power. This is due to the fact that the forest area creates additional
attenuation, especially at high frequencies. - At a frequency of 30 MHz, the signal power is reduced to 4.30×10^-8 watts, and at a frequency of 80 MHz — to 6.04×10^-16 watts.
The attenuation in the forest increases with increasing frequency, which leads to an exponential
decrease in signal power. For example, at a frequency of 80 MHz, the signal power becomes
almost insignificant.
Conclusion
In conclusion, we will compare the results.
- Without taking into account the forest, the signal power at all frequencies remains at a level sufficient
for reception (above the receiver sensitivity of 4×10^-6 watts). - Taking into account the forest, the signal power at all frequencies becomes significantly lower than the sensitivity of the receiver, which makes communication impossible.
This highlights the critical impact of woodlands on the propagation of radio waves, especially at high frequencies.
Based on the calculations, the following recommendations for improving the channel can be considered.
- To ensure communication in a wooded area, it is necessary either to increase the power of the transmitter
or to use lower frequencies where attenuation is lower. - You can also consider raising the antennas above the forest level
to minimize the effect of attenuation.