Evaluation of the characterisation of the ultrashort wave radio channel model¶
The purpose of this demonstration is to evaluate the performance of the VHF radio channel model in the frequency range from 30 to 80 MHz. First, let us declare the input values for our channel. These are the following values:
- elevation height of the transmitter antenna,
- the elevation of the receiver antenna,
- the transmitter antenna gain,
- receiver antenna gain,
- transmitted signal power,
- receiver sensitivity,
- distance between 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 the model of radio wave propagation in free space. of radio wave propagation in free space. It takes as input the power transmitter power P_tx, transmitter antenna gain G_tx and receiver antenna gain G_rx, the signal wavelength λ and the distance between the transmitter and receiver R. The formula, used in the function is based on the Friis equation, which describes the attenuation of a of a signal under ideal conditions: the received signal power is proportional to the to the product of the transmitter power, the antenna gains and the square of the wavelength 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 power in environments where there are no obstacles and no additional sources of attenuation. there are no obstacles and no 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 line of sight without taking into account the 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
Summarising the table without forest height, the following conclusions can be drawn.
- The received signal power (P_prm) decreases with increasing frequency. This is due to the fact that 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 approx. 6.81×10^-4 W, and at 80 MHz it decreases to 9.58×10^-5 W. This behaviour is consistent with the classical model of radio wave propagation in free space, where signal attenuation depends on distance and frequency.
Let us perform calculations for a forest area. For this purpose, let's supplement the previously implemented function.
- The new function calculates the signal attenuation 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 higher. If the antennas are above the forest, the attenuation is lower. Attenuation is expressed in decibels (dB) and then converted to times to multiply by the signal strength.
- The received signal power P_prm is multiplied by the attenuation_factor to account for the effect of the forest.
- The result table now shows the received signal power including attenuation in the forest.
This code allows a more realistic modelling of the radio channel in conditions where the signal passes through a forested 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
Summarising the data from the table with the forest height taken into account, the following conclusions can be drawn.
- The introduction of correction for signal attenuation in the forest significantly reduces the power of the received signal. This is due to the fact that the forest area creates additional attenuation, especially at high frequencies.
- At 30 MHz, the signal power decreases to 4.30×10^-8 W, and at 80 MHz it decreases to 6.04×10^-16 W. Attenuation in the forest increases with increasing frequency, resulting in an exponential decrease in signal power. For example, at 80 MHz, the signal power becomes practically insignificant.
Conclusion¶
Let us conclude by comparing 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 W). for reception (above the receiver sensitivity of 4×10^-6 W).
- With the forest taken into account, the signal power at all frequencies becomes well below the receiver sensitivity, making communication impossible. This emphasises the critical effect of the forest on radio wave propagation, especially at high frequencies.
Based on the calculations, the following channel improvement recommendations can be considered.
- To ensure communication in forested areas it is necessary either to increase the transmitter power, or use lower frequencies where attenuation is less. 2.
- Consideration could also be given to raising the antennas above the forest floor, to minimise the effects of attenuation.