LOS Channel

Attenuation or path loss in a wideband LOS channel consists of four components.

,

where:

Each component is measured in units of magnitude, not dB.

When the source and target are stationary relative to each other, the unit output can be written as . The value represents the delay and represents the propagation loss. The delay is calculated from , where is the propagation distance and is the propagation velocity. The free-space path loss is defined by the expression

,

where is the wavelength of the signal.

This formula assumes that the target is in the far zone of the transmitting element or array. In the near zone, the free-space propagation path loss formula is invalid and may result in a loss less than unity, which is equivalent to signal gain. For this reason, the loss is set equal to unity for range values .

When there is relative motion between source and target, processing also introduces a frequency shift. This shift corresponds to the Doppler shift between the source and target points. The frequency shift is for one-way propagation and for two-way propagation. The parameters is the relative velocity of the target relative to the source.

This model calculates the attenuation of signals propagating through atmospheric gases.

Electromagnetic signals are attenuated when propagating through the atmosphere. This effect is mainly due to the resonant absorption lines of oxygen and water vapour, with a smaller contribution from nitrogen. The model also includes a continuous absorption spectrum below 10 GHz. The model calculates specific attenuation (attenuation per kilometre) as a function of temperature, pressure, water vapour density and signal frequency. The atmospheric gas model is valid for frequencies 1-1000 GHz and is applicable to polarised and unpolarised fields.

The formula for the specific attenuation at each frequency is as follows:

.

The value is the imaginary part of the complex refractivity of the atmosphere and consists of spectral linear and continuous components:

.

The spectral component consists of the sum of the discrete spectral terms comprising the localised bandwidth function, , multiplied by the spectral line strength, . For atmospheric oxygen, the strength of each spectral line is equal to:

.

For atmospheric water vapour, the strength of each spectral line is equal to:

.

where:

The units of pressure are hectopascals (hPa) and the units of temperature are degrees Kelvin.

The specific pressure of water vapour, , is related to the density of water vapour, , as follows:

.

The total atmospheric pressure is equal to:

.

For each oxygen line, depends on two parameters, and . Similarly, each water vapour line depends on two parameters, and .

The localised bandwidth functions are complex functions of frequency. These functions depend on the empirical parameters of the model.

To calculate the total attenuation for narrowband signals in a path, the function multiplies the specific attenuation by the path length, . Then the total attenuation is equal to:

.

The attenuation model can be applied to broadband signals. First divide the broadband signal into frequency sub-bands and apply attenuation to each sub-band. Then sum all the attenuated sub-band signals into a total attenuated signal.

This model calculates the attenuation of signals propagating through fog or clouds.

Fog or clouds are the same atmospheric phenomenon. The model calculates the specific attenuation (attenuation per kilometre) of a signal as a function of liquid water density, signal frequency and temperature. The model is applicable to polarised and unpolarised fields. The formula for the specific attenuation at each frequency is as follows:

,

where:

The model of attenuation in clouds and fog is valid for frequencies 10-1000 GHz. The units of the specific attenuation coefficient are (dB/km)/(g/m3).

To calculate the total attenuation of narrowband signals on a path, the function multiplies the specific attenuation by the path length . The total attenuation is equal to .

The attenuation model can be applied to broadband signals. First divide the broadband signal into frequency sub-bands and apply narrowband attenuation to each sub-band. Then sum all the attenuated sub-band signals into a total attenuated signal.

This model calculates the attenuation of signals propagating through rainfall areas. Rainfall attenuation is the dominant attenuation mechanism and can vary from location to location and from year to year.

Electromagnetic signals are attenuated as they propagate through the rainfall region. The model calculates the specific attenuation (attenuation per kilometre) of a signal as a function of rain intensity, signal frequency, polarisation and elevation angle of the path. The specific attenuation, , is modelled as a power law as a function of rain intensity

,

where:

This attenuation model is valid for frequencies 1-1000 GHz.

To calculate the total attenuation of a narrowband signal path, the function multiplies the specific attenuation by the effective propagation distance, . Then the total attenuation is equal to .

The effective distance is the geometric distance , multiplied by a scaling factor:

,

where:

The precipitation rate , used in these calculations, is the long-term statistical precipitation rate . This is the precipitation rate that is exceeded 0.01% of the time.

The attenuation model can be applied to broadband signals. First divide the broadband signal into frequency sub-bands and apply attenuation to each sub-band. Then sum all the attenuated sub-band signals into a total attenuated signal.