Wideband LOS Channel

The attenuation or signal loss in a wideband LOS channel consists of four components:

,

where

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

When the signal source and receiver are stationary relative to each other, you can write the output of the free-space channel as , where is the signal delay and is the free-space propagation loss. The signal delay is calculated as , 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 field of the transmitting element or array. In the near field, the free-space propagation path loss formula is invalid and can result in loss values less than unity, which is equivalent to signal amplification. For this reason, the loss is set to unity for the values of .

If there is relative motion between the source and receiver, the Doppler frequency shift is taken into account. The frequency shift is for one-way propagation and for two-way propagation. The value is the relative velocity of the receiver 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 gas. The model also includes a continuous absorption spectrum below 10 GHz. The ITU (International Telecommunication Union) model given in [1] is used for the calculations. 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 refractive index of the atmosphere and consists of a spectral line component and a continuous component:

.

The spectral component consists of the sum of discrete spectral terms, which are the product of the localised frequency band function and the spectrum line intensity . For atmospheric oxygen, the line intensity of the spectrum is:

.

For atmospheric water vapour, the intensity of the spectrum line is:

,

where:

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

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

.

The total atmospheric pressure is .

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.

The calculation of the total attenuation of a narrowband signal is done by multiplying the specific attenuation by the path length . Then the total attenuation is equal to:

.

This model of signal attenuation can be applied to broadband signals. To do this, first divide the broadband signal into frequency sub-bands, calculate the attenuation for each sub-band, and 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 ITU model given in [2] is used for the calculations. 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).

The total attenuation of a narrowband signal is calculated by multiplying the specific attenuation by the path length . Then the total attenuation is equal to:

.

This model of signal attenuation can be applied to broadband signals. To do this, first divide the broadband signal into frequency sub-bands, calculate the attenuation for each sub-band, and then sum all the attenuated sub-band signals into a total attenuated signal.

This model calculates the attenuation of signals propagating through areas of precipitation. Precipitation 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 precipitation region. The ITU model given in [3] is used for the calculations. The model calculates the specific attenuation (attenuation per kilometre) of a signal as a function of precipitation intensity, signal frequency, polarisation and elevation angle. The specific attenuation depends on the precipitation intensity according to a power law:

,

where:

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

The calculation of the total attenuation of a narrowband signal is done by multiplying 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 is the frequency. A more detailed description of the attenuation calculation is given in [4].

The precipitation intensity , used in these calculations, is the long-term statistical precipitation intensity [5]. This is the precipitation intensity 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 the model to each sub-band. Then sum all attenuated sub-band signals into a total attenuated signal.

Sub-band processing divides a wideband signal into several sub-bands and applies narrowband processing to the signal in each sub-band. The signals from all sub-bands are summed to form the output signal.

When using wideband system objects or blocks, the number of sub-bands , into which the wideband signal is to be decomposed, is specified. The centre frequencies and sub-band widths are automatically calculated based on the total bandwidth and the number of sub-bands. The total bandwidth is centred on the carrier or operating frequency . The total bandwidth is determined by the sampling frequency . The sub-band frequency bandwidth is defined as . The centre frequencies of the sub-bands are defined as

- if is odd,

- if is odd.

Some system objects allow to get the centre frequencies of sub-bands as output data when the object is started. The returned sub-band frequencies are ordered according to the order of the discrete Fourier transform. Frequencies above the carrier are displayed first, then frequencies below the carrier.