Wideband LOS Channel

Signal attenuation or loss in a LOS broadband channel consists of four components:

,

where

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

When the signal source and receiver are stationary relative to each other, the output signal of the free space channel can be written as , where — signal delay, and — losses during propagation in free space. The signal delay is calculated as , where is the propagation distance, and — the speed of propagation. The losses on the way in free space are determined by the expression

,

where — 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 formula for losses along the propagation path in free space is invalid and can lead to loss values less than one, which is equivalent to signal amplification. For this reason, for the values losses are set at one.

If there is relative motion between the source and receiver, then the Doppler frequency shift is taken into account. The frequency shift is for unilateral distribution and for two-way distribution. Value — this is the relative speed of the receiver relative to the source.

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

Electromagnetic signals weaken as they propagate through the atmosphere. This effect is mainly due to the lines of resonant absorption of oxygen and water vapor, 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 calculations. The model calculates the specific attenuation (attenuation per kilometer) as a function of temperature, pressure, water vapor density, and signal frequency. The atmospheric gas model is valid for frequencies of 1-1000 GHz and is applicable to polarized and unpolarized fields.

The formula for the specific attenuation at each frequency is:

.

Value It is an 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 a localized function of the frequency band and the intensity of the spectrum line . For atmospheric oxygen, the intensity of the spectral line is:

.

For atmospheric water vapor, the intensity of the spectral line is:

,

where:

The units of measurement for pressure are hectopascals (gPa), and temperatures are degrees Kelvin.

Partial pressure of water vapor it is related to the density of water vapor , as follows:

.

The total atmospheric pressure is .

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

Localized frequency band functions they are complex functions of frequency. These functions depend on the empirical parameters of the model.

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

.

This signal attenuation model can be applied to broadband signals. To do this, first divide the broadband signal into frequency sub-bands, calculate the signal attenuation for each sub-band, and then sum all the attenuated sub-band signals into a common 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 calculations. The model calculates the specific attenuation (attenuation per kilometer) of a signal as a function of liquid water density, signal frequency, and temperature. The model is applicable to polarized and unpolarized fields. The formula for the specific attenuation at each frequency is:

,

where:

The attenuation model in clouds and fog is valid for frequencies of 10-1000 GHz. The units of measurement 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:

.

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

This model calculates the attenuation of signals propagating through areas where precipitation occurs. Precipitation attenuation is the dominant attenuation mechanism and can vary from place to place and from year to year.

Electromagnetic signals are attenuated as they propagate through the precipitation area. The ITU model given in [3] is used for calculations. The model calculates the specific attenuation (attenuation per kilometer) of a signal as a function of precipitation intensity, signal frequency, polarization, and elevation angle. Specific attenuation depends on the intensity of precipitation according to the power law:

,

where:

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

The total attenuation of a narrowband signal is calculated by multiplying the specific attenuation by the effective propagation distance, . Then the total attenuation is:

.

The effective distance is the geometric distance multiplied by the scale factor:

,

where — frequency. A more detailed description of the attenuation calculation is given in [4].

Precipitation intensity , used in these calculations, represents the long-term statistical intensity of precipitation [5]. This is the intensity of precipitation, which is exceeded in 0.01% of cases.

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 the attenuated subband signals into a total attenuated signal.

Subband processing divides the broadband signal into several subbands and applies narrowband processing to the signal in each subband. The signals of all sub-bands are combined to form an output signal.

When using broadband system objects or blocks, the number of sub-ranges is set. , into which the broadband signal needs to be decomposed. The center frequencies and subband widths are automatically calculated based on the total bandwidth and the number of subbands. The total frequency band is centered on the carrier or operating frequency . The total bandwidth is determined by the sampling rate . The width of the frequency subband is defined as . The central frequencies of the sub-bands are defined as

— if - even number,

— if "odd."

Some system objects allow you to get the central frequencies of the sub-bands as output data when starting the object. The returned subband frequencies are ordered according to the order of the discrete Fourier transform. The frequencies above the carrier are displayed first, then the frequencies below the carrier.