EngeeRadars.TwoRayChannel

The two-beam propagation channel is the next step in complexity after the free space channel and is the simplest case of a multipath propagation medium.

The free space channel models the beam line of sight from point 1 to point 2.

In a two-beam channel, the medium is specified as a homogeneous, isotropic medium with a reflective planar boundary. The boundary is always set as .

There are at most two rays propagating from point 1 to point 2. The first ray propagates along the same line-of-sight path as in the free-space channel. The line-of-sight path is often referred to as the straight ray. The second ray is reflected from the boundary before reaching point 2. According to the law of reflection, the angle of reflection is equal to the angle of incidence. In short-range simulations, such as cellular telephone systems or automobile radars, it may be assumed that the reflecting surface, the earth or ocean surface, is flat.

The EngeeRadars.TwoRayChannel system object simulates propagation time delay, phase shift, Doppler shift and loss effects for both paths. For the reflected path, the loss effects include reflection losses at the boundary.

The following figure shows the two propagation paths. From the source position, , and the receiver position, , you can calculate the angles of incidence for both paths, and . The angles of incidence are the angles of location and azimuth of the incoming radiation with respect to the local coordinate system. In this case, the local coordinate system is the same as the global coordinate system.

You can also calculate the propagation angles, and . In global coordinates, the reflection angle at the boundary coincides with the angles and . The reflection angle is important to know when you use angle-dependent reflection loss data.

The total path length for the line-of-sight path , which is equal to the geometric distance between the source and receiver, is shown in the figure.

The total path length for the reflected path is . The value is the distance between the source and the receiver.

You can easily derive exact formulas for path lengths and angles in terms of distance to the ground and height of objects in a global coordinate system.

Attenuation, or path loss in a two-beam channel, is the product of five components , where

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

Losses occur when a signal is reflected from a boundary. You can obtain a simple model of ground reflection loss by representing the electromagnetic field as a scalar field. This approach also works for acoustic and sonar systems.

Let be a free-space scalar electromagnetic field with amplitude at a reference distance from the transmitter (e.g. one metre). The free-space propagating field at a distance from the transmitter has the form

for the line-of-sight trajectory.

You can express the ground-reflected -field as

where is the distance of the reflected path.

The value represents the loss due to reflection from the ground plane. To specify , use the GroundReflectionCoefficient property. In general, depends on the angle of incidence of the field. The total field at the destination is the sum of the line-of-sight and reflected path fields.

For electromagnetic waves, a more complex but more realistic model uses a vector representation of the polarised field. You can decompose the incident electric field into two components. One component, , is parallel to the plane of incidence. The other component, , is perpendicular to the plane of incidence. The ground reflection coefficients for these components are different and can be written in terms of ground permeability and angle of incidence.

where is the impedance of the medium. Since the magnetic permeability of the earth is almost the same as that of air or free space, the impedance ratio depends primarily on the ratio of electrical permeabilities

where the value is the relative permeability of the ground, given by the GroundRelativePermittivity property. The angle is the angle of incidence, and the angle is the angle of refraction at the boundary. You can determine , using Snell’s law of refraction.

After reflection, the total field is reconstructed from the parallel and perpendicular components. The total attenuation in the ground plane, , is a combination of and .

When the origin and destination points are stationary relative to each other, you can write the output Y of an object as . The value is the signal delay, and is the free-space path loss. The delay is given by . - is either the line-of-sight propagation path distance or the reflection path distance, and is the propagation velocity. Path loss:

where is the wavelength of the signal.

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 from 1-1000 GHz and is applicable to polarised and unpolarised fields.

Formula for the specific attenuation at each frequency:

The value is the imaginary part of the complex atmospheric refractivity and consists of a spectral line component and a continuous component:

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:

is the pressure of dry air, is the partial pressure of water vapour, and is the ambient temperature. 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 ITU documentation at the end of this section contains tables of these parameters as functions of frequency.

The localised bandwidth functions are complex functions of frequency described in the ITU references below. These functions depend on empirical model parameters, which are also given in the references.

To calculate the total attenuation for narrowband signals on a path, the function multiplies the specific attenuation by the path length, . Then the total attenuation is .

You can apply the attenuation model 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 and cloud attenuation are the same atmospheric phenomenon. The ITU model used is IRU Recommendation-R P.840-6: Attenuation due to clouds and fog. 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 is the density of liquid water in gm/m3. The value represents the specific attenuation coefficient and is frequency dependent. The cloud and fog attenuation model is valid for frequencies 10-1000 GHz. The units of the specific attenuation coefficient are (dB/km)/(g/m3).

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

You can apply the attenuation model 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 that propagate through rainfall regions. Rain attenuation is the dominant attenuation mechanism and can vary from place to place and year to year.

Electromagnetic signals are attenuated when propagating through a rainfall region. Rain attenuation is calculated according to the ITU rain model "Recommendation ITU-R P.838-3: Specific rain attenuation model for usage in forecasting methods". The model calculates the specific attenuation (attenuation per kilometre) of a signal as a function of rain intensity, nominal signal frequency, polarisation and location angle. The specific attenuation, , is modelled as a power law as a function of rain rate:

Where is the rain rate. The units of measurement are mm/hour. The parameters and the exponent depend on frequency, polarisation state and elevation angle in the signal path. The specific attenuation model is valid for frequencies from 1-1000 GHz.

To calculate the total attenuation for narrowband signals in the path, the function multiplies the specific attenuation by the effective propagation distance, . Then the total attenuation is .

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

where is the frequency. The article "Recommendation ITU-R P.530-17 (12/2017): Propagation data and prediction methods required for the design of terrestrial line-of-sight systems" contains a full description of the attenuation calculation.

The rain rate, , used in these calculations is the long-term statistical rain rate, . This is the rain rate that is exceeded 0.01% of the time. The calculation of the statistical rainfall rate is discussed in "Recommendation ITU-R P.837-7 (06/2017): Precipitation characteristics for propagation modelling". This article also explains how to calculate attenuation for other percentages of the 0.01% value.

You can apply the attenuation model 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.