cranerainpl

RF signal attenuation due to rainfall using Crane model

Syntax

L = cranerainpl(range,freq,rainrate)

L = cranerainpl(range,freq,rainrate,elev)

L = cranerainpl(range,freq,rainrate,elev,tau)

Description

L = cranerainpl(range,freq,rainrate) returns the signal attenuation, L, due to rain based on the Crane rain model. Signal attenuation is a function of the signal path length, range, the signal frequency, freq, and the rain rate, rainrate. The rain rate is defined as the long-term statistical rain rate. The attenuation model applies only for frequencies from 1 GHz to 1000 GHz and is valid for ranges up to 22.5 km. The Crane model accounts for the cellular nature of rainstorms. For more information about the Crane rain model, see [1].

L = cranerainpl(range,freq,rainrate,elev) also specifies the elevation angle, elev, of the signal path.

L = cranerainpl(range,freq,rainrate,elev,tau) also specifies the polarization tilt angle, tau, of the signal.

Examples

Compare Attenuation for Two Rain Rates Using Crane Model

Use the Crane rain model to compute the signal attenuation caused by rain for a 20 GHz signal sent over a distance of 10 km. Use rain rates of 10.0 and 100.0 mm/hr.

First, set the rain rate to 10 mm/hr.

rr = 10.0;
L = cranerainpl(10e3,20.0e9,rr)

L = 
12.5988

Repeat the computation using a rain rate of 100.0 mm/hr.

rr = 100.0;
L = cranerainpl(10e3,20.0e9,rr)

L = 
73.1912

Rain Attenuation as a Function of Frequency Using Crane Model

Plot the signal attenuation due to rain for signals in the frequency range from 1 to 1000 GHz. Use the Crane model to compute the attenuation for a rain rate of 30.0 mm/hr and a signal path distance of 10 km.

rr = 30.0;
freq = [1:1000]*1e9;
L = cranerainpl(10e3,freq,rr);
semilogx(freq/1e9,L)
grid
xlabel('Frequency (GHz)')
ylabel('Attenuation (dB)')

Rain Attenuation as a Function of Elevation Using Crane Model

Plot the signal attenuation due to rain as a function of elevation angle. Elevation angles vary from 0 to 90 degrees. Assume a path distance of 10 km and a signal frequency of 10 GHz. The rain rate is 100 mm/hr.

rr = 100.0;

Set the elevation angles, frequency, and path length.

elev = [0:1:90];
freq = 10.0e9;
rng = 10e3*ones(size(elev));

Compute and plot the loss.

L = cranerainpl(rng,freq,rr,elev);
plot(elev,L)
grid
xlabel('Path Elevation (degrees)')
ylabel('Attenuation (dB)')

Rain Attenuation as a Function of Polarization Using Crane Model

Plot the signal attenuation due to rainfall as a function of the polarization tilt angle. Assume a path distance of 10 km, a signal frequency of 10 GHz, and a path elevation angle of 0 degrees. Set the rainfall rate to 70 mm/hour. Plot the signal attenuation against polarization tilt angle.

Set the polarization tilt angle to vary from -90 to 90 degrees.

tau = -90:90;

Set the elevation angle, frequency, path distance, and rain rate.

elev = 0;
freq = 10.0e9;
rng = 10e3*ones(size(tau));
rr = 70.0;

Compute and plot the attenuation.

L = cranerainpl(rng,freq,rr,elev,tau);
plot(tau,L)
grid
xlabel('Tilt Angle (degrees)')
ylabel('Attenuation (dB)')

Input Arguments

range — Signal path length in meters

positive scalar | real-valued 1-by-M vector of positive values | real-valued M-by-1 vector of positive values

Signal path length in meters, specified as a positive scalar, a real-valued 1-by-M vector of positive values, or real-valued M-by-1 vector of positive values.

Example: [13000.0,14000.0]

freq — Signal frequency in Hz

positive scalar | real-valued 1-by-N vector of positive values | real-valued N-by-1 vector of positive values

Signal frequency in Hz, specified as a positive scalar, a real-valued 1-by-N vector of positive values, or a real-valued N-by-1 vector of positive values. Frequencies must lie in the range 1–1000 GHz.

Example: [2.0:2:10.0]*1e9]

rainrate — Rain rate in mm/hr

nonnegative scalar

Rain rate in mm/hr, specified as a nonnegative scalar. Rain rate represents the long-term statistical rainfall rate provided by Crane (see [1]).

Example: 100.5

elev — Signal path elevation angle, in degrees

0.0 (default) | scalar | real-valued 1-by-M vector | real-valued M-by-1 vector

Signal path elevation angle, in degrees, specified as a real-valued scalar, or real-valued M-by-1 or real-valued 1-by-M vector. Units are in degrees between –90° and 90°.

• If elev is a scalar, all propagation paths have the same elevation angle.

• If elev is a vector, its length must match the length of range and each element in elev corresponds to a propagation range.

Example: [0,45]

tau — Tilt angle of signal polarization ellipse, in degrees

0.0 (default) | scalar | real-valued 1-by-M vector | real-valued M-by-1 vector

Tilt angle of the signal polarization ellipse, in degrees, specified as a scalar, a real-valued 1-by-M vector, or a real-valued M-by-1 vector. Tilt angle values are in the range –90° and 90°, inclusive.

• If tau is a scalar, all signals have the same tilt angle.

• If tau is a vector, its length must match the length of range. In that case, each element in tau corresponds to a propagation path in range.

The tilt angle is defined as the angle between the semimajor axis of the polarization ellipse and the x-axis. Because the ellipse is symmetrical, a tilt angle of 10° corresponds to the same polarization state as a tilt angle of -80°. Thus, the tilt angle need only be specified between ±90°.

Example: [45,30]

Output Arguments

L — Signal attenuation in dB

real-valued M-by-N matrix

Signal attenuation in dB, returned as a real-valued M-by-N matrix. Each matrix row represents a different path where M is the number of paths. Each column represents a different frequency where N is the number of frequencies.

More About

Crane Rainfall Attenuation Model

The Crane model calculates the attenuation of signals that propagate through regions of rainfall. The model was developed for use on Earth–space or terrestrial propagation paths and is a commonly-used method for the calculation of rain attenuation. The model is based on observations of rain rate, rain structure, and the vertical variation of temperature in the atmosphere. The Crane model (see Electromagnetic Wave Propagation through Rain) is primarily applicable to North America. The Crane model generally predicts losses greater than those of the ITU rain attenuation model used in the rainpl function. However, the uncertainty of both models and the short-term variation of fade can be large.

The ITU and Crane models are very similar but have some differences. The ITU and Crane rain attenuation models both require statistical annual rainfall rates and utilize an effective path length reduction factor to account for the cellular nature of storms. The 0.01% rainfall rate tables provided by Crane and the ITU are different. The Crane rainfall zones are similar to the ITU zones but more zones are defined in the US than in the ITU model. The ITU rainfall zones are discussed in ITU-R P.838-3: Specific attenuation model for rain for use in prediction methods. The Crane model is more complex consisting of a piecewise combination of path profiles composed of exponential functions.

The Crane model utilizes two exponential functions to span the distance from 0 to 22.5 km.

• For δ < D < 22.5,

  $$L=\gamma \left(\frac{e^{y\delta }-1}{y}-\frac{b^{\alpha }{e}^{z\delta }}{z}+\frac{b^{\alpha }{e}^{zD}}{z}\right)$$

• For 0 < D < δ,

  $$L=\gamma \left(\frac{e^{yD}-1}{y}\right)$$

where

• L = path attenuation (dB)

• 𝐷 = propagation distance (km)

• R = statistical 0.01% rain rate (mm/hr)

• γ = specific attenuation identical to that calculated in rainpl.

  $${\gamma }_R=k{R}^{\alpha },$$

  The parameters k and α depend on the frequency, the polarization state, and the elevation angle of the signal path. These coefficients, given by both Crane Electromagnetic Wave Propagation through Rain and the ITU-R P.838-3: Specific attenuation model for rain for use in prediction methods, are identical and are valid from 1 GHz to 1000 GHz. The specific attenuation model is valid for frequencies from 1–1000 GHz. Rainfall specific attenuation is computed according to the ITU rainfall model in ITU-R P.838-3: Specific attenuation model for rain for use in prediction methods.

The remaining parameters are empirical constants defined as:

• b = 2.3R^-0.17

• c = 0.026 - 0.03ln R

• δ = 3.8 - 0.6 ln R

• u = ln (be^cδ)/δ

• y = αu

• z = αc

To compute the total attenuation for narrowband signals along a path, the function multiplies the specific attenuation by the propagation distance.

You can also apply the attenuation model to wideband signals. First, divide the wideband signal into frequency subbands and apply attenuation to each subband. Then, sum all attenuated subband signals into the total attenuated signal.

References

[1] Crane, Robert K. Electromagnetic Wave Propagation through Rain. Wiley, 1996.

[2] Radiocommunication Sector of International Telecommunication Union. Recommendation ITU-R P.838-3: Specific attenuation model for rain for use in prediction methods. P Series, Radiowave Propagation 2005.

[3] Radiocommunication Sector of International Telecommunication Union. Recommendation ITU-R P.530-17: Propagation data and prediction methods required for the design of terrestrial line-of-sight systems. 2017.

[4] Radiocommunication Sector of International Telecommunication Union. Recommendation ITU-R P.837-7: Characteristics of precipitation for propagation modelling. 6/2017

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Does not support variable-size inputs.

Version History

Introduced in R2020a