# phased.LOSChannel

Narrowband LOS propagation channel

## Description

The `phased.LOSChannel`

models the propagation of
narrowband electromagnetic signals through a line-of-sight (LOS) channel from a source
to a destination. In an LOS channel, propagation paths are straight lines from point to
point. The propagation model in the LOS channel includes free-space attenuation in
addition to attenuation due to atmospheric gases, rain, fog, and clouds. You can use
`phased.LOSChannel`

to model the propagation of
signals between multiple points simultaneously.

While the System object™ works for all frequencies, the attenuation models for atmospheric gases and rain are valid for electromagnetic signals in the frequency range 1–1000 GHz only. The attenuation model for fog and clouds is valid for 10–1000 GHz. Outside these frequency ranges, the System object uses the nearest valid value.

The `phased.LOSChannel`

System object applies range-dependent time delays to the signals, as well as gains or
losses. When either the source or destination is moving, the System object applies Doppler shifts.

Like the `phased.FreeSpace`

System object, the `phased.LOSChannel`

System object supports two-way propagation.

To create and use a narrowband channel:

Create the

`phased.LOSChannel`

object and set its properties.Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

## Creation

### Description

creates
an LOS attenuating propagation channel System object, `channel`

= phased.LOSChannel`channel`

.

creates a System object, `channel`

= phased.LOSChannel(`Name`

=`Value`

)`channel`

, with each specified property
`Name`

set to the specified `Value`

.
You can specify additional name and value pair arguments in any order as
(`Name1=Value1`

,...,`NameN=ValueN`

).

## Properties

Unless otherwise indicated, properties are *nontunable*, which means you cannot change their
values after calling the object. Objects lock when you call them, and the
`release`

function unlocks them.

If a property is *tunable*, you can change its value at
any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

`PropagationSpeed`

— Signal propagation speed

`physconst('LightSpeed')`

(default) | positive scalar

Signal propagation speed, specified as a positive scalar. Units are in meters per second. The
default propagation speed is the value returned by
`physconst('LightSpeed')`

. See `physconst`

for more information.

**Example: **`3e8`

**Data Types: **`double`

`OperatingFrequency`

— Operating frequency

`300e6`

(default) | positive scalar

Operating frequency, specified as a positive scalar. Units are in Hz.

**Example: **`1e9`

**Data Types: **`double`

`SpecifyAtmosphere`

— Enable atmospheric attenuation model

`false`

(default) | `true`

Option to enable the atmospheric attenuation model, specified
as a `false`

or `true`

. Set this
property to `true`

to add signal attenuation caused
by atmospheric gases, rain, fog, or clouds. Set this property to `false`

to
ignore atmospheric effects in propagation.

Setting `SpecifyAtmosphere`

to `true`

,
enables the `Temperature`

, `DryAirPressure`

, `WaterVapourDensity`

, `LiquidWaterDensity`

,
and `RainRate`

properties.

**Data Types: **`logical`

`Temperature`

— Ambient temperature

`15`

(default) | real-valued scalar

Ambient temperature, specified as a real-valued scalar. Units are in degrees Celsius.

**Example: **`20.0`

#### Dependencies

To enable this property, set `SpecifyAtmosphere`

to `true`

.

**Data Types: **`double`

`DryAirPressure`

— Atmospheric dry air pressure

`101.325e3`

(default) | positive real-valued scalar

Atmospheric dry air pressure, specified as a positive real-valued scalar. Units are in pascals (Pa). The default value of this property corresponds to one standard atmosphere.

**Example: **`101.0e3`

#### Dependencies

To enable this property, set `SpecifyAtmosphere`

to `true`

.

**Data Types: **`double`

`WaterVapourDensity`

— Atmospheric water vapor density

`7.5`

(default) | positive real-valued scalar

Atmospheric water vapor density, specified as a positive real-valued
scalar. Units are in g/m^{3}.

**Example: **`7.4`

#### Dependencies

To enable this property, set `SpecifyAtmosphere`

to `true`

.

**Data Types: **`double`

`LiquidWaterDensity`

— Liquid water density

`0.0`

(default) | nonnegative real-valued scalar

Liquid water density of fog or clouds, specified as a nonnegative
real-valued scalar. Units are in g/m^{3}.
Typical values for liquid water density are 0.05 for medium fog and
0.5 for thick fog.

**Example: **`0.1`

#### Dependencies

To enable this property, set `SpecifyAtmosphere`

to `true`

.

**Data Types: **`double`

`RainRate`

— Rainfall rate

`0.0`

(default) | nonnegative scalar

Rainfall rate, specified as a nonnegative scalar. Units are in mm/hr.

**Example: **`10.0`

#### Dependencies

To enable this property, set `SpecifyAtmosphere`

to `true`

.

**Data Types: **`double`

`TwoWayPropagation`

— Enable two-way propagation

`false`

(default) | `true`

Enable two-way propagation, specified as a `false`

or
`true`

. Set this property to `true`

to perform
round-trip propagation between the signal origin and the destination. Set this property
to `false`

to perform only one-way propagation from the origin to the
destination.

**Example: **`true`

**Data Types: **`logical`

`SampleRate`

— Sample rate of signal

`1e6`

(default) | positive scalar

Sample rate of signal, specified as a positive scalar. Units are in Hz. The System object uses this quantity to calculate the propagation delay in units of samples.

**Example: **`1e6`

**Data Types: **`double`

`MaximumDistanceSource`

— Source of maximum one-way propagation distance

`'Auto'`

(default) | `'Property'`

Source of maximum one-way propagation distance, specified as `'Auto'`

or `'Property'`

.
The maximum one-way propagation distance is used to allocate sufficient
memory for signal delay computation. When you set this property to `'Auto'`

,
the System object automatically allocates memory. When you set
this property to `'Property'`

, you specify the maximum
one-way propagation distance using the value of the `MaximumDistance`

property.

**Data Types: **`char`

`MaximumDistance`

— Maximum one-way propagation distance

`10000`

(default) | positive real-valued scalar

Maximum one-way propagation distance, specified as a positive real-valued scalar. Units are in meters. Any signal that propagates more than the maximum one-way distance is ignored. The maximum distance must be greater than or equal to the largest position-to-position distance.

**Example: **`5000`

#### Dependencies

To enable this property, set the `MaximumDistanceSource`

property
to `'Property'`

.

**Data Types: **`double`

`MaximumNumInputSamplesSource`

— Source of maximum number of samples

`'Auto'`

(default) | `'Property'`

The source of the maximum number of samples of the input signal, specified as
`'Auto'`

or `'Property'`

. When you set this
property to `'Auto'`

, the propagation model automatically allocates
enough memory to buffer the input signal. When you set this property to
`'Property'`

, you specify the maximum number of samples in the
input signal using the `MaximumNumInputSamples`

property. Any input
signal longer than that value is truncated.

To use this object with variable-size signals in a MATLAB^{®} Function Block in Simulink^{®}, set the `MaximumNumInputSamplesSource`

property to
`'Property'`

and set a value for the
`MaximumNumInputSamples`

property.

**Example: **`'Property'`

#### Dependencies

To enable this property, set `MaximumDistanceSource`

to
`'Property'`

.

**Data Types: **`char`

`MaximumNumInputSamples`

— Maximum number of input signal samples

`100`

(default) | positive integer

Maximum number of input signal samples, specified as a positive integer. The input signal is the first argument of the object call. The size of the input signal is the number of rows in the input matrix. Any input signal longer than this number is truncated. To process signals completely, ensure that this property value is greater than any maximum input signal length.

The waveform-generating System objects determine the maximum signal size:

For any waveform, if the waveform

`OutputFormat`

property is set to`'Samples'`

, the maximum signal length is the value specified in the`NumSamples`

property.For pulse waveforms, if the

`OutputFormat`

is set to`'Pulses'`

, the signal length is the product of the smallest pulse repetition frequency, the number of pulses, and the sample rate.For continuous waveforms, if the

`OutputFormat`

is set to`'Sweeps'`

, the signal length is the product of the sweep time, the number of sweeps, and the sample rate.

**Example: **`2048`

#### Dependencies

To enable this property, set `MaximumNumInputSamplesSource`

to `'Property'`

.

**Data Types: **`double`

## Usage

### Description

returns the resulting signal, `prop_sig`

= channel(`sig`

,`origin_pos`

,`dest_pos`

,`origin_vel`

,`dest_vel`

)`prop_sig`

, when a narrowband
signal, `sig`

, propagates through a line-of-sight (LOS)
channel from a source located at the `origin_pos`

position to
a destination at the `dest_pos`

position. Only one of the
`origin_pos`

or `dest_pos`

arguments
can specify multiple positions. The other must contain a single position. The
velocity of the signal origin is specified in `origin_vel`

and the velocity of the signal destination is specified in
`dest_vel`

. The dimensions of
`origin_vel`

and `dest_vel`

must match
the dimensions of `origin_pos`

and
`dest_pos`

, respectively.

Electromagnetic fields propagating through an LOS channel can be polarized or
nonpolarized. For nonpolarized fields, the propagating signal field,
`sig`

, is a vector or matrix. For polarized fields,
`sig`

is an array of structures. The structure elements
represent an electric field vector in Cartesian form.

### Input Arguments

`sig`

— Narrowband signal

*M*-by-*N* complex-valued
matrix | 1-by-*N*
`struct`

array containing complex-valued fields

Narrowband signal, specified as a matrix or `struct`

array, depending on whether is signal or polarized or nonpolarized. The
quantity *M* is the number of samples in the signal,
and *N* is the number of LOS channels. Each channel
corresponds to a source-destination pair.

Narrowband nonpolarized scalar signal. Specify

`sig`

as an*M*-by-*N*complex-valued matrix. Each column contains one signal propagated along the line-of-sight path.The size of the first dimension of the input matrix can vary to simulate a changing signal length. A size change can occur, for example, in the case of a pulse waveform with variable pulse repetition frequency.

Narrowband polarized signal. Specify

`sig`

as a 1-by-*N*`struct`

array containing complex-valued fields. Each`struct`

represents a polarized signal propagated along the line-of-sight path. Each`struct`

element contains three*M*-by-1 complex-valued column vectors,`sig.X`

,`sig.Y`

, and`sig.Z`

. These vectors represent the*x*,*y*, and*z*Cartesian components of the polarized signal.The size of the first dimension of the matrix fields within the

`struct`

can vary to simulate a changing signal length such as a pulse waveform with variable pulse repetition frequency.

**Example: **`[1,1;j,1;0.5,0]`

**Data Types: **`double`

**Complex Number Support: **Yes

`origin_pos`

— Signal origins

3-by-1 real-valued column vector | 3-by-*N* real-valued matrix

Origin of signals, specified as a 3-by-1 real-valued column vector or
3-by-*N* real-valued matrix. The quantity
*N* is the number of LOS channels. If
`origin_pos`

is a column vector, it takes the
form `[x;y;z]`

. If `origin_pos`

is a
matrix, each column specifies a different signal origin and has the form
`[x;y;z]`

. Units are in meters.

You cannot specify both `origin_pos`

and
`dest_pos`

as matrices. At least one must be a
3-by-1 column vector.

**Example: **`[1000;100;500]`

**Data Types: **`double`

`dest_pos`

— Signal destinations

3-by-1 real-valued column vector | 3-by-*N* real-valued matrix

Destination position of the signal or signals, specified as a 3-by-1
real-valued column vector or 3-by-*N* real-valued
matrix. The quantity *N* is the number of LOS channels
propagating from or to *N* signal origins. If
`dest_pos`

is a 3-by-1 column vector, it takes
the form `[x;y;z]`

. If `dest_pos`

is
a matrix, each column specifies a different signal destination and takes
the form `[x;y;z]`

Position units are in meters.

You cannot specify both `origin_pos`

and
`dest_pos`

as matrices. At least one must be a
3-by-1 column vector.

**Example: **`[0;0;0]`

**Data Types: **`double`

`origin_vel`

— Velocities of signal origins

3-by-1 real-valued column vector | 3-by-*N* real-valued matrix

Velocity of signal origin, specified as a 3-by-1 real-valued column
vector or 3-by-*N* real-valued matrix. The dimensions
of `origin_vel`

must match the dimensions of
`origin_pos`

. If `origin_vel`

is a column vector, it takes the form `[Vx;Vy;Vz]`

. If
`origin_vel`

is a 3-by-*N*
matrix, each column specifies a different origin velocity and has the
form `[Vx;Vy;Vz]`

. Velocity units are in meters per
second.

**Example: **`[10;0;5]`

**Data Types: **`double`

`dest_vel`

— Velocities of signal destinations

3-by-1 real-valued column vector | 3-by-*N* real-valued matrix

Velocity of signal destinations, specified as a 3-by-1 real-valued
column vector or 3-by-*N* real-valued matrix. The
dimensions of `dest_vel`

must match the dimensions of
`dest_pos`

. If `dest_vel`

is a
column vector, it takes the form `[Vx;Vy;Vz]`

. If
`dest_vel`

is a 3-by-*N* matrix,
each column specifies a different destination velocity and has the form
`[Vx;Vy;Vz]`

Velocity units are in meters per
second.

**Example: **`[0;0;0]`

**Data Types: **`double`

### Output Arguments

`prop_sig`

— Narrowband propagated signal

*M*-by-*N* complex-valued
matrix | 1-by-*N*
`struct`

array containing complex-valued fields

Narrowband signal, returned as a matrix or `struct`

array, depending on whether signal is polarized or nonpolarized. The
quantity *M* is the number of samples in the signal and
*N* is the number of narrowband LOS channels. Each
channel corresponds to a source-destination pair.

Narrowband nonpolarized scalar signal.

`prop_sig`

is an*M*-by-*N*complex-valued matrix.Narrowband polarized scalar signal.

`prop_sig`

is a 1-by-*N*`struct`

array containing complex-valued fields. Each`struct`

element contains three*M*-by-1 complex-valued column vectors,`sig.X`

,`sig.Y`

, and`sig.Z`

. These vectors represent the*x*,*y*, and*z*Cartesian components of the polarized signal.

The `prop_sig`

output contains signal samples
arriving at the signal destination within the current time frame. The
current time frame is the time frame of the input signals to the object.
Whenever it takes longer than the current time frame for the signal to
propagate from the origin to the destination, the output might not
contain all contributions from the input of the current time frame. The
remaining output appears in the next call to the object.

## Object Functions

To use an object function, specify the
System object as the first input argument. For
example, to release system resources of a System object named `obj`

, use
this syntax:

release(obj)

## Examples

### Propagate Signal in LOS Channel

Propagate a sinusoidal signal in a line of sight (LOS) channel from a radar at *(1000,0,0)* meters to a target at *(10000,4000,500)* meters. Assume the signal propagates in medium fog specified by a liquid water density of 0.05 $$g/{m}^{3}$$. Assume that the radar and the target are stationary. The signal carrier frequency is 10 GHz. The signal frequency is 500 Hz and the sample rate is 8.0 kHz.

Set up the transmitted signal.

fs = 8.0e3; dt = 1/fs; fsig = 500.0; fc = 10.0e9; t = [0:dt:.01]; sig = sin(2*pi*fsig*t);

Set the liquid water density and specify the LOS channel System object™.

lwd = 0.05; channel = phased.LOSChannel('SampleRate',fs,'SpecifyAtmosphere',true,... 'LiquidWaterDensity',lwd,'OperatingFrequency',fc);

Set the origin and destination of the signal.

xradar = [1000,0,0].'; vradar = [0,0,0].'; xtgt = [10000,4000,500].'; vtgt = [0,0,0].';

Propagate the signal from origin to destination and plot the result.

prog_sig = channel(sig.',xradar,xtgt,vradar,vtgt); plot(t*1000,real(prog_sig)) grid xlabel('Time (milliseconds)') ylabel('Amplitude')

### Propagate Polarized Wave in LOS Channel

Propagate a polarized electromagnetic wave radiating from a short-dipole antenna element. The dipole is rotated 30° around the *y*-axis. Set the orientation of the local axis to coincide with the dipole. Assume the dipole radiates at 30.0 GHz. Propagate the signal toward a target approximately 10 km away.

Create the short-dipole antenna element and radiator System objects. Set the `Polarization`

property to `'Combined'`

to generate polarized waves.

freq = 30.0e9; c = physconst('LightSpeed'); antenna = phased.ShortDipoleAntennaElement('FrequencyRange',[100e6 40e9], ... 'AxisDirection','Z'); radiator = phased.Radiator('Sensor',antenna, ... 'PropagationSpeed',c, ... 'OperatingFrequency',freq, ... 'Polarization','Combined', ... 'WeightsInputPort',false);

Create a signal to radiate. The signal envelope consists of several cycles of a 4 kHz sinusoid with amplitude set to unity. Set the sampling frequency to 1 MHz.

fsig = 4.0e3; fs = 1.0e6; t = [1:1000]/fs; signal = sin(2*pi*fsig*t'); laxes = roty(30)*eye(3,3);

Use a `phased.FreeSpace`

System object™ to propagate the field from the origin to the destination in free space.

fschannel = phased.FreeSpace('PropagationSpeed',c,... 'OperatingFrequency',freq,... 'TwoWayPropagation',false,... 'SampleRate',fs);

Use a `phased.LOSChannel`

System object to propagate the field from the origin to the destination in the LOS channel. Attenuation is due to atmospheric gases and fog.

loschannel = phased.LOSChannel('PropagationSpeed',c,... 'OperatingFrequency',freq,... 'TwoWayPropagation',false,... 'SampleRate',fs,'SpecifyAtmosphere',true,'LiquidWaterDensity',0.5);

Set the signal origin, signal origin velocity, signal destination, and signal destination velocity.

source_pos = [0;0;0]; target_pos = [10000;200;0]; source_vel = [0;0;0]; target_vel = [0;0;0]; [~,radiatingAngles] = rangeangle(target_pos,source_pos,laxes);

Radiate the signal towards the target. The radiated signal is a `struct`

containing the polarized field.

rad_sig = radiator(signal,radiatingAngles,laxes);

Propagate the signals to the target in free space.

```
prop_sig = fschannel(rad_sig,source_pos,target_pos,...
source_vel,target_vel);
```

Propagate the signals to the target in the LOS channel.

```
prop_att_sig = loschannel(rad_sig,source_pos,target_pos,...
source_vel,target_vel);
```

Plot the z-components of both the free-space and LOS-channel-propagated signals.

plot(1e6*t,real(prop_sig.Z),1e6*t,real(prop_att_sig.Z)) grid xlabel('Time (\mu sec)') legend('z_{fsp}','z_{los}')

The LOS channel signal is attenuated as compared to the free-space signal.

## More About

### Path Attenuation or Loss

Attenuation or path loss in the LOS channel consists of four
components. *L = L _{fsp}L_{g}L_{c}L_{r}*,
where

*L*is the free space path attenuation_{fsp}*L*is the atmospheric path attenuation_{g}*L*is the fog and cloud path attenuation_{c}*L*is the rain path attenuation_{r}

Each path attenuation is in magnitude units, not in dB.

### Free-space Time Delay and Path Loss

When the origin and destination are stationary relative to each
other, you can write the output signal of a free-space channel as *Y(t)
= x(t-τ)/L _{fsp}*.
The quantity

*τ*is the signal delay and

*L*is the free-space path loss. The delay

_{fsp}*τ*is given by

*R/c*, where

*R*is the propagation distance and

*c*is the propagation speed. The free-space path loss is given by

$${L}_{fsp}=\frac{{(4\pi R)}^{2}}{{\lambda}^{2}},$$

where λ is the signal wavelength.

This formula assumes that the target is in the far field of
the transmitting element or array. In the near field, the free-space
path loss formula is not valid and can result in a loss smaller than
one, equivalent to a signal gain. Therefore, the loss is set to unity
for range values, *R ≤ λ/4π*.

When the origin and destination have relative motion, the processing
also introduces a Doppler frequency shift. The frequency shift is *v/λ* for
one-way propagation and *2v/λ* for two-way
propagation. The quantity *v* is the relative speed
of the destination with respect to the origin.

For more details on free-space channel propagation, see [5].

### Atmospheric Gas Attenuation Model

This model calculates the attenuation of signals that propagate through atmospheric gases.

Electromagnetic signals attenuate when they propagate through the atmosphere. This effect is
due primarily to the absorption resonance lines of oxygen and water vapor, with smaller
contributions coming from nitrogen gas. The model also includes a continuous absorption
spectrum below 10 GHz. The ITU model *Recommendation ITU-R P.676-10: Attenuation by
atmospheric gases* is used. The model computes 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 from 1–1000 GHz and
applies to polarized and nonpolarized fields.

The formula for specific attenuation at each frequency is

$$\gamma ={\gamma}_{o}(f)+{\gamma}_{w}(f)=0.1820f{N}^{\u2033}(f).$$

The quantity *N"()* is the imaginary part of the complex
atmospheric refractivity and consists of a spectral line component and a continuous component:

$${N}^{\u2033}(f)={\displaystyle \sum _{i}{S}_{i}{F}_{i}+{{N}^{\u2033}}_{D}^{}(f)}$$

The spectral component consists of a sum of discrete spectrum terms
composed of a localized frequency bandwidth function,
*F(f)*_{i}, multiplied by a spectral line strength,
*S*_{i}. For atmospheric oxygen, each spectral line
strength is

$${S}_{i}={a}_{1}\times {10}^{-7}{\left(\frac{300}{T}\right)}^{3}\mathrm{exp}\left[{a}_{2}(1-\left(\frac{300}{T}\right)\right]P.$$

For atmospheric water vapor, each spectral line strength is

$${S}_{i}={b}_{1}\times {10}^{-1}{\left(\frac{300}{T}\right)}^{3.5}\mathrm{exp}\left[{b}_{2}(1-\left(\frac{300}{T}\right)\right]W.$$

*P* is the dry air pressure, *W* is the
water vapor partial pressure, and *T* is the ambient temperature. Pressure
units are in hectoPascals (hPa) and temperature is in degrees Kelvin. The water vapor
partial pressure, *W*, is related to the water vapor density, ρ, by

$$W=\frac{\rho T}{216.7}.$$

The total atmospheric pressure is *P* +
*W*.

For each oxygen line, *S _{i}* depends on two parameters,

*a*and

_{1}*a*. Similarly, each water vapor line depends on two parameters,

_{2}*b*and

_{1}*b*. The ITU documentation cited at the end of this section contains tabulations of these parameters as functions of frequency.

_{2}The localized frequency bandwidth functions *F _{i}(f)* are
complicated functions of frequency described in the ITU references
cited below. The functions depend on empirical model parameters that
are also tabulated in the reference.

This model applies to both narrowband and wideband atmospheric attenuation. To compute the
total attenuation for narrowband signals along a path, the function multiplies the specific
attenuation by the path length, *R*. Then, the total attenuation is
*L _{g}= R(γ_{o} +
γ_{w})*. To 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.

### Fog and Cloud Attenuation Model

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

Fog and cloud attenuation are due to the same atmospheric phenomenon. The ITU model,
*Recommendation ITU-R P.840-6: Attenuation due to clouds and fog* is
used. The model computes the specific attenuation (attenuation per kilometer), of a signal
as a function of liquid water density, signal frequency, and temperature. The model applies
to polarized and nonpolarized fields. The formula for specific attenuation at each frequency is

$${\gamma}_{c}={K}_{l}\left(f\right)M,$$

where *M* is the liquid water density in
gm/m^{3}. The quantity
*K _{l}(f)* is the specific attenuation coefficient
and depends on frequency. The cloud and fog attenuation model is valid for frequencies
10–1000 GHz. Units for the specific attenuation coefficient are
(dB/km)/(g/m

^{3}).

To compute the total attenuation for narrowband signals along a path, the function multiplies
the specific attenuation by the path length *R*. Total attenuation is
*L _{c} = Rγ_{c}*. You can
also apply the attenuation model to wideband signals. First, divide the wideband signal into
frequency subbands, and apply narrowband attenuation to each subband. Then, sum all
attenuated subband signals into the total attenuated signal.

### Rainfall Attenuation Model

This model calculates the attenuation of signals that propagate through regions of rainfall. Rain attenuation is a dominant fading mechanism and can vary from location-to-location and from year-to-year.

Electromagnetic signals are attenuated when propagating through a region of rainfall. Rainfall
attenuation is computed according to the ITU rainfall model *Recommendation
ITU-R P.838-3: Specific attenuation model for rain for use in prediction
methods*. The model computes the specific attenuation (attenuation
per kilometer) of a signal as a function of rainfall rate, signal frequency,
polarization, and path elevation angle. The specific attenuation,
*ɣ*_{R}, is modeled as a power law with
respect to rain rate

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

where *R* is rain rate. Units are in mm/hr. The
parameter *k* and exponent *α* depend on the
frequency, the polarization state, and the elevation angle of the signal path. The
specific attenuation model is valid for frequencies from 1–1000 GHz.

To compute the total attenuation for narrowband signals along a path, the function multiplies
the specific attenuation by the an effective propagation distance,
*d*_{eff}. Then, the total attenuation
is *L =
d*_{eff}*γ*_{R}.

The effective distance is the geometric distance, *d*, multiplied by
a scale factor

$$r=\frac{1}{0.477{d}^{0.633}{R}_{0.01}^{0.073\alpha}{f}^{0.123}-10.579\left(1-\mathrm{exp}\left(-0.024d\right)\right)}$$

where *f* 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* presents a complete discussion for computing
attenuation.

The rain rate, *R*, used in these computations is the long-term
statistical rain rate, *R*_{0.01}. This is the
rain rate that is exceeded 0.01% of the time. The calculation of the statistical
rain rate is discussed in *Recommendation ITU-R P.837-7 (06/2017):
Characteristics of precipitation for propagation modelling*. This
article also explains how to compute the attenuation for other percentages from the
0.01% value.

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] Radiocommunication Sector of
the International Telecommunication Union. *Recommendation ITU-R P.676-10:
Attenuation by atmospheric gases*. 2013.

[2] Radiocommunication Sector of
the International Telecommunication Union. *Recommendation ITU-R P.840-6:
Attenuation due to clouds and fog*. 2013.

[3] Radiocommunication Sector of
the International Telecommunication Union. *Recommendation ITU-R P.838-3:
Specific attenuation model for rain for use in prediction methods*.
2005.

[4] Seybold, J.
*Introduction to RF Propagation*. New York: Wiley & Sons,
2005.

[5] Skolnik, M. *Introduction to Radar
Systems*, 3rd Ed. New York: McGraw-Hill, 2001.

## Extended Capabilities

### C/C++ Code Generation

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

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See System Objects in MATLAB Code Generation (MATLAB Coder).

## Version History

**Introduced in R2016a**

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