Scattering MIMO channel
The phased.ScatteringMIMOChannel
System object™ models a multipath propagation channel in which radiated signals from a
transmitting array are reflected from multiple scatterers back toward a receiving array.
In this channel, propagation paths are line of sight from point to point. The object
models range-dependent time delay, gain, Doppler shift, phase change, and atmospheric
loss due to gases, rain, fog, and clouds.
The attenuation models for atmospheric gases and rain are valid for electromagnetic signals in the frequency range from 1 through 1000 GHz. The attenuation model for fog and clouds is valid from 10 through 1000 GHz. Outside of these frequency ranges, the object uses the nearest valid value.
To compute the multipath propagation for specified source and receiver points:
Define and set up your scattering MIMO channel using the Construction procedure. You can set the System object properties during construction or leave them at their default values.
Call the step method to compute the
propagated signals using the properties of the phased.ScatteringMIMOChannel
System object. You can change tunable properties before or after any call to
the step method.
Note
Instead of using the step method to perform the
operation defined by the System object, you can call the object with arguments, as if it were a function. For
example, y = step(obj,x) and y = obj(x)
perform equivalent operations.
channel = phased.ScatteringMIMOChannel creates a scattering MIMO
propagation channel System object, channel.
channel = phased.ScatteringMIMOChannel(
creates a System object, 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).
TransmitArray — Transmitting arrayphased.ULA (default) | Phased Array System Toolbox™ antenna array System objectTransmitting array, specified as a Phased Array System Toolbox antenna array System object. The default value for this property is a phased.ULA array with its
default property values.
Example: phased.URA
ReceiveArray — Receiving arrayphased.ULA (default) | Phased Array System Toolbox antenna array System objectReceiving array, specified as a Phased Array System Toolbox antenna array System object. The default value for this property is a phased.ULA array with its
default property values.
Example: phased.URA
PropagationSpeed — Signal propagation speedphysconst('LightSpeed') (default) | positive scalarSignal 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
CarrierFrequency — Signal carrier frequency300e6 (default) | positive real-valued scalarSignal carrier frequency, specified as a positive real-valued scalar. Units are in Hz.
Example: 100e6
Data Types: double
Polarization — Polarization configuration'None' (default) | 'Combined' | 'Dual'Polarization configuration, specified as 'None',
'Combined', or 'Dual'. When you set this
property to 'None', the output field is considered a scalar field.
When you set this property to 'Combined', the radiated fields are
polarized and are interpreted as a single signal in the sensor's inherent polarization.
When you set this property to 'Dual', the H and
V polarization components of the radiated field are independent
signals.
Example: 'Dual'
Data Types: char
SpecifyAtmosphere — Enable atmospheric attenuation modelfalse (default) | trueOption 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 temperature15 (default) | real-valued scalarAmbient temperature, specified as a real-valued scalar. Units are in degrees Celsius.
Example: 20.0
To enable this property, set SpecifyAtmosphere to true.
Data Types: double
DryAirPressure — Atmospheric dry air pressure101.325e3 (default) | positive real-valued scalarAtmospheric 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
To enable this property, set SpecifyAtmosphere to true.
Data Types: double
WaterVapourDensity — Atmospheric water vapor density7.5 (default) | positive real-valued scalarAtmospheric water vapor density, specified as a positive real-valued scalar. Units are in g/m3.
Example: 7.4
To enable this property, set SpecifyAtmosphere to true.
Data Types: double
LiquidWaterDensity — Liquid water density0.0 (default) | nonnegative real-valued scalarLiquid water density of fog or clouds, specified as a nonnegative real-valued scalar. Units are in g/m3. Typical values for liquid water density are 0.05 for medium fog and 0.5 for thick fog.
Example: 0.1
To enable this property, set SpecifyAtmosphere to true.
Data Types: double
RainRate — Rainfall rate0.0 (default) | nonnegative scalarRainfall rate, specified as a nonnegative scalar. Units are in mm/hr.
Example: 10.0
To enable this property, set SpecifyAtmosphere to true.
Data Types: double
SampleRate — Sample rate of signal1e6 (default) | positive scalarSample 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
SimulateDirectPath — Enable propagation along direct pathfalse (default) | trueOption to enable signal propagation along the direct path, specified as
false or true. The direct path is
a line-of-sight path from the transmitting array to the receiving array with
no scattering.
Data Types: logical
ChannelResponseOutputPort — Enable output of channel responsefalse (default) | trueOption to enable output of channel response, specified as
false or true. Set this property
to trueto output the channel response and time delay by
using the chmatrix and tau output
arguments of the step method.
Data Types: logical
MaximumDelaySource — Source of maximum delay'Auto' (default) | 'Property'Source of the maximum delay value, specified as 'Auto' or 'Property'.
When you set this property to 'Auto', the channel
automatically allocates enough memory to simulate the propagation
delay. When you set this property to 'Property',
you can specify the maximum delay by using the MaximumDelay property.
Signals arriving after the maximum delay are ignored.
MaximumDelay — Maximum signal delay10e-6 (default) | positive scalarMaximum signal delay, specified as a positive scalar. Delays greater than this value are ignored. Units are in seconds.
To enable this property, set the
MaximumDelaySource property to
'Property'.
Data Types: double
TransmitArrayMotionSource — Source of transmitting array motion parameters'Property' (default) | 'Input port'Source of the transmitting array motion parameters, specified as
'Property' or 'Input port'.
When you set this property to 'Property',
the transmitting array is stationary. Then, you can specify the
location and orientation of the array using the
TransmitArrayPosition and
TransmitArrayOrientationAxes
properties.
When you set this property to 'Input port',
specify the transmitting array location, velocity, and
orientation by using the txpos,
txvel, and txaxes
input arguments of the step
method.
Data Types: char
TransmitArrayPosition — Position of transmitting array phase center[0;0;0] (default) | real-valued three-element vectorPosition of the transmitting array phase center, specified as a
real-valued three-element vector in Cartesian form,
[x;y;z], with respect to the global coordinate
system. Units are in meters.
Example: [1000;-200;55]
To enable this property, set the
TransmitArrayMotionSource property to
'Property'.
Data Types: double
TransmitArrayOrientationAxes — Orientation of transmitting arrayeye(3,3) (default) | real-valued 3-by-3 orthonormal matrixOrientation of transmitting array, specified as a real-valued 3-by-3 orthonormal matrix. The matrix specifies the three axes, (x,y,z), that define the local coordinate system of the array with respect to the global coordinate system. Matrix columns correspond to the axes of the local array coordinate system.
Example: rotz(45)
To enable this property, set the
TransmitArrayMotionSource property to
'Property'.
Data Types: double
ReceiveArrayMotionSource — Source of receiving array motion parameters'Property' (default) | 'Input port'Source of the receiving array motion parameters, specified as
'Property' or 'Input port'.
When you set this property to 'Property',
the receiving array is stationary. Then, you can specify the
location and orientation of the array by using the
ReceiveArrayPosition and
ReceiveArrayOrientationAxes properties.
When you set this property to 'Input port',
you can specify the receiving array location, velocity, and
orientation by using the rxpos,
rxvel, and rxaxes
input arguments of the step
method.
Data Types: char
ReceiveArrayPosition — Position of receiving array[0;0;0] (default) | real-valued three-element vectorPosition of the receiving array phase center, specified as a real-valued
three-element vector in Cartesian form,[x;y;z], with
respect to the global coordinate system. Units are in meters.
Example: [1000;-200;55]
To enable this property, set the
ReceiveArrayMotionSource property to
'Property'.
Data Types: double
ReceiveArrayOrientationAxes — Orientation of receiving arrayeye(3,3) (default) | real-valued 3-by-3 orthonormal matrixOrientation of receiving array, specified as a real-valued 3-by-3 orthonormal matrix. The matrix specifies the three axes, (x,y,z), that define the local coordinate system of the array with respect to the global coordinate system. Matrix columns correspond to the axes of the local array coordinate system.
Example: roty(60)
To enable this property, set the
ReceiveArrayMotionSource property to
'Property'.
Data Types: double
ScattererSpecificationSource — Source of scatterer parameters'Auto' (default) | 'Property' | 'Input port'Source of scatterer parameters, specified as 'Auto',
'Property', 'Input port'.
When you set this property to 'Auto', all
scatterer positions and coefficients are randomly generated.
Scatterer velocities are zero. The generated positions are
contained within the region defined by the
ScattererPositionBoundary. To set the
number of scatterers, use the NumScatterers
property.
When you set this property to 'Property',
you can set the scatterer positions by using the
ScattererPosition property and the
scattering coefficients by using the
ScattererCoefficient property. All
scatterer velocities are zero.
When you set this property to 'Input port',
you can specify the scatterer positions, velocities, and
scattering coefficients using the scatpos,
scatvel, and
scatcoef input arguments of the step
method.
Example: 'Input port'
Data Types: char
NumScatterers — Number of scatterers1 (default) | nonnegative integerNumber of scatterers, specified as a nonnegative integer.
Example: 9
To enable this property, set the
ScattererSpecificationSource property to
'Auto'.
Data Types: double
ScattererPositionBoundary — Boundary of scatterer positions[0,1000] (default) | 1-by-2 real-valued vector | 3-by-2 real-valued matrixBoundary of the scatterer positions, specified as a 1-by-2 real-valued row
vector or a 3-by-2 real-valued matrix. The vector specifies the minimum and
maximum, [minbdry maxbdry], for all three dimensions. The
matrix specifies boundaries in all three dimensions in the form
[x_minbdry x_maxbdry;y_minbdry y_maxbdry; z_minbdry
z_maxbdry].
Example: [-1000 500;-100 100;-200 0]
To enable this property, set the
ScattererSpecificationSource property to
'Auto'.
Data Types: double
ScattererPosition — Positions of scatterers[0;0;0] (default) | real-valued 3-by-K matrixPositions of the scatterers, specified as real-valued
3-by-K matrix. K is the number of
scatterers. Each column represents a different scatterer and has the
Cartesian form [x;y;z] with respect to the global
coordinate system. Units are in meters.
Example: [1050 -100;-300 55;0 -75]
To enable this property, set the
ScattererSpecificationSource property to
'Property'.
Data Types: double
ScattererCoefficient — Scattering coefficients1 (default) | complex-valued 1-by-K vectorScattering coefficients, specified as a complex-valued 1-by-K vector. K is the number of scatterers. Units are dimensionless.
Example: 2+1i
To enable this property, set the
ScattererSpecificationSource property to
'Property'.
Data Types: double
Complex Number Support: Yes
ScatteringMatrix — Scattering matrices[1 0;0 1] | complex–valued 2-by-2-by-Ns
arrayScattering matrices of the scatterers, specified as a complex–valued
2-by-2-by-Ns array where
Ns is the number of
scatterers. Each page of this array represents the scattering matrix of a
scatterer. Each scattering matrix has the form [s_hh s_hv;s_vh
s_vv]. For example, the component s_hv
specifies the complex scattering response when the input signal is
vertically polarized and the reflected signal is horizontally polarized. The
other components are defined similarly. Units are in square meters.
To enable this property, set the
ScatteringMatrixSource property to
'Property' and the
Polarization property to
'Combined' or 'Dual'.
Data Types: double
Complex Number Support: Yes
ScattererOrientationAxes — Orientation of scatterers[1 0 0;0 1 0;0 0 1] (default) | real–valued 3-by-3-by-Ns
arrayOrientation of the scatterers, specified as a real–valued 3-by-3-by-Ns array where Ns is the number of scatterers. Each page of this array is an orthonormal matrix. Matrix columns represent the axis of the local coordinates (x,y,z) of the scatterer with respect to the global coordinate system.
Example: roty(45)
To enable this property, set the
ScatteringMatrixSource property to
'Property' and the
Polarization property to
'Combined' or 'Dual'.
Data Types: double
SeedSource — Source of random number generator seed'Auto' (default) | 'Property'Source of random number generator seed, specified as
'Auto' or 'Property'.
When you set this property to 'Auto',
random numbers are generated using the default MATLAB® random number generator.
When you set this property to 'Property',
the object uses a private random number generator with the seed
specified by the value of the Seed
property.
To use this object with Parallel Computing Toolbox™ software, set this property to
'Auto'.
To enable this property, set the
ScattererSpecificationSource property to
'Auto'.
Seed — Random number generator seed0 (default) | nonnegative integerRandom number generator seed, specified as a nonnegative integer less than 232.
Example: 5005
To enable this property, set the
ScattererSpecificationSource property to
'Auto' and the SeedSource
property to 'Property'.
Data Types: double
| reset | Reset state of the System object |
| step | Propagate signals in scattering MIMO channel |
| Common to All System Objects | |
|---|---|
release | Allow System object property value changes |
Create a 30 GHz MIMO channel with random scatterers. The scenario contains a stationary 21-element transmitting ULA array and a stationary 15-element receiving ULA array. The transmitting antennas have cosine responses and the receiving antennas are isotropic. Element spacing for both arrays is less than one-half wavelength. The channel has 50 randomly generated static scatterers within a specified bounding box. The transmit array is located at [0;20;50] meters and the receive array is located at [200;10;10] meters. Compute the propagated signal through this channel. The sample rate for the signal is 10 MHz.
fc = 30e9; c = physconst('LightSpeed'); lambda = c/fc; fs = 10e6; txarray = phased.ULA('Element',phased.CosineAntennaElement,... 'NumElements',21,'ElementSpacing',0.45*lambda); rxarray = phased.ULA('Element',phased.IsotropicAntennaElement,... 'NumElements',15,'ElementSpacing',0.45*lambda); channel = phased.ScatteringMIMOChannel('TransmitArray',txarray,... 'ReceiveArray',rxarray,'PropagationSpeed',c,'CarrierFrequency',fc,... 'SampleRate',fs,'TransmitArrayPosition',[0;20;50],... 'ReceiveArrayPosition',[200;10;10],'NumScatterers',50,... 'ScattererPositionBoundary',[10 180; -30 30; -30 30]);
Create a random data signal of ones and zeros for each transmitter.
x = randi(2,[100 21]) - 1;
Compute the received signals after propagating through the channel.
y = channel(x);
Create a MIMO channel containing 3 fixed scatterers. The scenario contains a 21-element transmitting ULA array operating at 72 GHz, and a 15-element receiving ULA array. The transmitting elements have cosine response shapes and the receiving antennas are isotropic. Only the transmitting antenna is moving. Element spacing for both arrays is less than one-half wavelength. The transmitting array starts at (0,20,50) meters and moves towards the receiver at 2 m/s. The receiving array is located at (200,10,10) meters. Compute the propagated signal through this channel. The sample rate for the signal is 10 MHz.
fc = 72e9; c = physconst('LightSpeed'); lambda = c/fc; fs = 10e6; txplatform = phased.Platform('MotionModel','Velocity','InitialPosition', ... [0;20;50],'Velocity',[2;0;0]); txarray = phased.ULA('Element',phased.CosineAntennaElement, ... 'NumElements',21,'ElementSpacing',0.45*lambda); rxarray = phased.ULA('Element',phased.IsotropicAntennaElement, ... 'NumElements',15,'ElementSpacing',0.45*lambda); channel = phased.ScatteringMIMOChannel('TransmitArray',txarray, ... 'ReceiveArray',rxarray,'PropagationSpeed',c,'CarrierFrequency',fc,... 'SampleRate',fs,'TransmitArrayMotionSource','Input port', ... 'ReceiveArrayMotionSource','Property','ReceiveArrayPosition',[200;10;10],... 'ReceiveArrayOrientationAxes',rotz(180),... 'ScattererSpecificationSource','Property','ScattererPosition', ... [75 100 120; -10 20 12; 5 -5 8],'ScattererCoefficient',[1i,2+3i,-1+1i]);
Move the platforms for two time steps at one second intervals. For each time instance:
Create a random data signal of ones and zeros for each transmitter element.
Move the transmitter and receiver. The orientations are fixed.
Propagate the signals from transmitters to scatterers to receiver.
for k =1:2 x = randi(2,[100 21]) - 1; [txpos,txvel] = txplatform(1); txaxes = eye(3); y = channel(x,txpos,txvel,txaxes); end
Create a MIMO channel containing 3 fixed scatterers. The scenario contains a 21-element transmitting ULA array and a 15-element receiving ULA array. Both arrays operating at 72 GHz. The transmitting elements have cosine response shapes and the receiving antennas are isotropic. Only the receiving antenna is moving. Element spacing for both arrays is less than one-half wavelength. The transmitting array is located at (0,20,50) meters. The receiving array starts at (200,10,10) meters and moves toward the transmitter at 2 m/s. Compute the propagated signal through this channel. The sample rate for the signal is 10 MHz.
fc = 72e9; c = physconst('LightSpeed'); lambda = c/fc; fs = 10e6; rxplatform = phased.Platform('MotionModel','Velocity','InitialPosition',... [200;10;10],'Velocity',[-2;0;0]); txarray = phased.ULA('Element',phased.CosineAntennaElement, ... 'NumElements',21,'ElementSpacing',0.45*lambda); rxarray = phased.ULA('Element',phased.IsotropicAntennaElement, ... 'NumElements',15,'ElementSpacing',0.45*lambda); channel = phased.ScatteringMIMOChannel('TransmitArray',txarray, ... 'ReceiveArray',rxarray,'PropagationSpeed',c,'CarrierFrequency',fc, ... 'SampleRate',fs,'TransmitArrayMotionSource','Property',... 'TransmitArrayPosition',[0;20;50],'TransmitArrayOrientationAxes',eye(3,3), ... 'ReceiveArrayMotionSource','Input port','ScattererSpecificationSource', ... 'Property','ScattererPosition',[75 100 120; -10 20 12; 5 -5 8], ... 'ScattererCoefficient',[1i,2+3i,-1+1i],'SpecifyAtmosphere',false);
Move the platforms for two time steps at one-second intervals. For each time instance:
Create a random data signal of ones and zeros for each transmitter element.
Move the transmitter and receiver. Fix the array orientations.
Propagate the signals from transmitters to scatterers to receiver.
for k =1:2 x = randi(2,[100 21]) - 1; [rxpos,rxvel] = rxplatform(1); rxaxes = rotz(45); y = channel(x,rxpos,rxvel,rxaxes); end
Create a MIMO channel at 30 GHz with an 16-element transmit array and a 64-element receive array. Assume the elements are short-dipole antennas and the arrays are uniform linear arrays. The transmit array is located at [0;0;50] meters.
The receive array has an initial position at [200;0;0] meters and is moving at a speed of [10;0;0] meters/second. There are 200 static scatterers randomly located on the xy plane within a square centered at [200;0;0] and with a side length of 100 meters.
Use the channel to compute the propagated polarized signal. Assume the sample rate for the signal is 10 MHz and the frame length is 1000 samples. Collect 5 frames of received signal.
fc = 30e9; c = 3e8; lambda = c/fc; fs = 10e6; txarray = phased.ULA('Element',phased.ShortDipoleAntennaElement,... 'NumElements',16,'ElementSpacing',lambda/2); rxarray = phased.ULA('Element',phased.ShortDipoleAntennaElement,... 'NumElements',64,'ElementSpacing',lambda/2); Ns = 200; scatpos = [100*rand(1,Ns) + 150; 100*rand(1,Ns) + 150; zeros(1,Ns)]; temp = randn(1,Ns) + 1i*randn(1,Ns); scatcoef = repmat(eye(2),1,1,Ns).*permute(temp,[1 3 2]); scatax = repmat(eye(3),1,1,Ns); Nframesamp = 1000; Tframe = Nframesamp/fs; rxmobile = phased.Platform('InitialPosition',[200;0;0],... 'Velocity',[10;0;0],'OrientationAxesOutputPort',true); chan = phased.ScatteringMIMOChannel(... 'TransmitArray',txarray,... 'ReceiveArray',rxarray,... 'PropagationSpeed',c,... 'CarrierFrequency',fc,... 'SampleRate',fs,... 'Polarization','Dual',... 'TransmitArrayPosition',[0;0;50],... 'ReceiveArrayMotionSource','Input port',... 'ScattererSpecificationSource','Property',... 'ScattererPosition',scatpos,... 'ScatteringMatrix',scatcoef,... 'ScattererOrientationAxes',scatax); xh = randi(2,[Nframesamp 16])-1; xv = randi(2,[Nframesamp 16])-1; for m = 1:5 [rxpos,rxvel,rxax] = rxmobile(Tframe); [yh,yv] = chan(xh,xv,rxpos,rxvel,rxax); end
Attenuation or path loss in the scattering MIMO channel consists of four components. L = LfspLgLcLr, where:
Lfsp is the free-space path attenuation.
Lg is the atmospheric path attenuation.
Lc is the fog and cloud path attenuation.
Lr is the rain path attenuation.
Each component is in magnitude units, not in dB.
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)/Lfsp. The quantity τ is the signal delay and Lfsp is the free-space path loss. The delay 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
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 [8]
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
The quantity N"() 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 a sum of discrete spectrum terms composed of a localized frequency bandwidth function, F(f)i, multiplied by a spectral line strength, Si. For atmospheric oxygen, each spectral line strength is
For atmospheric water vapor, each spectral line strength is
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
The total atmospheric pressure is P + W.
For each oxygen line, Si depends on two parameters, a1 and a2. Similarly, each water vapor line depends on two parameters, b1 and b2. The ITU documentation cited at the end of this section contains tabulations of these parameters as functions of frequency.
The localized frequency bandwidth functions Fi(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.
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 Lg= R(γo + γw).
You can 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.
For a complete description of this model, see [4].
This model calculates the attenuation of signals that propagate through fog or clouds.
Fog and cloud attenuation are 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
where M is the liquid water density in gm/m3. The quantity Kl(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/m3).
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 Lc = Rγc.
You can 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.
For a complete description of this model, see [5]
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, ɣR, is modeled as a power law with respect to rain rate
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, deff. Then, the total attenuation is L = deffγR.
The effective distance is the geometric distance, d, multiplied by a scale factor
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, R0.01. 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 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.
[1] Heath, R. Jr. et al. “An Overview of Signal Processing Techniques for Millimeter Wave MIMO Systems”, arXiv.org:1512.03007 [cs.IT], 2015.
[2] Tse, D. and P. Viswanath, Fundamentals of Wireless Communications, Cambridge: Cambridge University Press, 2005.
[3] Paulraj, A. Introduction to Space-Time Wireless Communications, Cambridge: Cambridge University Press, 2003.
[4] Radiocommunication Sector of the International Telecommunication Union. Recommendation ITU-R P.676-10: Attenuation by atmospheric gases. 2013.
[5] Radiocommunication Sector of the International Telecommunication Union. Recommendation ITU-R P.840-6: Attenuation due to clouds and fog. 2013.
[6] Radiocommunication Sector of the International Telecommunication Union. Recommendation ITU-R P.838-3: Specific attenuation model for rain for use in prediction methods. 2005.
[7] Seybold, J. Introduction to RF Propagation. New York: Wiley & Sons, 2005.
[8] Skolnik, M. Introduction to Radar Systems, 3rd Ed. New York: McGraw-Hill, 2001.
Usage notes and limitations:
See System Objects in MATLAB Code Generation (MATLAB Coder).
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