phased.ScatteringMIMOChannel

Scattering MIMO channel

Description

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:

1. 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.

2. 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.

Construction

channel = phased.ScatteringMIMOChannel creates a scattering MIMO propagation channel System object, channel.

channel = phased.ScatteringMIMOChannel(Name,Value) creates a System object, 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

TransmitArray — Transmitting array

phased.ULA (default) | Phased Array System Toolbox™ element | Phased Array System Toolbox antenna array | Phased Array System Toolbox subarray

Transmitting array, specified as a Phased Array System Toolbox element, Phased Array System Toolbox antenna array, or Phased Array System Toolbox subarray. The default value for this property is a phased.ULA array with its default property values.

Example: phased.URA

ReceiveArray — Receiving array

phased.ULA (default) | Phased Array System Toolbox element | Phased Array System Toolbox antenna array | Phased Array System Toolbox subarray

Receiving array, specified as a Phased Array System Toolbox element, Phased Array System Toolbox antenna array, or Phased Array System Toolbox subarray. The default value for this property is a phased.ULA array with its default property values.

Example: phased.URA

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

CarrierFrequency — Signal carrier frequency

300e6 (default) | positive real-valued scalar

Signal 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 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/m³.

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/m³. 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

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

SimulateDirectPath — Enable propagation along direct path

false (default) | true

Option 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 response

false (default) | true

Option 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 delay

10e-6 (default) | positive scalar

Maximum signal delay, specified as a positive scalar. Delays greater than this value are ignored. Units are in seconds.

Dependencies

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 vector

Position 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]

Dependencies

To enable this property, set the TransmitArrayMotionSource property to 'Property'.

Data Types: double

TransmitArrayOrientationAxes — Orientation of transmitting array

eye(3,3) (default) | real-valued 3-by-3 orthonormal matrix

Orientation 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)

Dependencies

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 vector

Position 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]

Dependencies

To enable this property, set the ReceiveArrayMotionSource property to 'Property'.

Data Types: double

ReceiveArrayOrientationAxes — Orientation of receiving array

eye(3,3) (default) | real-valued 3-by-3 orthonormal matrix

Orientation 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)

Dependencies

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 scatterers

1 (default) | nonnegative integer

Number of scatterers, specified as a nonnegative integer.

Example: 9

Dependencies

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 matrix

Boundary 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]

Dependencies

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 matrix

Positions 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]

Dependencies

To enable this property, set the ScattererSpecificationSource property to 'Property'.

Data Types: double

ScattererCoefficient — Scattering coefficients

1 (default) | complex-valued 1-by-K vector

Scattering coefficients, specified as a complex-valued 1-by-K vector. K is the number of scatterers. Units are dimensionless.

Example: 2+1i

Dependencies

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-N_s array

Scattering matrices of the scatterers, specified as a complex–valued 2-by-2-by-N_s array where N_s 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.

Dependencies

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-N_s array

Orientation of the scatterers, specified as a real–valued 3-by-3-by-N_s array where N_s 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)

Dependencies

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'.

Dependencies

To enable this property, set the ScattererSpecificationSource property to 'Auto'.

Seed — Random number generator seed

0 (default) | nonnegative integer

Random number generator seed, specified as a nonnegative integer less than 2³².

Example: 5005

Dependencies

To enable this property, set the ScattererSpecificationSource property to 'Auto' and the SeedSource property to 'Property'.

Data Types: double

Methods

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

Examples

Propagate Signals in MIMO Channel

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);

Propagate Signals in MIMO Channel from Moving Transmitter

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

Propagate Signals Through MIMO Channel to Moving Receiver

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 operate 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

Propagate Polarized Signals in MIMO Channel

Create a MIMO channel at 30 GHz with a 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

More About

Attenuation and Loss Factors

Attenuation or path loss in the scattering MIMO channel consists of four components. L = L_fspL_gL_cL_r, where:

• L_fsp is the free-space path attenuation.

• L_g is the atmospheric path attenuation.

• L_c is the fog and cloud path attenuation.

• L_r is the rain path attenuation.

Each component is in magnitude units, not in dB.

Free-Space Time Delay and 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_fsp 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

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

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 [8]

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

$$\gamma ={\gamma }_o(f)+{\gamma }_w(f)=0.1820f{N}^{″}(f).$$

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

$$N^{″}(f)={\displaystyle \sum _i{S}_i{F}_i+{N^{″}}_D^{}(f)}$$

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

$$S_i=a_1\times {10}^{-7}{\left(\frac{300}{T}\right)}^3\exp \left[a_2(1-\left(\frac{300}{T}\right)\right]P.$$

For atmospheric water vapor, each spectral line strength is

$$S_i=b_1\times {10}^{-1}{\left(\frac{300}{T}\right)}^{3.5}\exp \left[b_2(1-\left(\frac{300}{T}\right)\right]W.$$

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, 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 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.

For a complete description of this model, see [4].

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/m³. 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/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 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.

For a complete description of this model, see [5]

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_effγ_R.

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

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

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] 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.

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

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

Version History

Introduced in R2017a

Steerable Subarrays

This release supports steerable subarrays by setting the EnablePanelSubarray and SubarraySteering properties.