twoRayChannel

Two-ray propagation channel

Since R2021a

Description

The twoRayChannel System object™ models a narrowband two-ray propagation channel. A two-ray propagation channel is the simplest type of multipath channel. You can use a two-ray channel to simulate propagation of signals in a homogeneous, isotropic medium with a single reflecting boundary. This type of medium has two propagation paths: a line-of-sight (direct) propagation path from one point to another and a ray path reflected from the boundary. You can use the twoRayChannel object for short-range radar and mobile communications applications where the signals propagate along straight paths and the earth is assumed to be flat. You can also use this object for sonar and microphone applications. For acoustic applications, you can choose the fields to be non-polarized and adjust the propagation speed to be the speed of sound in air or water. You can use twoRayChannel to model propagation from several points simultaneously.

While the twoRayChannel 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 twoRayChannel object uses the nearest valid value.

The twoRayChannel object applies range-dependent time delays to the signals, and as well as gains or losses, phase shifts, and boundary reflection loss. The twoRayChannel object also applies Doppler shift when either the source or destination is moving.

Signals at the channel output can be kept separate or be combined — controlled by the CombinedRaysOutput property. In the separate option, both fields arrive at the destination separately and are not combined. For the combined option, the two signals at the source propagate separately but are coherently summed at the destination into a single quantity. This option is convenient when the difference between the sensor or array gains in the directions of the two paths is not significant and need not be taken into account.

Unlike the phased.FreeSpace System object, the twoRayChannel System object does not support two-way propagation.

To perform two-ray channel propagation:

1. Create the twoRayChannel object and set its properties.

2. 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

Syntax

channel = twoRayChannel

channel = twoRayChannel(Name=Value)

Description

channel = twoRayChannel creates a two-ray propagation channel System object.

channel = twoRayChannel(Name=Value) creates a two-ray propagation channel System object with each specified property Name set to the corresponding Value. You can specify additional pairs of 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 (m/s)

physconst('LightSpeed') (default) | positive scalar

Signal propagation speed, specified as a positive scalar. Units are in meters per second (m/s). The default propagation speed is the value returned by physconst('LightSpeed'). See physconst for more information.

Example: 3e8

Data Types: double

OperatingFrequency — Signal carrier frequency (Hz)

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, WaterVaporDensity, LiquidWaterDensity, and RainRate properties.

Data Types: logical

Temperature — Ambient temperature (degrees Celsius)

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 (Pa)

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

WaterVaporDensity — Atmospheric water vapor density (g/m³)

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 (g/m³)

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 (mm/hr)

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 (Hz)

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. The default value corresponds to 1 MHz.

Example: 1e6

Data Types: double

EnablePolarization — Enable polarized fields

false (default) | true

Option to enable polarized fields, specified as false or true. Set this property to true to enable polarization. Set this property to false to ignore polarization.

Data Types: logical

GroundReflectionCoefficient — Ground reflection coefficient

-1 (default) | complex-valued scalar | complex-valued 1-by-N row vector

Ground reflection coefficient for the field at the reflection point, specified as a complex-valued scalar or a complex-valued 1-by-N row vector. Each coefficient has an absolute value less than or equal to one. The quantity N is the number of two-ray channels. Units are dimensionless. Use this property to model nonpolarized signals. To model polarized signals, use the GroundRelativePermittivity property.

Example: -0.5

Dependencies

To enable this property, set EnablePolarization to false.

Data Types: double
Complex Number Support: Yes

GroundRelativePermittivity — Ground relative permittivity

15 (default) | positive real-valued scalar | real-valued 1-by-Nrow vector of positive values

Relative permittivity of the ground at the reflection point, specified as a positive real-valued scalar or a 1-by-N real-valued row vector of positive values. The dimension N is the number of two-ray channels. Permittivity units are dimensionless. Relative permittivity is defined as the ratio of actual ground permittivity to the permittivity of free space. This property applies when you set the EnablePolarization property to true. Use this property to model polarized signals. To model nonpolarized signals, use the GroundReflectionCoefficient property.

Example: 5

Dependencies

To enable this property, set EnablePolarization to true.

Data Types: double

CombinedRaysOutput — Option to combine two rays at output

true (default) | false

Option to combine the two rays at channel output, specified as true or false. When this property is true, the object coherently adds the line-of-sight propagated signal and the reflected path signal when forming the output signal. Use this mode when you do not need to include the directional gain of an antenna or array in your simulation.

Data Types: logical

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 (m)

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 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

Syntax

prop_sig = channel(sig,origin_pos,dest_pos,origin_vel,dest_vel)

Description

prop_sig = channel(sig,origin_pos,dest_pos,origin_vel,dest_vel) returns the resulting signal, prop_sig, when a narrowband signal, sig, propagates through a two-ray channel from the origin_pos position to the dest_pos position. Either the origin_pos or dest_pos arguments can have multiple points but you cannot specify both as having multiple points. 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 agree with the dimensions of origin_pos and dest_pos, respectively.

Electromagnetic fields propagated through a two-ray channel can be polarized or nonpolarized. For, nonpolarized fields, such as an acoustic field, the propagating signal field, sig, is a vector or matrix. When the fields are polarized, sig is an array of structures. Every structure element represents an electric field vector in Cartesian form.

In the two-ray environment, there are two signal paths connecting every signal origin and destination pair. For N signal origins (or N signal destinations), there are 2N number of paths. The signals for each origin-destination pair do not have to be related. The signals along the two paths for any single source-destination pair can also differ due to phase or amplitude differences.

You can keep the two signals at the destination separate or combined — controlled by the CombinedRaysOutput property. Combined means that the signals at the source propagate separately along the two paths but are coherently summed at the destination into a single quantity. To use the separate option, set CombinedRaysOutput to false. To use the combined option, set CombinedRaysOutput to true. This option is convenient when the difference between the sensor or array gains in the directions of the two paths is not significant and need not be taken into account.

Input Arguments

channel — Narrowband two-ray channel object

twoRayChannel object

Narrowband two-ray channel, specified as a twoRayChannel System object.

sig — Narrowband signal

M-by-N complex-valued matrix | M-by-2N complex-valued matrix | 1-by-N struct array containing complex-valued fields | 1-by-2N struct array containing complex-valued fields

• Narrowband nonpolarized scalar signal, specified as an

  • M-by-N complex-valued matrix. Each column contains a common signal propagated along both the line-of-sight path and the reflected path. You can use this form when both path signals are the same.

  • M-by-2N complex-valued matrix. Each adjacent pair of columns represents a different channel. Within each pair, the first column represents the signal propagated along the line-of-sight path and the second column represents the signal propagated along the reflected path.

• Narrowband polarized signal, specified as a

  • 1-by-N struct array containing complex-valued fields. Each struct contains a common polarized signal propagated along both the line-of-sight path and the reflected path. Each structure element contains an M-by-1 column vector of electromagnetic field components (sig.X,sig.Y,sig.Z). You can use this form when both path signals are the same.

  • 1-by-2N struct array containing complex-valued fields. Each adjacent pair of array columns represents a different channel. Within each pair, the first column represents the signal along the line-of-sight path and the second column represents the signal along the reflected path. Each structure element contains an M-by-1 column vector of electromagnetic field components (sig.X,sig.Y,sig.Z).

For nonpolarized fields, the quantity M is the number of samples of the signal and N is the number of two-ray channels. Each channel corresponds to a source-destination pair.

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.

For polarized fields, the 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 — Origin of the signal or signals

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

Origin 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 two-ray 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]. Position units are meters.

origin_pos and dest_pos cannot both be specified as matrices — at least one must be a 3-by-1 column vector.

Example: [1000;100;500]

Data Types: double

dest_pos — Destination position of the signal or signals

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 two-ray 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 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 — Velocity of signal origin

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 — Velocity 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 — Propagated signal

M-by-N complex-valued matrix | M-by-2N complex-valued matrix | 1-by-N struct array containing complex-valued fields | 1-by-2N struct array containing complex-valued fields

• Narrowband nonpolarized scalar signal, returned as an:

  • M-by-N complex-valued matrix. To return this format, set the CombinedRaysOutput property to true. Each matrix column contains the coherently combined signals from the line-of-sight path and the reflected path.

  • M-by-2N complex-valued matrix. To return this format set the CombinedRaysOutput property to false. Alternate columns of the matrix contain the signals from the line-of-sight path and the reflected path.

• Narrowband polarized scalar signal, returned as:

  • 1-by-N struct array containing complex-valued fields. To return this format, set the CombinedRaysOutput property to true. Each column of the array contains the coherently combined signals from the line-of-sight path and the reflected path. Each structure element contains the electromagnetic field vector (prop_sig.X,prop_sig.Y,prop_sig.Z).

  • 1-by-2N struct array containing complex-valued fields. To return this format, set the CombinedRaysOutput property to false. Alternate columns contains the signals from the line-of-sight path and the reflected path. Each structure element contains the electromagnetic field vector (prop_sig.X,prop_sig.Y,prop_sig.Z).

The output prop_sig contains signal samples arriving at the signal destination within the current input time frame. Whenever it takes longer than the current time frame for the signal to propagate from the origin to the destination, the output may not contain all contributions from the input of the current time frame. The remaining output will appear 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)

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Scalar Field Propagating in Two-Ray Channel

This example illustrates the two-ray propagation of a signal, showing how the signals from the line-of-sight and reflected path arrive at the receiver at different times.

Create and Plot Propagating Signal

Create a nonpolarized electromagnetic field consisting of two rectangular waveform pulses at a carrier frequency of 100 MHz. Assume the pulse width is 10 ms and the sampling rate is 1 MHz. The bandwidth of the pulse is 0.1 MHz. Assume a 50% duty cycle in so that the pulse width is one-half the pulse repetition interval. Create a two-pulse wave train. Set the GroundReflectionCoefficient to 0.9 to model strong ground reflectivity. Propagate the field from a stationary source to a stationary receiver. The vertical separation of the source and receiver is approximately 10 km.

c = physconst('LightSpeed');
fs = 1e6;
pw = 10e-6;
pri = 2*pw;
PRF = 1/pri;
fc = 100e6;
lambda = c/fc;
waveform = phased.RectangularWaveform('SampleRate',fs,'PulseWidth',pw,...
    'PRF',PRF,'OutputFormat','Pulses','NumPulses',2);
wav = waveform();
n = size(wav,1);
figure;
plot((0:(n-1)),real(wav),'b.-');
xlabel('Time (samples)')
ylabel('Waveform magnitude')

Specify the Location of Source and Receiver

Place the source and receiver about 1000 meters apart horizontally and approximately 10 km apart vertically.

pos1 = [1000;0;10000];
pos2 = [0;100;100];
vel1 = [0;0;0];
vel2 = [0;0;0];

Compute the predicted signal delays in units of samples.

[rng,ang] = rangeangle(pos2,pos1,'two-ray');

Create a Two-Ray Channel System Object™

Create a two-ray propagation channel System object™ and propagate the signal along both the line-of-sight and reflected ray paths.

channel = twoRayChannel('SampleRate',fs,...
    'GroundReflectionCoefficient',.9,'OperatingFrequency',fc,...
    'CombinedRaysOutput',false);
prop_signal = channel([wav,wav],pos1,pos2,vel1,vel2);

Plot the Propagated Signals

• Plot the signal propagated along the line-of-sight.

• Then, overlay a plot of the signal propagated along the reflected path.

• Finally, overlay a plot of the coherent sum of the two signals.

n = size(prop_signal,1);
delay = 0:(n-1);
plot(delay,abs(prop_signal(:,1)),'g')
hold on
plot(delay,abs(prop_signal(:,2)),'r')
plot(delay,abs(prop_signal(:,1) + prop_signal(:,2)),'b')
hold off
legend('Line-of-sight','Reflected','Combined','Location','NorthWest')
xlabel('Delay (samples)')
ylabel('Signal Magnitude')

The plot shows that the delay of the reflected path signal agrees with the predicted delay. The magnitude of the coherently combined signal is less than either of the propagated signals indicating that there is some interference between the two signals.

Polarized Field Propagation in Two-Ray Channel

Create a polarized electromagnetic field consisting of linear FM waveform pulses. Propagate the field from a stationary source with a crossed-dipole antenna element to a stationary receiver approximately 10 km away. The transmitting antenna is 100 meters above the ground. The receiving antenna is 150 m above the ground. The receiving antenna is also a crossed-dipole. Plot the received signal.

Set Radar Waveform Parameters

Assume the pulse width is $$10\mu s$$ and the sampling rate is 10 MHz. The bandwidth of the pulse is 1 MHz. Assume a 50% duty cycle in which the pulse width is one-half the pulse repetition interval. Create a two-pulse wave train. Assume a carrier frequency of 100 MHz.

c = physconst('LightSpeed');
fs = 10e6;
pw = 10e-6;
pri = 2*pw;
PRF = 1/pri;
fc = 100e6;
bw = 1e6;
lambda = c/fc;

Set Up Required System Objects

Use a GroundRelativePermittivity of 10.

waveform = phased.LinearFMWaveform('SampleRate',fs,'PulseWidth',pw,...
    'PRF',PRF,'OutputFormat','Pulses','NumPulses',2,'SweepBandwidth',bw,...
    'SweepDirection','Up','Envelope','Rectangular','SweepInterval',...
    'Positive');
antenna = phased.CrossedDipoleAntennaElement(...
    'FrequencyRange',[50,200]*1e6);
radiator = phased.Radiator('Sensor',antenna,'OperatingFrequency',fc,...
    'Polarization','Combined');
channel = twoRayChannel('SampleRate',fs,...
    'OperatingFrequency',fc,'CombinedRaysOutput',false,...
    'EnablePolarization',true,'GroundRelativePermittivity',10);
collector = phased.Collector('Sensor',antenna,'OperatingFrequency',fc,...
    'Polarization','Combined');

Set Up Scene Geometry

Specify transmitter and receiver positions, velocities, and orientations. Place the source and receiver about 1000 m apart horizontally and approximately 50 m apart vertically.

posTx = [0;100;100];
posRx = [1000;0;150];
velTx = [0;0;0];
velRx = [0;0;0];
laxRx = rotz(180);
laxTx = rotx(1)*eye(3);

Create and Radiate Signals from Transmitter

Compute the transmission angles for the two rays traveling toward the receiver. These angles are defined with respect to the transmitter local coordinate system. The phased.Radiator System object™ uses these angles to apply separate antenna gains to the two signals.

[rng,angsTx] = rangeangle(posRx,posTx,laxTx,'two-ray');
wav = waveform();

Plot the transmitted Waveform

n = size(wav,1);
plot((0:(n-1))/fs*1000000,real(wav))
xlabel('Time ({\mu}sec)')
ylabel('Waveform')

sig = radiator(wav,angsTx,laxTx);

Propagate signals to receiver via two-ray channel

prop_sig = channel(sig,posTx,posRx,velTx,velRx);

Receive Propagated Signal

Compute the reception angles for the two rays arriving at the receiver. These angles are defined with respect to the receiver local coordinate system. The phased.Collector System object™ uses these angles to apply separate antenna gains to the two signals.

[~,angsRx] = rangeangle(posTx,posRx,laxRx,'two-ray');

Collect and combine received rays.

y = collector(prop_sig,angsRx,laxRx);

Plot received waveform

plot((0:(n-1))/fs*1000000,real(y))
xlabel('Time ({\mu}sec)')
ylabel('Received Waveform')

Compare Two-Ray with Free Space Propagation

Propagate a signal in a two-ray channel environment from a radar at (0,0,10) meters to a target at (300,200,30) meters. Assume that the radar and target are stationary and that the transmitting antenna has a cosine pattern. Compare the combined signals from the two paths with the single signal resulting from free space propagation. Set the CombinedRaysOutput to true to produce a combined propagated signal.

Create a Rectangular Waveform

Set the sample rate to 2 MHz.

fs = 2e6;
waveform = phased.RectangularWaveform('SampleRate',fs);
wavfrm = waveform();

Create the Transmitting Antenna and Radiator

Set up a phased.Radiator System object™ to transmit from a cosine antenna

antenna = phased.CosineAntennaElement;
radiator = phased.Radiator('Sensor',antenna);

Specify Transmitter and Target Coordinates

posTx = [0;0;10];
posTgt = [300;200;30];
velTx = [0;0;0];
velTgt = [0;0;0];

Free Space Propagation

Compute the transmitting direction toward the target for the free-space model. Then, radiate the signal.

[~,angFS] = rangeangle(posTgt,posTx); 
wavTx = radiator(wavfrm,angFS);

Propagate the signal to the target.

fschannel = phased.FreeSpace('SampleRate',waveform.SampleRate);
yfs = fschannel(wavTx,posTx,posTgt,velTx,velTgt);
release(radiator);

Two-Ray Propagation

Compute the two transmit angles toward the target for line-of-sight (LOS) path and reflected paths. Compute the transmitting directions toward the target for the two rays. Then, radiate the signals.

[~,angTwoRay] = rangeangle(posTgt,posTx,'two-ray');
wavTwoRay = radiator(wavfrm,angTwoRay);

Propagate the signals to the target.

channel = twoRayChannel('SampleRate',waveform.SampleRate,...
    'CombinedRaysOutput',true);
y2ray = channel(wavTwoRay,posTx,posTgt,velTx,velTgt);

Plot the Propagated Signals

Plot the combined signal against the free-space signal

plot(abs([y2ray yfs]))
legend('Two-ray','Free space')
xlabel('Samples')
ylabel('Signal Magnitude')

Two-Ray Propagation of LFM Waveform

Propagate a linear FM signal in a two-ray channel. The signal propagates from a transmitter located at (1000,10,10) meters in the global coordinate system to a receiver at (10000,200,30) meters. Assume that the transmitter and the receiver are stationary and that they both have cosine antenna patterns. Plot the received signal.

Set up the radar scenario. First, create the required System objects.

waveform = phased.LinearFMWaveform('SampleRate',1000000,...
    'OutputFormat','Pulses','NumPulses',2);
fs = waveform.SampleRate;
antenna = phased.CosineAntennaElement;
radiator = phased.Radiator('Sensor',antenna);
collector = phased.Collector('Sensor',antenna);
channel = twoRayChannel('SampleRate',fs,...
    'CombinedRaysOutput',false,'GroundReflectionCoefficient',0.95);

Set up the scene geometry. Specify transmitter and receiver positions and velocities. The transmitter and receiver are stationary.

posTx = [1000;10;10];
posRx = [10000;200;30];
velTx = [0;0;0];
velRx = [0;0;0];

Specify the transmitting and receiving radar antenna orientations with respect to the global coordinates. The transmitting antenna points along the +x direction and the receiving antenna points near but not directly in the -x direction.

laxTx = eye(3);
laxRx = rotx(5)*rotz(170);

Compute the transmission angles which are the angles that the two rays traveling toward the receiver leave the transmitter. The phased.Radiator System object™ uses these angles to apply separate antenna gains to the two signals. Because the antenna gains depend on path direction, you must transmit and receive the two rays separately.

[~,angTx] = rangeangle(posRx,posTx,laxTx,'two-ray');

Create and radiate signals from transmitter along the transmission directions.

wavfrm = waveform();
wavtrans = radiator(wavfrm,angTx);

Propagate signals to receiver via two-ray channel.

wavrcv = channel(wavtrans,posTx,posRx,velTx,velRx);

Collect signals at the receiver. Compute the angle at which the two rays traveling from the transmitter arrive at the receiver. The phased.Collector System object™ uses these angles to apply separate antenna gains to the two signals.

[~,angRcv] = rangeangle(posTx,posRx,laxRx,'two-ray');

Collect and combine the two received rays.

yR = collector(wavrcv,angRcv);

Plot the received signals.

dt = 1/fs;
n = size(yR,1);
plot((0:(n-1))*dt*1000000,real(yR))
xlabel('Time ({\mu}sec)')
ylabel('Signal Magnitude')

Two-Ray Propagation of LFM Waveform with Atmospheric Losses

Propagate a 100 Mhz linear FM signal into a two-ray channel. Assume there is signal loss caused by atmospheric gases and rain. The signal propagates from a transmitter located at (0,0,0) meters in the global coordinate system to a receiver at (10000,200,30) meters. Assume that the transmitter and the receiver are stationary and that they both have cosine antenna patterns. Plot the received signal. Set the dry air pressure to 102.5 Pa and the rain rate to 5 mm/hr.

Set Up Radar Scenario

waveform = phased.LinearFMWaveform('SampleRate',1e6,...
    'OutputFormat','Pulses','NumPulses',2);
antenna = phased.CosineAntennaElement;
radiator = phased.Radiator('Sensor',antenna);
collector = phased.Collector('Sensor',antenna);
channel = twoRayChannel('SampleRate',waveform.SampleRate,...
    'CombinedRaysOutput',false,'GroundReflectionCoefficient',0.95,...
    'SpecifyAtmosphere',true,'Temperature',20,...
    'DryAirPressure',102.5,'RainRate',5.0);

Set up the scene geometry giving. the transmitter and receiver positions and velocities. The transmitter and receiver are stationary.

posTx = [0;0;0];
posRx = [10000;200;30];
velTx = [0;0;0];
velRx = [0;0;0];

Specify the transmitting and receiving radar antenna orientations with respect to the global coordinates. The transmitting antenna points along the +x-direction and the receiving antenna points close to the –x-direction.

laxTx = eye(3);
laxRx = rotx(5)*rotz(170);

Compute the transmission angles which are the angles that the two rays traveling toward the receiver leave the transmitter. The phased.Radiator System object™ uses these angles to apply separate antenna gains to the two signals. Because the antenna gains depend on path direction, you must transmit and receive the two rays separately.

[~,angTx] = rangeangle(posRx,posTx,laxTx,'two-ray');

Create and Radiate Signals from Transmitter

Radiate the signals along the transmission directions.

wavfrm = waveform();
wavtrans = radiator(wavfrm,angTx);

Propagate signals to receiver via two-ray channel.

wavrcv = channel(wavtrans,posTx,posRx,velTx,velRx);

Collect Signal at Receiver

Compute the angle at which the two rays traveling from the transmitter arrive at the receiver. The phased.Collector System object™ uses these angles to apply separate antenna gains to the two signals.

[~,angRcv] = rangeangle(posTx,posRx,laxRx,'two-ray');

Collect and combine the two received rays.

yR = collector(wavrcv,angRcv);

Plot Received Signal

dt = 1/waveform.SampleRate;
n = size(yR,1);
plot((0:(n-1))*dt*1000000,real(yR))
xlabel('Time ({\mu}sec)')
ylabel('Signal Magnitude')

More About

Two-Ray Propagation Paths

A two-ray propagation channel is the next step up in complexity from a free-space channel and is the simplest case of a multipath propagation environment. The free-space channel models a straight-line line-of-sight path from point 1 to point 2. In a two-ray channel, the medium is specified as a homogeneous, isotropic medium with a reflecting planar boundary. The boundary is always set at z = 0. There are at most two rays propagating from point 1 to point 2. The first ray path propagates along the same line-of-sight path as in the free-space channel. The line-of-sight path is often called the direct path. The second ray reflects off the boundary before propagating to point 2. According to the Law of Reflection , the angle of reflection equals the angle of incidence. In short-range simulations such as cellular communications systems and automotive radars, you can assume that the reflecting surface, the ground or ocean surface, is flat.

The twoRayChannel and widebandTwoRayChannel System objects model propagation time delay, phase shift, Doppler shift, and loss effects for both paths. For the reflected path, loss effects include reflection loss at the boundary.

The figure illustrates two propagation paths. From the source position, s_s, and the receiver position, s_r, you can compute the arrival angles of both paths, θ′_los and θ′_rp. The arrival angles are the elevation and azimuth angles of the arriving radiation with respect to a local coordinate system. In this case, the local coordinate system coincides with the global coordinate system. You can also compute the transmitting angles, θ_los and θ_rp. In the global coordinates, the angle of reflection at the boundary is the same as the angles θ_rp and θ′_rp. The reflection angle is important to know when you use angle-dependent reflection-loss data. You can determine the reflection angle by using the rangeangle function and setting the reference axes to the global coordinate system. The total path length for the line-of-sight path is shown in the figure by R_los which is equal to the geometric distance between source and receiver. The total path length for the reflected path is R_rp= R₁ + R₂. The quantity L is the ground range between source and receiver.

You can easily derive exact formulas for path lengths and angles in terms of the ground range and object heights in the global coordinate system.

$$\begin{array}{l}\overrightarrow{R}={\overrightarrow{x}}_s-{\overrightarrow{x}}_r\\ R_{los}=\left|\overrightarrow{R}\right|=\sqrt{{\left(z_r-z_s\right)}^2+L^2}\\ R_1=\frac{z_r}{z_r+z_z}\sqrt{{\left(z_r+z_s\right)}^2+L^2}\\ R_2=\frac{z_s}{z_s+z_r}\sqrt{{\left(z_r+z_s\right)}^2+L^2}\\ R_{rp}=R_1+R_2=\sqrt{{\left(z_r+z_s\right)}^2+L^2}\\ \tan {\theta }_{los}=\frac{\left(z_s-z_r\right)}{L}\\ \tan {\theta }_{rp}=-\frac{\left(z_s+z_r\right)}{L}\\ {{\theta }^{\prime }}_{los}=-{\theta }_{los}\\ {{\theta }^{\prime }}_{rp}={\theta }_{rp}\end{array}$$

Two-Ray Attenuation

Attenuation or path loss in the two-ray channel is the product of five components, L = L_tworay L_G L_g L_c L_r, where

• L_tworay is the two-ray geometric path attenuation

• L_G is the ground reflection 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.

Ground Reflection and Propagation Loss

Losses occurs when a signal is reflected from a boundary. You can obtain a simple model of ground reflection loss by representing the electromagnetic field as a scalar field. This approach also works for acoustic and sonar systems. Let E be a scalar free-space electromagnetic field having amplitude E₀ at a reference distance R₀ from a transmitter (for example, one meter). The propagating free-space field at distance R_los from the transmitter is

$$E_{los}=E_0\left(\frac{R_0}{R_{los}}\right)e^{i\omega \left(t-R_{los}/c\right)}$$

for the line-of-sight path. You can express the ground-reflected E-field as

$$E_{rp}=L_G{E}_0\left(\frac{R_0}{R_{rp}}\right)e^{i\omega \left(t-R_{rp}/c\right)}$$

where R_rp is the reflected path distance. The quantity L_G represents the loss due to reflection at the ground plane. To specify L_G, use the GroundReflectionCoefficient property. In general, L_G depends on the incidence angle of the field. If you have empirical information about the angular dependence of L_G, you can use rangeangle to compute the incidence angle of the reflected path. The total field at the destination is the sum of the line-of-sight and reflected-path fields.

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

$$\begin{array}{l}{G}_p=\frac{Z_1\cos {\theta }_1-Z_2\cos {\theta }_2}{Z_1\cos {\theta }_1+Z_2\cos {\theta }_2}=\frac{\cos {\theta }_1-\frac{Z_2}{Z_1}\cos {\theta }_2}{\cos {\theta }_1+\frac{Z_2}{Z_1}\cos {\theta }_2}\\ G_s=\frac{Z_2\cos {\theta }_1-Z_1\cos {\theta }_2}{Z_2\cos {\theta }_1+Z_1\cos {\theta }_2}=\frac{\cos {\theta }_2-\frac{Z_2}{Z_1}\cos {\theta }_1}{\cos {\theta }_2+\frac{Z_2}{Z_1}\cos {\theta }_1}\\ Z_1=\sqrt{\frac{{\mu }_1}{{\epsilon }_1}}\\ Z_2=\sqrt{\frac{{\mu }_2}{{\epsilon }_2}}\end{array}$$

where Z is the impedance of the medium. Because the magnetic permeability of the ground is almost identical to that of air or free space, the ratio of impedances depends primarily on the ratio of electric permittivities

$$\begin{array}{l}{G}_p=\frac{\sqrt{\rho }\cos {\theta }_1-\cos {\theta }_2}{\sqrt{\rho }\cos {\theta }_1+\cos {\theta }_2}\\ G_s=\frac{\sqrt{\rho }\cos {\theta }_2-\cos {\theta }_1}{\sqrt{\rho }\cos {\theta }_2+\cos {\theta }_1}\end{array}$$

where the quantity ρ = ε₂/ε₁ is the ground relative permittivity set by the GroundRelativePermittivity property. The angle θ₁ is the incidence angle and the angle θ₂ is the refraction angle at the boundary. You can determine θ₂ using Snell’s law of refraction.

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

When the origin and destination are stationary relative to each other, you can write the output Y of the object as Y(t) = F(t-τ)/L. The quantity τ is the signal delay and L is the free-space path loss. The delay τ is given by R/c. R is either the line-of-sight propagation path distance or the reflected path distance, and c is the propagation speed. The path loss

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

where λ is the signal wavelength.

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.

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.

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] Saakian, A. Radio Wave Propagation Fundamentals. Norwood, MA: Artech House, 2011.

[2] Balanis, C. Advanced Engineering Electromagnetics. New York: Wiley & Sons, 1989.

[3] Rappaport, T. Wireless Communications: Principles and Practice, 2nd Ed New York: Prentice Hall, 2002.

[4] Radiocommunication Sector of the International Telecommunication Union. Recommendation ITU-R P.676-12: Attenuation by atmospheric gases. 2019.

[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.

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 R2021a