freeSpacePath

Monostatic free space propagation path

Since R2025a

Syntax

propPaths = freeSpacePath(freq,rdrPose,tgtPoses)

propPaths = freeSpacePath(freq,rdrPose,tgtPoses,Name=Value)

Description

propPaths = freeSpacePath(freq,rdrPose,tgtPoses) returns two-way monostatic free space propagation path structures, propPaths, for input radar transceiver rdrPose and target tgtPoses platform configurations.

propPaths = freeSpacePath(freq,rdrPose,tgtPoses,Name=Value) returns two-way monostatic free space propagation paths, with additional options specified using one or more name-value arguments. For example, you can specify the radar transceiver mounting location and angles.

Examples

Free Space Propagation Paths for Radar Transceiver

Calculate the free space propagation path for a radar transceiver configuration.

Create a radar transceiver with an isotropic antenna, transmitting a linear frequency modulated (LFM) pulse waveform with a 10 microsecond pulse width. Calculate the free space propagation paths assuming the radar is at the origin and the target is 5 km away. Return I/Q signals from the radar transceiver at the initial time and plot the results. Start by initializing the radar transceiver.

wav  = phased.LinearFMWaveform(PulseWidth=1e-5);
ant  = phased.IsotropicAntennaElement;
rdr  = radarTransceiver(Waveform=wav, ...
     TransmitAntenna=phased.Radiator(Sensor=ant), ...
     ReceiveAntenna=phased.Collector(Sensor=ant), ...
     RangeOutputPort=true);
freq = rdr.TransmitAntenna.OperatingFrequency; 

Define the radar position, target position, and target velocity. Calculate the free space propagation paths. The target is located 5 km away and is moving at 20 m/s in the y-direction.

rdrPose.Position = [0 0 0];   % Radar position (m)
tgtPose.Position = [0 5e3 0]; % Target position (m)
tgtPose.Velocity = [0 20 0];  % Target velocity (m/s) 
proppaths        = freeSpacePath(freq,rdrPose,tgtPose)

proppaths = struct with fields:
               PathLength: 10000
                 PathLoss: 191.9392
    ReflectionCoefficient: 11.2177
         AngleOfDeparture: [2×1 double]
           AngleOfArrival: [2×1 double]
             DopplerShift: -40.0277

Return I/Q signals from the radarTransceiver at a time of 0 seconds and plot the results. The target is located at 5 km.

t = 0; % Time (sec) 
[iq,rgrid] = rdr(proppaths,t);

% Plot 
figure
plot(rgrid*1e-3,mag2db(abs(sum(iq,2))))
grid on
hold on
xline(5,'r--')
xlabel('Range (km)')
ylabel('Magnitude (dB)')

Free Space Propagation Paths for Rotated Radar Transceiver

This example shows how to calculate the free space propagation path for a rotated radar transceiver configuration.

Create a radar transceiver with a directive sinc antenna with a 5 degree beamwidth. Rotate the radar to point in the direction of the target by modifying the mounting angle. Calculate the free space propagation path assuming the radar is at the origin and the target is 5 km away. The propagation paths calculated by freeSpacePath are in the radar mounting frame. Return I/Q signals from the radar transceiver at the initial time and plot the results. Start by initializing the radar transceiver.

mntAng = [90 0 0];           % Mounting angles (deg)
wav  = phased.LinearFMWaveform(PulseWidth=1e-5);
ant  = phased.IsotropicAntennaElement;
rdr  = radarTransceiver(Waveform=wav, ...
     TransmitAntenna=phased.Radiator(Sensor=ant), ...
     ReceiveAntenna=phased.Collector(Sensor=ant), ...
     RangeOutputPort=true);
freq = rdr.TransmitAntenna.OperatingFrequency; 

Define the radar position, target position, and target velocity. Calculate the free space propagation path in the radar mounting frame.

rdrPose.Position = [0 0 0];   % Radar position (m)
tgtPose.Position = [0 5e3 0]; % Target position (m)
tgtPose.Velocity = [0 20 0];  % Target velocity (m/s) 
proppaths        = freeSpacePath(freq,rdrPose,tgtPose)

proppaths = struct with fields:
               PathLength: 10000
                 PathLoss: 191.9392
    ReflectionCoefficient: 11.2177
         AngleOfDeparture: [2×1 double]
           AngleOfArrival: [2×1 double]
             DopplerShift: -40.0277

Return I/Q signals from radarTransceiver at a time of 0 seconds and plot the results. The target is located at 5 km.

t = 0;                        % Time (sec) 
[iq,rgrid] = rdr(proppaths,t);

% Plot 
figure
plot(rgrid*1e-3,mag2db(abs(sum(iq,2))))
grid on
hold on
xline(5,'r--')
xlabel('Range (km)')
ylabel('Magnitude (dB)')

Input Arguments

freq — Operating frequency (Hz)

positive scalar

Operating frequency of the radar transceiver, specified as a positive scalar in units of hertz (Hz).

Data Types: double

rdrPose — Transceiver platform configuration

struct

Transceiver platform configuration, specified as a struct that contains Position, Velocity, and Orientation fields. The platform configuration is defined relative to a global coordinate frame that is considered to have an origin at [0 0 0] in unrotated Cartesian x, y, z coordinates (see Radar Coordinate Systems and Frames for more information on reference frames).

Field	Description
Position	Position of the platform with respect to the global coordinate frame, specified as a 3-element row vector in the form of [x y z]. Units are in meters (m). There is no default value.
Velocity	Velocity of the platform with respect to the global coordinate frame, specified as a 3-element row vector in the form of [x y z]. Units are in meters per second (m/s). The default value is [0 0 0].
Orientation	Orientation of the platform with respect to the global coordinate frame, specified as a unitless scalar quaternion or a 3-by-3 rotation matrix in units of degrees (deg). Orientation defines the intrinsic frame rotation from the global coordinate frame to the current platform body frame. The default value is quaternion(1,0,0,0).

You can define platforms as platform objects in a radarScenario and then return the platform poses as structs using platformPoses. You can use a returned platform pose struct for this input argument because it contains Position, Velocity, and Orientation fields (irrelevant fields including PlatformID are ignored).

Data Types: struct

tgtPoses — Target platform configurations

struct | 1-by-T array of structs

Target platform configurations, specified as a struct or a 1-by-T array of structs that contain a Position, Velocity, Orientation, and Signatures field for each target, T. The platform configuration is defined relative to a global coordinate frame that is considered to have an origin at [0 0 0] in unrotated Cartesian x, y, z coordinates (see Radar Coordinate Systems and Frames for more information on reference frames).

Field	Description
Position	Position of the platform with respect to the global frame, specified as a 3-element row vector in the form of [x y z]. Units are in meters (m). There is no default value.
Velocity	Velocity of the platform with respect to the global frame, specified as a 3-element row vector in the form of [x y z]. Units are meters in per second (m/s). The default value is [0 0 0].
Orientation	Orientation of the platform with respect to the global coordinate frame, specified as a unitless scalar quaternion or a 3-by-3 rotation matrix in units of degrees. Orientation defines the intrinsic frame rotation from the global coordinate frame to the current platform body frame. Units are dimensionless. The default value is quaternion(1,0,0,0).
Signatures	Mean monostatic target radar cross section (RCS) signature, specified as a cell array of platform signature objects. If there are multiple cells, freeSpacePath selects the first rcsSignature object and any other signature objects are ignored. The default value is a cell array containing an rcsSignature object with default property values. Swerling fluctuations are not considered. Polarimetric signatures are not supported.

You can define platforms as platform objects in a radarScenario and then return the platform poses as structs using platformPoses. You can use the returned platform pose structs for this input argument because they contain Position, Velocity, and Orientation fields (irrelevant fields including PlatformID are ignored). However, the returned platform pose structs do not contain a Signatures fields. The Signatures field can be obtained using platformProfiles.

Data Types: struct

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: propPaths = freeSpacePath(txPose,rxPose,tgtPoses,IncludeDirectPath=false)

MountingLocation — Transceiver origin offset (m)

[0 0 0] (default) | 1-by-3 vector

Offset of the radar transceiver origin relative to the transceiver platform, specified as a 3-element row vector in the form [x_offset y_offset z_offset], where x_offset, y_offset, and z_offset are offsets measured along the x-, y-, and z-axes. The default value is [0 0 0]. Units are in meters (m).

The transceiver platform position is set by the Position field of the rdrPose input argument.

Data Types: double

MountingAngles — Rotation angles of the transceiver mounting frame (deg)

[0 0 0] (default) | 1-by-3 vector

Rotation angles of the radar transceiver mounting frame relative to the transceiver platform body frame, specified as a 3-element row vector of intrinsic Euler angles in the form [zyaw ypitch xroll], where zyaw, ypitch, and xroll are rotations measured about the z-, y-, and x-axes. Units are in degrees (deg).

Intrinsics rotations follow the right hand rule convention and are sequential:

• zyaw, or yaw angle, rotates the mounting frame around the z-axis of the platform body frame.

• ypitch, or pitch angle, rotates the mounting frame around the y-axis of the platform body frame. This rotation is relative to the mount orientation that results from the z_yaw rotation.

• xroll, or roll angle, rotates the mounting frame about the x-axis of the platform body frame. This rotation is relative to the mount orientation that results from the z_yaw and y_pitch rotations.

In other words, perform rotations in the order of yaw, pitch, and roll on the platform z-, y-, and x-axes to obtain the current mounting frame axes relative to the platform body frame. The transceiver platform orientation is set by the Orientation field of the rdrPose input argument. See Frame Rotation (Sensor Fusion and Tracking Toolbox) for more information on intrinsic rotations.

Data Types: double

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

Output Arguments

propPaths — Two-way monostatic propagation paths

1-by-T array of structs

Two-way monostatic free space propagation paths, returned as a 1-by-T array of path configuration structs, where T is the number of target poses in tgtPoses. Each propPaths struct describes a free space, single-bounce, propagation path between the radar transceiver transmit antenna, a target, and the radar transceiver receive antenna, and contains these fields:

Field	Description
PathLength	Propagation path length, returned as a nonnegative scalar in units of meters (m).
PathLoss	Propagation path loss, computed by summing the Free Space Path Loss along each path segment, returned as a scalar in units of decibels (dB).
ReflectionCoefficient	Reflection coefficient, returned as a scalar in linear units. The reflection coefficient value depends on the corresponding tgtPoses Signatures field value and the monostatic configuration. Scattering from other targets that may be present is not considered.
AngleOfDeparture	Propagation path angle of departure, returned as a two-element column vector in the form of [azimuth; elevation] in units of degrees (deg). The transmit antenna angle of departure is measured with respect to the radar transceiver mounting frame.
AngleOfArrival	Propagation path angle of arrival, returned as a two-element column vector in the form of [azimuth; elevation] in units of degrees (deg). The receive antenna angle of arrival is measured with respect to the radar transceiver mounting frame.
DopplerShift	Cumulative Doppler shift along the path, returned as a scalar in units of hertz (Hz).

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2025a