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phased.FreeSpace System object

Package: phased

Free space environment


The FreeSpace object models a free space environment.

To compute the propagated signal in free space:

  1. Define and set up your free space environment. See Construction.

  2. Call step to propagate the signal through a free space environment according to the properties of phased.FreeSpace. The behavior of step is specific to each object in the toolbox.


H = phased.FreeSpace creates a free space environment System object™, H. The object simulates narrowband signal propagation in free space, by applying range-dependent time delay, gain and phase shift to the input signal.

H = phased.FreeSpace(Name,Value) creates a free space environment object, H, with each specified property Name set to the specified Value. You can specify additional name-value pair arguments in any order as (Name1,Value1,...,NameN,ValueN).



Signal propagation speed

Specify the wave propagation speed (in meters per second) in free space as a scalar.

Default: Speed of light


Signal carrier frequency

A scalar containing the carrier frequency in hertz of the narrowband signal. The default value of this property corresponds to 300 MHz.

Default: 3e8


Perform two-way propagation

Set this property to true to perform round-trip propagation between the origin and destination that you specify in the step command. Set this property to false to perform one-way propagation from the origin to the destination.

Default: false


Sample rate

A scalar containing the sample rate (in hertz). The algorithm uses this value to determine the propagation delay in samples. The default value of this property corresponds to 1 MHz.

Default: 1e6


cloneCreate free space object with same property values
getNumInputsNumber of expected inputs to step method
getNumOutputsNumber of outputs from step method
isLockedLocked status for input attributes and nontunable properties
releaseAllow property value and input characteristics changes
resetReset internal states of propagation channel
stepPropagate signal from one location to another


expand all

Signal Propagation from Stationary Radar to Stationary Target

Calculate the result of propagating a signal in a free space environment from a radar at (1000, 0, 0) to a target at (300, 200, 50). Assume both the radar and the target are stationary.

henv = phased.FreeSpace('SampleRate',8e3);
y = step(henv,ones(10,1),[1000; 0; 0],[300; 200; 50],...

Signal Propagation from Moving Radar to Moving Target

Calculate the result of propagating a signal in a free space environment from a radar at (1000, 0, 0) to a target at (300, 200, 50). Assume the radar moves at 10 m/s in the direction of the x-axis, while the target moves at 15 m/s in the direction of the y-axis.

henv = phased.FreeSpace('SampleRate',8e3);
origin_pos = [1000; 0; 0];
dest_pos = [300; 200; 50];
origin_vel = [10; 0; 0];
dest_vel = [0; 15; 0];
y = step(henv,ones(10,1),origin_pos,dest_pos,...


When the origin and destination are stationary relative to each other, the output Y of step can be written as Y(t)=x(t–tau)/L. In this case, tau is the delay and L is the propagation loss. The delay tau is R/c, where R is the propagation distance and c is the propagation speed. The free space path loss is given by

where λ is the signal wavelength.

When there is relative motion between the origin and destination, the processing also introduces a frequency shift. This shift corresponds to the Doppler shift between the origin and destination. The frequency shift is v/λ for one-way propagation and 2v/λ for two-way propagation. In this case, v is the relative speed from the origin to the destination.

For further details, see [2].


[1] Proakis, J. Digital Communications. New York: McGraw-Hill, 2001.

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

See Also


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