Free space environment
The FreeSpace System object™ models a free space environment.
To compute the propagated signal in free space:
Define and set up your free space environment. See Construction.
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.
When propagating a signal in free-space to an object and back, you can either using a single FreeSpace System object to compute a two-way free space propagation delay or two FreeSpace System objects to perform one-way propagation delays in each direction. Because the free-space propagation delay is not necessarily an integer multiple of the sampling interval, it may turn out that the total round trip delay in samples when you use a two-way propagation phased.FreeSpace System object differs from the delay in samples when you use two one-way phased.FreeSpace System objects. For this reason, it is recommended that, when possible, you use a single two-way phased.FreeSpace System object.
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.
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.
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.
|clone||Create free space object with same property values|
|getNumInputs||Number of expected inputs to step method|
|getNumOutputs||Number of outputs from step method|
|isLocked||Locked status for input attributes and nontunable properties|
|release||Allow property value and input characteristics changes|
|reset||Reset internal states of propagation channel|
|step||Propagate signal from one location to another|
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],... [0;0;0],[0;0;0]);
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,... origin_vel,dest_vel);
When the origin and destination are stationary relative to each other, the output Y of step can be written as Y(t) = x(t-τ)/L. The quantity τ is the signal delay and L is the free-space path!gg loss. The delay τ is given by R/c, where R is the propagation distance and c is the propagation speed. The free space path loss is given by
where λ is the signal wavelength.
This formula assumes that the target is in the far-field of the transmitting element or array. In the near-field, the free-space path loss formula is not valid and can result in a loss less than one, equivalent to a signal gain. For this reason, the loss is set to unity for range values, R ≤ λ/4π.
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. The parameter v is the relative speed of the destination with respect to the origin.
For further details, see .
 Proakis, J. Digital Communications. New York: McGraw-Hill, 2001.
 Skolnik, M. Introduction to Radar Systems, 3rd Ed. New York: McGraw-Hill, 2001.