The phased.FreeSpace
System object™ models
narrowband signal propagation from one point to another in a freespace
environment. The object applies rangedependent time delay, gain and
phase shift to the input signal. The object accounts for doppler shift
when either the source or destination is moving. A freespace environment
is a boundaryless medium with a speed of signal propagation independent
of position and direction. The signal propagates along a straight
line from source to destination. For example, you can use this object
to model the propagation of a signal from a radar to a target and
back to the radar.
For nonpolarized signals, the FreeSpace
System object lets
you propagate signals from a single point to multiple points or from
multiple points to a single point. Multiplepoint to multiplepoint
propagation is not supported.
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 round trip signal in freespace, you can
either use one FreeSpace
System object to compute
the twoway propagation delay or two separate FreeSpace
System
objects to compute oneway propagation delays in each direction. Due
to filter distortion, the total round trip delay when you employ twoway
propagation can differ from the delay when you use two oneway phased.FreeSpace
System
objects. It is more accurate to use a single twoway phased.FreeSpace
System object.
This option is set by the TwoWayPropagation
property.
Note:
Starting in R2016b, instead of using the 
H = phased.FreeSpace
creates a free space
environment System object, H
.
H = phased.FreeSpace(
creates
a free space environment object, Name
,Value
)H
, with each specified
property Name set to the specified Value. You can specify additional
namevalue pair arguments in any order as (Name1
,Value1
,...,NameN
,ValueN
).

Signal propagation speed Specify signal wave propagation speed in free space as a real positive scalar. Units are meters per second. Default: Speed of light 

Signal carrier frequency A scalar containing the carrier frequency of the narrowband signal. Units are hertz. Default: 

Perform twoway propagation Set this property to Default: 

Sample rate A scalar containing the sample rate. Units of sample rate are hertz. The algorithm uses this value to determine the propagation delay in number of samples. Default: 

Source of maximum distance value Source of maximum distance value, specified as Default: 

Maximum oneway propagation distance Maximum oneway propagation distance, specified as a realvalued
positive scalar. Units are meters. This property applies when you
set the Default: 

Source of maximum number of samples The source of the maximum number of samples of the input signal,
specified as This property applies when you set the When you use propagation models in MATLAB^{®} Function Block
in Simulink^{®} with variablesize signals, you must set the Default: 

Maximum number of input signal samples Maximum number of samples in input signal, specified as a positive
integer. This property limits the size of the input signal. Any input
signal longer than this value is truncated. The input signal is the
first argument to the Default: 
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 
When the origin and destination are stationary relative to each other, the output signal of a freespace channel can be written as Y(t) = x(tτ)/L_{fsp}. The quantity τ is the signal delay and L_{fsp} is the freespace path loss. The delay τ is given by R/c, where R is the propagation distance and c is the propagation speed. The freespace 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 freespace path loss formula is not valid and can result in a loss smaller than one, equivalent to a signal gain. For this reason, 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 oneway propagation and 2v/λ for twoway 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 [2].
[1] Proakis, J. Digital Communications. New York: McGrawHill, 2001.
[2] Skolnik, M. Introduction to Radar Systems, 3rd Ed. New York: McGrawHill, 2001.