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 signal in freespace to an object and back,
you can either using a single FreeSpace
System object to
compute a twoway free space propagation delay or two FreeSpace
System
objects to perform oneway propagation delays in each direction. Because
the freespace 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 twoway propagation phased.FreeSpace
System object differs
from the delay in samples when you use two oneway phased.FreeSpace
System
objects. For this reason, it is recommended that, when possible, you
use a single twoway phased.FreeSpace
System object.
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: 
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 Y
of step
can
be written as Y(t) = x(tτ)/L.
The quantity τ is the signal delay and L 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 free space path loss is given by
$$L=\frac{{(4\pi R)}^{2}}{{\lambda}^{2}}$$
where λ is the signal wavelength.
This formula assumes that the target is in the farfield of the transmitting element or array. In the nearfield, the freespace 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 oneway propagation and 2v/λ for twoway propagation. The parameter v is the relative speed of the destination with respect to the origin.
For further details, see [2].
[1] Proakis, J. Digital Communications. New York: McGrawHill, 2001.
[2] Skolnik, M. Introduction to Radar Systems, 3rd Ed. New York: McGrawHill, 2001.