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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).
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(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
$$L=\frac{{(4\pi R)}^{2}}{{\lambda}^{2}}$$
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 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 [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.