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The `FreeSpace` 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.

`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,

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*–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.

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