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# phased.FreeSpace System object

Package: phased

Free space environment

## Description

The FreeSpace System object™ models a free space environment.

To compute the propagated signal in free space:

1. Define and set up your free space environment. See Construction.

2. 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.

## Construction

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).

## Properties

 PropagationSpeed Signal propagation speed Specify the wave propagation speed (in meters per second) in free space as a scalar. Default: Speed of light OperatingFrequency 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. Default: 3e8 TwoWayPropagation 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. Default: false SampleRate Sample rate 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. Default: 1e6

## Methods

 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

## Examples

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### Signal Propagation from Stationary Radar to Stationary Target

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]);```

### Signal Propagation from Moving Radar to Moving Target

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);```

## Algorithms

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

$L=\frac{{\left(4\pi R\right)}^{2}}{{\lambda }^{2}}$

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].

## References

[1] Proakis, J. Digital Communications. New York: McGraw-Hill, 2001.

[2] Skolnik, M. Introduction to Radar Systems, 3rd Ed. New York: McGraw-Hill, 2001.