# Free Space

Free space environment

**Library:**Phased Array System Toolbox / Environment and Target

## Description

The Free Space Channel block propagates a signal from one point to another in space. The block models propagation time, free space propagation loss and Doppler shift. The block assumes that the propagation speed is much greater than the target or array speed in which case the stop-and-hop model is valid.

When propagating a signal in free-space to an object and back, you have the choice of either using a single block to compute a two-way free space propagation delay or two blocks 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 block differs from the delay in samples when you use two one-way propagation blocks. For this reason, it is recommended that, when possible, you use a single two-way propagation block.

## Ports

### Input

### Output

## Parameters

## Algorithms

When the origin and destination are stationary relative to each other, the block
output can be written as *y(t) = x(t – τ)/L*. The quantity *τ* is the delay and
*L* is the propagation loss. The delay is computed from *τ = R/c* where *R* is the propagation distance and
*c* is the propagation speed. The free space 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 free-space path loss formula is not valid and can
result in losses smaller 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.

## Version History

**Introduced in R2014b**