# 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

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Narrowband signal, specified as an M-element complex-valued column vector or M-by-N complex-valued matrix. The quantity M is the number of sample values of the signal and N is the number of signals to propagate. When you specify N signals, you need to specify N signal origins or N signal destinations.

The size of the first dimension of the input matrix can vary to simulate a changing signal length. A size change can occur, for example, in the case of a pulse waveform with variable pulse repetition frequency.

Signal origin, specified as a 3-by-1 real-valued column vector or 3-by-N real-valued matrix. The quantity N is the number of propagated signals and equals the dimension specified in the signal into the port `X`. If `Pos1` is a column vector, it takes the form `[x; y; z]`. If `Pos1` is a matrix, each column specifies a different signal origin and has the form `[x; y; z]`. `Pos1` and `Pos2` cannot both be specified as matrices — at least one must be a 3-by-1 column vector. Position units are meters.

Data Types: `double`

Signal destination, specified as a 3-by-1 real-valued column vector or 3-by-N real-valued matrix. The quantity N is the number of propagated signals and equals the dimension specified in the signal into the port `X`. If `Pos2` is a column vector, it takes the form `[x; y; z]`. If `Pos2` is a matrix, each column specifies a different signal origin and has the form `[x; y; z]`. `Pos2` and `Pos1` cannot both be specified as matrices — at least one must be a 3-by-1 column vector. Position units are meters.

Data Types: `double`

Signal origin velocity, specified as a 3-by-1 real-valued column vector or 3-by-N real-valued matrix. The quantity N is the number of propagated signals and equals the dimension specified in the signal into the port `X`. If `Vel1` is a column vector, it takes the form `[Vx; Vy; zV]`. If `Vel1` is a matrix, each column specifies a different signal origin and has the form ```[Vx; Vy; Vz]```. `Vel1` and `Vel2` cannot both be specified as matrices — at least one must be a 3-by-1 column vector. Position units are meters.

Data Types: `double`

Signal destination velocity, specified as a 3-by-1 real-valued column vector or 3-by-N real-valued matrix. The quantity N is the number of propagated signals and equals the dimension specified in the signal into the port `X`. If `Vel2` is a column vector, it takes the form `[Vx; Vy; zV]`. If `Vel2` is a matrix, each column specifies a different signal origin and has the form ```[Vx; Vy; Vz]```. `Vel2` and `Vel1` cannot both be specified as matrices — at least one must be a 3-by-1 column vector. Position units are meters.

Data Types: `double`

### Output

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Propagated signal, returned as a M-element complex-valued column vector, M-by-N complex-valued matrix.

If `X` is a column vector or matrix, `Y` is also a column vector or matrix with the same dimensions.

The output `Y` contains signal samples arriving at the signal destination within the current time frame. The current time frame is defined as the time spanned by the current input. Whenever it takes longer than the current time frame for the signal to propagate from the origin to the destination, the output contains no contribution from the input of the current time frame.

## Parameters

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Signal propagation speed, specified as a real-valued positive scalar. The default value of the speed of light is the value returned by `physconst('LightSpeed')`.

Data Types: `double`

Signal carrier frequency, specified as a positive real-valued scalar. Units are in hertz.

Data Types: `double`

Select this check box to perform round-trip propagation between the origin and destination. Otherwise the block performs one-way propagation from the origin to the destination.

Select this parameter to inherit the sample rate from upstream blocks. Otherwise, specify the sample rate using the Sample rate (Hz) parameter.

Data Types: `Boolean`

Specify the signal sampling rate as a positive scalar. Units are in Hz.

#### Dependencies

To enable this parameter, clear the Inherit sample rate check box.

Data Types: `double`

The maximum distance, in meters, between the origin and the destination as a positive scalar. Amplitudes of any signals that propagate beyond this distance will be set to zero.

Block simulation, specified as `Interpreted Execution` or `Code Generation`. If you want your block to use the MATLAB® interpreter, choose `Interpreted Execution`. If you want your block to run as compiled code, choose ```Code Generation```. Compiled code requires time to compile but usually runs faster.

Interpreted execution is useful when you are developing and tuning a model. The block runs the underlying System object™ in MATLAB. You can change and execute your model quickly. When you are satisfied with your results, you can then run the block using ```Code Generation```. Long simulations run faster with generated code than in interpreted execution. You can run repeated executions without recompiling, but if you change any block parameters, then the block automatically recompiles before execution.

This table shows how the Simulate using parameter affects the overall simulation behavior.

When the Simulink® model is in `Accelerator` mode, the block mode specified using Simulate using overrides the simulation mode.

Acceleration Modes

 Block Simulation Simulation Behavior `Normal` `Accelerator` `Rapid Accelerator` `Interpreted Execution` The block executes using the MATLAB interpreter. The block executes using the MATLAB interpreter. Creates a standalone executable from the model. `Code Generation` The block is compiled. All blocks in the model are compiled.

## 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

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

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 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