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# step

System object: phased.FreeSpace
Package: phased

Propagate signal from one location to another

## Syntax

Y = step(H,X,origin_pos,dest_pos,origin_vel,dest_vel)

## Description

Y = step(H,X,origin_pos,dest_pos,origin_vel,dest_vel) returns the resulting signal, Y, when the narrowband signal X propagates in free space from origin_pos to dest_pos. The velocity of the signal origin is origin_vel and the velocity of the signal destination is dest_vel. Consider FreeSpace as a point-to-point propagation channel. For example, you can use it to model the propagation of a signal between a radar and a target.

 Note:   H specifies the System object™ on which to run this step method.The object performs an initialization the first time the step method is executed. This initialization locks nontunable properties and input specifications, such as dimensions, complexity, and data type of the input data. If you change a nontunable property or an input specification, the System object issues an error. To change nontunable properties or inputs, you must first call the release method to unlock the object.

## Input Arguments

 H Free space object. X Narrowband signal. The form of X depends upon whether polarization is simulated or not. If polarization is not simulated, X is a column vector. If polarization is simulated X is a MATLAB® struct containing two alternate ways of representing the polarized signal:X.X, X.Y, and X.Z representing the x, y, and z components of the polarized signal.X.H and X.V representing the horizontal and vertical components of the polarized signal. origin_pos Starting location of signal, specified as a 3-by-1 column vector in the form [x; y; z] (in meters). dest_pos Ending location of signal, specified as a 3-by-1 column vector in the form [x; y; z] (in meters). origin_vel Velocity of signal origin, specified as a 3-by-1 column vector in the form [Vx; Vy; Vz] (in meters/second). dest_vel Velocity of the signal destination, specified as a 3-by-1 column vector in the form [Vx; Vy; Vz] (in meters/second).

## Output Arguments

 Y Propagated signal, returned as a column vector or MATLAB struct, depending upon the form of the input argument X. If X is a column vector, Y is also a column vector with same dimensions. If X is a struct, Y is also a struct with the same fields. Each field in Y contains the resulting signal of the corresponding field in X. The output Y is the signal arriving at the propagation destination within the current time frame, which is the time occupied 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.

## 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.