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.

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.

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.

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

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

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 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.