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# step

Package: phased

Reflect incoming signal

## Syntax

• Y = step(H,X)
• Y = step(H,X,MEANRCS)
• Y = step(H,X,UPDATERCS)
• Y = step(H,X,MEANRCS,UPDATERCS)
• Y = step(H,X,ANGLE_IN,LAXES)
• Y = step(H,X,ANGLE_IN,ANGLE_OUT,LAXES)
• Y = step(H,X,ANGLE_IN,LAXES,SMAT)
• Y = step(H,X,ANGLE_IN,LAXES,UPDATESMAT)
• Y = step(H,X,ANGLE_IN,ANGLE_OUT,LAXES,SMAT,UPDATESMAT)

## Description

Y = step(H,X) returns the reflected signal Y due to the incident signal X. Use this syntax when you set the Model property of H to 'Nonfluctuating'. In this case, the value of the MeanRCS property is used as the Radar cross-section (RCS) value. This syntax applies only when the EnablePolarization property is set to false.

Y = step(H,X,MEANRCS) uses MEANRCS as the mean RCS value. This syntax is available when you set the MeanRCSSource property to 'Input port'. MEANRCS must be a positive scalar. This syntax applies only when the EnablePolarization property is set to false.

Y = step(H,X,UPDATERCS) uses UPDATERCS as the indicator of whether to update the RCS value. This syntax is available when you set the Model property to 'Swerling1', 'Swerling2', 'Swerling3', or 'Swerling4'. If UPDATERCS is true, a new RCS value is generated. If UPDATERCS is false, the previous RCS value is used. This syntax applies only when the EnablePolarization property is set to false.

Y = step(H,X,MEANRCS,UPDATERCS) lets you can combine optional input arguments when their enabling properties are set. This syntax applies only when the EnablePolarization property is set to false.

Y = step(H,X,ANGLE_IN,LAXES) returns the reflected signal Y from an incident signal X. This syntax applies only when the EnablePolarization property is set to true. The input argument, ANGLE_IN, specifies the direction of the incident signal with respect to the target's local coordinate system. The input argument, LAXES, specifies the direction of the local coordinate axes with respect to the global coordinate system. This syntax requires that you set the Model property to 'Nonfluctuating' and the Mode property to 'Monostatic'. In this case, the value of the ScatteringMatrix property is used as the scattering matrix value.

X is a row array of MATLAB® struct type, each member of the array representing a different signal. The struct contains three fields, X.X, X.Y, and X.Z. Each field corresponds to the x, y, and z components of the polarized input signal. Polarization components are measured with respect to the global coordinate system. Each field is a column vector representing a sequence of values for each incoming signal. The X.X, X.Y, and Y.Z fields must all have the same dimension. The argument, ANGLE_IN, is a 2-row matrix representing the signals' incoming directions with respect to the target's local coordinate system. Each column of ANGLE_IN specifies the incident direction of the corresponding signal in the form [AzimuthAngle; ElevationAngle]. Angle units are in degrees. The number of columns in ANGLE_IN must equal the number of members in the X array. The argument, LAXES, is a 3-by-3 matrix. Each column is a unit vector specifying the local coordinate system's orthonormal x, y, and z axes, respectively, with respect to the global coordinate system. Each columns is written in [x;y;z] form.

Y is a row array of struct type having the same size as X. Each struct contains the three reflected polarized fields, Y.X, Y.Y, and Y.Z. Each field corresponds to the x, y, and z component of the signal. Polarization components are measured with respect to the global coordinate system. Each field is a column vector representing one reflected signal.

Y = step(H,X,ANGLE_IN,ANGLE_OUT,LAXES), in addition, specifies the reflection angle, ANGLE_OUT, of the reflected signal when you set the Mode property to 'Bistatic'. This syntax applies only when the EnablePolarization property is set to true. ANGLE_OUT is a 2-row matrix representing the reflected direction of each signal. Each column of ANGLE_OUT specifies the reflected direction of the signal in the form [AzimuthAngle; ElevationAngle]. Angle units are in degrees. The number of columns in ANGLE_OUT must equal the number of members in the X array. The number of columns in ANGLE_OUT must equal the number of elements in the X array.

Y = step(H,X,ANGLE_IN,LAXES,SMAT) specifies SMAT as the scattering matrix. This syntax applies only when the EnablePolarization property is set to true. The input argument SMAT is a 2-by-2 matrix. You must set the ScatteringMatrixSource property 'Input port' to use SMAT.

Y = step(H,X,ANGLE_IN,LAXES,UPDATESMAT) specifies UPDATESMAT to indicate whether to update the scattering matrix when you set the Model property to 'Swerling1', 'Swerling2'', 'Swerling3', or 'Swerling4'. This syntax applies only when the EnablePolarization property is set to true. If UPDATESMAT is set to true, a scattering matrix value is generated. If UPDATESMAT is false, the previous scattering matrix value is used.

You can combine optional input arguments when their enabling properties are set. Optional inputs must be listed in the same order as the order of their enabling properties. For example,Y = step(H,X,ANGLE_IN,ANGLE_OUT,LAXES,SMAT,UPDATESMAT)

 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.

## Examples

Reflect a 250-Hz sine wave with unit amplitude off a target with a nonfluctuating RCS of 2 m2. The carrier frequency of the sine wave is 1 GHz.

### Reflection of Sine Wave

```htarget = phased.RadarTarget('Model','nonfluctuating',...
'MeanRCS',2,'OperatingFrequency',1e9);
t = linspace(0,1,1000);
sig = cos(2*pi*250*t)';
reflectedsig = step(htarget,sig);```

## Algorithms

The reflected signal is given by:

$Y=\sqrt{G}\cdot X$

where:

• X is the incoming signal

• G is the target gain factor, a dimensionless quantity given by

$G=\frac{4\pi \sigma }{{\lambda }^{2}}$

• σ is the mean RCS of the target

• λ is the wavelength of the incoming signal

Each element of the signal incident on the target is scaled by the gain factor.

For polarized waves, the scattering equation is more complicated. The single scalar signal, X, is replaced by a vector signal, (EH, EV), with horizontal and vertical components. A scattering matrix, S, replaces the scalar cross-section, σ. Through the scattering matrix, the incident horizontal and vertical polarized signals are converted into the reflected horizontal and vertical polarized signals

$\left[\begin{array}{c}{E}_{H}^{\left(scat\right)}\\ {E}_{V}^{\left(scat\right)}\end{array}\right]=\sqrt{\frac{4\pi }{{\lambda }^{2}}}\left[\begin{array}{cc}{S}_{HH}& {S}_{VH}\\ {S}_{HV}& {S}_{VV}\end{array}\right]\left[\begin{array}{c}{E}_{H}^{\left(inc\right)}\\ {E}_{V}^{\left(inc\right)}\end{array}\right]=\sqrt{\frac{4\pi }{{\lambda }^{2}}}\left[S\right]\left[\begin{array}{c}{E}_{H}^{\left(inc\right)}\\ {E}_{V}^{\left(inc\right)}\end{array}\right]$

For further details, see Mott [1] or Richards[2].

## References

[1] Mott, H. Antennas for Radar and Communications.John Wiley & Sons, 1992.

[2] Richards, M. A. Fundamentals of Radar Signal Processing. New York: McGraw-Hill, 2005.

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