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# step

System object: phased.RadarTarget
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

 Note:   Starting in R2016b, instead of using the `step` method to perform the operation defined by the System object™, you can call the object with arguments, as if it were a function. For example, ```y = step(obj,x)``` and `y = obj(x)` perform equivalent operations.
````Y = step(H,X)` returns the reflected signal `Y` due to the incident signal `X`. The argument `X` is a complex-valued N-by-1 column vector or N-by-M matrix. The value M is the number of signals. Each signal corresponds to a different target. The value N is the number of samples in each signal. 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`. If you specify M incident signals, you can specify the radar cross-section as a scalar or as a 1-by-M vector. For a scalar, the same value will be applied to all signals.The size of the first dimension of this input matrix can vary to simulate a changing signal length, such as a pulse waveform with variable pulse repetition frequency.```
````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'` and set `Model` to `'Nonfluctuating'`. The value of `MEANRCS` must be a nonnegative scalar or 1-by-M row vector for multiple targets. 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`. In this case, the value of the `MeanRCS` property is used as the radar cross-section (RCS) value.```
````Y = step(H,X,MEANRCS,UPDATERCS)` lets you can combine optional input arguments when their enabling properties are set. In this syntax, `MeanRCSSource` is set to `'Input port'` and `Model` is set to one of the `Swerling` models. This syntax applies only when the `EnablePolarization` property is set to `false`. For this syntax, changes in `MEANRCS` will be ignored after the first call to the `step` method.```
````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 1-by-M 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-by-M 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 signals in the `X` array. The argument, `LAXES,` is a 3-by-3 matrix. The columns are unit vectors specifying the local coordinate system's orthonormal x, y, and z axes, respectively, with respect to the global coordinate system. Each column 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.The size of the first dimension of the matrix fields within the `struct` can vary to simulate a changing signal length such as a pulse waveform with variable pulse repetition frequency.```
``` `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.```
````Y = step(H,X,ANGLE_IN,ANGLE_OUT,LAXES,SMAT,UPDATESMAT)`. 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.```
 Note:   The object performs an initialization the first time the `step` method is executed. This initialization locks nontunable properties (MATLAB) 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

expand all

Create two sinusoidal signals and compute the value of the reflected signals from targets having radar cross section of and , respectively. Set the radar cross sections in the `step` method by choosing `Input port` for the value of the `MeanRCSSource` property. Set the radar operating frequency to 600 MHz.

```sRadarTarget = phased.RadarTarget('Model','Nonfluctuating',... 'MeanRCSSource','Input port',... 'OperatingFrequency',600e6); t = linspace(0,1,1000); x = [cos(2*pi*250*t)',10*sin(2*pi*250*t)']; y = step(sRadarTarget,x,[5,10]); disp(y(1:3,1:2)) ```
``` 15.8643 0 -0.0249 224.3546 -15.8642 -0.7055 ```

## Algorithms

For a narrowband nonpolarized signal, the reflected signal, Y, is

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

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 radar cross-section (RCS) of the target.

• λ is the wavelength of the incoming signal.

The incident signal on the target is scaled by the square root of the gain factor.

For narrowband polarized waves, the single scalar signal, X, is replaced by a vector signal, (EH, EV), with horizontal and vertical components. The 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.

## See Also

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