# step

Package: phased

Reflect incoming signal

## 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 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.

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 object 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

expand all

Create two sinusoidal signals and compute the value of the reflected signals from targets having radar cross sections of $5{m}^{2}$ and $10{m}^{2}$, 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.

'MeanRCSSource','Input port',...
'OperatingFrequency',600e6);
t = linspace(0,1,1000);
x = [cos(2*pi*250*t)',10*sin(2*pi*250*t)'];
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.