# Documentation

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# phased.STAPSMIBeamformer System object

Package: phased

Sample matrix inversion (SMI) beamformer

## Description

The `SMIBeamformer` object implements a sample matrix inversion space-time adaptive beamformer. The beamformer works on the space-time covariance matrix.

To compute the space-time beamformed signal:

1. Define and set up your SMI beamformer. See Construction.

2. Call `step` to execute the SMI beamformer algorithm according to the properties of `phased.STAPSMIBeamformer`. The behavior of `step` is specific to each object in the toolbox.

 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.

## Construction

`H = phased.STAPSMIBeamformer` creates a sample matrix inversion (SMI) beamformer System object, `H`. The object performs the SMI space-time adaptive processing (STAP) on the input data.

`H = phased.STAPSMIBeamformer(Name,Value)` creates an SMI object, `H`, with each specified property Name set to the specified Value. You can specify additional name-value pair arguments in any order as (`Name1`,`Value1`,...,`NameN`,`ValueN`).

## Properties

`SensorArray`

Sensor array

Sensor array specified as an array System object belonging to the `phased` package. A sensor array can contain subarrays.

Default: `phased.ULA` with default property values

`PropagationSpeed`

Signal propagation speed

Specify the propagation speed of the signal, in meters per second, as a positive scalar.

Default: Speed of light

`OperatingFrequency`

System operating frequency

Specify the operating frequency of the system in hertz as a positive scalar. The default value corresponds to 300 MHz.

Default: `3e8`

`PRF`

Pulse repetition frequency

Specify the pulse repetition frequency (PRF) of the received signal in hertz as a scalar.

Default: `1`

`DirectionSource`

Source of targeting direction

Specify whether the targeting direction for the STAP processor comes from the `Direction` property of this object or from an input argument in `step`. Values of this property are:

 `'Property'` The `Direction` property of this object specifies the targeting direction. `'Input port'` An input argument in each invocation of `step` specifies the targeting direction.

Default: `'Property'`

`Direction`

Targeting direction

Specify the targeting direction of the SMI processor as a column vector of length 2. The direction is specified in the format of ```[AzimuthAngle; ElevationAngle]``` (in degrees). Azimuth angle should be between –180 and 180. Elevation angle should be between –90 and 90. This property applies when you set the `DirectionSource` property to `'Property'`.

Default: `[0; 0]`

`NumPhaseShifterBits`

Number of phase shifter quantization bits

The number of bits used to quantize the phase shift component of beamformer or steering vector weights. Specify the number of bits as a non-negative integer. A value of zero indicates that no quantization is performed.

Default: `0`

`DopplerSource`

Source of targeting Doppler

Specify whether the targeting Doppler for the STAP processor comes from the `Doppler` property of this object or from an input argument in `step`. Values of this property are:

 `'Property'` The `Doppler` property of this object specifies the Doppler. `'Input port'` An input argument in each invocation of `step` specifies the Doppler.

Default: `'Property'`

`Doppler`

Targeting Doppler frequency

Specify the targeting Doppler of the STAP processor as a scalar. This property applies when you set the `DopplerSource` property to `'Property'`.

Default: `0`

`WeightsOutputPort`

Output processing weights

To obtain the weights used in the STAP processor, set this property to `true` and use the corresponding output argument when invoking `step`. If you do not want to obtain the weights, set this property to `false`.

Default: `false`

`NumGuardCells`

Number of guarding cells

Specify the number of guard cells used in the training as an even integer. This property specifies the total number of cells on both sides of the cell under test.

Default: `2`, indicating that there is one guard cell at both the front and back of the cell under test

`NumTrainingCells`

Number of training cells

Specify the number of training cells used in the training as an even integer. Whenever possible, the training cells are equally divided before and after the cell under test.

Default: `2`, indicating that there is one training cell at both the front and back of the cell under test

## Methods

 clone Create space-time adaptive SMI beamformer object with same property values getNumInputs Number of expected inputs to step method getNumOutputs Number of outputs from step method isLocked Locked status for input attributes and nontunable properties release Allow property value and input characteristics changes step Perform SMI STAP processing on input data

## Examples

Process the data cube using an SMI processor. The weights are calculated for the 71st cell of a collected data cube pointing to the direction of [45; –35] degrees and the Doppler of 12980 Hz.

```load STAPExampleData; % load data Hs = phased.STAPSMIBeamformer('SensorArray',STAPEx_HArray,... 'PRF',STAPEx_PRF,... 'PropagationSpeed',STAPEx_PropagationSpeed,... 'OperatingFrequency',STAPEx_OperatingFrequency,... 'NumTrainingCells',100,... 'WeightsOutputPort',true,... 'DirectionSource','Input port',... 'DopplerSource','Input port'); [y,w] = step(Hs,STAPEx_ReceivePulse,71,[45; -35],12980); Hresp = phased.AngleDopplerResponse(... 'SensorArray',Hs.SensorArray,... 'OperatingFrequency',Hs.OperatingFrequency,... 'PRF',Hs.PRF,... 'PropagationSpeed',Hs.PropagationSpeed); plotResponse(Hresp,w);```

## Algorithms

The optimum beamformer weights are

`$w=k{R}^{-1}v$`

where:

• k is a scalar

• R represents the space-time covariance matrix

• v indicates the space-time steering vector

Because the space-time covariance matrix is unknown, you must estimate that matrix from the data. The sample matrix inversion (SMI) algorithm estimates the covariance matrix by designating a number of range gates to be training cells. Because you use the training cells to estimate the interference covariance, these cells should not contain target returns. To prevent target returns from contaminating the estimate of the interference covariance, you can specify insertion of a number of guard cells before and after the designated target cell.

To use the general algorithm for estimating the space-time covariance matrix:

1. Assume you have a M-by-N-by-K matrix. M represents the number of slow-time samples, and N is the number of array sensors. K is the number of training cells (range gates for training). Also assume that the number of training cells is an even integer and that you can designate K/2 training cells before and after the target range gate excluding the guard cells. Reshape the M-by-N-by-K matrix into a MN-by-K matrix by letting X denote the MN-by-K matrix.

2. Estimate the space-time covariance matrix as

`$\frac{1}{K}X{X}^{H}$`
3. Invert the space-time covariance matrix estimate.

4. Obtain the beamforming weights by multiplying the sample space-time covariance matrix inverse by the space-time steering vector.

## References

[1] Guerci, J. R. Space-Time Adaptive Processing for Radar. Boston: Artech House, 2003.

[2] Ward, J. "Space-Time Adaptive Processing for Airborne Radar Data Systems," Technical Report 1015, MIT Lincoln Laboratory, December, 1994.