phased.GSCBeamformer

Generalized sidelobe canceler beamformer

Description

The phased.GSCBeamformer System object™ implements a generalized sidelobe cancellation (GSC) beamformer. A GSC beamformer splits the incoming signals into two channels. One channel goes through a conventional beamformer path and the second goes into a sidelobe canceling path. The algorithm first pre-steers the array to the beamforming direction and then adaptively chooses filter weights to minimize power at the output of the sidelobe canceling path. The algorithm uses least mean squares (LMS) to compute the adaptive weights. The final beamformed signal is the difference between the outputs of the two paths.

To compute the beamformed signal:

1. Create the phased.GSCBeamformer object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

beamformer = phased.GSCBeamformer

beamformer = phased.GSCBeamformer(Name,Value)

Description

beamformer = phased.GSCBeamformer creates a GSC beamformer System object, beamformer, with default property values.

beamformer = phased.GSCBeamformer(Name,Value) creates a GSC beamformer object, beamformer, 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). Enclose each property name in single quotes.

Example: beamformer = phased.GSCBeamformer('SensorArray',phased.ULA('NumElements',20),'SampleRate',300e3) sets the sensor array to a uniform linear array (ULA) with default ULA property values except for the number of elements. The beamformer has a sample rate of 300 kHz.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

SensorArray — Sensor array

phased.ULA array with default array properties (default) | Phased Array System Toolbox™ array System object

Sensor array, specified as a Phased Array System Toolbox array System object. The array cannot contain subarrays.

Example: phased.URA

PropagationSpeed — Signal propagation speed

physconst('LightSpeed') (default) | real-valued positive scalar

Signal propagation speed, specified as a real-valued positive scalar. Units are in meters per second. The default propagation speed is the value returned by physconst('LightSpeed').

Example: 3e8

Data Types: single | double

SampleRate — Sample rate of signal

1e6 (default) | positive scalar

Sample rate of signal, specified as a positive scalar. Units are in Hz. The System object uses this quantity to calculate the propagation delay in units of samples.

Example: 1e6

Data Types: single | double

FilterLength — FIR filter length

1 (default) | positive integer

Length of the signal path FIR filters, specified as a positive integer. This property determines the adaptive filter size for the sidelobe canceling path. The FIR filter for the conventional beamforming path is a delta function of the same length.

Example: 4

Data Types: double | single

LMSStepSize — Adaptive filter step size factor

0.1 (default) | positive real-valued scalar

The adaptive filter step size factor, specified as a positive real-valued scalar. This quantity, when divided by the total power in the sidelobe canceling path, sets the actual adaptive filter step size that is used in the LMS algorithm.

Data Types: double | single

DirectionSource — Source of beamforming direction

'Property' (default) | 'Input port'

Source of beamforming direction, specified as 'Property' or 'Input port'. Specify whether the beamforming direction comes from the Direction property of this object or from the input argument, ANG. Values of this property are:

'Property'	Specify the beamforming direction using the Direction property.
'Input port'	Specify the beamforming direction using the input argument, ANG.

Data Types: char

Direction — Beamforming directions

[0;0] (default) | real-valued 2-by-1 vector | real-valued 2-by-L matrix

Beamforming directions, specified as a real-valued 2-by-1 vector or a real-valued 2-by-L matrix. For a matrix, each column specifies a different beamforming direction. Each column has the form [AzimuthAngle;ElevationAngle]. Azimuth angles must lie between –180° and 180° and elevation angles must lie between –90° and 90°. All angles are defined with respect to the local coordinate system of the array. Units are in degrees.

Example: [40;30]

Dependencies

To enable this property, set the DirectionSource property to 'Property'.

Data Types: single | double

Usage

Syntax

Y = beamformer(X)

Y = beamformer(X,ANG)

Description

Y = beamformer(X) performs GSC beamforming on the input, X, and returns the beamformed output, Y.

Y = beamformer(X,ANG) uses ANG as the beamforming direction. To use this syntax, set the DirectionSource property to 'Input port'.

Input Arguments

X — Input signal

complex-valued M-by-N matrix

Input signal, specified as a complex-valued M-by-N matrix. M is the signal length and N is the number of array elements specified in the SensorArray property. M must be larger than the length of the filter specified by the FilterLength property.

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.

Data Types: double | single
Complex Number Support: Yes

ANG — Beamforming directions

[0;0] (default) | real-valued 2-by-1 column vector | real-valued 2-by-L matrix

Beamforming directions, specified as a real-valued 2-by-1 column vector The vector has the form [AzimuthAngle;ElevationAngle]. Units are in degrees. The azimuth angle must lie between –180° and 180°, and the elevation angle must lie between –90° and 90°.

Example: [40;10]

Dependencies

To enable this argument, set the DirectionSource property to 'Input port'.

Data Types: double

Output Arguments

Y — Beamformed output

complex-valued 1-by-M vector

Beamformed output, returned as a complex-valued 1-by-Mvector, where M is the number of rows of the input X.

Data Types: double | single
Complex Number Support: Yes

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Generalized Sidelobe Cancellation on Uniform Linear Array

Create a GSC beamformer for a 11-element acoustic array in air. A chirp signal is incident on the array at $$-50^{\circ }$$ in azimuth and $$0^{\circ }$$ in elevation. Compare the GSC beamformed signal to a Frost beamformed signal. The signal propagation speed is 340 m/s and the sample rate is 8 kHz.

Create the microphone and array System objects. The array element spacing is one-half wavelength. Set the signal frequency to the one-half the Nyquist frequency.

c = 340.0;
fs = 8.0e3;
fc = fs/2;
lam = c/fc;
transducer = phased.OmnidirectionalMicrophoneElement('FrequencyRange',[20 20000]);
array = phased.ULA('Element',transducer,'NumElements',11,'ElementSpacing',lam/2);

Simulate a chirp signal with a 500 Hz bandwidth.

t = 0:1/fs:.5;
signal = chirp(t,0,0.5,500);

Create an incident wave arriving at the array. Add gaussian noise to the wave.

collector = phased.WidebandCollector('Sensor',array,'PropagationSpeed',c, ...
    'SampleRate',fs,'ModulatedInput',false,'NumSubbands',512);
incidentAngle = [-50;0];
signal = collector(signal.',incidentAngle);
noise = 0.5*randn(size(signal));
recsignal = signal + noise;

Perform Frost beamforming at the actual incident angle.

frostbeamformer = phased.FrostBeamformer('SensorArray',array,'PropagationSpeed', ...
    c,'SampleRate',fs,'Direction',incidentAngle,'FilterLength',15);
yfrost = frostbeamformer(recsignal);

Perform GSC beamforming and plot the beamformer output against the Frost beamformer output. Also plot the nonbeamformed signal arriving at the middle element of the array.

gscbeamformer = phased.GSCBeamformer('SensorArray',array, ...
    'PropagationSpeed',c,'SampleRate',fs,'Direction',incidentAngle, ...
    'FilterLength',15);
ygsc = gscbeamformer(recsignal);
plot(t*1000,recsignal(:,6),t*1000,yfrost,t,ygsc)
xlabel('Time (ms)')
ylabel('Amplitude')

Zoom in on a small portion of the output.

idx = 1000:1300;
plot(t(idx)*1000,recsignal(idx,6),t(idx)*1000,yfrost(idx),t(idx)*1000,ygsc(idx))
xlabel('Time (ms)')
legend('Received signal','Frost beamformed signal','GSC beamformed signal')

Generalized Sidelobe Cancellation in Two Directions

Create a GSC beamformer for an 11-element acoustic array in air. A chirp signal is incident on the array at $$-50^{\circ }$$ in azimuth and $$0^{\circ }$$ in elevation. Compute the beamformed signal in the direction of the incident wave and in another direction. Compare the two beamformed outputs. The signal propagation speed is 340 m/s and the sample rate is 8 kHz. Create the microphone and array System objects. The array element spacing is one-half wavelength. Set the signal frequency to the one-half the Nyquist frequency.

c = 340.0;
fs = 8.0e3;
fc = fs/2;
lam = c/fc;
transducer = phased.OmnidirectionalMicrophoneElement('FrequencyRange',[20 20000]);
array = phased.ULA('Element',transducer,'NumElements',11,'ElementSpacing',lam/2);

Simulate a chirp signal with a 500 Hz bandwidth.

t = 0:1/fs:0.5;
signal = chirp(t,0,0.5,500);

Create an incident wavefield hitting the array.

collector = phased.WidebandCollector('Sensor',array,'PropagationSpeed',c, ...
    'SampleRate',fs,'ModulatedInput',false,'NumSubbands',512);
incidentAngle = [-50;0];
signal = collector(signal.',incidentAngle);
noise = 0.1*randn(size(signal));
recsignal = signal + noise;

Perform GSC beamforming and plot the beamformer outputs. Also plot the nonbeamformed signal arriving at the middle element of the array.

gscbeamformer = phased.GSCBeamformer('SensorArray',array, ...
    'PropagationSpeed',c,'SampleRate',fs,'DirectionSource','Input port', ...
    'FilterLength',5);
ygsci = gscbeamformer(recsignal,incidentAngle);
ygsco = gscbeamformer(recsignal,[20;30]);
plot(t*1000,recsignal(:,6),t*1000,ygsci,t*1000,ygsco)
xlabel('Time (ms)')
ylabel('Amplitude')
legend('Received signal at element','GSC beamformed signal (incident direction)', ...
    'GSC beamformed signal (other direction)','Location','southeast')

Zoom in on a small portion of the output.

idx = 1000:1300;
plot(t(idx)*1000,recsignal(idx,6),t(idx)*1000,ygsci(idx),t(idx)*1000,ygsco(idx))
xlabel('Time (ms)')
legend('Received signal at element','GSC beamformed signal (incident direction)', ...
    'GSC beamformed signal (other direction)','Location','southeast')

Algorithms

Generalized Sidelobe Cancellation

The generalized sidelobe canceler (GSC) is an efficient implementation of a linear constraint minimum variance (LCMV) beamformer. LCMV beamforming minimizes the output power of an array while preserving the power in one or more specified directions. This type of beamformer is called a constrained beamformer. You can compute exact weights for the constrained beamformer but the computation is costly when the number of elements is large. The computation requires the inversion of a large spatial covariance matrix. The GSC formulation converts the adaptive constrained optimization LCMV problem into an adaptive unconstrained problem, which simplifies the implementation.

In the GSC algorithm, incoming sensor data is split into two signal paths as shown in the block diagram. The upper path is a conventional beamformer. The lower path is an adaptive unconstrained beamformer whose purpose is to minimize the GSC output power. The GSC algorithm consists of these steps:

1. Presteer the element sensor data by time-shifting the incoming signals. Presteering time-aligns all sensor element signals. The time shifts depend on the arrival angle of the signal.

2. Pass the presteered signals through the upper path into a conventional beamformer with fixed weights, w_conv.

3. Also pass the presteered signals through the lower path into the blocking matrix, B. The blocking matrix is orthogonal to the signal and removes the signal from the lower path.

4. Filter the lower path signals through a bank of FIR filters. The FilterLength property sets the length of the filters. The filter coefficients are the adaptive filter weights, w_ad.

5. Compute the difference between the upper and lower signal paths. This difference is the beamformed GSC output.

6. Feed the beamformed output back into the filter. The filter adapts its weights using a least mean-square (LMS) algorithm. The actual adaptive LMS step size is equal to the value of the LMSStepSize property divided by the total signal power.

For more information, see [1].

Data Precision

This System object supports single and double precision for input data, properties, and arguments. If the input data X is single precision, the output data is single precision. If the input data X is double precision, the output data is double precision. The precision of the output is independent of the precision of the properties and other arguments.

References

[1] Griffiths, L. J., and Charles W. Jim. "An alternative approach to linearly constrained adaptive beamforming." IEEE Transactions on Antennas and Propagation, 30.1 (1982): 27-34.

[2] Van Trees, H. Optimum Array Processing. New York: Wiley-Interscience, 2002.

[3] Johnson, D.H., and Dan E. Dudgeon, Array Signal Processing, Englewood Cliffs: Prentice-Hall, 1993.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Requires dynamic memory allocation. See Limitations for System Objects that Require Dynamic Memory Allocation.

• See System Objects in MATLAB Code Generation (MATLAB Coder).

• This System object supports single and double precision for input data, properties, and arguments. If the input data X is single precision, the output data is single precision. If the input data X is double precision, the output data is double precision. The precision of the output is independent of the precision of the properties and other arguments.

Version History

Introduced in R2016b