phased.MUSICEstimator2D

Estimate 2D direction of arrival using narrowband MUSIC algorithm

Description

The phased.MUSICEstimator2D System object™ implements the narrowband multiple signal classification (MUSIC) algorithm for 2-D planar or 3-D arrays such as a uniform rectangular array (URA). MUSIC is a high-resolution direction-finding algorithm capable of resolving closely-spaced signal sources. The algorithm is based on the eigenspace decomposition of the sensor covariance matrix.

To estimate directions of arrival (DOA):

1. Create the phased.MUSICEstimator2D 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

estimator = phased.MUSICEstimator2D

estimator = phased.MUSICEstimator2D(Name,Value)

Description

estimator = phased.MUSICEstimator2D creates a MUSIC DOA estimator System object, estimator.

estimator = phased.MUSICEstimator2D(Name,Value) creates a System object, estimator, 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

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.

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

OperatingFrequency — Operating frequency

300e6 (default) | positive scalar

Operating frequency, specified as a positive scalar. Units are in Hz.

Example: 1e9

Data Types: single | double

ForwardBackwardAveraging — Enable forward-backward averaging

false (default) | true

Enable forward-backward averaging, specified as false or true. Set this property to true to use forward-backward averaging to estimate the covariance matrix for sensor arrays with a conjugate symmetric array manifold.

Data Types: logical

AzimuthScanAngles — Azimuth scan angles

[-90:90] (default) | real-valued row vector

Azimuth scan angles, specified as a or real-valued row vector. Angle units are in degrees. The angle values must lie between –180° and 180°, inclusive, and be in ascending order.

Example: [-30:20]

Data Types: single | double

ElevationScanAngles — Elevation scan angles

0 (default) | real-valued row vector

Elevation scan angles, specified as a real-valued row vector. Angle units are in degrees. The angle values must lie between –90° and 90°, inclusive, and be in ascending order.

Example: [-70:75]

Data Types: single | double

DOAOutputPort — Enable directions of arrival output

false (default) | true

Option to enable directions-of-arrival (DOA) output, specified as false or true. To obtain the DOA of signals, set this property to true. The DOAs are returned in the second output argument when the object is executed.

Data Types: logical

NumSignalsSource — Source of number of signals

'Auto' (default) | 'Property'

Source of the number of arriving signals, specified as 'Auto' or 'Property'.

• 'Auto' — The System object estimates the number of arriving signals using the method specified in the NumSignalsMethod property.

• 'Property' — Specify the number of arriving signals using the NumSignals property.

Data Types: char

NumSignalsMethod — Method used to estimate number of arriving signals

'AIC' (default) | 'MDL'

Method used to estimate the number of arriving signals, specified as 'AIC' or 'MDL'.

• 'AIC' — Akaike Information Criterion

• 'MDL' — Minimum Description Length criterion

Dependencies

To enable this property, set NumSignalsSource to 'Auto'.

Data Types: char

NumSignals — Number of arriving signals

1 (default) | positive integer

Number of arriving signals for DOA estimation, specified as a positive integer.

Example: 3

Dependencies

To enable this property, set NumSignalsSource to 'Property'.

Data Types: single | double

Usage

Syntax

spectrum = estimator(X)

[spectrum,doa] = estimator(X)

Description

spectrum = estimator(X) returns the 2-D MUSIC spectrum of a signal specified in X.

[spectrum,doa] = estimator(X) also returns the signal directions of arrival angles, doa. To use this syntax, set the DOAOutputPort property to true.

Input Arguments

estimator — 2-D MUSIC estimator

phased.MUSICEstimator2D System object

2-D MUSIC estimator, specified as a phased.MUSICEstimator2D System object.

X — Received signal

M-by-N complex-valued matrix

Received signal, specified as an M-by-N complex-valued matrix. The quantity M is the number of sample values (snapshots) contained in the signal and N is the number of sensor elements in the array.

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.

Example: [[0;1;2;3;4;3;2;1;0],[1;2;3;4;3;2;1;0;0]]

Data Types: single | double
Complex Number Support: Yes

Output Arguments

spectrum — 2-D MUSIC spatial spectrum

nonnegative, real-valued K-length column vector

2-D MUSIC spatial spectrum, returned as a nonnegative, real-valued K-length column vector representing the magnitude of the estimated MUSIC spatial spectrum. Each entry corresponds to an angle specified by the AzimuthScanAngles and ElevationScanAngles properties.

doa — Directions of arrival

real-valued 2-by-L matrix

Directions of arrival of the signals, returned as a real-valued 2-by-L matrix. The direction of arrival angle is defined by the azimuth and elevation angles of the source with respect to the array local coordinate system. The first row of the matrix contains the azimuth angles and the second row contains the elevation angles. Angle units are in degrees. L is the number of signals specified by the NumSignals property or derived using the method specified by the NumSignalsMethod property.

Dependencies

To enable this output argument, set the DOAOutputPort property to true.

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)

Specific to phased.MUSICEstimator2D

plotSpectrum

Plot 2-D MUSIC spectrum

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

Estimate DOAs of Two Signals

Assume that two sinusoidal waves of frequencies 450 Hz and 600 Hz strike a URA from two different directions. Signals arrive from -37° azimuth, 0° elevation and 17° azimuth, 20° elevation. Use 2-D MUSIC to estimate the directions of arrival of the two signals. The array operating frequency is 150 MHz and the signal sampling frequency is 8 kHz.

f1 = 450.0;
f2 = 600.0;
doa1 = [-37;0];
doa2 = [17;20];
fc = 150e6;
c = physconst('LightSpeed');
lam = c/fc;
fs = 8000;

Create the URA with default isotropic elements. Set the frequency response range of the elements.

array = phased.URA('Size',[11 11],'ElementSpacing',[lam/2 lam/2]);
array.Element.FrequencyRange = [50.0e6 500.0e6];

Create the two signals and add random noise.

t = (0:1/fs:1).';
x1 = cos(2*pi*t*f1);
x2 = cos(2*pi*t*f2);
x = collectPlaneWave(array,[x1 x2],[doa1,doa2],fc);
noise = 0.1*(randn(size(x))+1i*randn(size(x)));

Create and execute the 2-D MUSIC estimator to find the directions of arrival.

estimator = phased.MUSICEstimator2D('SensorArray',array,...
    'OperatingFrequency',fc,...
    'NumSignalsSource','Property',...
    'DOAOutputPort',true,'NumSignals',2,...
    'AzimuthScanAngles',-50:.5:50,...
    'ElevationScanAngles',-30:.5:30);
[~,doas] = estimator(x + noise)

doas = 2×2

   -37    17
     0    20

The estimated DOAs exactly match the true DOAs.

Plot the 2-D spatial spectrum.

plotSpectrum(estimator);

Estimate DOAs of Two Signals at Disk Array

Assume that two sinusoidal waves of frequencies 1.6 kHz and 1.8 kHz strike a disk array from two different directions. The spacing between elements of the disk is 1/2 wavelength. Signals arrive from -31° azimuth, -11° elevation and 35° azimuth, 55° elevation. Use 2-D MUSIC to estimate the directions of arrival of the two signals. The array operating frequency is 300 MHz and the signal sampling frequency is 8 kHz.

f1 = 1.6e3;
f2 = 1.8e3;
doa1 = [-31;-11];
doa2 = [35;55];
fc = 300e6;
c = physconst('LightSpeed');
lam = c/fc;
fs = 8.0e3;

Create a conformal array with default isotropic elements. First, create a URA to get the element positions.

uraarray = phased.URA('Size',[21 21],'ElementSpacing',[lam/2 lam/2]);
pos = getElementPosition(uraarray);

Extract a subset of these to form an inscribed disk.

radius = 10.5*lam/2;
pos(:,sum(pos.^2) > radius^2) = [];

Then, create the conformal array using these positions.

confarray = phased.ConformalArray('ElementPosition',pos);
viewArray(confarray)

Set the frequency response range of the elements.

confarray.Element.FrequencyRange = [50.0e6 600.0e6];

Create the two signals and add random noise.

t = (0:1/fs:1.5).';
x1 = cos(2*pi*t*f1);
x2 = cos(2*pi*t*f2);
x = collectPlaneWave(confarray,[x1 x2],[doa1,doa2],fc);
noise = 0.1*(randn(size(x)) + 1i*randn(size(x)));

Create and execute the 2-D MUSIC estimator to find the directions of arrival.

estimator = phased.MUSICEstimator2D('SensorArray',confarray,...
    'OperatingFrequency',fc,...
    'NumSignalsSource','Property',...
    'DOAOutputPort',true,'NumSignals',2,...
    'AzimuthScanAngles',-60:.1:60,...
    'ElevationScanAngles',-60:.1:60);
[~,doas] = estimator(x + noise)

doas = 2×2

    35   -31
    55   -11

The estimated DOAs exactly match the true DOAs.

Plot the 2-D spatial spectrum.

plotSpectrum(estimator);

Algorithms

MUSIC Algorithm

MUSIC stands for MUltiple SIgnal Classification. MUSIC is a high-resolution direction-finding algorithm that estimates directions of arrival (DOA) of signals at an array from the covariance matrix of array sensor data. MUSIC belongs to the subspace-decomposition family of direction-finding algorithms. Unlike conventional beamforming, MUSIC can resolve closely-spaced signal sources.

Based on eigenspace decomposition of the sensor covariance matrix, MUSIC divides the observation space into orthogonal signal and noise subspaces. Eigenvectors corresponding to the largest eigenvalues span the signal subspace. Eigenvectors corresponding to the smaller eigenvalues span the noise subspace. Because arrival (or steering) vectors lie in the signal subspace, they are orthogonal to the noise subspace. The arrival vectors depend on the direction of arrival of a signals. For a 2-D or 3-D array. the directions are determined by the azimuth and elevation of the sources. By searching over a grid of arrival angles, the algorithm finds those arrival vectors whose projection into the noise subspace is zero or at least very small.

MUSIC requires that the number of source signals is known. The algorithm degrades if the number of specified sources does not match the actual number of sources. Generally, you must provide an estimate of the number of sources or use one of the built-in source number estimation methods. For a description of the methods used to estimate the number of sources, see the aictest or mdltest functions.

In place of the true sensor covariance matrix, the algorithm computes the sample covariance matrix from the sensor data. MUSIC applies to noncoherent signals but can be extended to coherent signals using forward-backward averaging techniques. For a high-level description of the algorithm, see MUSIC Super-Resolution DOA Estimation.

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

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

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