phased.MUSICEstimator

Estimate direction of arrival using narrowband MUSIC algorithm for ULA

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Description

Thephased.MUSICEstimatorSystem object™ implements the narrowband multiple signal classification (MUSIC) algorithm for uniform linear arrays (ULA). MUSIC is a high-resolution direction-finding algorithm capable of resolving closely-spaced signal sources. The algorithm is based on eigenspace decomposition of the sensor spatial covariance matrix.

To estimate directions of arrival (DOA):

Define and set up aphased.MUSICEstimatorSystem object. SeeConstruction.
Call thestepmethod to estimate the DOAs according to the properties ofphased.MUSICEstimator.

Note

Alternatively, instead of using thestep方法定义的操作来执行the System object, you can call the object with arguments, as if it were a function. For example,y = step(obj,x)andy = obj(x)perform equivalent operations.

Construction

estimator= phased.MUSICEstimatorcreates a MUSIC DOA estimator System object,estimator.

estimator= phased.MUSICEstimator(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

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`SensorArray`—ULA sensor array
`phased.ULA`System object(default)

ULA sensor array, specified as aphased.ULASystem object. If you do not specify any name-value pair properties for the ULA sensor array, the default properties of the array are used.

`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 byphysconst('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 asfalseortrue. Set this property totrueto use forward-backward averaging to estimate the covariance matrix for sensor arrays with a conjugate symmetric array manifold.

Data Types:logical

`ScanAngles`—Broadside scan angles
`[-90:90]`(default) |real-valuedK-length vector

Broadside scan angles, specified as a real-valued vector. Units are in degrees. Broadside angles are between the search direction and the ULA array axis. The angles lie between –90° and 90°, inclusive. Specify the angles in increasing value.

Example:[-20:20]

Data Types:single|double

`DOAOutputPort`—Enable directions of arrival output
`false`(default) |`true`

Option to enable directions-of-arrival (DOA) output, specified asfalseortrue. To obtain the DOA of signals, set this property totrue. 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 theNumSignalsMethodproperty.
'Property'— Specify the number of arriving signals using theNumSignalsproperty.

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, setNumSignalsSourceto'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, setNumSignalsSourceto'Property'.

Data Types:single|double

`SpatialSmoothing`—Enable spatial smoothing
0(default) |nonnegative integer

Option to enable spatial smoothing, specified as a nonnegative integer. Use spatial smoothing to compute the arrival directions of coherent signals. A value of zero specifies no spatial smoothing. A positive value represents the number of subarrays used to compute the smoothed (averaged) source covariance matrix. Each increment in this value lets you handle one additional coherent source, but reduces the effective number of array elements by one. The length of the smoothing aperture,L, depends on the array length,M, and the averaging number,K, byL = M – K + 1. The maximum value ofKisM – 2.

Example:5

Data Types:double

Methods

plotSpectrum	Plot MUSIC spectrum
reset	Reset states ofSystem object
step	Estimate direction of arrival using MUSIC

Common to All System Objects
`release`	Allow System object property value changes

Examples

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Plot MUSIC Spectrum of Two Signals Arriving at ULA

Open Live Script

Estimate the DOAs of two signals received by a standard 10-element ULA having an element spacing of 1 meter. Then plot the MUSIC spectrum.

Note:You can replace each call to the function with the equivalentstepsyntax. For example, replacemyObject(x)withstep(myObject,x).

Create the ULA array. The antenna operating frequency is 150 MHz.

fc = 150.0e6; array = phased.ULA('NumElements',10,'ElementSpacing',1.0);

Create the arriving signals at the ULA. The true direction of arrival of the first signal is 10° in azimuth and 20° in elevation. The direction of the second signal is 60° in azimuth and -5° in elevation.

fs = 8000.0; t = (0:1/fs:1).'; sig1 = cos(2*pi*t*300.0); sig2 = cos(2*pi*t*400.0); sig = collectPlaneWave(array,[sig1 sig2],[10 20; 60 -5]',fc); noise = 0.1*(randn(size(sig)) + 1i*randn(size(sig)));

Estimate the DOAs.

estimator = phased.MUSICEstimator('SensorArray',array,...'OperatingFrequency',fc,...'DOAOutputPort',true,'NumSignalsSource','Property',...'NumSignals',2); [y,doas] = estimator(sig + noise); doas = broadside2az(sort(doas),[20 -5])

doas =1×29.5829 60.3813

Plot the MUSIC spectrum.

plotSpectrum(estimator,'NormalizeResponse',真正的)

Figure contains an axes object. The axes object with title MUSIC Spatial Spectrum contains an object of type line. This object represents 1 GHz.

Compute DOA of Two Nearby Signals Using MUSIC

Open Live Script

First, estimate the DOAs of two signals received by a standard 10-element ULA having an element spacing of one-half wavelength.Then, plot the spatial spectrum.

Note:You can replace each call to the function with the equivalentstepsyntax. For example, replacemyObject(x)withstep(myObject,x).

The antenna operating frequency is 150 MHz. The arrival directions of the two signals are separated by 2°. The direction of the first signal is 30° azimuth and 0° elevation. The direction of the second signal is 32° azimuth and 0° elevation. Estimate the number of signals using the Minimum Description Length (MDL) criterion.

Create the signals arriving at the ULA.

fs = 8000; t = (0:1/fs:1).'; f1 = 300.0; f2 = 600.0; sig1 = cos(2*pi*t*f1); sig2 = cos(2*pi*t*f2); fc = 150.0e6; c = physconst('LightSpeed'); lam = c/fc; array = phased.ULA('NumElements',10,'ElementSpacing',0.5*lam); sig = collectPlaneWave(array,[sig1 sig2],[30 0; 32 0]',fc); noise = 0.1*(randn(size(sig)) + 1i*randn(size(sig)));

Estimate the DOAs.

estimator = phased.MUSICEstimator('SensorArray',array,...'OperatingFrequency',fc,'DOAOutputPort',true,...'NumSignalsSource','Auto','NumSignalsMethod','MDL'); [y,doas] = estimator(sig + noise); doas = broadside2az(sort(doas),[0 0])

doas =1×230.0000 32.0000

Plot the MUSIC spectrum.

plotSpectrum(estimator,'NormalizeResponse',真正的)

Figure contains an axes object. The axes object with title MUSIC Spatial Spectrum contains an object of type line. This object represents 1 GHz.

Algorithms

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MUSIC Algorithm

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. For ULAs, arrival vectors are functions of the broadside direction angles of the sources. The algorithm searches a grid of arrival angles to find the arrival vectors that have zero or small projections into the noise subspace. These angles are the directions of the sources.

MUSIC requires that the number of source signals is known. If the number of specified sources does not match the actual number of sources, the algorithm degrades. 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 theaictestormdltestfunctions.

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 usingspatial smoothingand/orforward-backward averagingtechniques. For a high-level description of the algorithm, see音乐超分辨率DOA估计.

Data Precision

This System object supports single and double precision for input data, properties, and arguments. If the input dataXis single precision, the output data is single precision. If the input dataXis 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:

SeeSystem Objects in MATLAB Code Generation(MATLAB Coder).

Version History

Introduced in R2016b

phased.MUSICEstimator

Description

Construction

Properties

`SensorArray`—ULA sensor array
`phased.ULA`System object(default)

`PropagationSpeed`—Signal propagation speed
`physconst('LightSpeed')`(default) |real-valued positive scalar

`OperatingFrequency`—Operating frequency
`300e6`(default) |positive scalar

`ForwardBackwardAveraging`—Enable forward-backward averaging
`false`(default) |`true`

`ScanAngles`—Broadside scan angles
`[-90:90]`(default) |real-valuedK-length vector

`DOAOutputPort`—Enable directions of arrival output
`false`(default) |`true`

`NumSignalsSource`—Source of number of signals
`'Auto'`(default) |`'Property'`

`NumSignalsMethod`—Method used to estimate number of arriving signals
`'AIC'`(default) |`'MDL'`

Dependencies

`NumSignals`—Number of arriving signals
`1`(default) |positive integer

Dependencies

`SpatialSmoothing`—Enable spatial smoothing
0(default) |nonnegative integer

Methods

Examples

Plot MUSIC Spectrum of Two Signals Arriving at ULA

Compute DOA of Two Nearby Signals Using MUSIC

Algorithms

MUSIC Algorithm

Data Precision

References

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

See Also

Functions

Objects

Topics

phased.MUSICEstimator

Description

Construction

Properties

SensorArray—ULA sensor arrayphased.ULASystem object(default)

PropagationSpeed—Signal propagation speedphysconst('LightSpeed')(default) |real-valued positive scalar

OperatingFrequency—Operating frequency300e6(default) |positive scalar

ForwardBackwardAveraging—Enable forward-backward averagingfalse(default) |true

ScanAngles—Broadside scan angles[-90:90](default) |real-valuedK-length vector

DOAOutputPort—Enable directions of arrival outputfalse(default) |true

NumSignalsSource—Source of number of signals'Auto'(default) |'Property'

NumSignalsMethod—Method used to estimate number of arriving signals'AIC'(default) |'MDL'

Dependencies

NumSignals—Number of arriving signals1(default) |positive integer

Dependencies

SpatialSmoothing—Enable spatial smoothing0(default) |nonnegative integer

Methods

Examples

Plot MUSIC Spectrum of Two Signals Arriving at ULA

Compute DOA of Two Nearby Signals Using MUSIC

Algorithms

MUSIC Algorithm

Data Precision

References

Extended Capabilities

C/C++ Code GenerationGenerate C and C++ code using MATLAB® Coder™.

Version History

See Also

Functions

Objects

Topics

`SensorArray`—ULA sensor array
`phased.ULA`System object(default)

`PropagationSpeed`—Signal propagation speed
`physconst('LightSpeed')`(default) |real-valued positive scalar

`OperatingFrequency`—Operating frequency
`300e6`(default) |positive scalar

`ForwardBackwardAveraging`—Enable forward-backward averaging
`false`(default) |`true`

`ScanAngles`—Broadside scan angles
`[-90:90]`(default) |real-valuedK-length vector

`DOAOutputPort`—Enable directions of arrival output
`false`(default) |`true`

`NumSignalsSource`—Source of number of signals
`'Auto'`(default) |`'Property'`

`NumSignalsMethod`—Method used to estimate number of arriving signals
`'AIC'`(default) |`'MDL'`

`NumSignals`—Number of arriving signals
`1`(default) |positive integer

`SpatialSmoothing`—Enable spatial smoothing
0(default) |nonnegative integer

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.