phased.MUSICEstimator

Estimate direction of arrival using narrowband MUSIC algorithm for ULA

Description

The phased.MUSICEstimator System 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):

1. Define and set up a phased.MUSICEstimator System object. See Construction.

2. Call the step method to estimate the DOAs according to the properties of phased.MUSICEstimator.

Note

Alternatively, 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

estimator = phased.MUSICEstimator creates 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

SensorArray — ULA sensor array

phased.ULA System object (default)

ULA sensor array, specified as a phased.ULA System 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 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

ScanAngles — Broadside scan angles

[-90:90] (default) | real-valued K-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 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

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, by L = M – K + 1. The maximum value of K is M – 2.

Example: 5

Data Types: double

Methods

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

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

Examples

Plot MUSIC Spectrum of Two Signals Arriving at ULA

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 equivalent step syntax. For example, replace myObject(x) with step(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 = 1×2

    9.5829   60.3813

Plot the MUSIC spectrum.

plotSpectrum(estimator,'NormalizeResponse',true)

Compute DOA of Two Nearby Signals Using MUSIC

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 equivalent step syntax. For example, replace myObject(x) with step(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 = 1×2

   30.0000   32.0000

Plot the MUSIC spectrum.

plotSpectrum(estimator,'NormalizeResponse',true)

Algorithms

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 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 spatial smoothing and/or 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