phased.RootMUSICEstimator System object

Package: phased

Root MUSIC direction of arrival (DOA) estimator


The RootMUSICEstimator object implements a root multiple signal classification (MUSIC) direction of arrival estimate for a uniform linear array.

To estimate the direction of arrival (DOA):

  1. Define and set up your DOA estimator. See Construction.

  2. Call step to estimate the DOA according to the properties of phased.RootMUSICEstimator. The behavior of step is specific to each object in the toolbox.


H = phased.RootMUSICEstimator creates a root MUSIC DOA estimator System object™, H. The object estimates the signal's direction of arrival using the root MUSIC algorithm with a uniform linear array (ULA).

H = phased.RootMUSICEstimator(Name,Value) creates 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).



Handle to sensor array

Specify the sensor array as a handle. The sensor array must be a phased.ULA object.

Default: phased.ULA with default property values


Signal propagation speed

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

Default: Speed of light


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


Perform forward-backward averaging

Set this property to true to use forward-backward averaging to estimate the covariance matrix for sensor arrays with conjugate symmetric array manifold.

Default: false


Spatial smoothing

Specify the number of averaging used by spatial smoothing to estimate the covariance matrix as a nonnegative integer. Each additional smoothing handles one extra coherent source, but reduces the effective number of element by 1. The maximum value of this property is M–2, where M is the number of sensors. The default value indicates no spatial smoothing.

Default: 0


Source of number of signals

Specify the source of the number of signals as one of 'Auto' or 'Property'. If you set this property to 'Auto', the number of signals is estimated by the method specified by the NumSignalsMethod property.

Default: 'Auto'


Method to estimate number of signals

Specify the method to estimate the number of signals as one of 'AIC' or 'MDL'. 'AIC' uses the Akaike Information Criterion and 'MDL' uses Minimum Description Length Criterion. This property applies when you set the NumSignalsSource property to 'Auto'.

Default: 'AIC'


Number of signals

Specify the number of signals as a positive integer scalar. This property applies when you set the NumSignalsSource property to 'Property'.

Default: 1


cloneCreate root MUSIC DOA estimator object with same property values
getNumInputsNumber of expected inputs to step method
getNumOutputsNumber of outputs from step method
isLockedLocked status for input attributes and nontunable properties
releaseAllow property value and input characteristics changes
stepPerform DOA estimation


Estimate the DOAs of two signals received by a standard 10-element ULA with element spacing 1 m. The antenna operating frequency is 150 MHz. The actual direction of the first signal is 10 degrees in azimuth and 20 degrees in elevation. The direction of the second signal is 45 degrees in azimuth and 60 degrees in elevation.

fs = 8000; t = (0:1/fs:1).';
x1 = cos(2*pi*t*300); x2 = cos(2*pi*t*400);
ha = phased.ULA('NumElements',10,'ElementSpacing',1);
ha.Element.FrequencyRange = [100e6 300e6];
fc = 150e6;
x = collectPlaneWave(ha,[x1 x2],[10 20;45 60]',fc);
rng default;
noise = 0.1/sqrt(2)*(randn(size(x))+1i*randn(size(x)));
hdoa = phased.RootMUSICEstimator('SensorArray',ha,...
doas = step(hdoa,x+noise);
az = broadside2az(sort(doas),[20 60])


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

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