phased.RootMUSICEstimator

Root MUSIC direction of arrival (DOA) estimator for ULA and UCA

Description

The RootMUSICEstimator object implements the root multiple signal classification (root-MUSIC) direction of arrival estimator for uniform linear arrays (ULA) and uniform circular arrays (UCA). When a uniform circular array is used, the algorithm transforms the input to a ULA-like structure using the phase mode excitation technique [2].

To estimate the direction of arrival (DOA):

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

Note

Starting in R2016b, 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

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).

Properties

`SensorArray`	Sensor array System object Sensor array specified as a System object. The sensor array must be a `phased.ULA` object or a `phased.UCA` object. Default: `phased.ULA` with default property values
`PropagationSpeed`	Signal propagation speed Specify the propagation speed of the signal, in meters per second, as a positive scalar. You can specify this property as single or double precision. Default: Speed of light
`OperatingFrequency`	System operating frequency Specify the operating frequency of the system in hertz as a positive scalar. The default value corresponds to 300 MHz. You can specify this property as single or double precision. Default: `3e8`
`ForwardBackwardAveraging`	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`
`SpatialSmoothing`	Spatial smoothing The averaging number used by spatial smoothing to estimate the covariance matrix, specified as a strictly positive integer. Each additional smoothing value handles one additional coherent source, but reduces the effective number of elements by one. The maximum value of this property is M-2. For a ULA, M is the number of sensors. For a UCA, M is the size of the internal ULA-like array structure defined by the phase mode excitation technique. The default value of zero indicates that no spatial smoothing is employed. You can specify this property as single or double precision. Default: `0`
`NumSignalsSource`	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. When spatial smoothing is employed on a UCA, you cannot set the `NumSignalsSource` property to`'Auto'` to estimate the number of signals. You can use the functions `aictest` or `mdltest` independently to determine the number of signals. Default: `'Auto'`
`NumSignalsMethod`	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'`
`NumSignals`	Number of signals Specify the number of signals as a positive integer scalar. This property applies when you set the `NumSignalsSource` property to `'Property'`. The number of signals must be smaller than the number of elements in the array specified in the `SensorArray` property. You can specify this property as single or double precision. Default: `1`

Methods

step	Perform DOA estimation

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

Examples

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Root-MUSIC Estimation of DOA for ULA

Open Live Script

Estimate the DOA's of two signals received by a standard 10-element uniform linear array (ULA) having an element spacing of 1 meter. 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);
sULA = phased.ULA('NumElements',10,...
    'ElementSpacing',1);
sULA.Element.FrequencyRange = [100e6 300e6];
fc = 150e6;
x = collectPlaneWave(sULA,[x1 x2],[10 20;45 60]',fc);
rng default;
noise = 0.1/sqrt(2)*(randn(size(x))+1i*randn(size(x)));
sDOA = phased.RootMUSICEstimator('SensorArray',sULA,...
    'OperatingFrequency',fc,...
    'NumSignalsSource','Property',...
    'NumSignals',2);
doas = step(sDOA,x + noise);
az = broadside2az(sort(doas),[20 60])

az = 1×2

   10.0001   45.0107

Algorithms

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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. Optimum Array Processing. New York: Wiley-Interscience, 2002.

[2] Mathews, C.P., Zoltowski, M.D., "Eigenstructure techniques for 2-D angle estimation with uniform circular arrays." IEEE Transactions on Signal Processing, vol. 42, No. 9, pp. 2395-2407, Sept. 1994.