rootmusicdoa

Direction of arrival using Root MUSIC

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Syntax

ang = rootmusicdoa(R,nsig)
ang = rootmusicdoa(___,'Name','Value')

Description

ang = rootmusicdoa(R,nsig) estimates the directions of arrival, ang, of a set of plane waves received on a uniform line array (ULA). The estimation uses the root MUSIC algorithm. The input arguments are the estimated spatial covariance matrix between sensor elements, R, and the number of arriving signals, nsig. In this syntax, sensor elements are spaced one-half wavelength apart.

example

ang = rootmusicdoa(___,'Name','Value') allows you to specify additional input parameters in the form of Name-Value pairs. This syntax can use any of the input arguments in the previous syntax.

example

Examples

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Open Live Script

Assume a half-wavelength spaced uniform line array with 10 elements. Three plane waves arrive from the 0°, –25°, and 30° azimuth directions. Elevation angles are 0°. The noise is spatially and temporally white Gaussian noise.

Set the SNR for each signal to 5 dB. Find the arrival angles.

N = 10;
d = 0.5;
elementPos = (0:N-1)*d;
angles = [0 -25 30];
Nsig = 3;
R = sensorcov(elementPos,angles,db2pow(-5));
doa = rootmusicdoa(R,Nsig)
doa = 1×3

   -0.0000  -25.0000   30.0000

These angles agree with the known input angles.

Open Live Script

Assume a uniform line array 10 elements, as in the previous example. But now the element spacing is smaller than one-half wavelength. Three plane waves arrive from the 0°, –25°, and 30° azimuth directions. Elevation angles are 0°. The noise is spatially and temporally white Gaussian noise. The SNR for each signal is 5 dB.

Set element spacing to 0.4 wavelengths using the ElementSpacing name-value pair. Then, find the arrival angles.

N = 10;
d = 0.4;
elementPos = (0:N-1)*d;
angles = [0 -25 30];
Nsig = 3;
R = sensorcov(elementPos,angles,db2pow(-5));
doa = rootmusicdoa(R,Nsig,'ElementSpacing',d)
doa = 1×3

   -0.0000  -25.0000   30.0000

The solution agrees with the known angles.

Input Arguments

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Spatial covariance matrix, specified as a complex-valued, positive-definite, N-by-N matrix. In this matrix, N represents the number of elements in the ULA array. If R is not Hermitian, a Hermitian matrix is formed by averaging the matrix and its conjugate transpose, (R+R')/2.

Example: [ 4.3162, –0.2777 –0.2337i; –0.2777 + 0.2337i , 4.3162]

Data Types: double
Complex Number Support: Yes

Number of arriving signals, specified as a positive integer. The number of signals must be smaller than the number of elements in the ULA array.

Example: 2

Data Types: double

Name-Value Arguments

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Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: ‘ElementSpacing’, 0.4

ULA element spacing, specified as a real-valued, positive scalar. Position units are measured in terms of signal wavelength.

Example: 0.4

Data Types: double

Output Arguments

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Directions of arrival angle, returned as a real-valued, 1-by-M vector. The dimension M is the number of arriving signals specified in the argument nsig. Angle units are degrees and angle values lie between –90° and 90°.

References

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

Extended Capabilities

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Version History

Introduced in R2013a

See Also

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