# espritdoa

Direction of arrival using TLS ESPRIT

## Description

example

ang = espritdoa(R,nsig) estimates the directions of arrival, ang, of a set of plane waves received on a uniform line array (ULA). The estimation employs the TLS ESPRIT, the total least-squares ESPRIT, 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 = espritdoa(___,Name,Value) estimates the directions of arrival with additional options specified by one or more Name,Value pair arguments. This syntax can use any of the input arguments in the previous syntax.

## Examples

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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. The SNR for each signal is 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 = espritdoa(R,Nsig)
doa = 1×3

30.0000    0.0000  -25.0000

The espritdoa function returns the correct angles.

Assume a uniform line array with 10 elements. The element spacing is 0.4 wavelength. Three plane waves arrive from the 0°, –25°, and 30° azimuth directions. Elevation angles are 0°. The noise is spatially and temporally white. The SNR for each signal is 5 dB. 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 = espritdoa(R,Nsig,'ElementSpacing',d)
doa = 1×3

-25.0000   -0.0000   30.0000

espritdoa returns the correct 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.

Example: 3

Data Types: double

### Name-Value Arguments

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’, 0.45

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

Row weights specified as a real-valued positive scalar. These weights are applied to the selection matrices which determine the ESPRIT subarrays. A larger value is generally better but the value must be less than or equal to (Ns–1)/2, where Ns is the number of subarray elements. The number of subarray elements is Ns = N–1. The value of N is the number of ULA elements, as specified by the dimensions of the spatial covariance matrix, R. A detailed discussion of selection matrices and row weighting can be found in Van Trees [1], p. 1178.

Example: 5

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. This angle is the broadside angle. 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.

## Version History

Introduced in R2013a