doa

Direction of arrival of signal

Since R2022a

Syntax

[phiArrival,thetaArrival] = doa(obj,freq)

Description

[phiArrival,thetaArrival] = doa(obj,freq) calculates the direction of arrival of a signal when the transmission source is either a single-feed antenna defined using a conformalArray object or an incident plane-wave defined using a planeWaveExcitation object.

Examples

Calculate Direction of Arrival Using Conformal Array Object

Visualize a transmitter-receiver system as a conformal array. Use a conformalArray object with a dipole antenna as the transmitter element and an array of dipoles as the receiver element. Specify an operating fequency of 70 MHz.

f = 70e6;
lambda = 3e8/f;

Specify the location coordinates of the transmitter and the receiver.

txCenterOffset = [200,50,370];
rxCenterOffset = [0,0,0];

Create the first and second element of the conformal array.

elem1 = design(dipole,f);
elem1.Tilt = 90;
elem2 = linearArray(Element=elem1, NumElements=4, ElementSpacing=0.4*lambda);

Create and view the conformal array.

c = conformalArray;
c.Element = {elem1 elem2};
c.ElementPosition = [txCenterOffset; rxCenterOffset];

Calculate the direction of arrival.

[phiArrival,thetaArrival] = doa(c,f)

phiArrival = 
14.0362

thetaArrival = 
27.9882

Calculate Direction of Arrival Using Plane-Wave Excitation Object

Calculate the direction of arrival of a signal using the plane-wave excitation object. Use a linear array of dipoles operating at 2.4 GHz as the receiver element and set the azimuth and elevation reference angles.

azimuthRef = 10;
elevationRef = 30;
f = 2.4e9;
lambda = 3e8/f;

Design a dipole antenna using the specified frequency.

d = design(dipole,f);
d.Tilt = 90;

Create and view a linear array.

ant = linearArray(Element=d, NumElements=10, ElementSpacing=0.5*lambda);
show(ant)

Create a plane-wave excitation object using the dipole array.

dir = [sind(elevationRef)*cosd(azimuthRef) sind(elevationRef)*sind(azimuthRef) -cosd(elevationRef)];
pol = [cosd(elevationRef)*cosd(azimuthRef) cosd(elevationRef)*sind(azimuthRef) sind(elevationRef)];
pw = planeWaveExcitation(Element=ant, Direction=dir, Polarization=pol);

Calculate the direction of arrival.

[phiArrival,thetaArrival] = doa(pw,f)

phiArrival = 
10

thetaArrival = 
29.8900

Input Arguments

obj — Transmitter-receiver system

conformalArray object | planeWaveExcitation object

Transmitter-receiver system, specified as a conformalArray object or a planeWaveExcitation object.

To define the transmitter-receiver system as a conformal array of two elements, specify this input as a conformalArray object. The first element of the conformal array is a single-feed antenna, and is the transmission signal source. The second element of the conformal array is the receiver array.

To define the transmitter-receiver system as a plane-wave excitation, specify this input as a planeWaveExcitation object. The plane-wave defined using the Direction and Polarization properties of the planeWaveExcitation object is the incident signal. The linear or rectangular array defined using the Element property of the planeWaveExcitation object is the receiver.

Note

The doa function accepts only linear or rectangular array configurations for the receiver array of the conformalArray and planeWaveExcitation objects. The number of elements along each axis of the receiver array must be even, and the center of the receiver array must be at the origin.

freq — Frequency of incident signal

nonnegative scalar | vector with nonnegative entries

Frequency of the incident signal in Hz. to use for the direction of arrival calculations, specified as a nonnegative scalar or a vector with nonnegative entries.

Example: f = 70e6

Data Types: double

Output Arguments

phiArrival — Azimuth angle of arrival of signal

scalar | vector

Azimuth angle of arrival of the signal in degrees, returned as a scalar or vector. The function calculates this output with reference to the center of the receiver array.

Data Types: double

thetaArrival — Elevation angle of arrival of signal

scalar | vector

Elevation angle of arrival of the signal in degrees, returned as a scalar or vector. The function calculates this output with reference to the center of the receiver array.

Data Types: double

Algorithms

To estimate the direction of arrival, the doa function uses the fundamentals of RF propagation from the transmission to the reception of the signal. The phase of a far-field received signal E_R(r) at an individual antenna is:

$$E_R(r)\alpha e^{j\beta r}(1)$$

where β is the propagation constant of the received signal and r is the distance between the transmit and receive elements.

For a given transmit antenna, the position of the antenna element is [x_tx, y_tx, z_tx], where

$$x_{tx}=\rho \cos (\phi )\sin (\theta )(2)$$

$$y_{tx}=\rho \sin (\phi )\sin (\theta )(3)$$

$$z_{tx}=\rho \cos (\theta )(4)$$

where ρ is the distance between the transmit element and the geometrical midpoint of the receive antenna array. θ is the elevation angle or the angular position of the transmit element from the z-axis and φ is the azimuth angle that lies in the xy-plane.

Assume that:

• The receiver array is a homogenous linear or rectangular array with identical elements.

• The separation between two adjacent elements of the receiver array is uniform. For a linear array, the element spacing is d_space. For a rectangular array, the row spacing is d_row and the column spacing is d_col.

• The receiver array has an equal number of elements along each axis. The number of elements along each axis of the array is even. For a linear array, the number of elements is N_elem. For a rectangular array, the number of elements in a row is N_row and the number of elements in a column is N_col.

For a uniform linear array (ULA) where the receive array elements lie along the x-axis, the position of the n^th elements is

$$x_{po{s}_n}=\frac{d_{space}}{2}(N_{elem}+1-2n)(5)$$

where N_elem is the number of elements in the ULA.

For the uniform rectangular array (URA), which lies in the xy-plane, the position of the receive array element in the n^th row and m^th column is [x_posn y_posn], where

$$x_{po{s}_n}=\frac{d_{col}}{2}(N_{elem}+1-2n)(6)$$

$$y_{po{s}_n}=\frac{d_{row}}{2}(M_{elem}+1-2m)(7)$$

Consider a single-antenna transmitter located at (x_tx, y_tx, z_tx). This equation determines the far-field separation r between the receiver array element and the transmitter for a ULA:

$$r_n=\sqrt{{(x_{tx}-x_{po{s}_n})}^2+{(y_{tx})}^2+{(z_{tx})}^2}\text{(ULA)}(8)$$

.

This equation determines the far-field separation r between the transmitter and the element in the m^th column and n^th row of a URA:

$$r_{m,n}=\sqrt{{(x_{tx}-x_{po{s}_n})}^2+{(y_{tx}-y_{po{s}_n})}^2+{(z_{tx})}^2}\text{(URA)}(9)$$

The function uses these equations to calculate the phase of the electric field by doing a full-wave electromagnetic simulation and uses this phase to calculate the direction of arrival in terms of the elevation and azimuth angles.

Version History

Introduced in R2022a