signal processing Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, Scalar potential, potential fields, Seismic tomograph ...

, direction of arrival (DOA) denotes the

direction Direction may refer to: *Body relative direction, for instance left, right, forward, backwards, up, and down ** Anatomical terms of location for those used in anatomy ** List of ship directions *Cardinal direction *Bearing (navigation) Mathemat ...

from which usually a

propagating Plant propagation is the process by which new plants grow from various sources, including seeds, cuttings, and other plant parts. Plant propagation can refer to both man-made and natural processes. Propagation typically occurs as a step in the o ...

wave In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance (change from List of types of equilibrium, equilibrium) of one or more quantities. ''Periodic waves'' oscillate repeatedly about an equilibrium ...

arrives at a point, where usually a set of sensors are located. These set of sensors forms what is called a

sensor array A sensor array is a group of sensors, usually deployed in a certain geometry pattern, used for collecting and processing electromagnetic or acoustic signals. The advantage of using a sensor array over using a single sensor lies in the fact that an ...

. Often there is the associated technique of

beamforming Beamforming or spatial filtering is a signal processing technique used in sensor arrays for directional signal transmission or reception. This is achieved by combining elements in an antenna array in such a way that signals at particular angles ...

which is estimating the signal from a given direction. Various engineering problems addressed in the associated literature are: *Find the direction relative to the array where the sound source is located *Direction of different sound sources around you are also located by you using a process similar to those used by the

algorithms In mathematics and computer science, an algorithm () is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for per ...

in the literature *

Radio telescopes A radio telescope is a specialized antenna (radio), antenna and radio receiver used to detect radio waves from astronomical radio sources in the sky. Radio telescopes are the main observing instrument used in radio astronomy, which studies the r ...

use these techniques to look at a certain location in the sky *Recently beamforming has also been used in

radio frequency Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the u ...

(RF) applications such as

wireless Wireless communication (or just wireless, when the context allows) is the transfer of information (''telecommunication'') between two or more points without the use of an electrical conductor, optical fiber or other continuous guided transm ...

communication. Compared with the spatial diversity techniques, beamforming is preferred in terms of complexity. On the other hand, beamforming in general has much lower data rates. In multiple access channels (

code-division multiple access Code-division multiple access (CDMA) is a channel access method used by various radio communication technologies. CDMA is an example of channel access method, multiple access, where several transmitters can send information simultaneously over ...

(CDMA),

frequency-division multiple access Frequency-division multiple access (FDMA) is a channel access method used in some multiple-access protocols. FDMA allows multiple users to send data through a single communication channel, such as a coaxial cable or microwave beam, by dividing ...

(FDMA),

time-division multiple access Time-division multiple access (TDMA) is a channel access method for shared-medium networks. It allows several users to share the same frequency channel by dividing the signal into different time slots. The users transmit in rapid succession, ...

(TDMA)), beamforming is necessary and sufficient *Various techniques for calculating the direction of arrival, such as

angle of arrival The angle of arrival (AoA) of a signal is the direction from which the signal (e.g. radio, optical or acoustic) is received. Measurement Measurement of AoA can be done by determining the direction of propagation of a radio-frequency wave incident ...

(AoA),

time difference of arrival Time is the continuous progression of existence that occurs in an apparently irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequence events, to compa ...

(TDOA),

frequency difference of arrival Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

(

FDOA Frequency difference of arrival (FDOA) or differential Doppler (DD), is a technique analogous to TDOA for estimating the location of a radio emitter based on observations from other points. (It can also be used for estimating one's own position ba ...

), or other similar associated techniques. *Limitations on the accuracy of estimation of direction of arrival signals in

digital antenna array Digital antenna array (DAA) is a smart antenna with multi channels digital beamforming, usually by using fast Fourier transform (FFT). The development and practical realization of digital antenna arrays theory started in 1962 under the guidanc ...

s are associated with

jitter In electronics and telecommunications, jitter is the deviation from true periodicity of a presumably periodic signal, often in relation to a reference clock signal. In clock recovery applications it is called timing jitter. Jitter is a signifi ...

ADC and DAC. Advanced sophisticated techniques perform joint direction of arrival and time of arrival (ToA) estimation to allow a more accurate localization of a node. This also has the merit of localizing more targets with less antenna resources. Indeed, it is well-known in the array processing community that, generally speaking, one can resolve

P

targets via

N > P

antennas. When JADE (joint angle and delay) estimation is employed, one can go beyond this limit.

Typical DOA estimation methods

Periodogram In signal processing, a periodogram is an estimate of the spectral density of a signal. The term was coined by Arthur Schuster in 1898. Today, the periodogram is a component of more sophisticated methods (see spectral estimation). It is the most ...

MUSIC Music is the arrangement of sound to create some combination of Musical form, form, harmony, melody, rhythm, or otherwise Musical expression, expressive content. Music is generally agreed to be a cultural universal that is present in all hum ...

* SAMV *

Maximum likelihood In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed stati ...

* ESPRIT * Root MUSIC Barabell, Arthur. "Improving the resolution performance of eigenstructure-based direction-finding algorithms." ICASSP'83. IEEE International Conference on Acoustics, Speech, and Signal Processing. Vol. 8. IEEE, 1983. * Weighted subspace fitting * Method of Direction Estimation (MODE)

References

Signal processing {{Signal-processing-stub