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, and scientific measurements. Signal processing techniq ...

, direction of arrival (DOA) denotes the direction from which usually a propagating

wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...

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

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 rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing c ...

in the literature *

Radio telescopes A radio telescope is a specialized 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 radio frequency po ...

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 upp ...

(RF) applications such as

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

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 multiple access, where several transmitters can send information simultaneously over a single communication ...

(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, o ...

(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 of arrival (TOA or ToA) is the absolute time instant when a radio signal emanating from a transmitter reaches a remote receiver. The time span elapsed since the time of transmission (TOT or ToT) is the ''time of flight'' (TOF or ToF). Time diff ...

(TDOA), frequency difference of arrival (

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 bas ...

), 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 guidance ...

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 significa ...

ADC ADC may refer to: Science and medicine * ADC (gene), a human gene * AIDS dementia complex, neurological disorder associated with HIV and AIDS * Allyl diglycol carbonate or CR-39, a polymer * Antibody-drug conjugate, a type of anticancer treatm ...

and DAC.

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 co ...

MUSIC Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspect ...

* SAMV *

Maximum likelihood In statistics, maximum likelihood estimation (MLE) is a method of estimation theory, estimating the Statistical parameter, parameters of an assumed probability distribution, given some observed data. This is achieved by Mathematical optimization, ...

* ESPRIT

References

Signal processing {{Signal-processing-stub