Digital antenna array (DAA) is a

smart antenna Smart antennas (also known as adaptive array antennas, digital antenna arrays, multiple antennas and, recently, MIMO) are antenna arrays with smart signal processing algorithms used to identify spatial signal signatures such as the direction of a ...

with multi channels digital beamforming, usually by using

fast Fourier transform A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in t ...

(FFT). The development and practical realization of digital antenna arrays theory started in 1962 under the guidance of Vladimir Varyukhin (

USSR The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen nation ...

History

The history of the DAA was started to emerge as a theory of multichannel analysis in the 1920s.Slyusar V. I. Origins of the Digital Antenna Array Theory.// International Conference on Antenna Theory and Techniques, 24–27 May 2017, Kyiv, Ukraine. – Pp. 199 - 20

/ref> In the 1940s this theory evolved to the theory of three-channel antenna analyzers. The implementation of effective signal processing in radars by the end of the 1950s predetermined the use of electronic computers in this field. In 1957, Ben S. Meltont and Leslie F. Bailey published article regarding using algebraic operations for signal processing with the help of electronic circuits or analog computer. Three years after in 1960 the idea of using high-speed computers to solve directional finding problems was embodied, initially to locate earthquake epicenter. B. A. Bolt was one of the first who implemented this idea in practice. Almost simultaneously a similar approach was used by Flinn, a research fellow of the Australian National University. Despite the fact that in the mentioned experiments the interaction between sensors and computers was implemented with the help of data input cards, such decision was a decisive step on the way of the appearance of the DAA. Then, it was needed only to solve the problem of direct digital data input into the computer from sensors, excluding the step of preparation of punch card and operator assistance as a surplus element. This step for radars theory was made after 1962 in the former USSR conducted with a solution to the problem of superRayleigh resolution of the emission sources.

Digital beamforming

The main approach to digital signal processing in DAA is the "digital beamforming" after

Analog-to-digital converter In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide ...

s (ADC) of receiver channels or before

Digital-to-analog converter In electronics, a digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function. There are several DAC archi ...

s (DAC) by transmission. Digital beamforming of DAA has advantages because the digital signals can be transformed and combined in parallel, to produce different output signals. The signals from every direction can be estimated simultaneously and integrated for a longer time to increasing of signals energy when detecting far-off objects and simultaneously integrated for a shorter time to detecting fast-moving close objects. Before digital beamforming operation should be used a correction of channels characteristics by a special test source or using the heterodyne signal. Such correction can be used not only for receiving channels but also in transmission channels of active DAA.Slyusar, V. I. Titov, I. V. Correction of characteristics of transmitting channels in an active digital antenna array// Radioelectronics and Communications Systems. – 2004, VOL 47; PART 8, pages 9 - 1

/ref> Limitations on the accuracy of estimation of

direction of arrival In signal processing, direction of arrival (DOA) denotes the direction from which usually a propagating wave 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 th ...

signals and depth of suppression of interferences in digital antenna arrays 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 ...

in ADCs and DACs.

Signal processing methods

Maximum likelihood beamformer

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 sta ...

beamformer (DML), the noise is modeled as a stationary Gaussian white random processes while the signal waveform as deterministic (but arbitrary) and unknown.

Bartlett beamformer

The Bartlett beamformer is a natural extension of conventional spectral analysis (

spectrogram A spectrogram is a visual representation of the spectrum of frequencies of a signal as it varies with time. When applied to an audio signal, spectrograms are sometimes called sonographs, voiceprints, or voicegrams. When the data are represen ...

) to the DAA. Its spectral power is represented by

\hat_(\theta)=\boldsymbol v^H \boldsymbol R \boldsymbol v \ \ (1)

. The angle that maximizes this power is an estimation of the angle of arrival.

Capon beamformer

Capon beamformer, also known as the minimum-variance distortionless response (MVDR) beamforming algorithm, has a power given by

\hat_(\theta)=\frac \ \ (2)

. The MVDR/Capon beamformer can achieve better resolution than the conventional (Bartlett) approach, but this algorithm has higher complexity due to the full-rank matrix inversion. Technical advances in

GPU computing General-purpose computing on graphics processing units (GPGPU, or less often GPGP) is the use of a graphics processing unit (GPU), which typically handles computation only for computer graphics, to perform computation in applications traditiona ...

have begun to narrow this gap and make real-time Capon beamforming possible.

MUSIC beamformer

MUSIC (

MUltiple SIgnal Classification MUSIC (MUltiple SIgnal Classification) is an algorithm used for frequency estimation and radio direction finding.Schmidt, R.O,Multiple Emitter Location and Signal Parameter Estimation" IEEE Trans. Antennas Propagation, Vol. AP-34 (March 1986), pp. ...

) beamforming algorithm starts with decomposing the covariance matrix for both the signal part and the noise part. The eigen-decomposition of is represented by

\boldsymbol R = \boldsymbol U_s \boldsymbol \Lambda_s \boldsymbol U_s^H + \boldsymbol U_n \boldsymbol \Lambda_n \boldsymbol U_n^H \ \ (3)

. MUSIC uses the noise sub-space of the spatial covariance matrix in the denominator of the Capon algorithm

\hat_(\theta)=\frac \ \ (4)

. Therefore MUSIC beamformer is also known as subspace beamformer. Compared to the Capon beamformer, it gives much better DOA estimation. As an alternative approach can be used

ESPRIT Esprit or L'Esprit may refer to: * the French for Spirit; as a loanword: ** Enthusiasm, intense interest or motivation ** Morale, motivation and readiness ** Geist "mind/spirit; intellect" * Esprit (name), a given name and surname * ''Esprit'' (m ...

algorithm as well.

Artificial Intelligence

The important trend in evolving digital signal processing for DAA is the use of

Artificial Intelligence Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machine A machine is a physical system using Power (physics), power to apply Force, forces and control Motion, moveme ...

technologies.

DAA Examples

Radars

F 220 Fregatte Hamburg.jpg, F220 ''Hamburg'' with SMART-L SmartLR.jpg, SMART-L onboard F221 ''Hessen'' Giraffe AFB-radar.jpg, Giraffe AMB, 2007. Voronezh-m-radar-lekhtusi.jpg, Voronezh-M radar, Lekhtusi. FBX T.jpg, Radar AN/TPY-2,

THAAD Terminal High Altitude Area Defense (THAAD), formerly Theater High Altitude Area Defense, is an American anti-ballistic missile defense system designed to shoot down short-, medium-, and intermediate-range ballistic missiles in their terminal ...

CAPTOR E.jpg, CAPTOR-E, DSEI-2019 DDG 124 with AMDR highlighted.png, AMDR AN/SPY-6 (digital beamformingKatherine Owens
New Navy destroyer radar conducts first flight test.
April 10, 2017.)

MIMO systems

DAA use to improve the performance of radio communications in

MIMO In radio, multiple-input and multiple-output, or MIMO (), is a method for multiplying the capacity of a radio link using multiple transmission and receiving antennas to exploit multipath propagation. MIMO has become an essential element of w ...

(Massive MIMO) systems.

Sonars and ultrasound sensors

DAA was implemented in a big lot of

sonar Sonar (sound navigation and ranging or sonic navigation and ranging) is a technique that uses sound propagation (usually underwater, as in submarine navigation) to navigate, measure distances ( ranging), communicate with or detect objects on ...

s and

medical ultrasound Medical ultrasound includes diagnostic techniques (mainly imaging techniques) using ultrasound, as well as therapeutic applications of ultrasound. In diagnosis, it is used to create an image of internal body structures such as tendons, muscl ...

sensors. File:ALOKA SSD-3500SV.jpg, ALOKA SSD-3500SV with 256 channels