Array processing: Difference between revisions

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{{Short description|Area of research in signal processing}}

{{distinguish|Array processor|Array data structure}}

{{more footnotes|date=November 2012}}

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Some common problem that are solved with array processing techniques are:

* determine number and locations of energy-radiating sources

* enhance the signal to noise ratio ([[Signal-to-noise_ratio|SNR]]) or "[[SINR|signal-to-interference-plus-noise ratio (SINR)]]"

* track moving sources

Array processing metrics are often assessed in noisy environments. The model for noise may be either one of spatially incoherent noise, or one with interfering signals following the same propagation physics. [[Estimation theory]] is an important and basic part of signal processing field, which used to deal with estimation problem in which the values of several parameters of the system should be estimated based on measured/empirical data that has a random component. As the number of applications increases, estimating temporal and spatial parameters become more important. Array processing emerged in the last few decades as an active area and was centered on the ability of using and combining data from different sensors (antennas) in order to deal with specific estimation task (spatial and temporal processing). In addition to the information that can be extracted from the collected data the framework uses the advantage prior knowledge about the geometry of the [[sensor array]] to perform the estimation task.

Array processing is used in [[radar]], [[sonar]], seismic exploration, anti-jamming and [[wireless]] communications. One of the main advantages of using array processing along with an array of sensors is a smaller foot-print. The problems associated with array processing include the number of sources used, their [[direction of arrival]]s, and their signal [[waveforms]].<ref name="utexas1">Torlak, M. [http://users.ece.utexas.edu/~bevans/courses/ee381k/lectures/13_Array_Processing/lecture13/lecture13.pdf Spatial Array Processing]. Signal and Image Processing Seminar. University of Texas at Austin.</ref><ref name="ref1">{{cite book|last=J Li|first=[[Peter Stoica]] (Eds)|title=MIMO Radar Signal Processing|year=2009|publisher=J Wiley&Sons|___location=USA}}</ref><ref name="ref2">{{cite book|last=[[Peter Stoica]]|first=R Moses|title=Spectral Analysis of Signals|year=2005|publisher=Prentice Hall|___location=NJ|url=http://user.it.uu.se/%7Eps/SAS-new.pdf}}</ref><ref name="ref3">{{cite book|last=J Li|first=[[Peter Stoica]] (Eds)|title=Robust Adaptive Beamforming|year=2006|publisher=J Wiley&Sons|___location=USA}}</ref>

[[File:Aray Prcessing Model.png|thumb|Sensors array]]

There are four assumptions in array processing. The first assumption is that there is uniform propagation in all directions of isotropic and non-dispersive medium. The second assumption is that for far field array processing, the radius of propagation is much greater than size of the array and that there is [[plane wave]] propagation. The third assumption is that there is a zero mean white noise and signal, which shows uncorrelation. Finally, the last assumption is that there is no coupling and the calibration is perfect.<ref name="utexas1"/>

==Applications==

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* Radar and Sonar Systems:

array processing concept was closely linked to radar and sonar systems which represent the classical applications of array processing. The antenna array is used in these systems to determine ___location(s) of source(s), cancel interference, suppress ground clutter. '''[[Radar|Radar systems]]''' used basically to detect objects by using radio waves. The range, altitude, speed and direction of objects can be specified. Radar systems started as military equipments then entered the civilian world. In radar applications, different modes can be used, one of these modes is the active mode. In this mode the antenna array based system radiates pulses and listens for the returns. By using the returns, the estimation of parameters such as velocity, range and DOAs (direction of arrival) of target of interest become possible. Using the passive far-field listening arrays, only the DOAs can be estimated. '''[[Sonar|Sonar systems]]''' (Sound Navigation and Ranging) use the sound waves that propagate under the water to detect objects on or under the water surface. Two types of sonar systems can be defined the active one and the passive one. In active sonar, the system emits pulses of sound and listens to the returns that will be used to estimate parameters. In the passive sonar, the system is essentially listening for the sounds made by the target objects. ItThere is very important to note thea difference between the radar system that uses radio waves and the sonar system that uses sound waves, the reason why the sonar uses the sound wave is because sound waves travel farther in the water than do radar and light waves. In passive sonar, the receiving array has the capability of detecting distant objects and their locations. Deformable array are usually used in sonar systems where the antenna is typically drawn under the water. In active sonar, the sonar system emits sound waves (acoustic energy) then listening and monitoring any existing echo (the reflected waves). The reflected sound waves can be used to estimate parameters, such as velocity, position and direction etc. Difficulties and limitations in sonar systems comparing to radar systems emerged from the fact that the propagation speed of sound waves under the water is slower than the radio waves. Another source of limitation is the high propagation losses and scattering. Despite all these limitations and difficulties, sonar system remains a reliable technique for range, distance, position and other parameters estimation for underwater applications.<ref name="ref2"/><ref name="ref6">{{citation |first1=Hema | last1= Singh |first2=RakeshMohan |last2=Jha| title=Trends in Adaptive Array Processing |year=2012}}</ref>

[[File:Radar System.png|thumb|Radar System]]

NORSAR is an independent geo-scientific research facility that was founded in Norway in 1968. NORSAR has been working with array processing ever since to measure seismic activity around the globe.<ref name=NORSAR>{{cite web|title=About Us|url=http://www.norsar.no/norsar/about-us/|publisher=NORSAR|accessdate=6 June 2013|archive-url=https://web.archive.org/web/20130620112533/http://www.norsar.no/norsar/about-us/|archive-date=20 June 2013|url-status=dead}}</ref> They are currently working on an International Monitoring System which will comprise 50 primary and 120 auxiliary seismic stations around the world. NORSAR has ongoing work to improve array processing to improve monitoring of seismic activity not only in Norway but around the globe.<ref>{{cite web |url=http://www.norsar.no/pc-31-83-Improving-IMS-array-processing.aspx |title=Improving IMS array processing |publisher=Norsar.no |accessdate=2012-08-06 |archive-url=https://web.archive.org/web/20120821220803/http://www.norsar.no/pc-31-83-Improving-IMS-array-processing.aspx |archive-date=2012-08-21 |url-status=dead }}</ref>

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== General model and problem formulation==

Consider a system that consists of array of '''r''' arbitrary sensors that have arbitrary locations and arbitrary directions (directional characteristics) which receive signals that generated by '''q''' narrow band sources of known center frequency ω and locations θ1, θ2, θ3, θ4 ... θq. since the signals are narrow band the [[propagation delay]] across the array is much smaller than the reciprocal of the signal bandwidth and it follows that by using a complex envelop representation the array output can be expressed (by the sense of superposition) as :<ref name="ref2"/><ref name="ref6"/><ref name="ref5"/><br>

<math>\textstyle x(t)=\sum_{K=1}^q a(\theta_k)s_k(t)+n(t)</math>

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==== Subspace-based technique ====

Many spectral methods in the past have called upon the spectral decomposition of a covariance matrix to carry out the analysis. A very important breakthrough came about when the eigen-structure of the covariance matrix was explicitly invoked, and its intrinsic properties were directly used to provide a solution to an underlying estimation problem for a given observed process. A class of spatial spectral estimation techniques is based on the eigen-value decomposition of the spatial covariance matrix. The rationale behind this approach is that one wants to emphasize the choices for the steering vector a(θ) which correspond to signal directions. The method exploits the property that the directions of arrival determine the eigen structure of the matrix.<br>

The tremendous interest in the subspace based methods is mainly due to the introduction of the [[MUSIC (algorithm)|MUSIC (Multiple Signal Classification)]] algorithm. MUSIC was originally presented as a DOA estimator, then it has been successfully brought back to the spectral analysis/system identification problem with its later development.<ref name="ref2"/><ref name="ref6"/><ref name="ref5"/>

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where the noise [[eigenvector matrix]] <math>E_{n}=[e_{d}+1, .... , e_{M}]</math>

MUSIC spectrum approaches use a single realization of the [[stochastic process]] that is represent by the snapshots x (t), t=1, 2 ...M. MUSIC estimates are consistent and they converge to true source bearings as the number of snapshots grows to infinity. A basic drawback of MUSIC approach is its sensitivity to model errors. A costly procedure of calibration is required in MUSIC and it is very sensitive to errors in the calibration procedure. The cost of calibration increases as the number of parameters that define the array manifold increases.

=== Parametric–based solutions ===