Editing Array processing (section)

{{Short description|Area of research in signal processing}}
{{distinguish|Array processor|Array data structure}}
{{more footnotes|date=November 2012}}
'''Array processing'''  is a wide area of research in the field of [[signal processing]] that extends from the simplest form of 1 dimensional line arrays to 2 and 3 dimensional array geometries. Array structure can be defined as a set of [[Sensor|sensors]] that are spatially separated, e.g. [[antenna (radio)|radio antenna]] and [[Seismic array|seismic arrays]]. The sensors used for a specific problem may vary widely, for example [[microphone]]s, [[accelerometer]]s and [[telescope]]s. However, many similarities exist, the most fundamental of which may be an assumption of [[wave propagation]]. Wave propagation means there is a systemic relationship between the signal received on spatially separated sensors. By creating a physical model of the wave propagation, or in [[machine learning]] applications a [[training data]] set, the relationships between the signals received on spatially separated sensors can be leveraged for many applications.

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"/>