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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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== 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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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 ===
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