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The ultimate goal of sensor array signal processing is to estimate the values of parameters by using available temporal and spatial information, collected through sampling a wavefield with a set of antennas that have a precise geometry description. The processing of the captured data and information is done under the assumption that the wavefield is generated by a finite number of signal sources (emitters), and contains information about signal parameters characterizing and describing the sources. There are many applications related to the above problem formulation, where the number of sources, their directions and locations should be specified. To motivate the reader, some of the most important applications related to array processing will be discussed.
array processing concept was closely linked to radar
[[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>
[[Communication theory|Communication]] can be defined as the process of exchanging of information between two or more parties. The last two decades witnessed a rapid growth of wireless communication systems. This success is a result of advances in communication theory and low power dissipation design process. In general, communication (telecommunication) can be done by technological means through either electrical signals (wired communication) or electromagnetic waves (wireless communication). Antenna arrays have emerged as a support technology to increase the usage efficiency of spectral and enhance the accuracy of wireless communication systems by utilizing spatial dimension in addition to the classical time and frequency dimensions. Array processing and estimation techniques have been used in wireless communication. During the last decade these techniques were re-explored as ideal candidates to be the solution for numerous problems in wireless communication. In wireless communication, problems that affect quality and performance of the system may come from different sources. The multiuser –medium multiple access- and multipath -signal propagation over multiple scattering paths in wireless channels- communication model is one of the most widespread communication models in wireless communication (mobile communication).
[[File:Multi-Path Communication.png|thumb|Multi-path communication problem in wireless communication systems]]
In the case of multiuser communication environment, the existence of multiuser increases the inter-user interference possibility that can affect quality and performance of the system adversely. In mobile communication systems the multipath problem is one of the basic problems that base stations have to deal with. Base stations have been using spatial diversity for combating fading due to the severe multipath. Base stations use an antenna array of several elements to achieve higher selectivity, so called [[beamforming]]. Receiving array can be directed in the direction of one user at a time, while avoiding the interference from other users.
===Sonar Array Processing===
* Medical applications▼
Sonar array processing plays a critical role in underwater communication and sensing by exploiting spatial diversity to enhance signal estimation in challenging acoustic environments. Sonar systems—particularly when equipped with arrays of vector and scalar sensors—can form directional beams and spatial filters to isolate desired signals while suppressing noise and interference from undesired directions. This spatial filtering capability is essential in time-spreading distortion channels, where multipath propagation from the sea surface, seabed, and various underwater obstacles causes significant signal degradation.
Multichannel array processing techniques utilize both scalar pressure measurements and particle velocity information provided by vector sensors to improve angular resolution and signal-to-noise ratio (SNR) in environments with severe multipath and noise interference <ref>R. Rashid, E. Zhang, A. Abdi, and Z. H. Michalopoulou. 2024. "Multichannel signal detection in time-spreading distortion underwater channels using vector and scalar sensors: Theory and experiments." IEEE J. Oceanic Engineering, vol. 49, pp. 1151–1159.</ref>. The addition of particle velocity components significantly enhances spatial discrimination, allowing for better signal localization and estimation in both active and passive sonar modes <ref>E. Zhang. 2023. "Particle velocity underwater data communication: Physics, channels, system and experiments." IEEE Journal of Oceanic Engineering, vol. 48, pp. 1338–1347.</ref>, <ref>R. Rashid. 2023. "Underwater acoustic signal acquisition and sensing using a ring vector sensor communication receiver: Theory and experiments." Sensors, vol. 23, issue 6917.</ref>, <ref>R. Rashid. 2024. "On the performance of a new wireless communication compact multichannel underwater receiver using a sphere vector sensor." IEEE Transactions on Vehicular Technology, vol. 73, pp. 1458–1461.</ref>.
In passive sonar applications, array processing supports the detection and classification of weak signals generated by marine sources or stealth targets. When combined with advanced estimation methods like dictionary learning, array systems can blindly extract signal features even in unknown environments with complex propagation effects <ref>Rami Rashid, Ali Abdi, and Zoi-Heleni Michalopoulou. 2025. "Blind weak signal detection via dictionary learning in time-spreading distortion channels using vector sensors." JASA Express Letters, vol. 5, 064803.</ref>, <ref>Rami Rashid, Ali Abdi, and Zoi-Heleni Michalopoulou. 2024. "Blind passive signal detection via dictionary learning in unknown multipath time-spreading distortion underwater channels." J. Acoust. Soc. Am., vol. 155, A84.</ref>.
Experimental results reinforce the effectiveness of sonar array processing using multichannel vector sensor receivers and MIMO configurations. These systems have demonstrated high-performance underwater signal acquisition and data transmission in real-world conditions, leveraging spatial diversity and adaptive processing algorithms to overcome time-spreading distortion and noise <ref>E. Zhang, R. Rashid, and A. Abdi. 2023. "Underwater communication experiments for transmitting multiple data streams using a vector acoustic MIMO system: OFDM and FSK modulations." In Proc. MTS/IEEE Oceans, Biloxi, MS, pp. 1–5.</ref>, <ref>E. Zhang, R. Rashid, and A. Abdi. 2023. "Experiments on a compact multichannel vector sensor receiver for signal acquisition in underwater communication systems." In Proc. MTS/IEEE Oceans, Biloxi, MS, pp. 1–4.</ref>, <ref>R. Rashid, E. Zhang, A. Abdi, and Z. H. Michalopoulou. 2022. "Theoretical and experimental multi-sensor signal detection in time spreading distortion underwater channels." In Proc. MTS/IEEE Oceans, Hampton Roads, VA, pp. 1–4.</ref>, <ref>Z. Qi, R. Rashid, A. Abdi, and D. Pompili. 2025. "Carrier frequency offset compensation for OSDM in underwater acoustic communications: Theory and experiments using a vector MIMO modem." In Proc. Conf. Inform. Sci. Syst., Johns Hopkins University, Baltimore, MD, pp. 1–6.</ref>.
Array processing techniques got on much attention from medical and industrial applications. In medical applications, the medical image processing field was one of the basic fields that use array processing. Other medical applications that use array processing: diseases treatment, tracking waveforms that have information about the condition of internal organs e.g. the heart, localizing and analyzing brain activity by using bio-magnetic sensor arrays.<ref name="ref5">{{citation |first1=Hamid| last1= Krim |first2=Mats |last2=Viberg | title=Sensor Array Signal Processing: Two Decades Later |year=1995}}</ref>
Speech enhancement and processing represents another field that has been affected by the new era of array processing. Most of the acoustic front end systems became fully automatic systems (e.g. telephones). However, the operational environment of these systems contains a mix of other acoustic sources; external noises as well as acoustic couplings of loudspeaker signals overwhelm and attenuate the desired speech signal. In addition to these external sources, the strength of the desired signal is reduced due to the relatively distance between speaker and microphones. Array processing techniques have opened new opportunities in speech processing to attenuate noise and echo without degrading the quality of and affecting adversely the speech signal. In general array processing techniques can be used in speech processing to reduce the computing power (number of computations) and enhance the quality of the system (the performance). Representing the signal as a sum of sub-bands and adapting cancellation filters for the sub-band signals can reduce the demanded computation power and lead to a higher performance system. Relying on multiple input channels allows designing systems of higher quality comparing to systems that use single channel and solving problems such as source localization, tracking and separation, which cannot be achieved in case of using single channel.<ref>Zelinski, Rainer. "A microphone array with adaptive post-filtering for noise reduction in reverberant rooms." Acoustics, Speech, and Signal Processing, 1988. ICASSP-88., 1988 International Conference on. IEEE, 1988.</ref>
Astronomical environment contains a mix of external signals and noises that affect the quality of the desired signals. Most of the arrays processing applications in astronomy are related to image processing. The array used to achieve a higher quality that is not achievable by using a single channel. The high image quality facilitates quantitative analysis and comparison with images at other wavelengths. In general, astronomy arrays can be divided into two classes: the beamforming class and the correlation class. Beamforming is a signal processing techniques that produce summed array beams from a direction of interest – used basically in directional signal transmission or reception- the basic idea is to combine elements in a phased array such that some signals experience destructive inference and other experience constructive inference. Correlation arrays provide images over the entire single-element primary beam pattern, computed off-line from records of all the possible correlations between the antennas, pairwise.
[[File:C G-K - DSC 0421.jpg|thumb|One antenna of the Allen Telescope Array]]
In addition to these applications, many applications have been developed based on array processing techniques: Acoustic Beamforming for Hearing Aid Applications, Under-determined Blind Source Separation Using Acoustic Arrays, Digital 3D/4D Ultrasound Imaging Array, Smart Antennas, Synthetic aperture radar, underwater acoustic imaging, and Chemical sensor arrays...etc.<ref name="ref2"/><ref name="ref3"/><ref name="ref6"/>
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