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| {{about|MIMO in wireless communication}}
| | == Vibram Shoes Greece καιροσκόπος == |
| [[File:Prinzip MIMO.svg|thumb|280px|Understanding of SISO, SIMO, MISO and MIMO (note that the terms ''input'' and ''output'' refer to the radio channel carrying the signal, not to the devices having antennas)]]
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| {{Antennas|Antenna Techniques}}
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| In [[radio]], '''multiple-input and multiple-output''', or '''MIMO''' (pronounced my-moh by some and me-moh by others), is the use of multiple antennas at both the transmitter and receiver to improve communication performance. It is one of several forms of [[smart antenna]] technology. Note that the terms ''input'' and ''output'' refer to the radio [[Channel (communications)|channel]] carrying the signal, not to the devices having antennas.
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| MIMO technology has attracted attention in [[wireless]] communications, because it offers significant increases in data throughput and link range without additional bandwidth or increased transmit power. It achieves this goal by spreading the same total transmit power over the antennas to achieve an [[array gain]] that improves the spectral efficiency (more bits per second per hertz of bandwidth) and/or to achieve a [[diversity gain]] that improves the link reliability (reduced [[fading]]). Because of these properties, MIMO is an important part of modern wireless communication standards such as [[IEEE 802.11n]] (Wi-Fi), [[4G]], [[3GPP Long Term Evolution]], [[WiMAX]] and [[Evolved HSPA|HSPA+]].
| | == New Balance Shoes == |
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| ==History of MIMO==
| | Όταν έχετε κάνει τα πάντα, φροντίστε να λίστα το στόχο σας, ας πούμε για όλο το [http://newbalancegreece.europeanhumanists2012.eu/ New Balance Shoes] μήνα Ιανουάριο θέλετε να πουλήσετε τέσσερις τράπεζα ιδιοκτησίας του Ελληνικού Δημοσίου. Πώς θα το κάνεις τότε; [http://timberlandgreece.europeanhumanists2012.eu/ Timberland Greece] Λοιπόν, πολύ απλά, υπάρχουν τέσσερις εβδομάδες σε ένα μήνα, ώστε το μόνο που χρειάζεται να πουλήσει τουλάχιστον μια φορά την εβδομάδα για να φτάσετε το στόχο σας. Κάθε επιχείρηση έχει το δικό του μερίδιο της σκαμπανεβάσματα. <br><br>Αξίζει σε αυτό, και οι περισσότερες συνδέσεις υπάρχουν, η πιο αξιόλογη πρέπει να είναι. Ποσότητα, βέβαια, δεν είναι το παν, και η ποιότητα των δεσμών [http://timberlandgreece.europeanhumanists2012.eu/ Timberland Shoes] αυτών είναι επίσης σημαντικό, το οποίο μετράται συνήθως από το Google PageRank της σελίδας στην οποία βρίσκεται ο σύνδεσμος. Μια σειρά από διαφορετικά προγράμματα υπάρχουν στοιχεία τα οποία θα ψάξει για το web για τις περιοχές που προσφέρουν υψηλό PageRank και [http://airjordangreece.europeanhumanists2012.eu/ Jordan Shoes Greece] λέξεις-κλειδιά που είναι παρόμοια με τη δική σας που θα μπορούσαν να καταστήσουν ελκυστικές συντρόφους σύνδεσμο. <br><br>Αν εισόδου αεροπλάνο Μοντέλο (ή το αεροπλάνο, Model), τότε μόνο τα αρχεία που περιέχουν και τις δύο λέξεις-κλειδιά θα πρέπει να επιστραφεί. Αναζήτηση για αεροπλάνο μοντέλο και το μοντέλο αεροπλάνο θα σας δώσει τα ίδια αποτελέσματα. Θα πρέπει επίσης να επισημανθεί ότι σε αυτήν την επιχείρηση, επιπλέον κενά μεταξύ των λέξεων-κλειδιών θα πρέπει να αγνοηθούν. <br><br>Ψάξτε για ανθρώπους που μπορεί να εγγυηθεί για να ανταποδώσει τη σύνδεσή σας σε μια δεδομένη (σύντομο) χρονικό διάστημα. Ψάξτε για τη γλώσσα που έχει επίγνωση του κινδύνου που παίρνετε με το χρόνο σας στη συμπλήρωση του εντύπου τους. Φυσικά, αυτό μπορεί να σημαίνει ότι είναι ιδιαίτερα κυνική για τη διαδικασία αυτή, αλλά η εμπειρία μας δείχνει ότι αυτός είναι ένας τρόπος για να κτυπήσει τις πιθανότητες. <br><br>Πέρυσι, μιλούσα με ένα φίλο μου που ήταν στην πρώτη του δουλειά μετά το πανεπιστήμιο, και πραγματικά δεν το απολαμβάνει. Η εταιρεία του τον κατάφερε άσχημα, κάνοντας τον να περνούν το χρόνο τους σε άσκοπες δραστηριότητες και υποβαθμίζοντας τις πραγματικές του ικανότητες, και ένιωθε σαν να πηγαίνεις στο έργο που δεν έχει πραγματικό αποτέλεσμα για τίποτα. Εκείνος μου έστειλε ένα σύνδεσμο σε αυτό το βίντεο κλιπ ενός εκπαιδευτή ενυδρείο και ένα χορό θαλάσσιο ίππο μαζί με τον Michael Jackson "Smooth Criminal και είπε:. <br><br>Εάν έχετε συμπεριλάβει τα βίντεο που δεν θέλετε να είναι στη γκαλερί της ιστοσελίδας, μπορείτε να αφαιρέσετε εύκολα. Επιλέξτε όλα τα βίντεο που θέλετε να αφαιρέσετε από τη συλλογή web site και επιλέξτε 'Διαγραφή επιλεγμένων. Κουμπί από τη γραμμή εργαλείων.<ul> |
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| ===First concepts===
| | <li>[http://gamescentral.com/activity/p/172384/ http://gamescentral.com/activity/p/172384/]</li> |
| The earliest ideas in this field go back to work by A.R. Kaye and D.A. George (1970), Branderburg and Wyner (1974)<ref>L. H. Brandenburg and A. D. Wyner, [http://www.alcatel-lucent.com/bstj/vol53-1974/bstj-vol53-issue05.html Capacity of the Gaussian Channel with Memory: The Multivariate Case] Bell Syst. Tech. J., vol. 53, no. 5, pp. 745–778, May/June 1974].</ref> and W. van Etten (1975, 1976). Jack Winters and Jack Salz at [[Bell Labs|Bell Laboratories]] published several papers on [[beamforming]] related applications in 1984 and 1986.<ref>J. Salz, “Digital transmission over cross-coupled linear channels,” AT&T Technical Journal, vol. 64, no. 6, pp. 1147–1159, July–August 1985.</ref>
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| | | <li>[http://annuncianimali.altervista.org/index.php?page=item&id=133835 http://annuncianimali.altervista.org/index.php?page=item&id=133835]</li> |
| ===Principle===
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| [[Arogyaswami Paulraj]] and [[Thomas Kailath]] proposed the concept of [[spatial multiplexing]] (SM) using MIMO in 1993. Their US patent (No. 5,345,599 issued in 1994<ref>http://www.google.com/patents/US5345599</ref>) emphasized "wireless broadcast communications" applications and splitting a high-rate signal "into several low-rate signals". The multi-user MIMO concept of [[space-division multiple access]] (SDMA) was proposed by Richard Roy and Björn Ottersten, researchers as [[ArrayComm]], in 1991. Their US patent (No. 5515378 issued in 1996<ref>http://www.google.com/patents/US5515378</ref>) emphasizes "an array of receiving antennas at the base station" and "plurality of remote users".
| | <li>[http://bbs.wufun.net/home.php?mod=space&uid=274061&do=blog&quickforward=1&id=374923 http://bbs.wufun.net/home.php?mod=space&uid=274061&do=blog&quickforward=1&id=374923]</li> |
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| In 1996, Greg Raleigh, [[Gerard J. Foschini]], and Emre Telatar refined new approaches to MIMO technology, considering a configuration where multiple transmit antennas are co-located at one transmitter to improve the link throughput effectively.<ref>Gregory G. Raleigh and John M. Cioffi, “Spatio-temporal coding for wireless communication,” IEEE Transactions on Communications, vol. 46, no. 3, pp. 357–366, March 1998.</ref><ref>G. J. Foschini, “Layered space–time architecture for wireless communication in a fading environment when using multiple antennas,” Bell Labs Syst. Tech. J., vol. 1, p. 41–59, Autumn 1996.</ref><ref name=telatar>{{cite journal|author=Emre Telatar|title=Capacity of Multi-antenna Gaussian Channels|journal=European Transactions on Telecommunications|pages=585–595|volume=10|year=1999|url=http://mars.bell-labs.com/papers/proof/|issue=6}}</ref>
| | <li>[http://verdamilio.info/org/spip.php?article573/ http://verdamilio.info/org/spip.php?article573/]</li> |
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| Bell Labs was the first to demonstrate a laboratory prototype of spatial multiplexing in 1998, where spatial multiplexing is a principal technology to improve the performance of MIMO communication systems.<ref>G. D. Golden, G. J. Foschini, R. A. Valenzuela, and P. W. Wolniansky, “Detection algorithm and initial laboratory results using V-BLAST space–time communication architecture,” Electron. Lett., vol. 35, pp.~14–16, Jan. 1999.</ref>
| | </ul> |
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| ===Wireless standards===
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| {{see also|MIMO technology in WiMAX|MIMO technology in 3G mobile standards}}
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| In the commercial area, [[Iospan Wireless Inc.]] developed the first commercial system in 2001 that used MIMO with [[orthogonal frequency-division multiple access]] technology (MIMO-OFDMA). Iospan technology supported both diversity coding and spatial multiplexing. In 2005, [[Airgo Networks]] had developed an [[IEEE 802.11n]] precursor implementation based on their patents on MIMO. Following that in 2006, several companies (including at least [[Broadcom]], [[Intel Corporation|Intel]], and [[Marvell Technology Group|Marvell]]) fielded a MIMO-OFDM solution based on a pre-standard for 802.11n Wi-Fi standard. Also in 2006, several companies (Beceem Communications, Samsung, Runcom Technologies, etc.) had developed MIMO-OFDMA based solutions for [[IEEE 802.16]]e WiMAX broadband mobile standard. All upcoming [[4G]] systems will also employ MIMO technology. Several research groups have demonstrated over 1 Gbit/s prototypes.
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| ==Functions of MIMO==
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| MIMO can be sub-divided into three main categories, [[precoding]], [[spatial multiplexing]] or SM, and [[Diversity Coding|diversity coding]].
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| '''[[Precoding]]''' is multi-stream [[beamforming]], in the narrowest definition. In more general terms, it is considered to be all spatial processing that occurs at the transmitter. In (single-stream) beamforming, the same signal is emitted from each of the transmit antennas with appropriate phase and gain weighting such that the signal power is maximized at the receiver input. The benefits of beamforming are to increase the received signal gain, by making signals emitted from different antennas add up constructively, and to reduce the multipath fading effect. In [[line-of-sight propagation]], beamforming results in a well defined directional pattern. However, conventional beams are not a good analogy in cellular networks, which are mainly characterized by [[multipath propagation]]. When the receiver has multiple antennas, the transmit beamforming cannot simultaneously maximize the signal level at all of the receive antennas, and precoding with multiple streams is often beneficial. Note that precoding requires knowledge of [[channel state information]] (CSI) at the transmitter and the receiver.
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| '''[[Spatial multiplexing]]''' requires MIMO antenna configuration. In spatial multiplexing, a high rate signal is split into multiple lower rate streams and each stream is transmitted from a different transmit antenna in the same frequency channel. If these signals arrive at the receiver antenna array with sufficiently different spatial signatures and the receiver has accurate CSI, it can separate these streams into (almost) parallel channels. Spatial multiplexing is a very powerful technique for increasing channel capacity at higher signal-to-noise ratios (SNR). The maximum number of spatial streams is limited by the lesser of the number of antennas at the transmitter or receiver. Spatial multiplexing can be used without CSI at the transmitter, but can be combined with [[precoding]] if CSI is available. Spatial multiplexing can also be used for simultaneous transmission to multiple receivers, known as [[space-division multiple access]] or [[multi-user MIMO]], in which case CSI is required at the transmitter.<ref>D. Gesbert, M. Kountouris, R. W. Heath, Jr., C.-B. Chae, and T. Sälzer, “Shifting the MIMO Paradigm: From Single User to Multiuser Communications,” IEEE Signal Processing Magazine, vol. 24, no. 5, pp. 36–46, Oct., 2007.</ref> The scheduling of receivers with different spatial signatures allows good separability.
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| '''[[Diversity Coding]]''' techniques are used when there is no [[channel state information|channel knowledge]] at the transmitter. In diversity methods, a single stream (unlike multiple streams in spatial multiplexing) is transmitted, but the signal is coded using techniques called [[space-time coding]]. The signal is emitted from each of the transmit antennas with full or near orthogonal coding. Diversity coding exploits the independent fading in the multiple antenna links to enhance signal diversity. Because there is no channel knowledge, there is no beamforming or [[array gain]] from diversity coding.
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| Diversity coding can be combined with spatial multiplexing when some channel knowledge is available at the transmitter.
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| ==Forms of MIMO==
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| [[File:LteMimoAntennen.jpg|thumb| Example of an antenna for [[3GPP Long Term Evolution|LTE]] with 2 ports [[antenna diversity]]]]
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| ===Multi-antenna types===
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| <!-- Deleted image removed: [[File:MIMO communications.svg|thumb|500px|MIMO communications]] --> | |
| Multi-antenna MIMO (or Single user MIMO) technology has been developed and implemented in some standards, e.g., 802.11n products.
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| * [[Single-Input and Single-Output|SISO]]/SIMO/MISO are special cases of MIMO
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| ** Multiple-input and single-output (MISO) is a special case when the receiver has a single antenna.
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| ** Single-input and multiple-output (SIMO) is a special case when the transmitter has a single antenna.
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| ** [[single-input single-output]] (SISO) is a conventional radio system where neither the transmitter nor receiver have multiple antenna.
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| <!-- Deleted image removed: [[File:Ltemimoantenna.jpg|thumb|LTE MIMO antenna for 2-port]] --> | |
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| * Principal single-user MIMO techniques
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| ** [[Bell Laboratories Layered Space-Time|Bell Laboratories Layered Space-Time (BLAST)]], Gerard. J. Foschini (1996)
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| ** Per Antenna Rate Control (PARC), Varanasi, Guess (1998), Chung, Huang, Lozano (2001)
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| ** Selective Per Antenna Rate Control (SPARC), Ericsson (2004)
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| * Some limitations
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| ** The physical antenna spacing is selected to be large; multiple [[wavelengths]] at the base station. The antenna separation at the receiver is heavily space constrained in hand sets, though advanced antenna design and algorithm techniques are under discussion. ''Refer to: [[multi-user MIMO]]''
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| ===Multi-user types===
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| {{main|Multi-user MIMO}}
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| Recently, results of research on multi-user MIMO technology have been emerging. While full multi-user MIMO (or network MIMO) can have a higher potential, practically, the research on (partial) multi-user MIMO (or multi-user and multi-antenna MIMO) technology is more active.
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| * [[Multi-user MIMO|Multi-user MIMO (MU-MIMO)]]
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| ** In recent [[3GPP]] and [[WiMAX]] standards, MU-MIMO is being treated as one of the candidate technologies adoptable in the specification by a number of companies, including Samsung, Intel, Qualcomm, Ericsson, TI, Huawei, Philips, Alcatel-Lucent, and Freescale. For these and other firms active in the mobile hardware market, MU-MIMO is more feasible for low complexity cell phones with a small number of reception antennas, whereas single-user SU-MIMO's higher per-user throughput is better suited to more complex user devices with more antennas.
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| ** [[PU2RC|PU<sup>2</sup>RC]] allows the network to allocate each antenna to a different user instead of allocating only a single user as in single-user MIMO scheduling. The network can transmit user data through a codebook-based spatial beam or a virtual antenna. Efficient user scheduling, such as pairing spatially distinguishable users with codebook based spatial beams, is additionally discussed for the simplification of wireless networks in terms of additional wireless resource requirements and complex protocol modification. Recently, PU<sup>2</sup>RC is included in the system description documentation (SDD) of IEEE 802.16m (WiMAX evolution to meet the ITU-R's IMT-Advance requirements).
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| ** Enhanced multiuser MIMO: 1) Employs advanced decoding techniques, 2) Employs advanced precoding techniques
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| **SDMA represents either [[space-division multiple access]] or super-division multiple access where ''super'' emphasises that orthogonal division such as frequency and time division is not used but non-orthogonal approaches such as superposition coding are used.
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| * [[Cooperative MIMO|Cooperative MIMO (CO-MIMO)]]
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| ** Uses distributed antennas which belong to other users.
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| *[[Macrodiversity]] MIMO
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| **A form of space diversity scheme which uses multiple transmit or receive base stations for communicating coherently with single or multiple users which are possibly distributed in the coverage area, in the same time and frequency resource.<ref name=Karakayali>M. K. Karakayali, G. J. Foschini, and R. A. Valenzuela, [http://dx.doi.org/10.1109/MWC.2006.1678166 Network coordination for spectrally efficient communications in cellular systems] IEEE Wireless Communication Magazine, vol. 13, no. 4, pp. 56-61, Aug. 2006.</ref><ref name=Gesbert2010>D. Gesbert, S. Hanly, H. Huang, S. Shamai, O. Simeone, W. Yu, [http://dx.doi.org/10.1109/JSAC.2010.101202 Multi-cell MIMO cooperative networks: A new look at interference] IEEE Journal on Selected Areas in Communications, vol. 28, no. 9, pp. 1380-1408, Dec. 2010.</ref><ref name=fnt2013>E. Björnson and E. Jorswieck, [http://kth.diva-portal.org/smash/get/diva2:608533/FULLTEXT01 Optimal Resource Allocation in Coordinated Multi-Cell Systems], Foundations and Trends in Communications and Information Theory, vol. 9, no. 2-3, pp. 113-381, 2013.</ref>
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| **The transmitters are far apart in contrast to traditional microdiversity MIMO schemes such as single-user MIMO. In multi-user macrodiversity MIMO scenario, users may also be far apart. Therefore, every constituent link in the virtual MIMO link has distinct average link [[Signal-to-noise ratio|SNR]]. This difference is mainly due to the different long-term channel impairments such as path loss and shadow fading which are experienced by different links.
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| **Macrodiversity MIMO schemes pose unprecedented theoretical and practical challenges. Among many theoretical challenges, perhaps the most fundamental challenge is to understand how the different average link SNRs affect the overall system capacity and individual user performance in fading environments.<ref name=Basnayaka>D. A. Basnayaka, P. J. Smith and P. A. Martin, [http://dx.doi.org/10.1109/TWC.2013.032113.120798 Performance analysis of macrodiversity MIMO systems with MMSE and ZF receivers in flat Rayleigh fading] IEEE Transactions on Wireless Communications, vol. 12, no. 5, pp. 2240 - 2251, May 2013.</ref>
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| * MIMO [[Routing]]
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| ** Routing a cluster by a cluster in each hop, where the number of nodes in each cluster is larger or equal to one. MIMO routing is different from conventional (SISO) routing since conventional routing protocols route node by node in each hop.<ref>{{cite journal|author=S. Cui, A. J. Goldsmith, and A. Bahai|title=Energy-efficiency of MIMO and Cooperative MIMO in Sensor Networks|journal=IEEE J. Select. Areas of Commun.|pages=1089–1098|volume=22|issue=6|date=August 2004|doi=10.1109/JSAC.2004.830916}}</ref>
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| ==Applications of MIMO==
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| Spatial multiplexing techniques make the receivers very complex, and therefore they are typically combined with [[Orthogonal frequency-division multiplexing]] (OFDM) or with [[Orthogonal Frequency Division Multiple Access]] (OFDMA) modulation, where the problems created by a multi-path channel are handled efficiently. The IEEE [[802.16e]] standard incorporates MIMO-OFDMA. The IEEE 802.11n standard, released in October 2009, recommends MIMO-OFDM.
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| MIMO is also planned to be used in [[Mobile radio telephone]] standards such as recent [[3GPP]] and [[3GPP2]]. In 3GPP, [[HSPA+|High-Speed Packet Access plus (HSPA+)]] and [[3GPP Long Term Evolution|Long Term Evolution (LTE)]] standards take MIMO into account. Moreover, to fully support cellular environments, MIMO research consortia including IST-MASCOT propose to develop advanced MIMO techniques, e.g., [[Multi-user MIMO|multi-user MIMO (MU-MIMO)]].
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| MIMO technology can be used in non-wireless communications systems. One example is the home networking standard [[ITU-T]] [[G.9963]], which defines a powerline communications system that uses MIMO techniques to transmit multiple signals over multiple AC wires (phase, neutral and ground).{{citation needed |date= July 2011}}
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| ==Mathematical description==
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| [[File:Kanalmatrix MIMO.png|thumb|280px|MIMO channel model]]
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| In MIMO systems, a transmitter sends multiple streams by multiple transmit antennas. The transmit streams go through a [[matrix (mathematics)|matrix]] channel which consists of all <math>N_t N_r</math> paths between the <math>N_t</math> transmit antennas at the transmitter and <math>N_r</math> receive antennas at the receiver. Then, the receiver gets the received signal [[Vector space|vectors]] by the multiple receive antennas and decodes the received signal vectors into the original information. A [[narrowband]] [[flat fading]] MIMO system is modelled as
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| :<math>\mathbf{y} = \mathbf{H}\mathbf{x} + \mathbf{n}</math>
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| where <math>\scriptstyle\mathbf{y}</math> and <math>\scriptstyle\mathbf{x}</math> are the receive and transmit vectors, respectively, and <math>\scriptstyle\mathbf{H}</math> and <math>\scriptstyle\mathbf{n}</math> are the channel matrix and the noise vector, respectively.
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| Referring to [[information theory]], the ergodic [[channel capacity]] of MIMO systems where both the transmitter and the receiver have perfect instantaneous [[channel state information]] is<ref name=dlove>D. Love, R. Heath, V. Lau, D. Gesbert, B. Rao and M. Andrews, [http://www.eurecom.fr/~gesbert/papers/JSAC_limitedfeedback_tutorial.pdf An overview of limited feedback in wireless communication systems], IEEE Journal on Selected Areas Communications, vol 26, pp. 1341–1365, 2008.</ref>
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| :<math>C_\mathrm{perfect-CSI} = E\left[\max_{\mathbf{Q}; \, \mbox{tr}(\mathbf{Q}) \leq 1} \log_2 \det\left(\mathbf{I} + \rho \mathbf{H}\mathbf{Q}\mathbf{H}^{H}\right)\right] = E\left[\log_2 \det\left(\mathbf{I} + \rho \mathbf{D}\mathbf{S} \mathbf{D} \right)\right]</math>
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| where <math>()^H</math> denotes [[Conjugate transpose|Hermitian transpose]] and <math>\rho</math> is the ratio between transmit power and noise power (i.e., transmit [[Signal-to-noise ratio|SNR]]). The optimal signal covariance <math>\scriptstyle \mathbf{Q}=\mathbf{VSV}^H</math> is achieved through [[singular value decomposition]] of the channel matrix <math>\scriptstyle\mathbf{UDV}^H \,=\, \mathbf{H}</math> and an optimal diagonal power allocation matrix <math>\scriptstyle \mathbf{S}=\textrm{diag}(s_1,\ldots,s_{\min(N_t, N_r)},0,\ldots,0)</math>. The optimal power allocation is achieved through waterfilling,<ref>D. Tse and P. Viswanath, [http://www.eecs.berkeley.edu/~dtse/book.html Fundamentals of Wireless Communication], Cambridge University Press, 2005.</ref> that is
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| :<math>s_i = \left(\mu - \frac{1}{\rho d_i^2} \right)^+, \quad \textrm{for} \,\, i=1,\ldots,\min(N_t, N_r),</math>
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| where <math>d_1,\ldots,d_{\min(N_t, N_r)}</math> are the diagonal elements of <math>\scriptstyle \mathbf{D}</math>, <math>(\cdot)^+</math> is zero if its argument is negative, and <math>\mu</math> is selected such that <math>s_1+\ldots+s_{\min(N_t, N_r)}=N_t</math>.
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| If the transmitter has only statistical [[channel state information]], then the ergodic [[channel capacity]] will decrease as the signal covariance <math>\scriptstyle \mathbf{Q}</math> can only be optimized in terms of the average [[mutual information]] as<ref name=dlove />
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| :<math>C_\mathrm{statistical-CSI} = \max_{\mathbf{Q}} E\left[\log_2 \det\left(\mathbf{I} + \rho \mathbf{H}\mathbf{Q}\mathbf{H}^{H}\right)\right].</math>
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| The [[Spatial Correlation|spatial correlation]] of the channel have a strong impact on the ergodic [[channel capacity]] with statistical information.
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| If the transmitter has no [[channel state information]] it can select the signal covariance <math>\scriptstyle \mathbf{Q}</math> to maximize channel capacity under worst-case statistics, which means <math>\scriptstyle \mathbf{Q}=1/N_t \mathbf{I}</math> and accordingly
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| :<math>C_\mathrm{no-CSI} = E\left[\log_2 \det\left(\mathbf{I} + \frac{\rho}{N_t}\mathbf{H}\mathbf{H}^{H}\right)\right].</math>
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| Depending on the statistical properties of the channel, the ergodic capacity is no greater than <math>\scriptstyle\min(N_t, N_r)</math> times larger than that of a SISO system.
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| ==MIMO testing==
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| MIMO signal testing focuses first on the transmitter/receiver system. The random phases of the sub-carrier signals can produce instantaneous power levels that cause the amplifier to compress, momentarily causing distortion and ultimately symbol errors. Signals with a high '''PAR''' ([[peak-to-average ratio]]) can cause amplifiers to compress unpredictably during transmission. OFDM signals are very dynamic and compression problems can be hard to detect because of their noise-like nature.<ref>Stefan Schindler, Heinz Mellein, [http://www.rohde-schwarz.com/appnote/1SP18.pdf, "Assessing a MIMO Channel"], Rohde & Schwarz, pg. 11.</ref>
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| Knowing the quality of the signal channel is also critical. A [[radio channel emulator|channel emulator]] can simulate how a device performs at the cell edge, can add noise or can simulate what the channel looks like at speed. To fully qualify the performance of a receiver, a calibrated transmitter, such as a [[Signal generator#Vector signal generators|vector signal generator]] (VSG), and channel emulator can be used to test the receiver under a variety of different conditions. Conversely, the transmitter's performance under a number of different conditions can be verified using a channel emulator and a calibrated receiver, such as a [[vector signal analyzer]] (VSA).
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| Understanding the channel allows for manipulation of the phase and amplitude of each transmitter in order to form a beam. To correctly form a beam, the transmitter needs to understand the characteristics of the channel. This process is called ''channel sounding'' or [[channel estimation]]. A known signal is sent to the mobile device that enables it to build a picture of the channel environment. The mobile device sends back the channel characteristics to the transmitter. The transmitter can then apply the correct phase and amplitude adjustments to form a beam directed at the mobile device. This is called a closed-loop MIMO system. For [[beamforming]], it is required to adjust the phases and amplitude of each transmitter. In a beamformer optimized for spatial diversity or spatial multiplexing, each antenna element simultaneously transmits a weighted combination of two data symbols.<ref>Agilent [http://cp.literature.agilent.com/litweb/pdf/5989-8973EN.pdf], ''Agilent MIMO Channel Modeling and Emulation Test Challenges'', pg. 10, January 22, 2010, accessed September 16, 2011.</ref>
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| ==MIMO literature==
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| ===Principal researches===
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| Papers by Gerard J. Foschini and Michael J. Gans,<ref>{{cite journal|author=Gerard J. Foschini and Michael. J. Gans|title=On limits of wireless communications in a fading environment when using multiple antennas|journal=Wireless Personal Communications|pages=311–335|volume=6|issue=3|date=January 1998|doi=10.1023/A:1008889222784}}</ref> Foschini<ref>{{cite journal|author=Gerard J. Foschini|title=Layered space-time architecture for wireless communications in a fading environment when using multi-element antennas|journal=Bell Labs Technical Journal |pages=41–59|volume=1|date=autumn 1996|doi=10.1002/bltj.2015|issue=2}}</ref> and Emre Telatar<ref name=telatar/> have shown that the [[channel capacity]] (a theoretical upper bound on system throughput) for a MIMO system is increased as the number of antennas is increased, proportional to the smaller of the number of transmit antennas and the number of receive antennas. This is known as the multiplexing gain and this basic finding in [[information theory]] is what led to a spurt of research in this area. Despite the simple propagation models used in the aforementioned seminal works, the multiplexing gain is a fundamental property that can be proved under almost any physical channel propagation model and with practical hardware that is prone to transceiver impairments.<ref>{{cite journal|author=Emil Björnson, Per Zetterberg, Mats Bengtsson, Björn Ottersten|title=Capacity Limits and Multiplexing Gains of MIMO Channels with Transceiver Impairments|journal=IEEE Communications Letters |pages=91–94|volume=17|date=January 2013|url=http://arxiv.org/pdf/1209.4093|issue=1}}</ref>
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| Papers by Fernando Rosas and Christian Oberli have shown that the entire MIMO SVD link can be approximated by the average of the SER of Nakagami-m channels.<ref>{{cite journal|author=Rosas, F. and Oberli, C.|title=Nakagami-m approximations for multiple-input multiple-output singular value decomposition transmissions|journal=Communications, IET|pages=554–561|volume=7|issue=6|date=April 16, 2013|doi=10.1049/iet-com.2012.0400}}</ref> This leads to characterise the eigenchannels of N × N MIMO channels with N larger than 14, showing that the smallest eigenchannel distributes as a Rayleigh channel, the next four eigenchannels closely distributes as Nakagami-m channels with m = 4, 9, 25 and 36, and the N - 5 remaining eigenchannels have statistics similar to an additive white Gaussian noise (AWGN) channel within 1 dB signal-to-noise ratio. It is also shown that 75% of the total mean power gain of the MIMO SVD channel goes to the top third of all the eigenchannels.
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| A textbook by A. Paulraj, R. Nabar and D. Gore has published an introduction to this area.<ref>{{cite book|author=A. Paulraj, R. Nabar and D. Gore|title=Introduction to Space-time Communications|work= Cambridge University Press|year=2003}}</ref> There are many other principal textbooks available as well.<ref>{{cite book|author= David Tse, Pramod Viswanath|title=Fundamentals of Wireless Communication|work=Cambridge |year=2005}}</ref><ref>{{cite book|author=Claude Oestges, Bruno Clerckx|title=MIMO Wireless Communications: From Real-world Propagation to Space-time Code Design|work=Academic Press |year=2007}}</ref><ref>{{cite book|author= Ezio Biglieri, Robert Calderbank, Anthony Constantinides, Andrea Goldsmith, Arogyaswami Paulraj, H. Vincent Poor|title=MIMO Wireless Communications|work=Cambridge University Press |year=2010}}</ref> Mobile Experts has published a [http://mobile-experts.net/product_info.php?products_id=46 research report] which predicts the use of MIMO technology in 500 million PCs, tablets, and smartphones by 2016.
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| ===Diversity-multiplexing tradeoff (DMT)=== | |
| There exists a fundamental tradeoff between transmit diversity and spatial multiplexing gains in a MIMO system (Zheng and Tse, 2003).<ref>{{cite journal|author=L. Zheng and D. N. C. Tse|title=Diversity and multiplexing: A fundamental tradeoff in multiple-antenna channels|journal=IEEE Trans. Inf. Th.|pages=1073–1096|volume=49|issue=5|date=May 2003|doi=10.1109/TIT.2003.810646}}</ref> In particular, achieving high spatial multiplexing gains is of profound importance in modern wireless systems.<ref>{{cite journal|author=A. Lozano and N. Jindal|title=Transmit diversity vs. spatial multiplexing in modern MIMO systems|journal=IEEE Trans. Wireless Commun.|pages=186–197|volume=9|issue=1|year=2010|url=http://www.dtic.upf.edu/~alozano/papers/Diversity.pdf}}</ref>
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| ===Other applications===
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| Given the nature of MIMO, it is not limited to wireless communication. It can be used for [[wire line]] communication as well. For example, a new type of [[DSL]] technology (gigabit DSL) has been proposed based on binder MIMO channels.
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| ===Sampling theory in MIMO systems===
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| An important question which attracts the attention of engineers and mathematicians is how to use the multi-output signals at the receiver to recover the multi-input signals at the transmitter. In Shang, Sun and Zhou (2007), sufficient and necessary conditions are established to guarantee the complete recovery of the multi-input signals.<ref>{{cite journal|author=Z. Shang, W. Sun and X. Zhou|title= Vector sampling expansions in shift invariant subspaces |journal= Journal of Mathematical Analysis and Applications|pages=898–919|volume=325|issue=2|date=January 2007|doi=10.1016/j.jmaa.2006.02.033}}</ref>
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| ==See also==
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| {{columns-list|3|
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| * [[Channel bonding]]
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| * [[Duplex (telecommunications)]]
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| * [[Single-frequency network]] (SFN)
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| * [[WiMAX MIMO]]
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| * [[Wi-Fi]]
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| * [[Phased array]]
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| * [[Smart Antennas]]
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| * [[Antenna diversity]]
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| * [[Beamforming]]
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| * [[Channel state information]]
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| * [[Dirty paper coding (DPC)]]
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| * [[Precoding]]
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| * [[Space–time block code]]
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| * [[Space–time code]]
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| * [[Spatial multiplexing]]
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| * [[Multi-user MIMO]]
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| * [[802.11]]
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| * [[802.16]]
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| * [[Macrodiversity]]
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| * [[History of smart antennas]]
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| }}
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| ==References==
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| {{reflist|3}}
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| ==External links==
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| {{external links|date=May 2012}}
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| * [http://engineering.cttc.es/gedomis GEDOMIS (GEneric hardware DemOnstrator for MIMO Systems)]
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| * [http://www-x.antd.nist.gov/uwb/main.html NIST UWB-MIMO Channel Propagation Measurements in the 2–8 GHz Spectrum]
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| * [http://wcsp.eng.usf.edu/MIMO_links.html Links to suggested readings in MIMO] - WCSP Group — University of South Florida (USF)
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| * [http://www.ieee.li/pdf/viewgraphs/wireless_mimo.pdf Introduction to Wireless MIMO - Theory and Applications]
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| * [http://www.ieee.li/pdf/viewgraphs/introduction_orthogonal_frequency_division_multiplex.pdf Introduction to Orthogonal Frequency Division Multiplexing (covers OFDM and MIMO radio configurations)]
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| * Computerworld QuickStudy [http://www.computerworld.com/action/article.do?command=viewArticleBasic&articleId=109410 MIMO]
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| * [http://www.rfglobalnet.com/article.mvc/Meeting-The-Test-Challenges-Of-4G-LTE-0001 Meeting The Test Challenges Of 4G LTE]
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| * [http://www.rfglobalnet.com/article.mvc/The-Basics-Of-OFDM-0001 The Basics Of OFDM]
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| * [http://www.rfglobalnet.com/article.mvc/MIMO-The-Future-Of-Wireless-0001 MIMO: The Future Of Wireless: Test Challenges For WiMAX, HSPA+, And LTE]
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| * [http://mobiledevdesign.com/hardware_news/radio_challenges_moving_mimo/ The challenges of moving to MIMO systems]
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| * [http://rfdesign.com/microwave_millimeter_tech/test_and_measurement/711RFD30.pdf RF test system tackles 4 × 4 MIMO signals]
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| * [http://www.rfglobalnet.com/article.mvc/EVM-Measurements-In-Amplifier-Modulation-0001 The Role Of EVM Measurements In Characterizing Amplifier Modulation Performance]
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| * [http://www.rfglobalnet.com/article.mvc/Industry-Views-4G-Systems-Bring-New-Design-An-0002 Industry Views: 4G Systems Bring New Design And Testing Challenges]
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| * [http://www.tmworld.com/article/CA6488248.html Instruments test MIMO data transmissions]
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| * [http://www.ofcom.org.uk/static/archive/ra/topics/research/topics/propagation/mimo.pdf Literature review of MIMO]
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| * [http://www.ztecinstruments.com/zconnect/?p=1635 Overview of MIMO & MIMO RFIC Test Architectures]
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| {{DEFAULTSORT:Mimo}}
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| [[Category:IEEE 802]]
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| [[Category:Information theory]]
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| [[Category:Radio resource management]]
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| [[bn:মাইমো]]
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