Multiple-input multiple-output - Revision history

Onnowpurbo: /* Mathematical description */

2010-12-28T12:08:52Z

Mathematical description

Onnowpurbo: /* Multi-antenna types */

2010-12-28T12:08:16Z

Multi-antenna types

Onnowpurbo: /* Wireless standards */

2010-12-28T12:05:02Z

Wireless standards

Onnowpurbo at 12:04, 28 December 2010

2010-12-28T12:04:35Z

Onnowpurbo: New page: {{about|MIMO in wireless communication}} Understanding of SISO, SIMO, MISO and MIMO In radio, '''multiple-input and multiple-output''', or '''M...

2010-12-28T11:58:31Z

New page: {{about|MIMO in wireless communication}} thumb|280px|Understanding of SISO, SIMO, MISO and MIMO In radio, '''multiple-input and multiple-output''', or '''M...

New page

{{about|MIMO in wireless communication}}

[[Image:Prinzip MIMO.png|thumb|280px|Understanding of SISO, SIMO, MISO and MIMO]]

In [[radio]], '''multiple-input and multiple-output''', or '''MIMO''' (commonly pronounced my-moh or me-moh), 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.

MIMO technology has attracted attention in [[wireless]] communications, because it offers significant increases in data throughput and link range without additional bandwidth or transmit power. It achieves this by higher spectral efficiency (more bits per second per hertz of bandwidth) and link reliability or diversity (reduced fading). Because of these properties, MIMO is an important part of modern wireless communication standards such as [[IEEE 802.11n]] (Wifi), [[4G]], [[3GPP Long Term Evolution]], [[WiMAX]] and [[Evolved HSPA|HSPA+]].

==History of MIMO==
===Background technologies===
The earliest ideas in this field go back to work by A.R. Kaye and D.A. George (1970) 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.

===Principle===
Arogyaswami Paulraj and Thomas Kailath proposed the concept of [[spatial multiplexing|spatial multiplexing (SM)]] using MIMO in 1993. Their US Patent No. 5,345,599 issued 1994. on Spatial Multiplexing emphasized applications to wireless broadcast.

In 1996, Greg Raleigh and [[Gerard J. Foschini]] refine new approaches to MIMO technology, which considers a configuration where multiple transmit antennas are co-located at one transmitter to improve the link throughput effectively.

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.

===Wireless standards===
{{see also|MIMO technology in WiMAX|MIMO technology in 3G mobile standards}}

In the commercial arena, [[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 a 802.11n precursor implementation based on their patents on MIMO. Following that in 2006, several companies (including at least Broadcom, Intel, and Marvell) have fielded a MIMO-OFDM solution based on a pre-standard for 802.11n WiFi standard. Also in 2006, several companies (Beceem Communications, Samsung, Runcom Technologies, etc.) have 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.

==Functions of MIMO==
MIMO can be sub-divided into three main categories, [[precoding]], [[spatial multiplexing]] or SM, and [[Diversity Coding|diversity coding]].

'''[[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-layer) beamforming, the same signal is emitted from each of the transmit antennas with appropriate phase (and sometimes 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 the absence of scattering, beamforming results in a well defined directional pattern, but in typical cellular conventional beams are not a good analogy. 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 used. Note that precoding requires knowledge of [[channel state information]] (CSI) at the transmitter.

'''[[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, the receiver 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 in the number of antennas at the transmitter or receiver. Spatial multiplexing can be used with or without transmit channel knowledge. Spatial multiplexing can also be used for simultaneous transmission to multiple receivers, known as [[space-division multiple access]]. By scheduling receivers with different spatial signatures, good separability can be assured.

'''[[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.

Spatial multiplexing can also be combined with precoding when the channel is known at the transmitter or combined with diversity coding when decoding reliability is in trade-off.

==Forms of MIMO==
===Multi-antenna types===
[[Image:MIMO communications.svg|thumb|500px|MIMO communications]]
Up to now,{{when}} multi-antenna MIMO (or Single user MIMO) technology has been mainly developed and is implemented in some standards, e.g. 802.11n products.
* [[Single-Input and Single-Output|SISO]]/SIMO/MISO are [[Degeneracy_(mathematics)|degenerate]] cases of MIMO
** Multiple-input and single-output (MISO) is a degenerate case when the receiver has a single antenna.
** Single-input and multiple-output (SIMO) is a degenerate case when the transmitter has a single antenna.
** [[single-input single-output]] (SISO) is a radio system where neither the transmitter nor receiver have multiple antenna.

* Principal single-user MIMO techniques
** [[Bell Laboratories Layered Space-Time|Bell Laboratories Layered Space-Time (BLAST)]], Gerard. J. Foschini (1996)
** Per Antenna Rate Control (PARC), Varanasi, Guess (1998), Chung, Huang, Lozano (2001)
** Selective Per Antenna Rate Control (SPARC), Ericsson (2004)

* Some limitations
** The physical antenna spacing are 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: [[Advanced MIMO communications|Advanced MIMO]]''

===Multi-user types===
{{main|Multi-user MIMO}}
Recently, the research on multi-user MIMO technology has been emerging. While full multi-user MIMO (or network MIMO) can have higher potentials, from its practicality the research on (partial) multi-user MIMO (or multi-user and multi-antenna MIMO) technology is more active.

* [[Multi-user MIMO|Multi-user MIMO (MU-MIMO)]]
** In recent [[3GPP]] and [[WiMAX]] standards, MU-MIMO is being treated as one of candidate technologies adoptable in the specification by a lot of companies including Samsung, Intel, Qualcomm, Ericsson, TI, Huawei, Philips, Alcatel-Lucent, Freescale, et al. since MU-MIMO is more feasible to low complexity mobiles with small number of reception antennas than SU-MIMO with the high system throughput capability.
** [[PU2RC|PU<sup>2</sup>RC]] allows the network to allocate each antenna to the different users instead of allocating only 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, are 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 the system description documentation (SDD) of IEEE 802.16m (WiMAX evolution to meet the ITU-R's IMT-Advance requirements).
** Enhanced multiuser MIMO: 1)Employ advanced decoding techniques, 2) Employ advanced precoding techniques
**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 super-position coding are used.

* [[Cooperative MIMO|Cooperative MIMO (CO-MIMO)]]
** Utilizes distributed antennas which belong to other users.

* MIMO [[Routing]]
** 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 a node by a node in each hop.

==Applications of MIMO==
Spatial multiplexing techniques makes the receivers very complex, and therefore it is typically combined with [[Orthogonal frequency-division multiplexing]] (OFDM) or with [[Orthogonal Frequency Division Multiple Access]] (OFDMA) modulation, where the problems created by 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.

MIMO is also planned to be used in [[Mobile radio telephone]] standards such as recent [[3GPP]] and [[3GPP2]] standards. 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 [http://www.ist-mascot.org/ IST-MASCOT] propose to develop advanced MIMO techniques, i.e., [[Multi-user MIMO|multi-user MIMO (MU-MIMO)]].

==Mathematical description==
[[Image:Kanalmatrix MIMO.png|thumb|280px|MIMO channel model]]
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
:<math>\mathbf{y} = \mathbf{H}\mathbf{x} + \mathbf{n}</math>
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.

{{Merge to |Channel capacity |date=October 2010}}
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
:<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>
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, that is
:<math>s_i = \left(\mu - \frac{1}{\rho d_i^2} \right)^+, \quad \textrm{for} \,\, i=1,\ldots,\min(N_t, N_r),</math>
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>.

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
:<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>
The [[Spatial Correlation|spatial correlation]] of the channel have a strong impact on the ergodic [[channel capacity]] with statistical information.

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
:<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>

Depending on the statistical properties of the channel, the ergodic capacity is mostly <math>\scriptstyle\min(N_t, N_r)</math> times larger than that of a SISO system.

==MIMO testing==
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) 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.

Knowing the quality of the signal channel is also critical. A 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 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).

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 state information#Estimation of CSI|channel estimation]]. A known signal is sent to the mobile device that enables it to build a picture of the channel environment. The phone then sends back the channel characteristics to the transmitter. The transmitter then can 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.

==MIMO literature==
===Principal researches===
Papers by Gerard J. Foschini and Michael J. Gans, Foschini and Emre [http://web.mit.edu/6.454/www/www_fall_2004/alex_o/Telatar99.pdf#search=%22telatar%22 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 minimum number of transmit and receive antennas. This basic finding in [[information theory]] is what led to a spurt of research in this area. A text book by A. Paulraj, R. Nabar and D. Gore has published an introduction to this area.

===Diversity-Multiplexing Tradeoff (DMT)===
There exists a fundamental tradeoff between diversity and multiplexing in a MIMO system (Zheng and Tse, 2003).

===Other applications===
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.

==See also==
* [[Channel bonding]]
* [[Mimax]]
* [[Single-frequency network]] (SFN)
* [[WiMAX MIMO]]

===Intelligent antenna technology===
* [[Phased array]]
* [[Smart Antennas]]

===Spatial techniques===
* [[Antenna diversity]]
* [[Beamforming]]
* [[Channel state information]]
* [[Dirty paper coding (DPC)]]
* [[Precoding]]
* [[Space–time block code]]
* [[Space–time code]]
* [[Spatial multiplexing]]
* [[Multi-user MIMO]]
* [[802.11]]
* [[802.16]]

==References==

==External links==
===Web sites===
* [http://wikieng.cttc.es/index.php/GEDOMIS GEDOMIS® (GEneric hardware DemOnstrator for MIMO Systems)]
* [http://www-x.antd.nist.gov/uwb/main.html NIST UWB-MIMO Channel Propagation Measurements in the 2-8 GHz Spectrum]
* D. Gesbert, M. Kountouris, R. W. Heath, Jr., C.-B. Chae, and T. Salzer, [http://www.eurecom.fr/%7Egesbert/papers/TutorialMUMIMOv3.pdf Shifting the MIMO Paradigm: From Single User to Multiuser Communications], IEEE Signal Processing Magazine, vol. 24, no. 5, pp. 36–46, Oct., 2007
* [http://wcsp.eng.usf.edu/MIMO_links.html Links to suggested readings in MIMO] - WCSP Group — University of South Florida (USF)
* [http://www.ieee.li/pdf/viewgraphs/wireless_mimo.pdf Introduction to Wireless MIMO - Theory and Applications]
* [http://www.ieee.li/pdf/viewgraphs/introduction_orthogonal_frequency_division_multiplex.pdf Introduction to Orthogonal Frequency Division Multiplexing (covers OFDM and MIMO radio configurations)]
* [http://www.ece.ualberta.ca/~HCDC/mimohistory.html Introduction to MIMO]
* Computerworld QuickStudy [http://www.computerworld.com/action/article.do?command=viewArticleBasic&articleId=109410 MIMO]
* [http://www.mwjournal.com/Journal/article.asp?HH_ID=AR_7230 Developing Strategies for MIMO Testing]
* [http://www.rfglobalnet.com/article.mvc/Meeting-The-Test-Challenges-Of-4G-LTE-0001 Meeting The Test Challenges Of 4G LTE ]
* [http://www.rfglobalnet.com/article.mvc/The-Basics-Of-OFDM-0001 The Basics Of OFDM]
* [http://www.rfglobalnet.com/article.mvc/MIMO-The-Future-Of-Wireless-0001 MIMO: The Future Of Wireless: Test Challenges For WiMAX, HSPA+, And LTE]
* [http://www.mwrf.com/Articles/Index.cfm?ArticleID=18032 OFDM Will Soon Be Dominant Form Of Digital Modulation]
* [http://mobiledevdesign.com/hardware_news/radio_challenges_moving_mimo/ The challenges of moving to MIMO systems ]
* [http://rfdesign.com/microwave_millimeter_tech/test_and_measurement/711RFD30.pdf RF test system tackles 4 x 4 MIMO signals]
* [http://www.rdmag.com/ShowPR_Print~PUBCODE~014~ACCT~1400000100~ISSUE~0802~RELTYPE~PR~Cat~14~SubCat~20~PRODCODE~00000000~PRODLETT~KW~CALLFROM~PR~CompName~R~D.html Increasing Mobile Systems Raises RF Test Throughput Issues]
* [http://www.rfglobalnet.com/article.mvc/EVM-Measurements-In-Amplifier-Modulation-0001 The Role Of EVM Measurements In Characterizing Amplifier Modulation Performance]
* [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]
* [http://electronicdesign.com/Articles/Index.cfm?ArticleID=17368 Test System Pushes MIMO Standards Into The Spotlight]
* [http://www.tmworld.com/article/CA6488248.html Instruments test MIMO data transmissions]

===Books===
* Claude Oestges, Bruno Clerckx, "MIMO Wireless Communications : From Real-world Propagation to Space-time Code Design," Academic, 2007.07.16, 448p, [http://www.amazon.com/MIMO-Wireless-Communications-Real-World-Propagation/dp/0123725356 ISBN : 0123725356]

[[Category:IEEE 802]]
[[Category:Information theory]]
[[Category:Radio resource management]]

← Older revision		Revision as of 12:08, 28 December 2010
Line 69:		Line 69:
	MIMO is also planned to be used in [[Mobile radio telephone]] standards such as recent [[3GPP]] and [[3GPP2]] standards. 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 [http://www.ist-mascot.org/ IST-MASCOT] propose to develop advanced MIMO techniques, i.e., [[Multi-user MIMO\|multi-user MIMO (MU-MIMO)]].		MIMO is also planned to be used in [[Mobile radio telephone]] standards such as recent [[3GPP]] and [[3GPP2]] standards. 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 [http://www.ist-mascot.org/ IST-MASCOT] propose to develop advanced MIMO techniques, i.e., [[Multi-user MIMO\|multi-user MIMO (MU-MIMO)]].

−	~~==Mathematical description==~~
−	~~[[Image:Kanalmatrix MIMO.png\|thumb\|280px\|MIMO channel model]]~~
−	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
−	~~:<math>\mathbf{y} = \mathbf{H}\mathbf{x} + \mathbf{n}</math>~~
−	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.

−	~~{{Merge to \|Channel capacity \|date=October 2010}}~~
−	~~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~~
−	:<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>
−	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, that is
−	~~:<math>s_i = \left(\mu - \frac{1}{\rho d_i^2} \right)^+, \quad \textrm{for} \,\, i=1,\ldots,\min(N_t, N_r),</math>~~
−	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>.
−
−	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
−	~~:<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>~~
−	~~The [[Spatial Correlation\|spatial correlation]] of the channel have a strong impact on the ergodic [[channel capacity]] with statistical information.~~
−
−	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
−	~~:<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>~~
−
−	~~Depending on the statistical properties of the channel, the ergodic capacity is mostly <math>\scriptstyle\min(N_t, N_r)</math> times larger than that of a SISO system.~~

	==MIMO testing==		==MIMO testing==

← Older revision		Revision as of 12:05, 28 December 2010
Line 17:		Line 17:

	===Wireless standards===		===Wireless standards===
−	~~{{see also\|MIMO technology in WiMAX\|MIMO technology in 3G mobile standards}}~~

	In the commercial arena, [[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 a 802.11n precursor implementation based on their patents on MIMO. Following that in 2006, several companies (including at least Broadcom, Intel, and Marvell) have fielded a MIMO-OFDM solution based on a pre-standard for 802.11n WiFi standard. Also in 2006, several companies (Beceem Communications, Samsung, Runcom Technologies, etc.) have 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.		In the commercial arena, [[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 a 802.11n precursor implementation based on their patents on MIMO. Following that in 2006, several companies (including at least Broadcom, Intel, and Marvell) have fielded a MIMO-OFDM solution based on a pre-standard for 802.11n WiFi standard. Also in 2006, several companies (Beceem Communications, Samsung, Runcom Technologies, etc.) have 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.

← Older revision		Revision as of 12:04, 28 December 2010
Line 1:		Line 1:
−	~~{{about\|MIMO in wireless communication}}~~	+	[[Image:Prinsip-mimo.jpeg\|thumb\|280px\|Understanding of SISO, SIMO, MISO and MIMO]]
−
−	[[Image:~~Prinzip MIMO~~.~~png~~\|thumb\|280px\|Understanding of SISO, SIMO, MISO and MIMO]]

	In [[radio]], '''multiple-input and multiple-output''', or '''MIMO''' (commonly pronounced my-moh or me-moh), 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.		In [[radio]], '''multiple-input and multiple-output''', or '''MIMO''' (commonly pronounced my-moh or me-moh), 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.

@@ Line 33: / Line 33: @@
 ==Forms of MIMO==
 ===Multi-antenna types===
-[[Image:MIMO communications.svg|thumb|500px|MIMO communications]]
+[[Image:Mimo-communications.jpeg|thumb|500px|MIMO communications]]
 Up to now,{{when}} multi-antenna MIMO (or Single user MIMO) technology has been mainly developed and is implemented in some standards, e.g. 802.11n products.
 * [[Single-Input and Single-Output|SISO]]/SIMO/MISO are [[Degeneracy_(mathematics)|degenerate]] cases of MIMO