# MIMO

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In radio, multiple-input and multiple-output, or MIMO (), is a method for multiplying the capacity of a radio link using multiple transmission and receiving antennas to exploit multipath propagation. [1] MIMO has become an essential element of wireless communication standards including IEEE 802.11n (Wi-Fi), IEEE 802.11ac (Wi-Fi), HSPA+ (3G), WiMAX (4G), and Long Term Evolution (4G LTE). More recently, MIMO has been applied to power-line communication for 3-wire installations as part of ITU G.hn standard and HomePlug AV2 specification. [2] [3]

In radio engineering, an antenna is the interface between radio waves propagating through space and electric currents moving in metal conductors, used with a transmitter or receiver. In transmission, a radio transmitter supplies an electric current to the antenna's terminals, and the antenna radiates the energy from the current as electromagnetic waves. In reception, an antenna intercepts some of the power of a radio wave in order to produce an electric current at its terminals, that is applied to a receiver to be amplified. Antennas are essential components of all radio equipment.

In wireless telecommunications, multipath is the propagation phenomenon that results in radio signals reaching the receiving antenna by two or more paths. Causes of multipath include atmospheric ducting, ionospheric reflection and refraction, and reflection from water bodies and terrestrial objects such as mountains and buildings.

## Contents

At one time, in wireless the term "MIMO" referred to the use of multiple antennas at the transmitter and the receiver. In modern usage, "MIMO" specifically refers to a practical technique for sending and receiving more than one data signal simultaneously over the same radio channel by exploiting multipath propagation. MIMO is fundamentally different from smart antenna techniques developed to enhance the performance of a single data signal, such as beamforming and diversity.

Beamforming or spatial filtering is a signal processing technique used in sensor arrays for directional signal transmission or reception. This is achieved by combining elements in an antenna array in such a way that signals at particular angles experience constructive interference while others experience destructive interference. Beamforming can be used at both the transmitting and receiving ends in order to achieve spatial selectivity. The improvement compared with omnidirectional reception/transmission is known as the directivity of the array.

Antenna diversity, also known as space diversity or spatial diversity, is any one of several wireless diversity schemes that uses two or more antennas to improve the quality and reliability of a wireless link. Often, especially in urban and indoor environments, there is no clear line-of-sight (LOS) between transmitter and receiver. Instead the signal is reflected along multiple paths before finally being received. Each of these bounces can introduce phase shifts, time delays, attenuations, and distortions that can destructively interfere with one another at the aperture of the receiving antenna.

## History

### Early research

MIMO is often traced back to 1970s research papers concerning multi-channel digital transmission systems and interference (crosstalk) between wire pairs in a cable bundle: AR Kaye and DA George (1970), [4] Branderburg and Wyner (1974), [5] and W. van Etten (1975, 1976). [6] Although these are not examples of exploiting multipath propagation to send multiple information streams, some of the mathematical techniques for dealing with mutual interference proved useful to MIMO development. In the mid-1980s Jack Salz at Bell Laboratories took this research a step further, investigating multi-user systems operating over "mutually cross-coupled linear networks with additive noise sources" such as time-division multiplexing and dually-polarized radio systems. [7]

Nokia Bell Labs is an industrial research and scientific development company owned by Finnish company Nokia. Its headquarters are located in Murray Hill, New Jersey. Other laboratories are located around the world. Bell Labs has its origins in the complex past of the Bell System.

Methods were developed to improve the performance of cellular radio networks and enable more aggressive frequency reuse in the early 1990s. Space-division multiple access (SDMA) uses directional or smart antennas to communicate on the same frequency with users in different locations within range of the same base station. An SDMA system was proposed by Richard Roy and Björn Ottersten, researchers at ArrayComm, in 1991. Their US patent (No. 5515378 issued in 1996 [8] ) describes a method for increasing capacity using "an array of receiving antennas at the base station" with a "plurality of remote users."

Space-division multiple access (SDMA) is a channel access method based on creating parallel spatial pipes next to higher capacity pipes through spatial multiplexing and/or diversity, by which it is able to offer superior performance in radio multiple access communication systems. In traditional mobile cellular network systems, the base station has no information on the position of the mobile units within the cell and radiates the signal in all directions within the cell in order to provide radio coverage. This method results in wasting power on transmissions when there are no mobile units to reach, in addition to causing interference for adjacent cells using the same frequency, so called co-channel cells. Likewise, in reception, the antenna receives signals coming from all directions including noise and interference signals. By using smart antenna technology and differing spatial locations of mobile units within the cell, space-division multiple access techniques offer attractive performance enhancements. The radiation pattern of the base station, both in transmission and reception, is adapted to each user to obtain highest gain in the direction of that user. This is often done using phased array techniques.

Björn Ottersten is a Swedish educator, researcher, and electrical engineer who is the co-inventor of Space/Spatial Division Multiple Access (SDMA) technology. He has made contributions in array signal processing and wireless communications and has received many notable awards in these areas. Currently, he is a Professor of Signal Processing at Royal Institute of Technology (KTH), Stockholm, Sweden, and the founding director of the Interdisciplinary Centre for Security, Reliability and Trust, at University of Luxembourg, Luxembourg. He is a Fellow of the IEEE and EURASIP.

ArrayComm is a wireless communications software company founded in San Jose, California, in Silicon Valley. Co-founded in 1992 by Martin Cooper, a pioneer of the wireless industry. The company is wholly owned by Ygomi LLC, under principal investor T. Russell Shields. The current headquarters is Buffalo Grove, Illinois.

### Invention

Arogyaswami Paulraj and Thomas Kailath proposed an SDMA-based inverse multiplexing technique in 1993. Their US patent (No. 5,345,599 issued in 1994 [9] ) described a method of broadcasting at high data rates by splitting a high-rate signal "into several low-rate signals" to be transmitted from "spatially separated transmitters" and recovered by the receive antenna array based on differences in "directions-of-arrival." Paulraj was awarded the prestigious Marconi Prize in 2014 for "his pioneering contributions to developing the theory and applications of MIMO antennas. ... His idea for using multiple antennas at both the transmitting and receiving stations – which is at the heart of the current high speed WiFi and 4G mobile systems – has revolutionized high speed wireless." [10]

Arogyaswami J. Paulraj is an Indian-American electrical engineer. He is a Professor Emeritus in the Department of Electrical Engineering at Stanford University.

Thomas Kailath is an electrical engineer, information theorist, control engineer, entrepreneur and the Hitachi America Professor of Engineering, Emeritus, at Stanford University. Professor Kailath has authored several books, including the well-known book Linear Systems, which ranks as one of the most referenced books in the field of linear systems. In 2012, Kailath was awarded the National Medal of Science, presented by President Barack Obama in 2014 for "transformative contributions to the fields of information and system science, for distinctive and sustained mentoring of young scholars, and for translation of scientific ideas into entrepreneurial ventures that have had a significant impact on industry." Kailath is listed as an ISI highly cited researcher and is generally recognized as one of the preeminent figures of twentieth-century electrical engineering.

In an April 1996 paper and subsequent patent, Greg Raleigh proposed that natural multipath propagation can be exploited to transmit multiple, independent information streams using co-located antennas and multi-dimensional signal processing. [11] The paper also identified practical solutions for modulation (MIMO-OFDM), coding, synchronization, and channel estimation. Later that year (September 1996) Gerard J. Foschini submitted a paper that also suggested it is possible to multiply the capacity of a wireless link using what the author described as "layered space-time architecture." [12]

Gregory “Greg” Raleigh, is an American radio scientist, inventor, and entrepreneur who has made contributions in the fields of wireless communication, information theory, mobile operating systems, medical devices, and network virtualization. His discoveries and inventions include the first wireless communication channel model to accurately predict the performance of advanced antenna systems, the MIMO-OFDM technology used in contemporary Wi-Fi and 4G wireless networks and devices, higher accuracy radiation beam therapy for cancer treatment, improved 3D surgery imaging, and a cloud-based Network Functions Virtualization platform for mobile network operators that enables users to customize and modify their smartphone services.

Multiple-input, multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) is the dominant air interface for 4G and 5G broadband wireless communications. It combines multiple-input, multiple-output (MIMO) technology, which multiplies capacity by transmitting different signals over multiple antennas, and orthogonal frequency-division multiplexing (OFDM), which divides a radio channel into a large number of closely spaced subchannels to provide more reliable communications at high speeds. Research conducted during the mid-1990s showed that while MIMO can be used with other popular air interfaces such as time-division multiple access (TDMA) and code-division multiple access (CDMA), the combination of MIMO and OFDM is most practical at higher data rates.

Gerard Joseph Foschini, is an American telecommunications engineer who has worked for Bell Laboratories since 1961. His research has covered many kinds of data communications, particularly wireless communications and optical communications. Foschini has also worked on point-to-point systems and networks.

Greg Raleigh, V. K. Jones, and Michael Pollack founded Clarity Wireless in 1996, and built and field-tested a prototype MIMO system. [13] Cisco Systems acquired Clarity Wireless in 1998. [14] Bell Labs built a laboratory prototype demonstrating its V-BLAST (Vertical-Bell Laboratories Layered Space-Time) technology in 1998. [15] Arogyaswami Paulraj founded Iospan Wireless in late 1998 to develop MIMO-OFDM products. Iospan was acquired by Intel in 2003. [16] V-BLAST was never commercialized, and neither Clarity Wireless nor Iospan Wireless shipped MIMO-OFDM products before being acquired. [17]

### Standards and commercialization

MIMO technology has been standardized for wireless LANs, 3G mobile phone networks, and 4G mobile phone networks and is now in widespread commercial use. Greg Raleigh and V. K. Jones founded Airgo Networks in 2001 to develop MIMO-OFDM chipsets for wireless LANs. The Institute of Electrical and Electronics Engineers (IEEE) created a task group in late 2003 to develop a wireless LAN standard delivering at least 100 Mbit/s of user data throughput. There were two major competing proposals: TGn Sync was backed by companies including Intel and Philips, and WWiSE was supported by companies including Airgo Networks, Broadcom, and Texas Instruments. Both groups agreed that the 802.11n standard would be based on MIMO-OFDM with 20 MHz and 40 MHz channel options. [18] TGn Sync, WWiSE, and a third proposal (MITMOT, backed by Motorola and Mitsubishi) were merged to create what was called the Joint Proposal. [19] In 2004, Airgo became the first company to ship MIMO-OFDM products. [20] Qualcomm acquired Airgo Networks in late 2006. [21] The final 802.11n standard supported speeds up to 600 Mbit/s (using four simultaneous data streams) and was published in late 2009. [22]

Surendra Babu Mandava and Arogyaswami Paulraj founded Beceem Communications in 2004 to produce MIMO-OFDM chipsets for WiMAX. The company was acquired by Broadcom in 2010. [23] WiMAX was developed as an alternative to cellular standards, is based on the 802.16e standard, and uses MIMO-OFDM to deliver speeds up to 138 Mbit/s. The more advanced 802.16m standard enables download speeds up to 1 Gbit/s. [24] A nationwide WiMAX network was built in the United States by Clearwire, a subsidiary of Sprint-Nextel, covering 130 million points of presence (PoP) by mid-2012. [25] Sprint subsequently announced plans to deploy LTE (the cellular 4G standard) covering 31 cities by mid-2013 [26] and to shut down its WiMAX network by the end of 2015. [27]

The first 4G cellular standard was proposed by NTT DoCoMo in 2004. [28] Long term evolution (LTE) is based on MIMO-OFDM and continues to be developed by the 3rd Generation Partnership Project (3GPP). LTE specifies downlink rates up to 300 Mbit/s, uplink rates up to 75 Mbit/s, and quality of service parameters such as low latency. [29] LTE Advanced adds support for picocells, femtocells, and multi-carrier channels up to 100 MHz wide. LTE has been embraced by both GSM/UMTS and CDMA operators. [30]

The first LTE services were launched in Oslo and Stockholm by TeliaSonera in 2009. [31] There are currently more than 360 LTE networks in 123 countries operational with approximately 373 million connections (devices). [32]

## Functions

MIMO can be sub-divided into three main categories: precoding, spatial multiplexing (SM), and 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-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.

Spatial multiplexing requires MIMO antenna configuration. In spatial multiplexing, [33] [34] 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. [35] The scheduling of receivers with different spatial signatures allows good separability.

Diversity coding techniques are used when there is no 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. Diversity coding can be combined with spatial multiplexing when some channel knowledge is available at the transmitter.

## Forms

### Multi-antenna types

Multi-antenna MIMO (or Single user MIMO) technology has been developed and implemented in some standards, e.g., 802.11n products.

• SISO/SIMO/MISO are special cases of MIMO
• Multiple-input and single-output (MISO) is a special case when the receiver has a single antenna.
• Single-input and multiple-output (SIMO) is a special case when the transmitter has a single antenna.
• Single-input single-output (SISO) is a conventional radio system where neither transmitter nor receiver has multiple antenna.
• Principal single-user MIMO techniques
• Some limitations
• 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 handsets, though advanced antenna design and algorithm techniques are under discussion. Refer to: multi-user MIMO

### Multi-user types

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. [36] [33]

• Multi-user MIMO (MU-MIMO)
• 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, Nokia, 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.
• Enhanced multiuser MIMO: 1) Employs advanced decoding techniques, 2) Employs 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 superposition coding are used.
• Cooperative MIMO (CO-MIMO)
• Uses multiple neighboring base stations to jointly transmit/receive data to/from users. As a result, neighboring base stations don't cause intercell interference as in the conventional MIMO systems. [33]
• Macrodiversity MIMO
• 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. [37] [38] [39]
• The transmitters are far apart in contrast to traditional microdiversity MIMO schemes such as single-user MIMO. In a multi-user macrodiversity MIMO scenario, users may also be far apart. Therefore, every constituent link in the virtual MIMO link has distinct average link 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.
• 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. [40]
• 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 node-by-node in each hop. [41]
• Massive MIMO
• a technology where the number of terminals is much less than the number of base station (mobile station) antennas. [42] In a rich scattering environment, the full advantages of the massive MIMO system can be exploited using simple beamforming strategies such as maximum ratio transmission (MRT), [43] maximum ratio-combining (MRC) [44] or zero forcing (ZF). To achieve these benefits of massive MIMO, accurate CSI must be available perfectly. However, in practice, the channel between the transmitter and receiver is estimated from orthogonal pilot sequences which are limited by the coherence time of the channel. Most importantly, in a multicell setup, the reuse of pilot sequences of several co-channel cells will create pilot contamination. When there is pilot contamination, the performance of massive MIMO degrades quite drastically. To alleviate the effect of pilot contamination, the work of [45] proposes a simple pilot assignment and channel estimation method from limited training sequences. However, in 2018 research by Emil Björnson, Jakob Hoydis, Luca Sanguinetti was published which has shown that pilot contamination is soluble and have found that capacity of a channel can always be increased, both in theory and practice by increasing the number of antennas. [46]

## Applications

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.

MIMO is also planned to be used in Mobile radio telephone standards such as recent 3GPP and 3GPP2. In 3GPP, High-Speed Packet Access plus (HSPA+) and 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 (MU-MIMO).

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). [2]

## Mathematical description

In MIMO systems, a transmitter sends multiple streams by multiple transmit antennas. [33] The transmit streams go through a matrix channel which consists of all ${\displaystyle \scriptstyle N_{t}N_{r}}$ paths between the ${\displaystyle \scriptstyle N_{t}}$ transmit antennas at the transmitter and ${\displaystyle \scriptstyle N_{r}}$ receive antennas at the receiver. Then, the receiver gets the received signal 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: [47]

${\displaystyle \mathbf {y} =\mathbf {H} \mathbf {x} +\mathbf {n} }$

where ${\displaystyle \scriptstyle \mathbf {y} }$ and ${\displaystyle \scriptstyle \mathbf {x} }$ are the receive and transmit vectors, respectively, and ${\displaystyle \scriptstyle \mathbf {H} }$ and ${\displaystyle \scriptstyle \mathbf {n} }$ are the channel matrix and the noise vector, respectively.

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 [49]

${\displaystyle C_{\mathrm {perfect-CSI} }=E\left[\max _{\mathbf {Q} ;\,{\mbox{tr}}(\mathbf {Q} )\leq 1}\log _{2}\det \left(\mathbf {I} +\rho \mathbf {H} \mathbf {Q} \mathbf {H} ^{H}\right)\right]=E\left[\log _{2}\det \left(\mathbf {I} +\rho \mathbf {D} \mathbf {S} \mathbf {D} \right)\right]}$

where ${\displaystyle \scriptstyle ()^{H}}$ denotes Hermitian transpose and ${\displaystyle \scriptstyle \rho }$ is the ratio between transmit power and noise power (i.e., transmit SNR). The optimal signal covariance ${\displaystyle \scriptstyle \mathbf {Q} =\mathbf {VSV} ^{H}}$ is achieved through singular value decomposition of the channel matrix ${\displaystyle \scriptstyle \mathbf {UDV} ^{H}\,=\,\mathbf {H} }$ and an optimal diagonal power allocation matrix ${\displaystyle \scriptstyle \mathbf {S} ={\textrm {diag}}(s_{1},\ldots ,s_{\min(N_{t},N_{r})},0,\ldots ,0)}$. The optimal power allocation is achieved through waterfilling, [50] that is

${\displaystyle s_{i}=\left(\mu -{\frac {1}{\rho d_{i}^{2}}}\right)^{+},\quad {\textrm {for}}\,\,i=1,\ldots ,\min(N_{t},N_{r}),}$

where ${\displaystyle \scriptstyle d_{1},\ldots ,d_{\min(N_{t},N_{r})}}$ are the diagonal elements of ${\displaystyle \scriptstyle \mathbf {D} }$, ${\displaystyle \scriptstyle (\cdot )^{+}}$ is zero if its argument is negative, and ${\displaystyle \mu }$ is selected such that ${\displaystyle \scriptstyle s_{1}+\ldots +s_{\min(N_{t},N_{r})}=N_{t}}$.

If the transmitter has only statistical channel state information, then the ergodic channel capacity will decrease as the signal covariance ${\displaystyle \scriptstyle \mathbf {Q} }$ can only be optimized in terms of the average mutual information as [49]

${\displaystyle C_{\mathrm {statistical-CSI} }=\max _{\mathbf {Q} }E\left[\log _{2}\det \left(\mathbf {I} +\rho \mathbf {H} \mathbf {Q} \mathbf {H} ^{H}\right)\right].}$

The spatial correlation of the channel has 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 ${\displaystyle \scriptstyle \mathbf {Q} }$ to maximize channel capacity under worst-case statistics, which means ${\displaystyle \scriptstyle \mathbf {Q} =1/N_{t}\mathbf {I} }$ and accordingly

${\displaystyle C_{\mathrm {no-CSI} }=E\left[\log _{2}\det \left(\mathbf {I} +{\frac {\rho }{N_{t}}}\mathbf {H} \mathbf {H} ^{H}\right)\right].}$

Depending on the statistical properties of the channel, the ergodic capacity is no greater than ${\displaystyle \scriptstyle \min(N_{t},N_{r})}$ times larger than that of a SISO system.

## 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) 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. [51]

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 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. [52]

## Literature

### Principal researchers

Papers by Gerard J. Foschini and Michael J. Gans, [53] Foschini [54] and Emre Telatar [55] 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. [56]

Papers by Dr. Fernando Rosas and Dr. Christian Oberli have shown that the entire MIMO SVD link can be approximated by the average of the SER of Nakagami-m channels. [57] 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.

A textbook by A. Paulraj, R. Nabar and D. Gore has published an introduction to this area. [58] There are many other principal textbooks available as well. [59] [60] [61]

There exists a fundamental tradeoff between transmit diversity and spatial multiplexing gains in a MIMO system (Zheng and Tse, 2003). [62] In particular, achieving high spatial multiplexing gains is of profound importance in modern wireless systems. [63]

### 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.

### Sampling theory in MIMO systems

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. [64]

## Related Research Articles

In telecommunications, orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies. OFDM has developed into a popular scheme for wideband digital communication, used in applications such as digital television and audio broadcasting, DSL internet access, wireless networks, power line networks, and 4G mobile communications.

Smart antennas are antenna arrays with smart signal processing algorithms used to identify spatial signal signatures such as the direction of arrival (DOA) of the signal, and use them to calculate beamforming vectors which are used to track and locate the antenna beam on the mobile/target. Smart antennas should not be confused with reconfigurable antennas, which have similar capabilities but are single element antennas and not antenna arrays.

An adaptive beamformer is a system that performs adaptive spatial signal processing with an array of transmitters or receivers. The signals are combined in a manner which increases the signal strength to/from a chosen direction. Signals to/from other directions are combined in a benign or destructive manner, resulting in degradation of the signal to/from the undesired direction. This technique is used in both radio frequency and acoustic arrays, and provides for directional sensitivity without physically moving an array of receivers or transmitters.

In wireless communications, channel state information (CSI) refers to known channel properties of a communication link. This information describes how a signal propagates from the transmitter to the receiver and represents the combined effect of, for example, scattering, fading, and power decay with distance. The method is called Channel estimation. The CSI makes it possible to adapt transmissions to current channel conditions, which is crucial for achieving reliable communication with high data rates in multiantenna systems.

In the field of wireless communication, macrodiversity is a kind of space diversity scheme using several receiver antennas and/or transmitter antennas for transferring the same signal. The distance between the transmitters is much longer than the wavelength, as opposed to microdiversity where the distance is in the order of or shorter than the wavelength.

Radio resource management (RRM) is the system level management of co-channel interference, radio resources, and other radio transmission characteristics in wireless communication systems, for example cellular networks, wireless local area networks, wireless sensor systems radio broadcasting networks. RRM involves strategies and algorithms for controlling parameters such as transmit power, user allocation, beamforming, data rates, handover criteria, modulation scheme, error coding scheme, etc. The objective is to utilize the limited radio-frequency spectrum resources and radio network infrastructure as efficiently as possible.

Spatial multiplexing is a transmission technique in MIMO wireless communication, Fibre-optic communication and other communications technologies to transmit independent and separately encoded data signals, known as "streams". Therefore, the space dimension is reused, or multiplexed, more than one time.

Precoding is a generalization of beamforming to support multi-stream transmission in multi-antenna wireless communications. In conventional single-stream beamforming, the same signal is emitted from each of the transmit antennas with appropriate weighting such that the signal power is maximized at the receiver output. When the receiver has multiple antennas, single-stream beamforming cannot simultaneously maximize the signal level at all of the receive antennas. In order to maximize the throughput in multiple receive antenna systems, multi-stream transmission is generally required.

Multi-user MIMO (MU-MIMO) is a set of multiple-input and multiple-output (MIMO) technologies for wireless communication, in which a set of users or wireless terminals, each with one or more antennas, communicate with each other. In contrast, single-user MIMO considers a single multi-antenna transmitter communicating with a single multi-antenna receiver. In a similar way that OFDMA adds multiple access (multi-user) capabilities to OFDM, MU-MIMO adds multiple access (multi-user) capabilities to MIMO. MU-MIMO has been investigated since the beginning of research into multi-antenna communication, including work by Telatar on the capacity of the MU-MIMO uplink.

Carrier Interferometry(CI) is a spread spectrum scheme designed to be used in an Orthogonal Frequency-Division Multiplexing (OFDM) communication system for multiplexing and multiple access, enabling the system to support multiple users at the same time over the same frequency band.

In radio, Cooperative multiple-input multiple-output is an advanced technology that can effectively exploit the spatial domain of mobile fading channels to bring significant performance improvements to wireless communication systems. It is also called Network MIMO, Distributed MIMO, Virtual MIMO, and Virtual Antenna Arrays.

WiMAX MIMO refers to the use of Multiple-input multiple-output communications (MIMO) technology on WiMAX, which is the technology brand name for the implementation of the standard IEEE 802.16.

3G MIMO describes MIMO techniques which have been considered as 3G standard techniques.

Theoretically, the performance of wireless communication systems can be improved by having multiple antennas at the transmitter and the receiver. The idea is that if the propagation channels between each pair of transmit and receive antennas are statistically independent and identically distributed, then multiple independent channels with identical characteristics can be created by precoding and be used for either transmitting multiple data streams or increasing the reliability. In practice, the channels between different antennas are often correlated and therefore the potential multi antenna gains may not always be obtainable. This is called spatial correlation as it can be interpreted as a correlation between a signal's spatial direction and the average received signal gain.

Many antennas is a smart antenna technique which overcomes the performance limitation of single user multiple-input multiple-output (MIMO) techniques. In cellular communication, the maximum number of considered antennas for downlink is 2 and 4 to support 3GPP Long Term Evolution (LTE) and IMT Advanced requirements, respectively. Since the available spectrum band will probably be limited while the data rate requirement will continuously increase beyond IMT-A to support the mobile multimedia services, it is highly probable that the number of transmit antennas at the base station must be increased to 8–64 or more. The installation of many antennas at single base stations introduced many challenges and required development of several high technologies: a new SDMA engine, a new beamforming algorithm and a new antenna array.

The first smart antennas were developed for military communications and intelligence gathering. The growth of cellular telephone in the 1980s attracted interest in commercial applications. The upgrade to digital radio technology in the mobile phone, indoor wireless network, and satellite broadcasting industries created new opportunities for smart antennas in the 1990s, culminating in the development of the MIMO technology used in 4G wireless networks.

Per-user unitary rate control (PU2RC) is a multi-user MIMO scheme. PU2RC uses both transmission pre-coding and multi-user scheduling. By doing that, the network capacity is further enhanced than the capacity of the single-user MIMO scheme.

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