# MIMO

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In radio, multiple-input and multiple-output, or MIMO (pronounced mee-moh or my-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 (SA), and the state of the art of SA technology.

MIMO technology has attracted attention in wireless communications, since 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 a current theme of international wireless research. (Refer to: Research trend in MIMO literature)

## History of MIMOEdit

Main article: History of MIMO

## Functions of MIMOEdit

MIMO can be sub-divided into three main categories, precoding, spatial multiplexing, or SM, and diversity coding.

Precoding is multi-layer beamforming in a narrow sense or all spatial processing at the transmitter in a wide-sense. 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 signal gain from constructive combining 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 antenna and precoding is used. Note that precoding requires knowledge of the 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, creating parallel channels for free. Spatial multiplexing is a very powerful technique for increasing channel capacity at higher Signal to Noise Ratio (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.

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 using certain principles of full or near orthogonal coding. Diversity 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 Edit

### Multi-antenna types Edit

Up to now, multi-antenna MIMO (or Single user MIMO) technology has been mainly developed and is implemented in some standards, e.g. 802.11n (draft) products.

• SISO/SIMO/MISO are 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
• 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

### Multi-user types Edit

Main article: Multi-user MIMO

Recently, the research on multi-user MIMO technology is 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 (MU-MIMO)
• In 3GPP/3GPP2, there have been active discussions with many companies including Samsung, Qualcomm, Ericsson, TI, Huawei, Philips, Alcatel-Lucent, Freescale, et al.
• PU2RC 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 physical 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.
• 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.
• 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[1].

## Applications of MIMOEdit

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, which is expected to be finalized soon, recommends MIMO-OFDM.

MIMO is also planned to be used in Mobile radio telephone standards such as recent 3GPP and 3GPP2 standards. 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, i.e., multi-user MIMO (MU-MIMO).

## Mathematical descriptionEdit

Main article: Capacity of MIMO

In MIMO systems, a transmitter sends multiple streams by multiple transmit antennas. The transmit streams go through a matrix channel which consists of multiple paths between multiple transmit antennas at the transmitter and multiple 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. Here is a MIMO system model:

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

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

Referring to information theory, the average capacity of a MIMO system is as follows:

• Closed loop MIMO can achieve
$C_\mathrm{CL} = E[\max_{\mathbf{Q}} \log_2 (\mathbf{I} + \mathbf{H}\mathbf{Q}\mathbf{H}^{H})] = E[\log_2 (\mathbf{I} + \mathbf{U}\mathbf{S}\mathbf{U}^{H})]$
where we have used that $\mathbf{UDV}^H = \mathrm{svd}(\mathbf{H})$ and $\mathbf{S} = \mathrm{waterfilling(\mathbf{D}^2)}$. The functions of svd() and waterfilling() represent singular value decomposition and power allocation by the water filling rule, respectively.
• Open loop MIMO can achieve
$C_\mathrm{OL} = \max_{\mathbf{Q}} E[\log_2 (\mathbf{I} + \mathbf{H}\mathbf{Q}\mathbf{H}^{H})] = E[\log_2 (\mathbf{I} + \mathbf{H}\mathbf{H}^{H})]$
since any unitary matrix of $\mathbf{Q}$ can achieve the capacity of a open-loop MIMO system, which is mostly $\min(N_t, N_r)$ times larger than that of a SISO system

## MIMO literatureEdit

### Principal researches Edit

Papers by Gerard J. Foschini and Michael J. Gans[2], Foschini[3] and Emre Telatar have show 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 [4].

There exists a fundamental tradeoff between diversity and multiplexing in a MIMO system (Zheng and Tse, 2003) [5].

### Research trend Edit

In the IEEE international VTC 2007 fall conference (30 September – 3 October 2007, Renaissance Harborplace Hotel, Baltimore), approximately 130 MIMO, or spatial processing, based papers were presented among 420 other wireless communication papers. Those about MIMO treat not only antenna processing but also various wireless technologies over MIMO configurations. Some of those papers take into account multi-user MIMO in addition to multi-antenna MIMO. Multi-user type techniques consider multiple active users as a basic unit of multiple element processing while multi-antenna type techniques consider multiple antenna elements.

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.