MIMO (), or multiple-input multiple-output, is a wireless technology that multiplies the capacity of a radio link using multiple transmit and receive antennas. MIMO has become a core technology for broadband wireless communications, including mobile standards—4G WiMAX (802.16 e, m), and 3GPP 4G LTE and 5G NR, as well as Wi-Fi standards, IEEE 802.11n, ac, and ax. MIMO uses the spatial diversity to increase link capacity. The technology requires multiple antennas at both the transmitter and receiver, along with associated signal processing, to deliver data rate speedups roughly proportional to the number of antennas at each end. MIMO starts with a high-rate data stream, which is demultiplexed into multiple, lower-rate streams. Each of these streams is then modulated and transmitted in parallel with different coding from the transmit antennas, with all streams in the same frequency channel. These co-channel, mutually interfering streams arrive at the receiver's antenna array, each having a different spatial signature—gain phase pattern at the receiver’s antennas. These distinct array signatures allow the receiver to separate these co-channel streams, demodulate them, and re-multiplex them to reconstruct the original high-rate data stream. This process is sometimes referred to as spatial multiplexing. The key to MIMO is the sufficient differences in the spatial signatures of the different streams to enable their separation. This is achieved through a combination of angle spread of the multipaths and sufficient spacing between antenna elements. In environments with a rich multipath and high angle spread, common in cellular and Wi-Fi deployments, an antenna element spacing at each end of just a few wavelengths can suffice. However, in the absence of significant multipath spread, larger element spacing (wider angle separation) is required at either the transmit array, the receive array, or at both.
History
Early research in multiple antennas 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), Branderburg and Wyner (1974), and W. van Etten (1975, 1976). 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. 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) describes a method for increasing capacity using "an array of receiving antennas at the base station" with a "plurality of remote users."
MIMO invention In December 1991, while working on a DARPA project involving signal separation algorithms at Stanford University, Arogyaswami Paulraj discovered that signals from two phones held in one hand could be separated using a three-element receive antenna array in a rich multipath environment. This discovery led to the foundational patent on MIMO, filed in February 1992 with Professor Thomas Kailath as a co-inventor. The patent proposed a method for increasing data rates on MIMO links in proportion to the number of antennas used. While Paulraj’s patent initially emphasized applications in broadcast TV, which he believed would be an early adopter of the technology, it also proposed broader uses for MIMO in cellular communications. Paulraj joined the Stanford faculty in 1993, where he built a research group on MIMO. Later in 1998 and 2004, he founded two startups (Iospan Wireless and Beceem Communications) to commercialize MIMO for mobile networks. Paulraj has received many recognitions for his work. These include the Royal Academy of Engineering (RAE) Prince Philip Medal, the Institution of Engineering and Technology (IET) Faraday Medal, the IEEE Alexander G. Bell Medal, the Marconi Prize, and induction into the U.S. Patent and Trademark Office's National Inventors Hall of Fame.
MIMO advancements In 1995, G. Foschini and Michael Gans of Bell Labs wrote influential papers on MIMO wireless capacity and proposed the BLAST (Bell Labs Layered Space-Time) scheme to layer MIMO data streams and maximize channel capacity. Foschini received the IEEE Alexander Graham Bell Medal. Many other key publications followed, significantly advancing the field: G. Raleigh and V. Jones introduced space-time methods. E. Telatar established the fundamental capacity limits of MIMO channels. S. Alamouti developed a simple but effective transmit diversity scheme that has been widely adopted. R. Calderbank et al. made crucial contributions to the development of space-time codes. H. Sampath et al. described the first MIMO-OFDM cellular system developed by Iospan Wireless. R. Heath advanced the areas of limited feedback and multi-user MIMO systems. A torrent of research has followed, and as of 2024, there are over 450,000 research publications on MIMO technology and more than 570,000 global patent publications referencing MIMO or its related techniques.
MIMO commercialization
Mobile networks
Iospan Wireless began in late 1998 to develop a MIMO-OFDM physical-layer-based cellular system. Iospan’s product (Airburst) consisted of a core network, base stations, and CPE terminals. Airburst did not initially support mobile handovers. The system was trialed in Santa Clara during 2000-2002 and underwent a customer trial in Dubai in 2002. Following the 2001 collapse of the Dot-Com bubble, Iospan could not raise additional venture funding and was acquired by Intel in 2003. Intel integrated Iospan’s MIMO-OFDM technology into the WiMAX broadband mobile standard, IEEE 802.16e standard in 2004. In the early 2000s, several semiconductor companies also entered the MIMO-OFDM-based WiMAX technology market. They included Sequans, Samsung, Intel, Alvarion, and Beceem Communications, which developed modem semiconductors for WiMAX phones. Beceem gained 65% share of the global market and was acquired by Broadcom Corp. The 3rd Generation Partnership Project (3GPP) standards body adopted MIMO for HSPA+ (Release 7) in 20XX and MIMO-OFDM-based 4G Long Term Evolution (LTE) (Release 8) in 2008. MIMO-OFDM has since remained the core technology since 2008 for mobile networks, including 5G NR. 5G added native support for MU-MIMO.
WiFi networks In the early 2000s, several companies—Atheros, Cisco, Broadcom, Intel, and Airgo Networks—entered the MIMO‑OFDM Wi‑Fi semiconductor market. Due to competing proposals within the IEEE 802.11, the first MIMO‑OFDM Wi‑Fi standard (802.11n) was not finalized until 2009. Several pre-standard products were developed, but the market grew only after the 802.11n standard was ratified. Airgo Networks was acquired by Qualcomm in December 2006, and Atheros was also acquired by Qualcomm in May 2011. Sequans did an IPO in 2011 and Alviron filed for bankruptcy in 2013. Wi-Fi 6 added native support for MU-MIMO.
MIMO economic impact Currently, 4G/5G and Wi-Fi powered by MIMO enable approximately 70% of internet-based services, accounting for 10% of global GDP. The GSMA industry alliance estimated the global economic value of mobile networks at $5.7 trillion, and the WiFi alliance estimated the corresponding value for WiFi networks at $3.5 trillion in 2023.
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. Precoding requires knowledge of channel state information (CSI) at the transmitter and the receiver. 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. 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 receiver.
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 single-output (MISO) is a special case when the receiver has a single antenna. Single-input 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 antennas. Principal single-user MIMO techniques 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 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
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 employs advanced decoding and 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 conventional MIMO systems. 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. 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 a 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. MIMO routing Routing a cluster by a cluster in each hop, where the number of nodes in each cluster is larger than or equal to one. MIMO routing is different from conventional (SISO) routing since conventional routing protocols route node-by-node in each hop. Massive MIMO (mMIMO) A technology where the number of terminals is much less than the number of base station (mobile station) antennas. 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), maximum ratio-combining (MRC) 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, Tadilo E. Bogale and Long B. Le propose a simple pilot assignment and channel estimation method from limited training sequences. However, in 2018, research by Emil Björnson, Jakob Hoydis, and Luca Sanguinetti was published which shows that pilot contamination is solvable and that the capacity of a channel can always be increased, both in theory and in practice, by increasing the number of antennas. Holographic MIMO Another recent technology is holographic MIMO to realize high energy and spectral efficiency with very high spatial resolution. Holographic MIMO is a key conceptual key enabler that is recently gaining increasing popularity, because of its low-cost, transformative wireless structure consisting of sub-wavelength metallic or dielectric scattering particles, which is capable of deforming electromagnetic wave properties, according to some desirable objectives.
Applications
Third generation (3G) (CDMA and UMTS) allows for implementing space-time transmit diversity schemes, in combination with transmit beamforming at base stations. Fourth generation (4G) LTE and LTE Advanced define very advanced air interfaces extensively relying on MIMO techniques. LTE primarily focuses on single-link MIMO relying on spatial multiplexing and space-time coding, while LTE-Advanced further extends the design to multi-user MIMO. In wireless local area networks (WLAN), the IEEE 802.11n (Wi-Fi), MIMO technology is implemented in the standard using three different techniques: antenna selection, space-time coding and possibly beamforming. 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 used in mobile radio telephone standards such as 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 wireless communications architectures and processing techniques can be applied to sensing problems. This is studied in a sub-discipline called MIMO radar. 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).
Mathematical description
In MIMO systems, a transmitter sends multiple streams by multiple transmit antennas. The transmit streams go through a matrix channel which consists of all N t N r {\displaystyle N_{t}N_{r}} paths between the N t {\displaystyle N_{t}} transmit antennas at the transmitter and N r {\displaystyle 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 modeled as:
y = H x + n {\displaystyle \mathbf {y} =\mathbf {H} \mathbf {x} +\mathbf {n} }
where y {\displaystyle \mathbf {y} } and x {\displaystyle \mathbf {x} } are the receive and transmit vectors, respectively, and H {\displaystyle \mathbf {H} } and n {\displaystyle \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
C p e r f e c t − C S I = E [ max Q ; tr ( Q ) ≤ 1 log 2 det ( I + ρ H Q H H ) ] = E [ log 2 det ( I + ρ D S D ) ] {\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 ( ) H {\displaystyle ()^{H}} denotes Hermitian transpose and ρ {\displaystyle \rho } is the ratio between transmit power and noise power (i.e., transmit SNR). The optimal signal covariance Q = V S V H {\displaystyle \mathbf {Q} =\mathbf {VSV} ^{H}} is achieved through singular value decomposition of the channel matrix U D V H = H {\displaystyle \mathbf {UDV} ^{H}\,=\,\mathbf {H} } and an optimal diagonal power allocation matrix S = diag ( s 1 , … , s min ( N t , N r ) , 0 , … , 0 ) {\displaystyle \mathbf {S} ={\textrm {diag}}(s_{1},\ldots ,s_{\min(N_{t},N_{r})},0,\ldots ,0)} . The optimal power allocation is achieved through waterfilling, that is
s i = ( μ − 1 ρ d i 2 ) + , for i = 1 , … , min ( N t , N r ) , {\displaystyle s_{i}=\left(\mu -{\frac {1}{\rho d_{i}^{2}}}\right)^{+},\quad {\textrm {for}}\,\,i=1,\ldots ,\min(N_{t},N_{r}),}
where d 1 , … , d min ( N t , N r ) {\displaystyle d_{1},\ldots ,d_{\min(N_{t},N_{r})}} are the diagonal elements of D {\displaystyle \mathbf {D} } , ( ⋅ ) + {\displaystyle (\cdot )^{+}} is zero if its argument is negative, and μ {\displaystyle \mu } is selected such that s 1 + … + s min ( N t , N r ) = N t {\displaystyle 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 Q {\displaystyle \mathbf {Q} } can only be optimized in terms of the average mutual information as
C s t a t i s t i c a l − C S I = max Q E [ log 2 det ( I + ρ H Q H H ) ] . {\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 Q {\displaystyle \mathbf {Q} } to maximize channel capacity under worst-case statistics, which means Q = 1 / N t I {\displaystyle \mathbf {Q} =1/N_{t}\mathbf {I} } and accordingly
C n o − C S I = E [ log 2 det ( I + ρ N t H H H ) ] . {\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 min ( N t , N r ) {\displaystyle \min(N_{t},N_{r})} times larger than that of a SISO system.
MIMO detection The MIMO system can be described by: y = H x + n {\displaystyle \mathbf {y} =\mathbf {H} \mathbf {x} +\mathbf {n} } , where y {\displaystyle \mathbf {y} } is the received vector, H {\displaystyle \mathbf {H} } is the channel matrix, x {\displaystyle \mathbf {x} } is the transmitted vector, and n {\displaystyle \mathbf {n} } is the noise vector. The goal of MIMO detection is to estimate x {\displaystyle \mathbf {x} } from y {\displaystyle \mathbf {y} } given knowledge of H {\displaystyle \mathbf {H} } .This can be posed as a statistical detection problem, and addressed using a variety of techniques including zero-forcing, successive interference cancellation a.k.a. V-blast, maximum likelihood estimation and recently, neural network MIMO detection. Such techniques commonly assume that the channel matrix H {\displaystyle \mathbf {H} } is known at the receiver. In practice, in communication systems, the transmitter sends a pilot signal and the receiver learns the state of the channel (i.e., H {\displaystyle \mathbf {H} } ) from the received signal Y {\displaystyle Y} and the pilot signal X {\displaystyle X} . Recently, there are works on MIMO detection using deep learning tools which have shown to work better than other methods such as zero-forcing.
Zero forcing The zero forcing (ZF) detector simply solves for the unknown transmitted signals regardless of the noise. The ZF solution takes the form of:
x ^ Z F = G Z F z , {\displaystyle {\hat {x}}_{ZF}=G_{ZF}z,} where G Z F {\displaystyle G_{ZF}} is the pseudo-inverse of matrix H {\displaystyle H} and is given by:
G Z F = H † = ( H H H ) − 1 H H . {\displaystyle G_{ZF}=H^{\dagger }=(H^{H}H)^{-1}H^{H}.}
Despite its simplicity, this approach suffers from noise enhancement. After decoupling by Equation, the ZF solution x ^ Z F {\displaystyle {\hat {x}}_{ZF}} is either quantized and demapped to binary bits or used to compute the LLR. Note that such an approximation introduces negligible error rate degradation and significantly reduces the computation needed. As the ZF detection decouples the multiple correlated streams into independent streams, the extrinsic LLR of the j {\displaystyle j} th bit of the current symbol in the p {\displaystyle p} th stream resembles the soft-output equalization, and is given by:
L j ( p ) , E = 1 ‖ g p ‖ 2 ( max X ( p ) ∈ χ 1 , j [ − | X ^ Z F ( p ) − X ( p ) | 2 ] − max X ( p ) ∈ χ − 1 , j [ − | X ^ Z F ( p ) − X ( p ) | 2 ] ) , {\displaystyle L_{j}^{(p),E}={\frac {1}{\|g_{p}\|^{2}}}\left(\max _{X^{(p)}\in \chi _{1,j}}\left[-|{\hat {X}}_{ZF}^{(p)}-X^{(p)}|^{2}\right]-\max _{X^{(p)}\in \chi _{-1,j}}\left[-|{\hat {X}}_{ZF}^{(p)}-X^{(p)}|^{2}\right]\right),}
where g p {\displaystyle g_{p}} denotes the p {\displaystyle p} th column vector of matrix G Z F T {\displaystyle G_{ZF}^{T}} , X ^ Z F ( p ) {\displaystyle {\hat {X}}_{ZF}^{(p)}} is the p {\displaystyle p} th element of the symbol vector x ^ Z F {\displaystyle {\hat {x}}_{ZF}} , and χ b , j {\displaystyle \chi _{b,j}} indicates the subset of constellation points whose j {\displaystyle j} th bit has value b {\displaystyle b} .
Minimum mean squared error The minimum mean squared error (MMSE) algorithm detects the transmitted signals, x ~ {\displaystyle {\tilde {\mathbf {x} }}} , through minimizing the mean squared error (MSE), E { ( x ~ − x ) (