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IEEE Communications Magazine • February 2014 186 0163-6804/14/$25.00 © 2014 IEEE GOING LARGE: MASSIVE MIMO Massive multiple-input multiple-output (MIMO) is an emerging technology that scales up MIMO by possibly orders of magnitude compared to the current state of the art. In this article, we follow up on our earlier exposition [1], with a focus on the developments in the last three years; most particularly, energy efficiency, exploitation of excess degrees of freedom, time-division duplex (TDD) calibration, techniques to combat pilot contamination, and entirely new channel mea- surements. With massive MIMO, we think of systems that use antenna arrays with a few hundred antennas simultaneously serving many tens of terminals in the same time-frequency resource. The basic premise behind massive MIMO is to reap all the benefits of conventional MIMO, but on a much greater scale. Overall, massive MIMO is an enabler for the development of future broadband (fixed and mobile) networks, which will be energy-efficient, secure, and robust, and will use the spectrum efficiently. As such, it is an enabler for the future digital society infra- structure that will connect the Internet of people and Internet of Things with clouds and other network infrastructure. Many different configu- rations and deployment scenarios for the actual antenna arrays used by a massive MIMO system can be envisioned (Fig. 1). Each antenna unit would be small and active, preferably fed via an optical or electric digital bus. Massive MIMO relies on spatial multiplexing, which in turn relies on the base station having good enough channel knowledge, on both the uplink and the downlink. On the uplink, this is easy to accomplish by having the terminals send pilots, based on which the base station estimates the channel responses to each of the terminals. The downlink is more difficult. In conventional MIMO systems such as the Long Term Evolu- tion (LTE) standard, the base station sends out pilot waveforms, based on which the terminals estimate the channel responses, quantize the thus obtained estimates, and feed them back to the base station. This will not be feasible in mas- sive MIMO systems, at least not when operating in a high-mobility environment, for two reasons. First, optimal downlink pilots should be mutually orthogonal between the antennas. This means that the amount of time-frequency resources needed for downlink pilots scales with the num- ber of antennas, so a massive MIMO system would require up to 100 times more such resources than a conventional system. Second, ABSTRACT Multi-user MIMO offers big advantages over conventional point-to-point MIMO: it works with cheap single-antenna terminals, a rich scat- tering environment is not required, and resource allocation is simplified because every active ter- minal utilizes all of the time-frequency bins. However, multi-user MIMO, as originally envi- sioned, with roughly equal numbers of service antennas and terminals and frequency-division duplex operation, is not a scalable technology. Massive MIMO (also known as large-scale antenna systems, very large MIMO, hyper MIMO, full-dimension MIMO, and ARGOS) makes a clean break with current practice through the use of a large excess of service antennas over active terminals and time-division duplex operation. Extra antennas help by focus- ing energy into ever smaller regions of space to bring huge improvements in throughput and radiated energy efficiency. Other benefits of massive MIMO include extensive use of inexpen- sive low-power components, reduced latency, simplification of the MAC layer, and robustness against intentional jamming. The anticipated throughput depends on the propagation environ- ment providing asymptotically orthogonal chan- nels to the terminals, but so far experiments have not disclosed any limitations in this regard. While massive MIMO renders many traditional research problems irrelevant, it uncovers entirely new problems that urgently need attention: the challenge of making many low-cost low-precision components that work effectively together, acquisition and synchronization for newly joined terminals, the exploitation of extra degrees of freedom provided by the excess of service anten- nas, reducing internal power consumption to achieve total energy efficiency reductions, and finding new deployment scenarios. This article presents an overview of the massive MIMO con- cept and contemporary research on the topic. ACCEPTED FROM OPEN CALL Erik G. Larsson, ISY, Linköping University, Sweden Ove Edfors and Fredrik Tufvesson, Lund University, Sweden Thomas L. Marzetta, Bell Labs, Alcatel-Lucent, United States Massive MIMO for Next Generation Wireless Systems

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Page 1: Massive MIMO for next generation wireless systems

IEEE Communications Magazine • February 2014186 0163-6804/14/$25.00 © 2014 IEEE

GOING LARGE: MASSIVE MIMOMassive multiple-input multiple-output (MIMO)is an emerging technology that scales up MIMOby possibly orders of magnitude compared to thecurrent state of the art. In this article, we follow

up on our earlier exposition [1], with a focus onthe developments in the last three years; mostparticularly, energy efficiency, exploitation ofexcess degrees of freedom, time-division duplex(TDD) calibration, techniques to combat pilotcontamination, and entirely new channel mea-surements.

With massive MIMO, we think of systemsthat use antenna arrays with a few hundredantennas simultaneously serving many tens ofterminals in the same time-frequency resource.The basic premise behind massive MIMO is toreap all the benefits of conventional MIMO, buton a much greater scale. Overall, massive MIMOis an enabler for the development of futurebroadband (fixed and mobile) networks, whichwill be energy-efficient, secure, and robust, andwill use the spectrum efficiently. As such, it is anenabler for the future digital society infra-structure that will connect the Internet of peopleand Internet of Things with clouds and othernetwork infrastructure. Many different configu-rations and deployment scenarios for the actualantenna arrays used by a massive MIMO systemcan be envisioned (Fig. 1). Each antenna unitwould be small and active, preferably fed via anoptical or electric digital bus.

Massive MIMO relies on spatial multiplexing,which in turn relies on the base station havinggood enough channel knowledge, on both theuplink and the downlink. On the uplink, this iseasy to accomplish by having the terminals sendpilots, based on which the base station estimatesthe channel responses to each of the terminals.The downlink is more difficult. In conventionalMIMO systems such as the Long Term Evolu-tion (LTE) standard, the base station sends outpilot waveforms, based on which the terminalsestimate the channel responses, quantize thethus obtained estimates, and feed them back tothe base station. This will not be feasible in mas-sive MIMO systems, at least not when operatingin a high-mobility environment, for two reasons.First, optimal downlink pilots should be mutuallyorthogonal between the antennas. This meansthat the amount of time-frequency resourcesneeded for downlink pilots scales with the num-ber of antennas, so a massive MIMO systemwould require up to 100 times more suchresources than a conventional system. Second,

ABSTRACT

Multi-user MIMO offers big advantages overconventional point-to-point MIMO: it workswith cheap single-antenna terminals, a rich scat-tering environment is not required, and resourceallocation is simplified because every active ter-minal utilizes all of the time-frequency bins.However, multi-user MIMO, as originally envi-sioned, with roughly equal numbers of serviceantennas and terminals and frequency-divisionduplex operation, is not a scalable technology.Massive MIMO (also known as large-scaleantenna systems, very large MIMO, hyperMIMO, full-dimension MIMO, and ARGOS)makes a clean break with current practicethrough the use of a large excess of serviceantennas over active terminals and time-divisionduplex operation. Extra antennas help by focus-ing energy into ever smaller regions of space tobring huge improvements in throughput andradiated energy efficiency. Other benefits ofmassive MIMO include extensive use of inexpen-sive low-power components, reduced latency,simplification of the MAC layer, and robustnessagainst intentional jamming. The anticipatedthroughput depends on the propagation environ-ment providing asymptotically orthogonal chan-nels to the terminals, but so far experimentshave not disclosed any limitations in this regard.While massive MIMO renders many traditionalresearch problems irrelevant, it uncovers entirelynew problems that urgently need attention: thechallenge of making many low-cost low-precisioncomponents that work effectively together,acquisition and synchronization for newly joinedterminals, the exploitation of extra degrees offreedom provided by the excess of service anten-nas, reducing internal power consumption toachieve total energy efficiency reductions, andfinding new deployment scenarios. This articlepresents an overview of the massive MIMO con-cept and contemporary research on the topic.

ACCEPTED FROM OPEN CALL

Erik G. Larsson, ISY, Linköping University, Sweden

Ove Edfors and Fredrik Tufvesson, Lund University, Sweden

Thomas L. Marzetta, Bell Labs, Alcatel-Lucent, United States

Massive MIMO for Next GenerationWireless Systems

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IEEE Communications Magazine • February 2014 187

the number of channel responses each terminalmust estimate is also proportional to the numberof base station antennas. Hence, the uplinkresources needed to inform the base station ofthe channel responses would be up to 100 timeslarger than in conventional systems. Generally,the solution is to operate in TDD mode, andrely on reciprocity between the uplink and down-link channels, although frequency-divisionduplext (FDD) operation may be possible in cer-tain cases [2].

While the concepts of massive MIMO havebeen mostly theoretical so far, stimulating muchresearch particularly in random matrix theoryand related mathematics, basic testbeds arebecoming available [3], and initial channel mea-surements have been performed [4, 5].

THE POTENTIAL OF MASSIVE MIMOMassive MIMO technology relies on phase-coherent but computationally very simple pro-cessing of signals from all the antennas at thebase station. Some specific benefits of a massiveMU-MIMO system are:

•Massive MIMO can increase the capacity 10times or more and simultaneously improve theradiated energy efficiency on the order of 100times. The capacity increase results from theaggressive spatial multiplexing used in massiveMIMO. The fundamental principle that makesthe dramatic increase in energy efficiency possibleis that with a large number of antennas, energycan be focused with extreme sharpness intosmall regions in space (Fig. 2). The underlyingphysics is coherent superposition of wavefronts.By appropriately shaping the signals sent out bythe antennas, the base station can make surethat all wavefronts collectively emitted by allantennas add up constructively at the locationsof the intended terminals, but destructively (ran-domly) almost everywhere else. Interferencebetween terminals can be suppressed even fur-ther by using, for example, zero-forcing (ZF).This, however, may come at the cost of moretransmitted power, as illustrated in Fig. 2.

More quantitatively, Fig. 3 (from [6]) depictsthe fundamental trade-off between energy effi-ciency in terms of the total number of bits (sumrate) transmitted per Joule per terminal receiv-ing service of energy spent, and spectral efficiencyin terms of total number of bits (sum rate) trans-mitted per unit of radio spectrum consumed.The figure illustrates the relation for the uplink,from the terminals to the base station (the down-link performance is similar). The figure showsthe trade-off for three cases: • A reference system with one single antenna

serving a single terminal (purple)• A system with 100 antennas serving a single

terminal using conventional beamforming(green)

• A massive MIMO system with 100 antennassimultaneously serving multiple (about 40here) terminals (red, using maximum ratiocombining, and blue, using ZF).The attractiveness of maximum ratio combin-

ing (MRC) compared with ZF is not only itscomputational simplicity — multiplication of thereceived signals by the conjugate channel

responses — but also that it can be performed ina distributed fashion, independently at eachantenna unit. While ZF also works fairly well fora conventional or moderately sized MIMO sys-tem, MRC generally does not. The reason thatMRC works so well for massive MIMO is thatthe channel responses associated with differentterminals tend to be nearly orthogonal when thenumber of base station antennas is large.

The prediction in Fig. 3 is based on an infor-mation-theoretic analysis that takes into accountintracell interference, as well as the bandwidthand energy cost of using pilots to acquire chan-nel state information in a high-mobility environ-ment [6]. With the MRC receiver, we operate inthe nearly noise-limited regime of informationtheory. This means providing each terminal witha rate of about 1 b/complex dimension (1b/s/Hz). In a massive MIMO system, when usingMRC and operating in the “green” regime (i.e.,scaling down the power as much as possiblewithout seriously affecting the overall spectralefficiency), multiuser interference and effectsfrom hardware imperfections tend to be over-whelmed by the thermal noise. The reason thatthe overall spectral efficiency still can be 10times higher than in conventional MIMO is thatmany tens of terminals are served simultaneous-ly, in the same time-frequency resource. Whenoperating in the 1 b/dimension/terminal regime,there is also some evidence that intersymbolinterference can be treated as additional thermalnoise [7], hence offering a way of disposing withorthogonal frequency-division multiplexing(OFDM) as a means of combatting intersymbolinterference.

To understand the scale of the capacity gainsmassive MIMO offers, consider an array consist-ing of 6400 omnidirectional antennas (total formfactor 6400 × (l/2)2 40 m2) transmitting with atotal power of 120 W (i.e., each antenna radiat-

Figure 1. Some possible antenna configurations and deployment scenarios fora massive MIMO base station.

Distributed

Cylindrica

l

Rectangular

Linear

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IEEE Communications Magazine • February 2014188

ing about 20 mW) over a 20 MHz bandwidth inthe personal communications services (PCS)band (1900 MHz). The array serves 1000 fixedterminals randomly distributed in a disk of radius6 km centered on the array, each terminal hav-ing an 8 dB gain antenna. The height of theantenna array is 30 m, and the height of the ter-minals is 5 m. Using the Hata-COST231 model,we find that the path loss is 127 dB at 1 kmrange, and the range-decay exponent is 3.52.There is also log-normal shadow fading with 8dB standard deviation. The receivers have a 9dB noise figure. One-quarter of the time is spenton transmission of uplink pilots for TDD chan-nel estimation, and it is assumed that the chan-nel is substantially constant over intervals of 164ms in order to estimate the channel gains withsufficient accuracy. Downlink data is transmittedvia maximum ratio transmission (MRT) beam-forming combined with power control, where the5 percent of terminals with the worst channelsare excluded from service. We use a capacitylower bound from [8] extended to accommodateslow fading, near/far effects and power control,which accounts for receiver noise, channel esti-mation errors, the overhead of pilot transmis-sion, and the imperfections of MRTbeamforming. We use optimal max-min power

control, which confers an equal signal-to-inter-ference-plus-noise ratio on each of the 950 ter-minals and therefore equal throughput.Numerical averaging over random terminal loca-tions and the shadow fading shows that 95 per-cent of the terminals will receive a throughput of21.2 Mb/s/terminal. Overall, the array in thisexample will offer the 1000 terminals a totaldownlink throughput of 20 Gb/s, resulting in asum-spectral efficiency of 1000 b/s/Hz. Thiswould be enough, for example, to provide 20Mb/s broadband service to each of 1000 homes.The max-min power control provides equal ser-vice simultaneously to 950 terminals. Other typesof power control combined with time-divisionmultiplexing could accommodate heterogeneoustraffic demands of a larger set of terminals.

The MRC receiver (for the uplink) and itscounterpart MRT precoding (for the downlink)are also known as matched filtering (MF) in theliterature. • Massive MIMO can be built with inexpen-

sive, low-power components.Massive MIMO is a game changing technolo-

gy with regard to theory, systems, and implemen-tation. With massive MIMO, expensiveultra-linear 50 W amplifiers used in conventionalsystems are replaced by hundreds of low-cost

Figure 2. Relative field strength around a target terminal in a scattering environment of size 800 l × 800 l when the base station isplaced 1600 l to the left. Average field strengths are calculated over 10,000 random placements of 400 scatterers when two differentlinear precoders are used: a) MRT precoders; b) ZF precoders. Left: pseudo-color plots of average field strengths, with target user posi-tions at the center () and four other users nearby (). Right: average field strengths as surface plots, allowing an alternate view of thespatial focusing.

Area with 400 random scatterers

Incoming narrow beam

400 λ

800 λ

800

λ

Narrow beam

Wide beam

Area with 400 random scatterers

100-elementλ/2-spacedlinear array

1600 λa) MRT precoding

(dB)

[dB]

-10400 λ

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5

800

λ

Incoming wide beam

400 λ

(dB)

[dB]

-10400 λ

-15

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1600 λb) ZF precoding

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≤ −15

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5

-10

≤ 15

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5

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IEEE Communications Magazine • February 2014 189

amplifiers with output power in the milli-Wattrange. The contrast to classical array designs,which use few antennas fed from high-poweramplifiers, is significant. Several expensive andbulky items, such as large coaxial cables, can beeliminated altogether. (The typical coaxial cablesused for tower-mounted base stations today aremore than 4 cm in diameter!)

Massive MIMO reduces the constraints onaccuracy and linearity of each individual amplifi-er and RF chain. All that matters is their com-bined action. In a way, massive MIMO relies onthe law of large numbers to make sure thatnoise, fading, and hardware imperfections aver-age out when signals from a large number ofantennas are combined in the air. The sameproperty that makes massive MIMO resilientagainst fading also makes the technologyextremely robust to failure of one or a few of theantenna unit(s).

A massive MIMO system has a large surplusof degrees of freedom. For example, with 200antennas serving 20 terminals, 180 degrees offreedom are unused. These degrees of freedomcan be used for hardware-friendly signal shap-ing. In particular, each antenna can transmit sig-nals with very small peak-to-average ratio [9] oreven constant envelope [10] at a very modestpenalty in terms of increased total radiatedpower. Such (near-constant) envelope signalingfacilitates the use of extremely cheap and power-efficient RF amplifiers. The techniques in [9,10] must not be confused with conventionalbeamforming techniques or equal-magnitude-weight beamforming techniques. This distinctionis explained in Fig. 4. With (near) constant-envelope multiuser precoding, no beams areformed, and the signals emitted by each antennaare not formed by weighing a symbol. Rather, awavefield is created such that when this wave-field is sampled at the spots where the terminalsare located, the terminals see precisely the sig-nals we want them to see. The fundamentalproperty of the massive MIMO channel thatmakes this possible is that the channel has alarge nullspace: almost anything can be put intothis nullspace without affecting what the termi-nals see. In particular, components can be putinto this nullspace that make the transmittedwaveforms satisfy the desired envelope con-straints. Notwithstanding, the effective channelsbetween the base station and each of the termi-nals can take any signal constellation as inputand do not require the use of phase shift keying(PSK) modulation.

The drastically improved energy efficiencyenables massive MIMO systems to operate witha total output RF power two orders of magni-tude less than with current technology. This mat-ters, because the energy consumption of cellularbase stations is a growing concern worldwide. Inaddition, base stations that consume many ordersof magnitude less power could be powered bywind or solar, and hence easily deployed whereno electricity grid is available. As a bonus, thetotal emitted power can be dramatically cut, andtherefore the base station will generate substan-tially less electromagnetic interference. This isimportant due to the increased concerns regard-ing electromagnetic exposure.

•Massive MIMO enables a significant reduc-tion of latency on the air interface.

The performance of wireless communicationssystems is normally limited by fading. Fading canrender the received signal strength very small atcertain times. This happens when the signal sentfrom a base station travels through multiplepaths before it reaches the terminal, and thewaves resulting from these multiple paths inter-fere destructively. It is this fading that makes ithard to build low-latency wireless links. If theterminal is trapped in a fading dip, it has to waituntil the propagation channel has sufficientlychanged until any data can be received. MassiveMIMO relies on the law of large numbers andbeamforming in order to avoid fading dips, sofading no longer limits latency.

•Massive MIMO simplifies the multiple accesslayer.

Due to the law of large numbers, the chan-nel hardens so that frequency domain schedul-ing no longer pays off. With OFDM, eachsubcarrier in a massive MIMO system will havesubstantially the same channel gain. Each ter-minal can be given the whole bandwidth, whichrenders most of the physical layer control sig-naling redundant.

•Massive MIMO increases the robustnessagainst both unintended man-made interferenceand intentional jamming.

Intentional jamming of civilian wireless sys-tems is a growing concern and a serious cyber-security threat that seems to be little known tothe public. Simple jammers can be bought offthe Internet for a few hundred dollars, andequipment that used to be military-grade can beput together using off-the-shelf software radio-based platforms for a few thousand dollars.

Figure 3. Half the power — twice the force (from [6]): Improving uplink spec-tral efficiency 10 times and simultaneously increasing the radiated power effi-ciency 100 times with massive MIMO technology, using extremely simplesignal processing, taking into account the energy and bandwidth costs ofobtaining channel state information.

Spectral efficiency (b/s/Hz)100

100

10–1

Rela

tive

ene

rgy

effic

ienc

y (b

/J)/(

b/J)

101

102

103

104

20 30 40 50 60 70 80

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90

100 antennas,single terminal

100 antennas,multiple terminals,MRC processing

100 antennas,multiple terminals,ZF processing

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IEEE Communications Magazine • February 2014190

Numerous recent incidents, especially in publicsafety applications, illustrate the magnitude ofthe problem. During the EU summit in Gothen-burg, Sweden, in 2001, demonstrators used ajammer located in a nearby apartment, and dur-ing critical phases of riots, the chief commandercould not reach any of the 700 police officersengaged [11].

Due to the scarcity of bandwidth, spreadinginformation over frequency just is not feasible,so the only way of improving robustness ofwireless communications is to use multipleantennas. Massive MIMO offers many excessdegrees of freedom that can be used to cancelsignals from intentional jammers. If massiveMIMO is implemented using uplink pilots forchannel estimation, smart jammers could causeharmful interference with modest transmissionpower. However, more clever implementationsusing joint channel estimation and decodingshould be able to substantially diminish thatproblem.

LIMITING FACTORS OFMASSIVE MIMOCHANNEL RECIPROCITY

Time-division duplexing operation relies onchannel reciprocity. There appears to be a rea-sonable consensus that the propagation channelitself is essentially reciprocal unless the propaga-tion is affected by materials with strange mag-netic properties. However, the hardware chainsin the base station and terminal transceivers maynot be reciprocal between the uplink and thedownlink. Calibration of the hardware chains

does not seem to constitute a serious problem,and there are calibration-based solutions thathave already been tested to some extent in prac-tice [3, 12]. Specifically, [3] treats reciprocity cal-ibration for a 64-antenna system in some detailand claims a successful experimental implemen-tation.

Note that calibration of the terminal uplinkand downlink chains is not required in order toobtain the full beamforming gains of massiveMIMO: if the base station equipment is properlycalibrated, the array will indeed transmit acoherent beam to the terminal. (There will stillbe some mismatch within the receiver chain ofthe terminal, but this can be handled by trans-mitting pilots through the beam to the terminal;the overhead for these supplementary pilots isvery small.) Absolute calibration within the arrayis not required. Instead, as proposed in [3], oneof the antennas can be treated as a reference,and signals can be traded between the referenceantenna and each of the other antennas to derivea compensation factor for that antenna. It maybe possible to entirely forgo reciprocity calibra-tion within the array; for example if the maxi-mum phase difference between the uplink anddownlink chains were less than 60˚, coherentbeamforming would still occur (at least withMRT beamforming), albeit with a possible 3 dBreduction in gain.

PILOT CONTAMINATIONIdeally, every terminal in a massive MIMO sys-tem is assigned an orthogonal uplink pilotsequence. However, the maximum number oforthogonal pilot sequences that can exist isupper-bounded by the duration of the coherenceinterval divided by the channel delay spread. In

Figure 4. Conventional MIMO beamforming contrasted with per-antenna constant envelope transmission in massive MIMO. Left: con-ventional beamforming, where the signal emitted by each antenna has a large dynamic range. Right: per-antenna constant envelopetransmission, where each antenna sends out a signal with a constant envelope.

ejφ1

ejφm

ejφM

α1

Per-antennavaryingenvelope

Combinedvaryingenvelopeαmuk

uK

fc

u1

αM

Line

ar e

ncod

erα

= W

(H)u

Per-antennaconstantenvelope

Combinedvaryingenvelopeuk

uK

fc

u1

Phas

e-on

ly e

ncod

erφ

= f

(u,H

)

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[13], for a typical operating scenario, the maxi-mum number of orthogonal pilot sequences in a1 ms coherence interval is estimated to be about200. It is easy to exhaust the available supply oforthogonal pilot sequences in a multicellular sys-tem.

The effect of reusing pilots from one cell toanother and the associated negative conse-quences is termed pilot contamination. Morespecifically, when the service array correlatesits received pilot signal with the pilot sequenceassociated with a particular terminal, it actual-ly obtains a channel estimate that is contami-nated by a linear combination of channels withother terminals that share the same pilotsequence. Downlink beamforming based onthe contaminated channel estimate results ininterference directed at those terminals thatshare the same pilot sequence. Similar inter-ference is associated with uplink transmissionsof data. This directed interference grows withthe number of service antennas at the samerate as the desired signal [13]. Even partiallycorrelated pilot sequences result in directedinterference.

Pilot contamination as a basic phenomenon isnot really specific to massive MIMO, but itseffect on massive MIMO appears to be muchmore profound than in classical MIMO [13, 14].In [13] it was argued that pilot contaminationconstitutes an ultimate limit on performancewhen the number of antennas is increased with-out bound, at least with receivers that rely onpilot-based channel estimation. While this argu-ment has been contested recently [15], at leastunder some specific assumptions on the powercontrol used, it appears likely that pilot contami-nation must be dealt with in some way. This canbe done in several ways:

•The allocation of pilot waveforms can beoptimized. One possibility is to use a less aggres-sive frequency reuse factor for the pilots (butnot necessarily for the payload data); say, 3 or 7.This pushes mutually contaminating cells fartherapart. It is also possible to coordinate the use ofpilots or adaptively allocate pilot sequences tothe different terminals in the network [16]. Cur-rently, the optimal strategy is unknown.

•Clever channel estimation algorithms [15],or even blind techniques that circumvent the useof pilots altogether [17], may mitigate or elimi-nate the effects of pilot contamination. The mostpromising direction seems to be blind techniquesthat jointly estimate the channels and the pay-load data.

•New precoding techniques that take intoaccount the network structure, such as pilotcontamination precoding [18], can utilize coop-erative transmission over a multiplicity of cells— outside of the beamforming operation — tonullify, at least partially, the directed interfer-ence that results from pilot contamination.Unlike coordinated beamforming over multiplecells, which requires estimates of the actualchannels between the terminals and the servicearrays of the contaminating cells, pilot contam-ination precoding requires only the corre-sponding slow-fading coefficients. Practicalpilot contamination precoding remains to bedeveloped.

RADIO PROPAGATION AND ORTHOGONALITY OFCHANNEL RESPONSES

Massive MIMO (and especially MRC/MRT pro-cessing) relies to a large extent on a property ofthe radio environment called favorable propaga-tion. Simply stated, favorable propagation meansthat the propagation channel responses from thebase station to different terminals are sufficient-ly different. To study the behavior of massiveMIMO systems, channel measurements have tobe performed using realistic antenna arrays. Thisis so because the channel behavior using largearrays differs from that usually experiencedusing conventional smaller arrays. The mostimportant differences are that:• There might be large-scale fading over the

array.• The small-scale signal statistics may also

change over the array. Of course, this isalso true for physically smaller arrays withdirectional antenna elements pointing invarious directions.Figure 5 shows pictures of the two massive

MIMO arrays used for the measurements report-ed in this article. On the left is a compact circu-lar massive MIMO array with 128 antenna ports.This array consists of 16 dual-polarized patchantenna elements arranged in a circle, with 4such circles stacked on top of each other. Besideshaving the advantage of being compact, thisarray also provides the possibility to resolve scat-terers at different elevations, but it suffers fromworse resolution in azimuth due to its limitedaperture. To the right is a physically large linear(virtual) array, where a single omnidirectionalantenna element is moved to 128 different posi-tions in an otherwise static environment to emu-late a real array with the same dimensions.

One way of quantifying how different thechannel responses to different terminals are is tolook at the spread between the smallest andlargest singular values of the matrix that containsthe channel responses. Figure 6 illustrates thisfor a case with 4 user terminals and a base sta-tion having 4, 32, and 128 antenna ports, respec-tively, configured as either a physically largesingle-polarized linear array or a compact dual-polarized circular array. More specifically, thefigure shows the cumulative density function(CDF) of the difference between the smallestand largest singular values for the different mea-sured (narrowband) frequency points in the dif-ferent cases. As a reference, we also showsimulated results for ideal independent identical-ly distributed (i.i.d.) channel matrices, often usedin theoretical studies. The measurements wereperformed outdoors in the Lund University cam-pus area. The center frequency was 2.6 GHz andthe measurement bandwidth 50 MHz. Whenusing the cylindrical array, the RUSK Lundchannel sounder was employed, while a networkanalyzer was used for the synthetic linear arraymeasurements. The first results from the cam-paign were presented in [4].

For the 4-element array, the median of thesingular value spread is about 23–18 dB. Thisnumber is a measure of the fading margin, theadditional power that has to be used in order toserve all users with a reasonable received signal

Massive MIMO (and

especially MRC/MRT

processing) relies to

a large extent on a

property of the radio

environment called

favorable propaga-

tion. Simply stated,

favorable propaga-

tion means that the

propagation channel

responses from the

base station to dif-

ferent terminals are

sufficiently different.

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power. With the massive linear array, the spreadis less than 3 dB. In addition, note that none ofthe curves has any substantial tail. This meansthat the probability of seeing a singular valuespread larger than 3 dB anywhere over the mea-sured bandwidth is essentially negligible.

To further illustrate the influence of differentnumbers of antenna elements at the base stationand antenna configuration, we plot in Fig. 7 thesum rate for 4 closely spaced users (less than 2m between users at a distance of about 40 mfrom the base station) in a non line-of-sight(NLOS) scenario when using MRT as precoding.The transmit power is normalized so that onaverage, the interference-free signal-to-noise-ratio at the terminals is 10 dB.

As can be seen in Fig. 7, the sum rateapproaches that of the theoretical interference-free case as the number of antennas at the basestation increases. The shaded areas in red (forthe linear array) and blue (for the circular array)shows the 90 percent confidence intervals of thesum rates for the different narrowband frequencyrealizations. As before, the variance of the sumrate decreases as the number of antennas increas-es, but slowly for the measured channels. Theslow decrease can, at least partially, be attributedto the shadow fading occurring across the arrays:for the linear array in the form of shadowing byexternal objects along the array, and for thecylindical array in the form of shadowing causedby directive antenna elements pointing in thewrong direction. The performance of the physi-cally large array approaches that of the theoreti-cal i.i.d. case when the number of antennas growslarge. The compact circular array has inferiorperformance compared to the linear array due toits smaller aperture — it cannot resolve the scat-terers as well as the physically large array — andits directive antenna elements sometimes point-ing in the wrong direction. Also, due to the factthat most of the scatterers are seen at the samehorizontal angle, the possibility to resolve scattersat different elevations gives only marginal contri-butions to the sum rate in this scenario.

It should be mentioned here that when usingsomewhat more complex, but still linear, pre-coding methods such as ZF or minimum meansquare error, the convergence to the i.i.d. chan-nel performance is faster and the variance of thesum rate lower as the number of base stationantennas is increased; see [4] for further details.Also, another aspect worth mentioning is thatfor a very tricky propagation scenario, such asclosely spaced users in line-of-sight conditions, itseems that the large array is able to separate theusers to a reasonable extent using the differentspatial signatures the users have at the base sta-tion due to the enhanced spatial resolution. Thiswould not be possible with conventional MIMO.These conclusions are also in line with the obser-vations in [5], where another outdoor measure-ment campaign is described and analyzed.

Figure 5. Massive MIMO antenna arrays used for the measurements.

Figure 6. CDF of the singular value spread for MIMO systems with 4 terminalsand three different numbers of base station antennas: 4, 32, and 128. The the-oretical i.i.d. channel is shown as a reference, while the other two cases aremeasured channels with linear and cylindrical array structures at the base sta-tion. Note that the curve for the linear array coincides with that of the i.i.d.channel for four base stations.

Singular value spread (dB)100

0.1

0

CDF

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Overall, there is compelling evidence that theassumptions on favorable propagation underpin-ning massive MIMO are substantially valid inpractice. Depending on the exact configurationof the large array and the precoding algorithmsused, the convergence toward the ideal perfor-mance may be faster or slower as the number ofantennas is increased. However, with about 10times more base station antennas than the num-ber of users, it seems that it is possible to getstable performance not far from the theoreticallyideal performance also under what are normallyconsidered very difficult propagation conditions.

MASSIVE MIMO: A GOLD MINE OFRESEARCH PROBLEMS

While massive MIMO renders many traditionalproblems in communication theory less relevant,it uncovers entirely new problems that needresearch.

Fast and distributed coherent signal process-ing: Massive MIMO arrays generate vastamounts of baseband data that must be pro-cessed in real time. This processing will have tobe simple, and simple means linear or nearly lin-ear. Fundamentally, this is good in many cases(Fig. 3). Much research needs be invested in thedesign of optimized algorithms and their imple-mentation. On the downlink, there is enormouspotential for ingenious precoding schemes. Someexamples of recent work in this direction include[19].

The challenge of low-cost hardware: Buildinghundreds of RF chains, up/down converters,analog-to-digital (A/D)-digital-to-analog (D/A)converters, and so forth, will require economy ofscale in manufacturing comparable to what wehave seen for mobile handsets.

Hardware impairments: Massive MIMOrelies on the law of large numbers to average outnoise, fading and to some extent, interference.In reality, massive MIMO must be built withlow-cost components. This is likely to mean thathardware imperfections are larger: in particular,phase noise and I/Q imbalance. Low-cost andpower-efficient A/D converters yield higher lev-els of quantization noise. Power amplifiers withvery relaxed linearity requirements will necessi-tate the use of per-antenna low peak-to-averagesignaling, which, as already noted, is feasiblewith a large excess of transmitter antennas. Withlow-cost phase locked loops or even free-runningoscillators at each antenna, phase noise maybecome a limiting factor. However, what ulti-mately matters is how much the phase will driftbetween the point in time when a pilot symbol isreceived and the point in time when a data sym-bol is received at each antenna. There is greatpotential to get around the phase noise problemby design of smart transmission physical layerschemes and receiver algorithms.

Internal power consumption: Massive MIMOoffers the potential to reduce the radiated power1000 times and at the same time drastically scaleup data rates. However, in practice, the totalpower consumed must be considered, includingthe cost of baseband signal processing. Muchresearch must be invested in highly parallel, per-

haps dedicated, hardware for the baseband sig-nal processing.

Channel characterization: There are addi-tional properties of the channel to considerwhen using massive MIMO instead of conven-tional MIMO. To facilitate a realistic perfor-mance assessment of massive MIMO systems, itis necessary to have channel models that reflectthe true behavior of the radio channel (i.e., thepropagation channel including effects of realisticantenna arrangements). It is also important todevelop more sophisticated analytical channelmodels. Such models need not necessarily becorrect in every fine detail, but they must cap-ture the essential behavior of the channel. Forexample, in conventional MIMO the Kroneckermodel is widely used to model channel correla-tion. This model is not an exact representationof reality, but provides a useful model for certaintypes of analysis despite its limitations. A similarway of thinking could probably be adopted formassive MIMO channel modeling.

Cost of reciprocity calibration: TDD willrequire reciprocity calibration. How often mustthis be done, and what is the best way of doingit? What is the cost, in terms of time- and fre-quency resources needed to do the calibration,and in terms of additional hardware componentsneeded?

Pilot contamination: It is likely that pilot con-tamination imposes much more severe limita-tions on massive MIMO than on traditionalMIMO systems. We have discussed some of theissues in detail and outlined some of the mostrelevant research directions earlier.

Non-CSI@TX operation: Before a link hasbeen established with a terminal, the base sta-tion has no way of knowing the channel responseto the terminal. This means that no array beam-forming gain can be harnessed. In this case,probably some form of space-time block coding

Figure 7. Achieved downlink sum rates using MRT precoding, with 4 single-antenna terminals and between 4 and 128 base station antennas.

Number of base station antennas200

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e (b

/s/H

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Average and 90 percent conf. interval

Interference free → 13.8 b/s/Hz

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is optimal. Once the terminal has been contact-ed and sent a pilot, the base station can learnthe channel response and operate in coherentMU-MIMO beamforming mode, reaping thepower gains offered by having a very large array.

New deployment scenarios: It is consideredextraordinarily difficult to introduce a radicalnew wireless standard. One possibility is to intro-duce dedicated applications of massive MIMOtechnology that do not require backward com-patibility. For example, as discussed earlier, inrural areas, a billboard-sized array could provide20 Mb/s service to each of 1000 homes usingspecial equipment that would be used solely forthis application. Alternatively, a massive arraycould provide the backhaul for base stations thatserve small cells in a densely populated area.Thus, rather than thinking of massive MIMO asa competitor to LTE, it can be an enabler forsomething that was just never before consideredpossible with wireless technology.

System studies and relation to small-cell andheterogeneous network solutions: The drivingmotivation of massive MIMO is to simultaneous-ly and drastically increase data rates and overallenergy efficiency. Other potential ways of reach-ing this goal are network densification by thedeployment of small cells, resulting in a hetero-geneous architecture, or coordination of thetransmission of multiple individual base stations.From a purely fundamental perspective, the ulti-mately limiting factor of the performance of anywireless network appears to be the availability ofgood enough channel state information (CSI) tofacilitate phase-coherent processing at multipleantennas or multiple access points [20]. Consid-ering factors like mobility, Doppler shifts, phasenoise, and clock synchronization, acquiring high-quality CSI seems to be easier with a collocatedmassive array than in a system where the anten-nas are distributed over a large geographicalarea. But at the same time, a distributed array orsmall cell solution may offer substantial path lossgains and would also provide some diversityagainst shadow fading. The deployment costs ofa massive MIMO array and a distributed orsmall cell system are also likely to be very differ-ent. Hence, both communication-theoretic andtechno-economic studies are needed to conclu-sively determine which approach is superior.However, it is likely that the winning solutionwill comprise a combination of all available tech-nologies.

Prototype development: While massiveMIMO is in its infancy, basic prototyping workon various aspects of the technology is going onin different parts of the world. The Argos testbed[3] was developed at Rice University in coopera-tion with Alcatel-Lucent, and shows the basicfeasibility of the massive MIMO concept using64 coherently operating antennas. In particular,the testbed shows that TDD operation relyingon channel reciprocity is possible. One of thevirtues of the Argos testbed in particular is thatit is entirely modular and scalable, and builtaround commercially available hardware (theWARP platform). Other test systems around theworld have also demonstrated the basic feasibili-ty of scaling up the number of antennas. TheNgara testbed in Australia [21] uses a 32-ele-

ment base station array to serve up to 18 userssimultaneously with true spatial multiplexing.Continued testbed development is highly desiredto both prove the massive MIMO concept witheven larger numbers of antennas and discoverpotentially new issues that urgently needresearch.

CONCLUSIONS AND OUTLOOKIn this article we have highlighted the largepotential of massive MIMO systems as a keyenabling technology for future beyond fourthgeneration (4G) cellular systems. The technologyoffers huge advantages in terms of energy effi-ciency, spectral efficiency, robustness, and relia-bility. It allows for the use of low-cost hardwareat both the base station and the mobile unit side.At the base station the use of expensive andpowerful, but power-inefficient, hardware isreplaced by massive use of parallel low-cost low-power units that operate coherently together.There are still challenges ahead to realize thefull potential of the technology, for example,computational complexity, realization of dis-tributed processing algorithms, and synchroniza-tion of the antenna units. This gives researchersin both academia and industry a gold mine ofentirely new research problems to tackle.

ACKNOWLEDGMENTSThe authors would like to thank Xiang Gao,doctoral student at Lund University, for heranalysis of the channel measurements presentedin Fig. 6 and Fig. 7, and the Swedish organiza-tions ELLIIT, VR, and SSF for their funding ofparts of this work.

REFERENCES[1] F. Rusek et al., “Scaling Up MIMO: Opportunities and

Challenges with Very Large Arrays,” IEEE Sig. Proc.Mag., vol. 30, Jan. 2013, pp. 40–60.

[2] J. Nam et al., “Joint Spatial Division and Multiplexing:Realizing Massive MIMO Gains with Limited ChannelState Information,” 46th Annual Conf. Information Sci-ences and Systems, 2012.

[3] C. Shepard et al., “Argos: Practical Many-Antenna BaseStations,” ACM Int’l. Conf. Mobile Computing and Net-working, Istanbul, Turkey, Aug. 2012.

[4] X. Gao et al., “Measured Propagation Characteristics forVery-Large MIMO at 2.6 GHz,” Proc. 46th Annual Asilo-mar Conf. Signals, Systems, and Computers, PacificGrove, CA, Nov. 2012.

[5] J. Hoydis et al., “Channel Measurements for LargeAntenna Arrays,” IEEE Int’l. Symp. Wireless Commun.Systems, Paris, France, Aug. 2012.

[6] H. Q. Ngo, E. G. Larsson, and T. L. Marzetta, “Energy andSpectral Efficiency of Very Large Multiuser MIMO Systems,”IEEE Trans. Commun., vol. 61, Apr. 2013, pp. 1436–49.

[7] A. Pitarokoilis, S. K. Mohammed, and E. G. Larsson, “Onthe Optimality of Single-Carrier Transmission in Large-Scale Antenna Systems,” IEEE Wireless Commun. Lett.,vol. 1, no. 4, Aug. 2012, pp. 276–79.

[8] H. Yang and T. L. Marzetta, “Performance of Conjugate andZero-Forcing Beamforming in Large-Scale Antenna Sys-tems,” IEEE JSAC, vol. 31, no. 2, Feb. 2013, pp. 172–79.

[9] C. Studer and E. G. Larsson, “PAR-Aware Large-ScaleMulti-User MIMO-OFDM Downlink,” IEEE JSAC, vol. 31,Feb. 2013, pp. 303–13.

[10] S. K. Mohammed and E. G. Larsson, “Per-AntennaConstant Envelope Precoding for Large Multi-UserMIMO Systems,” IEEE Trans. Commun., vol. 61, Mar.2013, pp. 1059–71.

[11] P. Stenumgaard et al., “An Early-Warning Service forEmerging Communication Problems in Security andSafety Applications,” IEEE Commun. Mag., vol. 51, no.5, Mar. 2013, pp. 186–92.

Continued testbed

development is

highly desired to

both prove the

massive MIMO

concept with even

larger numbers of

antennas and discov-

er potentially new

issues that urgently

need research.

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[12] F. Kaltenberger et al., “Relative Channel ReciprocityCalibration in MIMO/TDD Systems,” Proc. Future Net-work and Mobile Summit, 2010, 2010.

[13] T. L. Marzetta, “Noncooperative Cellular Wireless withUnlimited Numbers of Base Station Antennas,” IEEETrans. Wireless Commun., vol. 9, no. 11, Nov. 2010,pp. 3590–600.

[14] J. Hoydis, S. ten Brink, and M. Debbah, “MassiveMIMO in the UL/DL of Cellular Networks: How ManyAntennas Do We Need?,” IEEE JSAC, vol. 31, no. 2,Feb. 2013, pp. 160–71.

[15] R. Müller, M. Vehkaperä, and L. Cottatellucci, “BlindPilot Decontamination,” Proc. ITG Wksp. Smart Anten-nas, Stuttgart, Mar. 2013.

[16] H. Yin et al., “A Coordinated Approach to ChannelEstimation in Large-Scale Multiple-Antenna Systems,”IEEE JSAC, vol. 31, no. 2, Feb. 2013, pp. 264–73.

[17] H. Q. Ngo and E. G. Larsson, “EVD-Based Channel Esti-mations for Multicell Multiuser MIMO with Very LargeAntenna Arrays,” Proc. IEEE Int’l. Conf. Acoustics,Speed and Sig. Proc., Mar. 2012.

[18] A. Ashikhmin and T. L. Marzetta, “Pilot ContaminationPrecoding in Multi-Cell Large Scale Antenna Systems,”IEEE Int’l. Symp. Information Theory, Cambridge, MA,July 2012.

[19] J. Zhang, X. Yuan, and L. Ping, “Hermitian Precodingfor Distributed MIMO Systems with Individual ChannelState Information,” IEEE JSAC, vol. 31, no. 2, Feb.2013, pp. 241–50.

[20] A. Lozano, R.W. Heath Jr, and J. G. Andrews, “Funda-mental Limits of Cooperation,” IEEE Trans. Info. Theory,vol. 59, Sept. 2013, pp. 5213–26.

[21] H. Suzuki et al., “Highly Spectrally Efficient NgaraRural Wireless Broadband ACCESS Demonstrator,” Proc.IEEE Int’l. Symp. Commun. and Information Technolo-gies, Oct. 2012.

BIOGRAPHIESERIK G. LARSSON is a professor and head of the Division forCommunication Systems in the Department of ElectricalEngineering at Linköping University, Sweden. He has pub-lished some 100 journal papers on signal processing andcommunications, and is a co-author of the textbook Space-Time Block Coding for Wireless Communications. He is anAssociate Editor for IEEE Transactions on Communications,and he received the IEEE Signal Processing Magazine BestColumn Award 2012.

OVE EDFORS is a professor of radio systems in the Depart-ment of Electrical and Information Technology, Lund Uni-versity, Sweden. His research interests include statisticalsignal processing and low-complexity algorithms withapplications in wireless communications. In the context ofmassive MIMO, his research focus is on how realistic prop-agation characteristics influence system performance andbaseband processing complexity.

FREDRIK TUFVESSON received his Ph.D. in 2000 from Lund Uni-versity. After almost two years at a startup company, Fiber-less Society, he is now an associate professor in theDepartment of Electrical and Information Technology, LundUniversity. His main research interests are channel mea-surements and modeling for wireless communication,including channels for both MIMO and UWB systems.Besides these, he also works on distributed antenna sys-tems and radio-based positioning.

THOMAS L. MARZETTA [F’03] received his Ph.D. in electricalengineering from the Massachusetts Institute of Technolo-gy. He joined Bell Laboratories in 1995. Within the formerMathematical Sciences Research Center he was director ofthe Communications and Statistical Sciences Department.He was an early proponent of massive MIMO, which canprovide huge improvements in wireless spectral efficiencyand energy efficiency over 4G technologies. He receivedthe 1981 ASSP Paper Award and received the 2013 IEEEGuglielmo Marconi Best Paper Award.

There are still

challenges ahead to

realize the full

potential of the

technology, for

example, when it

comes to

computational

complexity,

realization of

distributed process-

ing algorithms, and

synchronization of

the antenna units.

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