Scaling up MIMO: Opportunities and
Challenges with Very Large Arrays
Fredrik Rusek, Daniel Persson, Buon Kiong Lau, Erik G. Larsson,
Thomas L. Marzetta, Ove Edfors and Fredrik Tufvesson
Linköping University Post Print
N.B.: When citing this work, cite the original article.
©2011 IEEE. Personal use of this material is permitted. However, permission to
reprint/republish this material for advertising or promotional purposes or for creating new
collective works for resale or redistribution to servers or lists, or to reuse any copyrighted
component of this work in other works must be obtained from the IEEE.
Fredrik Rusek, Daniel Persson, Buon Kiong Lau, Erik G. Larsson, Thomas L. Marzetta, Ove
Edfors and Fredrik Tufvesson, Scaling up MIMO: Opportunities and Challenges with Very
Large Arrays, accepted IEEE signal processing magazine.
Postprint available at: Linköping University Electronic Press
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-71581
1
Scaling up MIMO: Opportunities and
Challenges with Very Large Arrays
Fredrik Rusek
†
, Daniel Persson
‡
, Buon Kiong Lau
†
, Erik G. Larsson
‡
,
Thomas L. Marzetta
§
, Ove Edfors
†
, and Fredrik Tufvesson
†
I. INTRODUCTION
MIMO technology is becoming mature, and incorporated into emerging wireless
broadband standards like LTE [1]. For example, the LTE standard allows for up to 8
antenna ports at the base station. Basically, the more antennas the transmitter/receiver
is equipped with, and the more degrees of freedom that the propagation channel can
provide, the better the performance in terms of data rate or link reliability. More
precisely, on a quasi-static channel where a codeword spans across only one time
and frequency coherence interval, the reliability of a point-to-point MIMO link scales
according to Prob(link outage) ∼ SNR
−n
t
n
r
where n
t
and n
r
are the numbers of
transmit and receive antennas, respectively, and SNR is the Signal-to-Noise Ratio.
On a channel that varies rapidly as a function of time and frequency, and where
circumstances permit coding across many channel coherence intervals, the achievable
rate scales as min(n
t
, n
r
) log(1+SNR). The gains in multiuser systems are even more
impressive, because such systems offer the possibility to transmit simultaneously to
several users and the flexibility to select what users to schedule for reception at any
given point in time [2].
The price to pay for MIMO is increased complexity of the hardware (number of RF
chains) and the complexity and energy consumption of the signal processing at both
ends. For point-to-point links, complexity at the receiver is usually a greater concern
than complexity at the transmitter. For example, the complexity of optimal signal
detection alone grows exponentially with n
t
[3], [4]. In multiuser systems, complexity
at the transmitter is also a concern since advanced coding schemes must often be
†
Dept. of Electrical and Information Technology, Lund University, Lund, Sweden
‡
Dept. of Electrical Engineering (ISY), Link¨oping University, Sweden
§
Bell Laboratories, Alcatel-Lucent, Murray Hill, NJ
Contact authors: Fredrik Rusek fredrik.rusek@eit.lth.se and Daniel Persson daniel.persson@isy.liu.se
October 21, 2011 DRAFT
2
used to transmit information simultaneously to more than one user while maintaining
a controlled level of inter-user interference. Of course, another cost of MIMO is that
of the physical space needed to accommodate the antennas, including rents of real
estate.
With very large MIMO, we think of systems that use antenna arrays with an order of
magnitude more elements than in systems being built today, say a hundred antennas or
more. Very large MIMO entails an unprecedented number of antennas simultaneously
serving a much smaller number of terminals. The disparity in number emerges as a
desirable operating condition and a practical one as well. The number of terminals that
can be simultaneously served is limited, not by the number of antennas, but rather by
our inability to acquire channel-state information for an unlimited number of terminals.
Larger numbers of terminals can always be accommodated by combining very large
MIMO technology with conventional time- and frequency-division multiplexing via
OFDM. Very large MIMO arrays is a new research field both in communication theory,
propagation, and electronics and represents a paradigm shift in the way of thinking
both with regards to theory, systems and implementation. The ultimate vision of very
large MIMO systems is that the antenna array would consist of small active antenna
units, plugged into an (optical) fieldbus.
We foresee that in very large MIMO systems, each antenna unit uses extremely low
power, in the order of mW. At the very minimum, of course, we want to keep total
transmitted power constant as we increase n
t
, i.e., the power per antenna should be
∝ 1/n
t
. But in addition we should also be able to back off on the total transmitted
power. For example, if our antenna array were serving a single terminal then it can be
shown that the total power can be made inversely proportional to n
t
, in which case the
power required per antenna would be ∝ 1/n
2
t
. Of course, several complications will
undoubtedly prevent us from fully realizing such optimistic power savings in practice:
the need for multi-user multiplexing gains, errors in Channel State Information (CSI),
and interference. Even so, the prospect of saving an order of magnitude in transmit
power is important because one can achieve better system performance under the same
regulatory power constraints. Also, it is important because the energy consumption
of cellular base stations is a growing concern. As a bonus, several expensive and
bulky items, such as large coaxial cables, can be eliminated altogether. (The coaxial
cables used for tower-mounted base stations today are up to four centimeters in
diameter!) Moreover, very-large MIMO designs can be made extremely robust in
October 21, 2011 DRAFT
3
that the failure of one or a few of the antenna units would not appreciably affect
the system. Malfunctioning individual antennas may be hotswapped. The contrast to
classical array designs, which use few antennas fed from a high-power amplifier, is
significant.
So far, the large-number-of-antennas regime, when n
t
and n
r
grow without bound,
has mostly been of pure academic interest, in that some asymptotic capacity scaling
laws are known for ideal situations. More recently, however, this view is changing,
and a number of practically important system aspects in the large-(n
t
, n
r
) regime have
been discovered. For example, [5] showed that asymptotically as n
t
→ ∞ and under
realistic assumptions on the propagation channel with a bandwidth of 20 MHz, a time-
division multiplexing cellular system may accommodate more than 40 single-antenna
users that are offered a net average throughput of 17 Mbits per second both in the
reverse (uplink) and the forward (downlink) links, and a throughput of 3.6 Mbits per
second with 95% probability! These rates are achievable without cooperation among
the base stations and by relatively rudimentary techniques for CSI acquisition based
on uplink pilot measurements.
Several things happen when MIMO arrays are made large. First, the asymptotics
of random matrix theory kick in. This has several consequences. Things that were
random before, now start to look deterministic. For example, the distribution of the
singular values of the channel matrix approaches a deterministic function [6]. Another
fact is that very tall or very wide matrices tend to be very well conditioned. Also when
dimensions are large, some matrix operations such as inversions can be done fast, by
using series expansion techniques (see the sidebar). In the limit of an infinite number of
antennas at the base station, but with a single antenna per user, then linear processing
in the form of maximum-ratio combining for the uplink (i.e., matched filtering with the
channel vector, say h) and maximum-ratio transmission (beamforming with h
H
/||h||)
on the downlink is optimal. This resulting processing is reminiscent of time-reversal,
a technique used for focusing electromagnetic or acoustic waves [7], [8].
The second effect of scaling up the dimensions is that thermal noise can be averaged
out so that the system is predominantly limited by interference from other transmitters.
This is intuitively clear for the uplink, since coherent averaging offered by a receive
antenna array eliminates quantities that are uncorrelated between the antenna elements,
that is, thermal noise in particular. This effect is less obvious on the downlink, however.
Under certain circumstances, the performance of a very large array becomes limited
October 21, 2011 DRAFT
4
by interference arising from re-use of pilots in neighboring cells. In addition, choosing
pilots in a smart way does not substantially help as long as the coherence time of the
channel is finite. In a Time-Division Duplex (TDD) setting, this effect was quantified
in [5], under the assumption that the channel is reciprocal and that the base stations
estimate the downlink channels by using uplink received pilots.
Finally, when the aperture of the array grows, the resolution of the array increases.
This means that one can resolve individual scattering centers with unprecedented
precision. Interestingly, as we will see later on, the communication performance of
the array in the large-number-of-antennas regime depends less on the actual statistics
of the propagation channel but only on the aggregated properties of the propagation
such as asymptotic orthogonality between channel vectors associated with distinct
terminals.
Of course, the number of antennas in a practical system cannot be arbitrarily large
owing to physical constraints. Eventually, when letting n
r
or n
t
tend to infinity,
our mathematical models for the physical reality will break down. For example,
the aggregated received power would at some point exceed the transmitted power,
which makes no physical sense. But long before the mathematical models for the
physics break down, there will be substantial engineering difficulties. So, how large is
“infinity” in this paper? The answer depends on the precise circumstances of course,
but in general, the asymptotic results of random matrix theory are accurate even for
relatively small dimensions (even 10 or so). In general, we think of systems with at
least a hundred antennas at the base station, but probably less than a thousand.
Taken together, the arguments presented motivate entirely new theoretical research
on signal processing and coding and network design for very large MIMO systems.
This article will survey some of these challenges. In particular, we will discuss ultimate
information-theoretic performance limits, some practical algorithms, influence of chan-
nel properties on the system, and practical constraints on the antenna arrangements.
A. Outline and key results
The rest of the paper is organized as follows. We start with a brief treatment
of very large MIMO from an information-theoretic perspective. This provides an
understanding for the fundamental limits of MIMO when the number of antennas
grows without bound. Moreover, it gives insight into what the optimal transmit and
receive strategies look like with an infinite number of antennas at the base station.
October 21, 2011 DRAFT
![Fig. 3. Diagram of a MIMO system with antenna impedance matrices and matching networks at both link ends (freely reproduced from [23]).](/figures/fig-3-diagram-of-a-mimo-system-with-antenna-impedance-597mvdhd.webp)
