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Massive MIMO（大规模多输入多输出技术）是一种无线通信领域中的前沿技术，通过在基站安装大量天线来实现显著的性能提升。自提出以来，它就受到了学术界和工业界的广泛关注。在本文中，我们将介绍Massive MIMO的基本概念、优势、实现过程中的挑战以及未来在无线通信系统中实施Massive MIMO的机遇和挑战。一、Massive MIMO概念和优势 Massive MIMO技术是指在蜂窝基站配备数十至数百根天线，与传统的多输入多输出（MIMO）技术相比，其天线数目更多，因此被称为“大规模”。这种技术通过使用相对简单的线性处理方式，有望使频谱效率和能量效率提高数个数量级。Massive MIMO的优势主要体现在以下几方面： 1. 高频谱效率：增加基站天线数量可以显著提升无线通信系统的频谱效率，使得在同一频谱资源下，通信速率得到极大提升。 2. 高能量效率：大量的天线有助于优化信号的发送和接收过程，减少能耗，从而提高整个系统的能量效率。 3. 更好的信号覆盖和网络容量：由于采用了大规模天线阵列，基站可以同时服务于更多的用户，提高网络容量。二、Massive MIMO实现中的挑战和问题 Massive MIMO在理论上具有很大优势，但在实际的无线通信环境中面临着诸多挑战： 1. 信道估计：信道估计是指通过已知信息获取信道状态的过程，在Massive MIMO系统中，由于天线数量的激增，信道估计变得更加复杂。 2. 检测和预编码方案：在Massive MIMO系统中，数据的发送和接收需要复杂的检测算法和预编码方案，以确保信号的正确接收。 3. 导频污染：导频污染是指邻近小区的用户使用非正交导频序列导致的干扰问题。在Massive MIMO系统中，由于大量用户同时发送导频信号，导频污染成为需要解决的关键问题。三、Massive MIMO的能量效率和传输方式尽管Massive MIMO技术在提高频谱效率方面具有优势，但其对能量效率的提高也是研究的热点之一。Massive MIMO系统中天线的大量增加，为有效实施单载波传输提供了可能。此外，Massive MIMO系统在提供大量自由度的同时，也必须考虑实际部署时所需的硬件和能量消耗，以平衡系统性能和能效。四、Massive MIMO的未来机遇和挑战未来无线通信系统中实现Massive MIMO技术，面临着巨大的机遇和挑战。从机遇角度看，Massive MIMO有可能成为下一代通信标准的一部分，帮助实现更高数据速率、更低延迟和更广覆盖的通信网络。然而，挑战也相伴而生，包括需要对现有的无线通信架构进行重大修改、提高基站的计算能力和存储能力、解决大规模天线阵列部署的物理和经济成本等。五、结束语 Massive MIMO技术是无线通信领域的一项颠覆性创新，它提供了一个在频谱和能效方面实现巨大提升的可能途径。本文从信息论角度分析了Massive MIMO的优势，探讨了实现该技术所面临的挑战，并对未来实施 Massive MIMO系统的机遇和挑战进行了讨论。随着无线通信技术的不断发展，Massive MIMO技术有望在未来的通信系统中发挥关键作用。

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742 IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, VOL. 8, NO. 5, OCTOBER 2014

An Overview of Massive MIMO:

Beneﬁts and Challenges

Lu Lu, Student Member, IEEE, Geoffrey Ye Li, Fellow, IEEE, A. Lee Swindlehurst, Fellow, IEEE,

Alexei Ashikhmin, Senior Member, IEEE, and Rui Zhang, Member, IEEE

Abstract—Massive multiple-input multiple-output (MIMO) wire-

less communications refers to the idea equipping cellular base

stations (BSs) with a very large number of antennas, and has been

shown to potentially allow for orders of magnitude improvement

in spectral and energy e fﬁciency using relatively simple (linear)

processing. In this paper, we present a comprehensive overview of

state-of-the-art research on the topic, which has recently attracted

considerable attention. We begin with an information theoretic

analysis to illustrate the conjectured advantages of massive

MIMO, and then we address implementation issues related to

channel estimation, detection and precoding sch emes. We partic-

ularly focus on the potential impact of pilot contamination caused

by the use of non-orthogonal pilot sequences by users in adjacent

cells. We also analyze the energy efﬁcien cy achieved by massive

MIMO systems, and demonstrate how the degrees of freedom

provided by massive MIMO systems enable efﬁcient single-carrier

transmission. Finally, the challenges and opportunities associated

with implementing massive MIMO in future wireless communica-

tions systems are discussed.

Index Terms—Channel estimation, energy efﬁciency, mas-

sive MIMO systems, orthogonal frequency division m ultiplexing

(OFDM), pilot contamination, precoding and detection, single-car-

rier transmission, spectral efﬁciency, time-division duplexing

(TDD).

I. INTRODUCTION

ULTIPLE-

INPUT m ultip le-output (MIMO) technolog y

has been widely studied during the last two decades and

applied to many wireless standards since it can signiﬁcantly im-

prove th

e capacity and reliability of wireless systems. W hile

initial work on the problem focused on point-to-point MIMO

links where two devices with multiple antennas communicate

with e

ach other, focus has shifted in recent years to more prac-

tical mult i- user MIM O (MU -MIMO) systems, where typically a

Manuscript received September 30, 2013; revised December 30, 2013; ac-

cepted March 28, 2014. Date of publication April 15, 2014; date of current

version September 11, 2014. The guest editor coordinating the review of this

manuscript and approving it for publication was Prof. Fernando Pereira.

L. Lu and G. Y. Li are with the School of Electrical and Computer En-

gineering, Georgia Ins titu te of Technolog y, Atlanta, GA 30332 USA (e-mail:

lulu@ece.gatec h.edu; liye@ece.gatech.edu).

A. L. Swindlehurst is with the Henry Samueli School of Engineering, Uni-

versity of California, Irvine, CA 92697-2625 USA (e-mail: swindle@uci.edu).

A. Ashikhmin is with the Co mmunications and Statistical Sciences Depart-

ment, B ell Laboratories, Lucent Technologies, Murray Hill, NJ 07974-06 36

USA ( e-m ail: aea@al catel-lucent.com).

R. Zhang is with the Department of Electrical and Computer Engineering,

National University of Singapore, Singapore 117516 (e-mail: elezhang@nus.

edu.sg).

Color versions of one or more of the ﬁgures in this paper are available online

at http://ieeexplore.i eee.org.

Digital Object Identiﬁer 10.1109/JSTSP.2014.2317671

Fig. 1. Illustration of Massive MU- MIMO system s.

base station (BS) with multiple antennas simultaneously serves

a set of single-antenna users and the m ultiplexing gain can be

shared by all users.

In this way, expensive equipment i s only

needed on the BS end of the link, and the user terminals can

be relatively cheap single-antenna devices. Furthermore, due

to m ulti-user di

versity, the performance of MU-MIMO systems

is generally less sens iti ve to the propagation environment than

in the point-to-point MIMO case. As a result, MU-MIMO has

become an integ

ral part of comm unications standards, such as

802.11 (WiFi), 802.16 (WiMAX), LTE, and is progressively

being deplo yed throughout the world. For most MIMO imple-

mentations,

the BS typically employs only a few (i.e., fewer than

10) antennas, an d the correspond ing improvement in spectral ef-

ﬁciency, while important, is still relatively modest.

In a recent ef

fort to achieve m ore dramatic gains as well as

to simplify the required signal processing, massive MIMO sys-

tems o r large-scale antenna systems (LSAS) have been pro-

posedin[1

], [2], where each BS is equipped with orders of mag-

nitude m ore antennas, e.g., 100 or m ore. A massive MU-MIMO

network is depicted in Fig. 1. Asymptotic arguments based on

random ma

trix theory [2] demonstrate that the effects of u ncor-

related noise and small-scale fading are eliminated, the nu mber

of users per cell are independent of th e size of the cell, and

the req

uired transmitted energy per b it vanishes as the number

of antennas in a M IMO cell grows to inﬁnity. Furthermore,

simple linear signal processing approaches, such as matched-

ﬁlter

(MF) precoding/detection, can be used in massive MIMO

systems to achieve these advantages.

It is shown in [2] that u nder realistic propagation assump-

tions

, MF-b ased non-co operativ e massive MIMO systems could

in principle achieve a data rate of 17 Mb/s for each of 40 users

in a 20 MHz channel in both the uplink (reverse link) and down-

link

(forward link) directions, with an average throughp ut of 73 0

Mb/s per cell and an overall spectral efﬁciency of 26.5 bps/Hz.

Since the number of antennas at the BS is typically assumed to

See http://www.ieee.org/publications_standards/publications/rights/index.html for more inform ation.

LU et al.: OVERVIEW OF MASSIVE MIMO: BENEFITS AND CHALLENGES 743

be signiﬁcantly larger than the number of users, a large number

of degrees of freedom are available and can be used to shape

the transmitted signals in a hardware-friendly way or to null

interference [3]. To make such a system practical, algorithms

for massive MIMO sy stem s are required to keep the c om plexity

low.

Another advantage of m assive MIMO lies in its potential

energy efﬁciency com pared to a corresponding single-antenna

system. It is shown in [4] that each single-antenna user in a mas-

sive MIMO system can scale down its transmit power propor-

tional to the number of antennas at the BS with perfect channel

state information (CSI) or to the square root of the numb e r o f

BS antennas with imperfect CSI, to get the same performance as

a correspondin g single-input single-output (SIS O) syste

m. This

leads to hig her energy efﬁciency and is very important for fu-

ture wireless networks where excessiv e energy consumption is a

growing concern [5], [6 ]. On the other hand, if adequate tr

ansmit

power is available, then a massive MIMO system could signif-

icantly extend th e range of operation com pared wi th a single

antenna system. Even though the conclusions in [4]

ignore the

power consumption of the rad io fro nt-end, massive MIMO is

still a promising can didate for improving energy-efﬁciency of

future networks.

The observations described above have recently sparked a

ﬂurry of research activities aimed at understanding the signal

processing and information theoretic ramiﬁ

cations of massive

MIMO system designs. In [7], massive MIMO systems are

reviewed from various perspectives, including fu ndam ental

information theoretical gains, antenna a

nd propagation aspects,

and transceiver design. A follow-up tutorial [8] brieﬂy discusses

recent work. In this paper, we provide a more comprehensive

and detailed overview of state-of-the-a

rt research on this topic.

In Section I I, the opportunities of massive MIMO systems

are viewed fro m an information theoretic perspective. Issues

on channel estimation and sign al det

ection are then discussed

in Section III, and transmit precoding schemes are presented

in Section IV. Besides the MF precoder/detector, other linear

schemes such as minimu m mean-squar

ed error (MMSE) and

zero-forcing (ZF) precoders/detectors are discussed based on ei-

ther single-cell processing or multi-cell coordinated processing.

In Section V, the so-called pilo

t contamination effect, caused

by employing non-orthog onal p ilot sequences at different users

in different cells, is discussed in detail. The energy efﬁciency of

massive M IMO systems is then a

nalyzed in Section VI. Instead

of using orthogonal frequency division multiplexing (OFDM )

as in most MU -MIMO im plementations today, the possibility

of single-carrier modulat

ion for massive MIMO systems is

discussedinSectionVII.Finally, the challenges and potentials

related to applications of m assive MIM O in future wireless

communications are id ent

iﬁed in Section V I II and conclusions

are provided i n Section IX.

Notation

Boldface lower and upper case symbols represent vectors and

matrices, respectively. The transpose, conjugate, and Hermitian

transpose operators are denoted by

, ,and , respec-

tively. The Moore-Penrose pseudoinverse operator is denoted

. The determ inant and trace operators are denoted by

and , respectively. The norm of a vector is denoted

,and means is m uch greater than .

II. F

ROM REGULAR TO MASSIVE MIMO

In this section, the advantages of m assive MIMO systems

are reviewed from an information theoretic point of view. We

start with point-to-po int MIMO system s to reveal the poten-

tial opportunities that arise by equipping the ter minals with a

large number of antennas, and then we discuss the performance

of MU-MIMO sy stems, where multiple single-antenna users

are communicating w ith a BS equipped with a large number

of antennas. Most results in this section are based on [7], [9],

and [10].

A. Point-to-Point MIMO

We consider a point-to-p oin t MIMO transmission ﬁrst, where

the transmitter and the receiver are equipped with

and

antennas, respectively. We focus on the narrow-band time-in-

variant channel with a deterministic and constant channel ma-

trix

. OFDM-based schemes are normally used to

convert a frequency-selective wide-band channel into multiple

parallel ﬂat-fading narrow-band channels [11].

The received signal vector,

, can be expressed as

(1)

where

is the transmit signal vector and

represents noise and interference. We focus on the case that

the total power of the transmit signal is normalized, i.e.,

, and the noise is zero-mean circularly symmetric

complex Gaussian with an identity covariance matrix

.With

these assum ptions, the scalar

is the transmit power.

If we assume independent and identica lly distributed (i.i.d.)

Gaussian transmit signals and that perfect CSI is available at the

receiver, the instantaneous achievable rate can be expressed as

(2)

When the propagation coefﬁcients in t he channel matrix

are

normalized as

, upper and lower bounds

on the capacity are derived in [7] w ith the help of Jensen’s in-

equality:

(3)

The actual achievable rate depends on the distribution of t he

singular values of

. Among all chann els with the same

normalization, those whose singular v alues are all equal achieve

the highest rate, i.e., th e upper bound in (3), while those with

only one non-zero s in gular value have the lo west rate, i.e., the

lower bound in (3). The best case can be approached in the limit

by a scenario where all of the propagation coefﬁcients in the

channel matrix are i.i.d., w hile the worst case corresponds for

example to a scenario with line-of-sight (LO S) propagation.

Next we discuss two extreme cases, where either the number

of transm it or the number of receive antennas goes to inﬁnity.

744 IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, VOL. 8, NO. 5, OCTOBER 2014

1) and : When the number of transmit

antennas goes to inﬁnity while the number of receive antennas

is constant, i.e.,

, the row vectors o f are

asymptotically orthogonal, and hence we have

(4)

In this case, the achievable rate in (2) can be approximated as

(5)

which achieves the upper bound in (3).

and : Using similar derivations as in

Case 1),wehave

(6)

which achieves the upper bound in (3 ) as well.

The results in (5) and (6) show the advantages of equipping

the arrays i n a MIMO link with a large number of antennas. Note

that the above discussion depends on the assumption that the

row or the column vectors of

are asy mp totically orthogonal,

which is an o ptimistic assumption regarding the p rop agation co-

efﬁcients. The multiplexing gain disappears in LO S propagation

environments, as s how n in [7].

B. Multi-User MIMO

MU-MIM O systems can obtain the promising multiplexing

gain of m assive point-to-point M IMO systems wh ile elimi-

nating pro blems due to unfav orable propagation environments.

Consider a MU-MIMO system with

cells, where each cell

has

served single-antenna users and one BS with antennas.

Denote the channel coefﬁcient from the

-th user in the -th cell

to the

-th antenna of the -th BS as , which is equal to

a complex small-scale fading factor times an amplitude factor

that accounts for geometric attenu ation and large-scale fading:

(7)

where

and represent complex small-scale

fading and large-scale fading coefﬁcients, respectively. The

small-scale fading coefﬁcients are assumed to be different

for different users or for different antennas at each BS while

the large-scale fading coefﬁcients are the same for different

antennas at the same BS, but are user-dependent. Then, the

channel matrix from all

users in the -th cell to the -th BS

can be expressed as

(8)

where

(9)

(10)

Consider a single-cell (

) MU-MIMO system with

single-antenna users and a BS with antennas. For simplicity,

the cell and the BS indices are dropped when single-cell systems

are considered.

1) Uplink: For uplink signal transmission, the received

signal vector at a single B S, which we denote by

has the same expression as in (1):

(11)

where

is the sig nal vector from all users,

is the uplink ch a nnel matrix deﬁned i n (8) by dropping

the cell and the B S indices,

is a zero-mean noise

vector with com plex Gaussian distribution and identity covari-

ance matrix, and

is the u plink transmit power. The trans-

mitted symbol from the

-th user, ,isthe -th el e men t of

with .

Basedontheassumptionthatthe small-scale fading coefﬁ-

cients for different users are ind e pendent, the column channel

vectors from different u sers are asymptotically orthog onal as the

number of antennas at the BS,

, grows to inﬁnity [2]. Then,

we have

(12)

A detailed discussion of this result can be found in [9]. Based on

the result in (12), the ov erall achievable rate of all users becomes

(13)

In th e followin g, we show that simple MF processing at the

BS can achieve the capacity in (13). When MF processing is

used, the BS processes the signal vector by multiplying the con-

jugate-transpose of the channel, as

(14)

where (12) is used. Note that the channel vectors are asymptot-

ically orthogonal wh en the number of an tenn as at the BS grows

to inﬁnity. Therefore,

does not color the noise. Since is

a diagonal matrix , the M F processing separates the sign als from

different users into different streams and there is asymptotically

no inter-user interference. The signal transmissions from each

user can thus be treated as if originating from a SISO channel.

From (14), the signal-to-noise ratio (SNR) for the

-th user is

. Consequently, the rate achievable by u sing MF is the

same as the limit in (13), which implies that simple MF p ro-

cessing at the BS is optimal when the number of antennas at t he

BS,

, grows to inﬁnity.

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