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### MIMO系统概述：实现千兆无线通信的关键技术 #### 引言随着无线通信技术的飞速发展，人们对于高数据速率的需求日益增长。在新兴的无线局域网（WLAN）和家庭音频/视频（A/V）网络中，接近1Gb/s传输速率的无线通信变得尤为重要。当前，WLAN提供的峰值速率约为10Mb/s，而不久将来将提升至50-100Mb/s。然而，即便如此高的速率，在面对诸如高清视频流、大规模文件传输等需求时仍然显得不足。因此，如何设计出能在非视距（NLOS）环境下提供良好服务质量和服务范围的非常高速的无线链路，成为了研究与工程领域的一大挑战。 #### 多输入多输出（MIMO）技术概览 MIMO（Multiple-Input Multiple-Output）是一种利用多个发射天线和接收天线来显著提高无线通信系统的性能的技术。这一技术为实现1Gb/s的无线通信提供了可行的解决方案，并且正逐渐成为一种成本效益高的技术选择。MIMO技术通过空间复用和空间分集等手段提高了系统的容量和可靠性，从而克服了传统单输入单输出（SISO）系统在非视距环境中的局限性。 ### MIMO技术的关键要素 #### 1. 通道模型 MIMO系统中的通道模型是理解信号如何从发射端到接收端的基础。这些模型考虑了路径损耗、多径传播以及各种衰落效应等因素的影响。常见的MIMO通道模型包括瑞利衰落模型、莱斯衰落模型等。通道模型的准确性直接影响到后续的信号处理策略的设计。 #### 2. 性能限制 MIMO系统的性能受到多种因素的限制，包括但不限于信道带宽、发射功率、噪声水平等。这些因素共同决定了系统的最大数据传输速率。例如，为了达到1Gb/s的数据传输速率，需要确保带宽和频谱效率的乘积至少等于10^9。然而，由于成本、技术和监管方面的约束，单纯依靠增加带宽的方法并不总是可行的。 #### 3. 编码技术空间时间编码（Space-Time Coding, STC）是MIMO系统中的关键技术之一，它通过在时间和空间维度上对信号进行编码来提高系统的可靠性和吞吐量。STC可以分为两种主要类型：分组编码和连续编码。前者适用于低至中等的数据率场景，而后者更适合于高数据率的应用。 #### 4. 发射机和接收机设计 MIMO系统的发射机和接收机设计对于实现高性能通信至关重要。发射机需要能够有效地发送经过编码的信号，而接收机则需要准确地解码接收到的信号。这涉及到复杂的信号处理算法和技术，如预编码、波束成形、干扰抑制等。 #### 5. 正交频分复用（OFDM） MIMO-OFDM结合了MIMO技术和正交频分复用（Orthogonal Frequency Division Multiplexing, OFDM），可以在宽带多径信道中实现高效的频谱利用率和稳健的传输性能。MIMO-OFDM通过将高频带宽分割成许多并行的窄带子载波来降低多径衰落的影响，从而改善了系统的整体性能。 ### 结论 MIMO技术作为实现高速无线通信的关键技术之一，正在不断推动无线通信的发展。通过合理设计通道模型、优化性能限制、采用先进的编码技术和改进发射机及接收机的设计，MIMO系统能够在非视距环境中提供接近1Gb/s的传输速率。随着技术的进步和应用场景的扩展，MIMO技术将在未来的无线通信系统中发挥更加重要的作用。

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An Overview of MIMO Communications—A

Key to Gigabit Wireless

AROGYASWAMI J. PAULRAJ, FELLOW, IEEE

, DHANANJAY A. GORE,

ROHIT U. NABAR

, MEMBER, IEEE

AND

HELMUT BÖLCSKEI, SENIOR MEMBER, IEEE

Invited Paper

High data rate wireless communications, nearing 1-Gb/s trans-

mission rates, is of interest in emerging wireless local area net-

works and home audio/visual networks. Designing very high speed

wireless links that offer good quality-of-service and range capa-

bility in non-line-of-sight (NLOS) environments constitutes a signif-

icant research and engineering challenge. Ignoring fading in NLOS

environments, we can, in principle, meet the 1-Gb/s data rate re-

quirement with a single-transmit single-receive antenna wireless

system if the product of bandwidth (measured in hertz) and spectral

efficiency (measured in bits per second per hertz) is equal to 10

.As

we shall outline in this paper, a variety of cost, technology and reg-

ulatory constraints make such a brute force solution unattractive if

not impossible. The use of multiple antennas at transmitter and re-

ceiver, popularly known as multiple-input multiple-output (MIMO)

wireless is an emerging cost-effective technology that offers sub-

stantial leverages in making 1-Gb/s wireless links a reality. This

paper provides an overview of MIMO wireless technology covering

channel models, performance limits, coding, and transceiver de-

sign.

Keywords—Capacity, channel models, multiple-input multiple-

output (MIMO), MIMO orthogonal frequency division multiplexing

(MIMO-OFDM), performance limits, receiver design, space–time

coding, spatial multiplexing.

I. INTRODUCTION

High data rate wireless communications, nearing 1-Gb/s

transmission rates, is of interest in emerging wireless

local area networks (WLANs) and home audio/visual

(A/V) networks. Currently, WLANs offer peak rates of

10 Mb/s, with 50–100 Mb/s becoming available soon.

However, even 50 Mb/s is inadequate when faced with the

Manuscript received October 16, 2002; revised November 6, 2003.

A. J. Paulraj is with the Information Systems Laboratory, Stanford Uni-

versity, Stanford, CA 94305 USA (e-mail: apaulraj@stanford.edu).

D. Gore is with Qualcomm Inc., San Diego, CA 92121 USA (e-mail:

dgore@qualcomm.com).

R. U. Nabar and H. Bölcskei are with the Communication Technology

Laboratory, Swiss Federal Institute of Technology (ETH) Zürich, Zürich,

Switzerland (e-mail: nabar@nari.ee.ethz.ch; boelcskei@nari.ee.ethz.ch).

Digital Object Identifier 10.1109/JPROC.2003.821915

demand for higher access speeds due to the increase in

rich media content and competition from 10-Gb/s wired

LANs. Additionally, future home A/V networks will be

required to support multiple high-speed high-definition

television (HDTV) A/V streams, which again demand near

1-Gb/s data rates. Another challenge faced by WLANs and

home A/V environments as well as outdoor wireless wide

area network (WWAN) systems for fixed/nomadic access

is non-line-of-sight (NLOS) propagation, which induces

random fluctuations in signal level, known as fading.

Designing very high speed wireless links that offer good

quality-of-service (QoS) and range capability in NLOS

environments constitutes a significant research and engi-

neering challenge. Ignoring fading for the moment, we

can, in principle, meet the 1-Gb/s data rate requirement if

the product of bandwidth (measured in Hz) and spectral

efficiency (measured in b/s/Hz) equals 10

. As we shall

describe in the following, a variety of cost, technology,

and regulatory constraints make such a brute force solution

unattractive, if not impossible. In this paper, we provide

an overview of an emerging technology, known as mul-

tiple-input multiple-output (MIMO) wireless, that offers

significant promise in making 1-Gb/s wireless links in

NLOS environments a reality.

Several efforts are currently underway to build sub-Gb/s

NLOS broadband wireless systems. In WWANs (corre-

sponding standards are currently under development by

IEEE 802.16), Iospan Wireless (founded by the first author

of this paper and acquired by Intel Corp.) successfully

developed a MIMO wireless system (physical layer and

medium access control layer technology) using orthogonal

frequency division multiplexing (OFDM) modulation for

NLOS environments. The system is designed for a cellular

plan with a reuse factor of two and delivers a peak spectral

efficiency of 12 b/s/Hz. Current chipsets offer 13-Mb/s

goodput in a 2-MHz channel. Future releases will support

a goodput of 45 Mb/s in a 7-MHz channel. The system is

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aimed at fixed and nomadic/low mobility applications with

cell sizes up to 4 mi. In mobile access, there is an effort under

the International Telecommunications Union (ITU) working

group to integrate MIMO techniques into the high-speed

downlink packet access (HSDPA) channel, which is a part of

the Universal Mobile Telecommunications System (UMTS)

standard. Lucent Technologies recently announced a chip

for MIMO enhancement of UMTS/HSDPA, but has released

no further details. Preliminary efforts are also underway to

define a MIMO overlay for the IEEE 802.11 standard for

WLANs under the newly formed Wireless Next Generation

(WNG) group. With the exception of Iospan’s product, the

other efforts in MIMO technology are expected to take three

to four years to reach deployment status. These efforts can

serve as a good learning base for next-generation gigabit

wireless systems. In this paper, we outline the value of

MIMO technology in the development of viable gigabit

wireless systems and provide an overview of this technology.

A. Organization of the Paper

The remainder of this paper is organized as follows. Sec-

tion II discusses the design tradeoffs in building gigabit wire-

less systems and highlights the leverages of MIMO tech-

nology. Section III introduces a MIMO channel model for

NLOS environments. In Section IV, we study the capacity

gains resulting from the use of MIMO technology, while

Sections V and VI review signaling and receiver design for

MIMO systems, respectively. Section VII explores funda-

mental performance limits in communicating over MIMO

channels. In Section VIII, we briefly review MIMO-OFDM,

an increasingly popular modulation technique in broadband

MIMO wireless channels. We present our conclusions in Sec-

tion IX.

B. Notation

The superscripts

, , and stand for transposition, con-

jugate transposition, and elementwise conjugation, respec-

tively.

denotes the expectation operator while is the con-

volution operator with

stands for the identity matrix, denotes the

all zeros matrix of appropriate dimensions.

, det ,

and Tr

stand for the Frobenius norm, determinant, and

trace, respectively, of the matrix

. denotes the Eu-

clidean norm of the vector

. stands for the element

in the

th row and th column of . For an matrix

, we define the 1 vector vec

. A complex random variable

is if and are independent identically dis-

tributed (i.i.d.)

II. B

UILDING GIGABIT WIRELESS LINKS

As noted in the preceding section, we can, in principle,

reach 1-Gb/s link speed in a standard single-input single-

output (SISO) wireless link by employing sufficiently high

bandwidth along with coding and modulation that achieves

the required spectral efficiency. However, there are several

problems with such a simplistic approach.

Let us start by discussing how transmit power and receive

signal-to-noise ratio (SNR) constraints limit the maximum

achievable spectral efficiency in SISO links. First, the

transmit power in a terminal used by or located near human

beings is limited to less than 1 W in indoor environments due

to biohazard considerations. These limits are about a factor

of ten higher in outdoor tower-based base stations. Second,

the peak SNR limit in a wireless receiver rarely exceeds

30–35 dB because of the difficulty in building (at reasonable

cost) highly linear receivers with low phase noise. More gen-

erally, the signal-to-interference-and-noise ratio (SINR) in

cellular systems is capped due to the presence of cochannel

interference. It is well known that aggressive cellular reuse

with a low target SINR is advantageous for achieving

high multicell spectral efficiency. Also, channel fading in

the presence of imperfect power control and peak power

limitations at the transmitter results in the peak achievable

SINR being lower than the received SNR limit of 30–35

dB. The average SINR in a cellular reuse scheme lies in the

range of 10–20 dB at best. This implies that increasing the

spectral efficiency in a SISO NLOS cellular network beyond

a peak value of 4–6 b/s/Hz (average value of 2–4 b/s/Hz)

is not possible. In pure line-of-sight (LOS) links, practical

SISO systems have reached spectral efficiencies of up to 9

b/s/Hz. However, such systems rely on fixed point-to-point

links with very high gain directional antennas and Fresnel

clearance to almost completely eliminate fading. The advan-

tage of high-gain antennas in reducing the transmit power

constraint is not available in NLOS environments, where

large angle spread due to scattering can make such antennas

highly inefficient.

Let us next consider the implications of simply using the

appropriate bandwidth and spectral efficiency product to

achieve 1-Gb/s date rate. Consider a system that realizes

a nominal spectral efficiency of 4 b/s/Hz over 250-MHz

bandwidth, so that the data rate is 1 Gb/s. Two hundred

fifty megahertz of bandwidth is scarce, if not impossible to

obtain, particularly in frequency bands below 6 GHz, where

NLOS networks are feasible. Two hundred fifty megahertz

of bandwidth is easier to obtain in the 40-GHz frequency

range. However, at frequencies higher than 6 GHz, the

increased shadowing by obstructions in the propagation

path render NLOS links unusable. Since transmit power and

receive SNR are capped as pointed out above, a 250-MHz

bandwidth will mean a reduction in range. Assuming a path

(propagation) loss exponent of 3.0, the range reduces by

a factor of two (or cell area by a factor of four) for every

factor of eight increase in bandwidth. Therefore, compared

to a 10-MHz bandwidth system used today, the range of a

250-MHz system will drop by a factor of 3 and the cell area

by a factor of nine. On the positive side, a high bandwidth

results in frequency diversity, which reduces the fade margin

(excess transmit power required) in fading NLOS links.

We should finally note that in a cellularized system, a total

bandwidth of six to nine times the link bandwidth is needed

in order to support a cellular reuse plan. This clearly places

impossible bandwidth demands on SISO gigabit wireless

systems.

PAULRAJ et al.: AN OVERVIEW OF MIMO COMMUNICATIONS—A KEY TO GIGABIT WIRELESS 199

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Fig. 1. Bandwidth requirement and range of a 1-Gb/s link using MIMO technology.

We summarize our discussion by noting that Gb/s wire-

less links in NLOS (and perhaps cellularized) networks using

conventional approaches are in general not feasible due to

peak and average SNR limits in practical receivers. Addition-

ally, there is a serious range penalty to be paid for high band-

width systems. MIMO wireless constitutes a technological

breakthrough that will allow Gb/s speeds in NLOS wireless

networks. The following example is designed to illustrate the

performance gains delivered by MIMO. Consider a Rayleigh

fading NLOS link with an average receive SNR of 20 dB and

a constant total transmit power (independent of the number of

transmit antennas). Let the coherence bandwidth be 20 MHz

(typical value for indoor scenarios). The bandwidth needed to

ensure 99% link reliability is obtained by computing the 1%

outage capacity (see Section IV for details). Fig. 1 plots the

bandwidth and range of symmetrical MIMO links (i.e., links

with an equal number of transmit and receive antennas

)

needed to support 1-Gb/s link speed. The range is normal-

ized to unity with reference to a SISO system with 10-MHz

bandwidth. For

, we have a standard SISO link with

a required bandwidth of 220 MHz, and a reduction in range

to 35% of the reference system. On the other hand, a 10

MIMO system can deliver 1-Gb/s performance with only

20-MHz bandwidth and still support 80% of the reference

range. Clearly, MIMO technology offers a substantial per-

formance improvement. Note that a MIMO system does not

require additional transmit power or receive SNR to deliver

such performance gains. Furthermore, the spectral efficiency

achieved over a 20-MHz bandwidth by the 10

10 MIMO

channel is 50 b/s/Hz, which shows that high transmit power

is not necessarily required to reach spectral efficiencies in

excess of 10 b/s/Hz. We note that the downside of using a

MIMO system is the increased transceiver complexity.

The performance improvements resulting from the use of

MIMO systems are due to array gain, diversity gain, spatial

multiplexing gain, and interference reduction. We briefly re-

view each of these leverages in the following considering a

system with

transmit and receive antennas.

A. Array Gain

Array gain can be made available through processing at

the transmitter and the receiver and results in an increase

in average receive SNR due to a coherent combining effect.

Transmit/receive array gain requires channel knowledge in

the transmitter and receiver, respectively, and depends on the

number of transmit and receive antennas. Channel knowl-

edge in the receiver is typically available whereas channel

state information in the transmitter is in general more diffi-

cult to maintain.

B. Diversity Gain

Signal power in a wireless channel fluctuates randomly

(or fades). Diversity is a powerful technique to mitigate

fading in wireless links. Diversity techniques rely on trans-

mitting the signal over multiple (ideally) independently

fading paths (in time/frequency/space). Spatial (or antenna)

diversity is preferred over time/frequency diversity as it

does not incur an expenditure in transmission time or band-

width. If the

links composing the MIMO channel

fade independently and the transmitted signal is suitably

constructed, the receiver can combine the arriving signals

such that the resultant signal exhibits considerably reduced

amplitude variability in comparison to a SISO link and we

get

th-order diversity. Extracting spatial diversity

gain in the absence of channel knowledge at the transmitter

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is possible using suitably designed transmit signals. The

corresponding technique is known as space–time coding

[1]–[4].

C. Spatial Multiplexing Gain

MIMO channels offer a linear (in

) increase

in capacity for no additional power or bandwidth expenditure

[5]–[8]. This gain, referred to as spatial multiplexing gain, is

realized by transmitting independent data signals from the

individual antennas. Under conducive channel conditions,

such as rich scattering, the receiver can separate the different

streams, yielding a linear increase in capacity.

D. Interference Reduction

Cochannel interference arises due to frequency reuse in

wireless channels. When multiple antennas are used, the

differentiation between the spatial signatures of the desired

signal and cochannel signals can be exploited to reduce

interference. Interference reduction requires knowledge of

the desired signal’s channel. Exact knowledge of the inter-

ferer’s channel may not be necessary. Interference reduction

(or avoidance) can also be implemented at the transmitter,

where the goal is to minimize the interference energy sent

toward the cochannel users while delivering the signal to

the desired user. Interference reduction allows aggressive

frequency reuse and thereby increases multicell capacity.

We note that in general it is not possible to exploit all

the leverages of MIMO technology simultaneously due to

conflicting demands on the spatial degrees of freedom (or

number of antennas). The degree to which these conflicts are

resolved depends upon the signaling scheme and transceiver

design.

III. MIMO C

HANNEL MODEL

We consider a MIMO channel with transmit and

receive antennas. The time-varying channel impulse re-

sponse between the

th ( ) transmit antenna

and the

th ( ) receive antenna is denoted as

. This is the response at time to an impulse applied

at time

. The composite MIMO channel response is

given by the

matrix with

(1)

The vector

referred to as the spatio-temporal signature induced by

the

th transmit antenna across the receive antenna array.

Furthermore, given that the signal

is launched from the

th transmit antenna, the signal received at the th receive

antenna is given by

(2)

where

is additive noise in the receiver.

Fig. 2. Schematic of wavefront impinging on an antenna array.

Under the narrowband assumption the antenna outputs

(

)

and

(

)

are identical except for a phase shift.

A. Construction of the MIMO Channel Through a Physical

Scattering Model

In the following, we derive a MIMO wireless channel

model from a simplistic physical scattering description. For

convenience, we suppress the time-varying nature of the

channel and use the narrowband array assumption described

in brief below.

Consider a signal wavefront

impinging at angle on

an antenna array comprising two antennas spaced

apart (see

Fig. 2). We assume that the impinging wavefront has a band-

width of

and is represented as

(3)

where

is the complex envelope of the signal (with band-

width

) and is the carrier frequency in radians.

Under the narrowband assumption, we take the bandwidth

to be much smaller than the reciprocal of the transit time

of the wavefront across the antenna array, i.e.,

. Denoting the signal received at the first antenna by

, the signal received at the second antenna is then given

(4)

where

is the wavelength of the signal wavefront. It is

clear from (4) that the signals received at the two antennas

are identical, except for a phase shift that depends on the

array geometry and the angle of arrival of the wavefront. This

result can be extended to arrays with more than two antennas

in a straightforward way. We emphasize that the narrowband

assumption does not imply that the channel is frequency-flat

fading.

We shall next make use of the narrowband assumption

in constructing the MIMO channel below. For the sake

of simplicity we assume a single bounce based scattering

model and consider a scatterer located at angle

and delay

with respect to the receive array and with complex amplitude

(see Fig. 3). The same scatterer appears at angle

with respect to the transmit antenna array. Thus, given the

overall geometries of transmit and receive arrays, any two of

the variables

, , and define the third one. The

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