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### OFDM及其无线应用 #### 一、引言随着移动通信技术的不断发展，高数据速率传输成为众多应用场景的核心需求。然而，在实现高速率传输的过程中，符号持续时间的缩短会导致无线信道中的色散衰落引起更为严重的符号间干扰（ISI）。传统的单载波调制方式（如TDMA或GSM）难以有效应对这一挑战。为了解决这个问题，正交频分复用（Orthogonal Frequency-Division Multiplexing，简称OFDM）作为一种关键的技术手段被广泛应用。 #### 二、OFDM基本原理与优势 **1. 基本原理** OFDM是一种多载波调制技术，其核心思想是将一个高速的数据流分解成多个低速的子数据流，并通过一组相互正交的子载波进行并行传输。这样做的好处是可以显著提高频谱效率，同时减少符号间干扰（ISI）的影响。在OFDM系统中，整个可用带宽被分割成许多个窄带子信道，每个子信道上分别承载一部分数据信号。通过采用正交子载波，可以确保不同子信道之间的信号不会相互干扰，从而实现高效的数据传输。 **2. 技术优势** - **抵抗ISI的能力**：由于OFDM可以显著增加符号持续时间，因此能够有效对抗由无线信道延迟扩展引起的符号间干扰。 - **频谱效率高**：通过将频谱分割成多个子信道并并行传输，OFDM能够更有效地利用频谱资源。 - **灵活的带宽配置**：可以根据实际需求调整子载波的数量，实现对不同带宽需求的支持。 - **易于实现MIMO技术**：OFDM天然支持多输入多输出（Multiple-Input Multiple-Output，简称MIMO）技术的应用，进一步提升系统的容量和性能。 #### 三、OFDM的关键技术 **1. 信道估计** 为了确保OFDM系统的稳定性和可靠性，准确的信道估计是非常重要的。通常使用导频符号来进行信道状态信息的测量，基于这些测量结果，接收端可以估算出信道响应，进而进行正确的解调和数据恢复。 **2. 信号检测** 信号检测是OFDM系统中的另一个关键技术点。在接收到OFDM信号后，需要对其进行精确的检测和解调。常用的检测方法包括最大似然检测（MLD）、最小均方误差检测（MMSE）等。 **3. 时间偏移和频率偏移校正** 时间偏移和频率偏移是OFDM系统中常见的同步问题，它们会引入额外的相位旋转和子载波间的干扰。通过准确估计和校正这些偏移量，可以有效改善系统的性能。 **4. 峰均功率比（PAPR）降低** 高峰均功率比（Peak-to-Average Power Ratio，简称PAPR）是OFDM技术的一个主要缺点，它会导致放大器工作在线性区之外，产生非线性失真。为了克服这一问题，研究者们提出了多种PAPR降低技术，如选择性映射（SLM）、部分传输序列（PTS）等。 **5. 多输入多输出（MIMO）技术** MIMO技术利用多个天线在发送端和接收端之间传输多个独立的数据流，从而提高无线通信系统的容量和可靠性。结合OFDM使用时，MIMO能够进一步提升系统的性能。 #### 四、OFDM在现有系统和标准中的应用目前，OFDM已经被广泛应用于多种无线通信标准和技术中，包括但不限于： - **无线局域网（Wi-Fi）**：IEEE 802.11a/g/n/ac等标准都采用了OFDM技术。 - **数字地面电视广播（DVB-T/T2）**：欧洲、亚洲等地使用的DVB-T标准也基于OFDM。 - **长期演进（LTE）/5G**：4G和5G移动通信标准中大量运用了OFDM及其变种如OFDMA。 OFDM作为一种重要的多载波调制技术，凭借其在抵抗符号间干扰、提高频谱效率等方面的优势，在无线通信领域发挥了不可替代的作用。随着技术的不断进步，OFDM将继续在未来的无线通信系统中扮演着关键角色。

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 4, MAY 2009 1673

OFDM and Its Wireless Applications: A Survey

Taewon Hwang, Chenyang Yang, Senior Member, IEEE,GangWu,Member, IEEE, Shaoqian Li, and

Geoffrey Ye Li, Fellow, IEEE

(Invited Paper)

Abstract—Orthogonal frequency-division multiplexing

(OFDM) effectively mitigates intersymbol interference (ISI)

caused by the delay spread of wireless channels. Therefore,

it has been used in many wireless systems and adopted by

various standards. In this paper, we present a comprehensive

survey on OFDM for wireless communications. We address

basic OFDM and related modulations, as well as techniques to

improve the performance of OFDM for wireless communications,

including channel estimation and signal detection, time- and

frequency-offset estimation and correction, peak-to-average

power ratio reduction, and multiple-input–multiple-output

(MIMO) techniques. We also describe the applications of OFDM

in current systems and standards.

Index Terms—Channel estimation, frequency-offset estima-

tion, intercarrier interference (ICI), multicarrier (MC), multiple-

input–multiple-output (MIMO) orthogonal frequency-division

multiplexing (OFDM), peak-to-average power reduction, t ime-

offset estimation, wireless standards.

I. INTRODUCTION

IGH-DATA-RATE transmission over mobile or wireless

channels is required by many applications. However, the

symbol duration reduces with the increase of the data rate, and

dispersive fading of the wireless channels will cause more se-

vere intersymbol interference (ISI) if single-carrier modulation,

such as in time-division multiple access (TDMA) or Global

System for Mobile Communications (GSM), is still used. From

[1], to reduce the effect of ISI, the symbol duration must be

much larger than the delay spread of wireless channels. In

orthogonal frequency-division multiplexing (OFDM) [2]–[4],

the entire channel is divided into many narrow-band subchan-

nels,

which are transmitted in parallel to maintain high-data-

Manuscript received February 14, 2008; revised June 16, 2008. First pub-

lished August 26, 2008; current version published April 22, 2009. The review

of this paper was coordinated by Dr. W. Zhuang.

T. Hwang is with the School of Electrical and Electronic Engineering, Yonsei

University, Seoul 120-749, Korea.

C. Yang is with the School of Electronics and Information Engineering,

Beihang University, Beijing 100083, China.

G. Wu and S. Li are with the National Key Laboratory of Communications,

University of Electronic Science and Technology of China, Chengdu 610054,

China.

G. Y. Li is with the School of Electrical and Computer Engineering,

Georgia Institute of Technology, Atlanta, GA 30332-0250 USA (e-mail:

liye@ece.gatech.edu).

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

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TVT.2008.2004555

It is also called the subcarrier or tone in the literature.

rate transmission and, at the same time, to increase the symbol

duration to combat ISI.

OFDM is a special form of multicarrier (MC) that dates back

to 1960s. The concept of MC transmission was ﬁrst explicitly

proposed by Chang [5] in 1966. A detailed description of MC

can also be found in [6] and [7]. Before Chang, Doelz et al. [8]

had implemented a special MC system for a single-sideband

voice channel in 1957, and Holsinger [9] had implicitly intro-

duced the MC system in his dissertation at the Massachusetts

Institute of Technology in 1964. In 1971, Weinstein and Ebert

[3] proposed time-limited MC transmission, which is what

we call OFDM today. The implementation of MC systems

with equalization was investigated by Hirosaki et al. [10] and

[11] and Peled and Ruiz [12]. Zimmerman and Kirsch [13]

published one of the earliest papers in the application of MC in

HF radio in 1967. More materials on the HF application of MC

can be found in [14] and the references therein. The capacity of

OFDM was investigated in [15] and [16]. In 1985, Cimini ﬁrst

applied OFDM in mobile wireless communications [2]. In [17],

Casas and Leung discussed the application of MC over mobile

radio FM channels. Bingham [18] studied the performance and

complexity of MC modulation and concluded that the time for

MC has come. The application of original OFDM, clustered

OFDM, and MC code-division multiple access (CDMA) in

mobile wireless systems can be found in [19]–[26].

The ﬂexibility of OFDM provides opportunities to use ad-

vanced techniques, such as adaptive loading, transmit diver-

sity, and receiver diversity, to improve transmission efﬁciency.

Shannon’s classical paper in 1948 [27] suggested that the

highest data rate can be achieved for frequency-selective chan-

nels by using an MC system with an inﬁnitely dense set of

subchannels and adapting transmission powers and data rates

according to the signal-to-noise ratio (SNR) at different sub-

channels. Based on his theory, a water-ﬁlling principle has been

derived [28]. Ciofﬁ and his group have extensively investigated

OFDM with performance optimization for asymmetric digital

subscriber line, which they more often called discrete multiple

tone (DMT). Some of their earlier inventions on practical

loading algorithms for OFDM or DMT systems were in [29].

More results on this topic can be found in [30]–[32].

The capacity of a wireless system can signiﬁcantly be

improved if multiple transmit and receive antennas are

used to form multiple-input–multiple-output (MIMO) channels

[33]–[37]. It is proved in [33] that, compared with a single-

input–single-output (SISO) system, a MIMO system can im-

prove the capacity by a factor of the minimum number of

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1674 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 4, MAY 2009

Fig. 1. Function of the CP.

transmit and receive antennas for ﬂat fading or narrow-band

channels. For wideband transmission, it is natural to combine

OFDM with space–time coding (STC) or spatial–temporal

processing to deal with frequency selectivity of wireless chan-

nels and to obtain diversity and/or capacity gains. Therefore,

MIMO-OFDM has widely been used in various wireless sys-

tems and standards.

In this paper, we present a comprehensive survey of OFDM

for wireless communications. We start with basic OFDM

systems and techniques to improve the system performance

in Section II. Then, we address various OFDM-related

modulations in Section III. Next, we brieﬂy introduce MIMO

techniques for OFDM and its applications in current systems

and standards in Sections IV and V, respectively. Finally, we

present our concluding remarks in Section VI.

II. B

ASIC OFDM

In this section, we will ﬁrst describe basic OFDM and then

introduce techniques to improve the performance of OFDM

for wireless communications, including channel estimation,

time- and frequency-varying impairment mitigation, and peak-

to-average power ratio (PAPR) reduction techniques.

A. OFDM

Let {s

n,k

}

N−1

k=0

with E|s

n,k

= σ

be the complex symbols

to be transmitted at the nth OFDM block, then the OFDM-

modulated signal can be represented by

(t)=

N−1



k=0

n,k

j2πkΔft

, 0 ≤ t ≤ T

(1)

where T

, Δf, and N are the symbol duration, the subchannel

space, and the number of subchannels of OFDM signals, re-

spectively. For the receiver to demodulate the OFDM signal, the

symbol duration should be long enough such that T

Δf =1,

which is also called the orthogonal condition since it makes

−j2πkΔft

orthogonal to each other for different k. With the

orthogonal condition, the transmitted symbols s

n,k

can be

detected at the receiver by

n,k



(t)e

−j2πkΔft

dt (2)

if there is no channel distortion.

The sampled version of the baseband OFDM signal s(t) in

(1) can be expressed as





N−1



k=0

n,k

j2πkΔfm

N−1



k=0

n,k

2πmk

(3)

which is actually the inverse discrete Fourier transform (IDFT)

of the transmitted symbols {s

n,k

}

N−1

k=0

and can efﬁciently be

calculated by fast Fourier transform (FFT). It can easily be seen

that demodulation at the receiver can be performed using DFT

instead of the integral in (2).

A cyclic preﬁx (CP) or guard interval is critical for OFDM

to avoid interblock interference (IBI) caused by the delay

spread of wireless channels. They are usually inserted between

adjacent OFDM blocks. Fig. 1 shows the function of the CP.

Without the CP, the length of the OFDM symbol is T

,as

shown in (1). With the CP, the transmitted signal is extended

to T = T

+ T

and can be expressed as

˜s

(t)=

N−1



k=0

n,k

j2πkΔft

, −T

≤ t ≤ T

It is obvious that ˜s

(t)=s

(t + T

) for −T

≤ t ≤ 0, which

is why it is called the CP.

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HWANG et al.: OFDM AND ITS WIRELESS APPLICATIONS: A SURVEY 1675

The impulse response of a wireless channel can be expressed

by [38]

h(t)=



δ(t − τ

) (4)

where τ

and γ

are the delay and the complex amplitude

of the ith path, respectively. Then, the received signal can be

expressed as

(t)=



¯s

(t − τ

)+n(t)

where n(t) represents the additive white Gaussian noise

(AWGN) at the receiver. As demonstrated in Fig. 1, x

(t)

consists of only the signal component from the nth OFDM

block when τ

≤ t ≤ τ

, where τ

= −T

+ τ

, τ

= T

, τ

= min

{τ

}, and τ

= max

{τ

}; otherwise, the re-

ceived signal consists of signals from different OFDM blocks.

If τ

≤ 0 and τ

≥ T

, then

n,k



(t)e

−j2πf







¯s

(t − τ

)+n(t)



−j2πf

= H

n,k

+ n

(5)

for 0 ≤ k ≤ N − 1 and all n, where H

denotes the frequency

response of the wireless channel at the kth subchannel and is

deﬁned as



−j2πkΔfτ

and n

is the impact of AWGN and is deﬁned as



n(t)e

−j2πf

dt.

It can be proved that n

are independent identically distributed

complex circular Gaussian with zero mean and variance σ

With H

, transmitted symbols can be estimated. For single-

carrier systems, the received signal is the convolution of the

transmitted sequences or symbols and the impulse response of

wireless channels in addition to AWGN, whereas the impact of

the channel is only a multiplicative distortion at each subchan-

nel for OFDM systems, which makes signal detection in OFDM

systems very simple and is also one of the reasons why OFDM

is very popular nowadays.

As we have seen from the previous discussion, the CP or

guard interval effectively avoids IBI. More comments on the

CP and guard interval are listed here.

1) If a guard interval is used instead of the CP, that is,

transmitting no signal in the place of the CP in Fig. 1, the

When Doppler spread exists, γ

changes with time and will be a narrow-

band stochastic process.

IBI and intercarrier interference (ICI) can also be avoided

by the following simple processing:

˜x

(t)=

⎧

⎨

⎩

(t + T

), if 0 ≤ t ≤ τ

(t)+x

(t + T

), if τ

<t<τ

(t), if τ

≤ t ≤ T

It can easily be seen that if x

(t) in (5) is substi-

tuted by ˜x

(t), then the demodulated signal can also be

expressed as

˜x

n,k



˜x

(t)e

−j2πf

dt = H

n,k

+˜n

(6)

if τ

≤ 0 and τ

≥ T

. However, the power of the demod-

ulated noise ˜n

is a little bit higher than that in (5) since

the noise power in ˜x

(t) for t ∈ (τ

,τ

) is doubled.

2) τ

≤ 0 and τ

≥ T

are not the necessary conditions for

(5) or (6) to hold. By selecting the proper starting time of

the integral, the condition can be relaxed into τ

− τ

≥

or, equivalently, τ

− τ

≤ T

. The time difference

between the ﬁrst and last paths of a wireless channel τ

− τ

is also called the delay span, which is different

from the frequently used delay spread.

3) As indicated in [4], if there is no CP or guard interval, or

its length is not long enough, the delay spread of wireless

channels will cause both IBI and ICI.

To further improve the performance of OFDM systems,

link adaptation, including adapting transmission power or data

rate of each subchannel, has extensively been investigated

[29]–[32]. Link adaptation exploits the frequency-selectivity

nature of wideband channels. It is performed in a subchannel-

by-subchannel basis and may sometimes result in a signaling

overhead. A historical review on the topic has been addressed

in [39] and the references therein.

From the aforementioned discussion, channel state informa-

tion (CSI) is required for coherent detection. Various channel

estimation approaches have been developed for OFDM com-

munications [40]. In Section II-B, we will discuss the different

channel estimation approaches.

Similar to single-carrier modulation, time- and frequency-

varying wireless channels affect the performance of OFDM

systems. Time-varying impairments may come from the carrier

frequency offset (CFO) caused by the mismatch of frequencies

between the oscillators at the transmitter and the receiver, or

from the Doppler spread due to the relative movement between

the transmitter and the receiver. Frequency-varying impair-

ments are from the timing offset or the delay spread of wireless

channels. Since the duration of the OFDM symbol is longer and

its bandwidth is narrower compared with single-carrier modu-

lation, OFDM systems are more robust to frequency-selective

fading but more sensitive to the time-varying impairment of

The delay spread of a wireless channel is deﬁned as τ

spread





(τ

− ¯τ)



,whereσ

= E|γ

,and¯τ =



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1676 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 4, MAY 2009

Fig. 2. Typical training blocks and comb pilots. (a) Comb pilots. (b) Preamble.

channels. In Section II-C, we will present approaches for time-

and frequency-varying impairment mitigation.

From (1), the transmitted signal is a linear combination

of the transmitted symbols. Therefore, s(t) is Gaussian alike

from the central limit theorem in probability theory and has a

very large PAPR compared with the signal from single-carrier

modulation, which may cause nonlinear distortion of the

ampliﬁer at the transmitter. There have been many approaches

to reduce the PAPR of OFDM signals. We will summarize

them in Section II-D.

The multiple-receive antenna array, also called the adaptive

antenna array (AAA), can be used in OFDM for interference

suppression. AAA techniques have ﬁrst been proposed for

narrow-band TDMA in [41] to suppress cochannel interfer-

ence. A comprehensive introduction of AAA techniques and

beamforming can be found in [42]. The AAA techniques de-

veloped for ﬂat fading channels can directly be applied to each

subchannel in OFDM systems. The only challenge is how to

estimate the spatial correlation of cochannel interference, which

is required in ﬁnding the weights for interference suppression.

By exploiting the correlation of cochannel interference at dif-

ferent subchannels in OFDM, instantaneous spatial correlation

has successfully been obtained in [43]. MIMO techniques can

also be used in OFDM to form MIMO-OFDM for perfor-

mance and capacity improvement, which will be discussed

in Section IV.

B. Channel Estimation

In OFDM systems, CSI can be estimated using training sym-

bols known at both the transmitter and the receiver. The training

symbols may be inserted at different subchannels of different

OFDM blocks, as shown in Fig. 2(a). These training symbols

are more often called pilots. The CSI corresponding to the

pilot subchannels is ﬁrst estimated, and then, that corresponding

to the data-bearing subchannels is obtained by interpolation.

This is called pilot-aided channel estimation (PACE) [44]–[46].

In addition to interleaving the training symbols and the in-

formative symbols by such frequency-division multiplexing,

they may also be superimposed, which can be regarded as a

special form of pilots [47]. This kind of training symbols are

usually called superimposed pilots, which were ﬁrst proposed

to phase synchronization and originally called spread-spectrum

pilots [48] and were later applied for channel estimation

[49]–[53]. On the other hand, all training symbols may be

arranged at the ﬁrst (or couple of) OFDM blocks, as shown in

Fig. 2(b). The training blocks in this case are sometimes called

preamble. The CSI corresponding to the training blocks are

ﬁrst estimated, and that corresponding to the subsequent data

blocks can be tracked and further improved with the help of

the demodulated data. This is called decision-directed channel

estimation (DDCE) [54], [55].

When channel statistics are unknown and CSI is treated as

a deterministic parameter, maximum-likelihood (ML) channel

estimation will be optimal and will approach the Cramer–Rao

bound (CRB) [44]. For channels with AWGN, ML estimation

of channel parameters is equivalent to ﬁnding channel parame-

ters to minimize

x − S

H

where x and H are the received signal vector and chan-

nel frequency response vector, respectively, which are de-

ﬁned as

x =

⎛

⎝

N−1

⎞

⎠

H =

⎛

⎝

N−1

⎞

⎠

and S

is the pilot symbol matrix, which is deﬁned as

⎛

⎜

⎝

0 ··· 0

0 s

0 ··· 0 s

N−1

⎞

⎟

⎠

The index that indicates the OFDM block is omitted in the subsequent

discussion of this paper for simplicity.

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