第9章 正交频分复用技术

9.1 引言 正交频分复用（OFDM，Orthogonal Frequency Division Multiplexing）

是一种特殊的多载波传输方式，它可以被看作一种调制技术，也可以被

当作一种复用技术。OFDM最早源于20世纪50年代中期，在60年代已经

形成了使用并行数据传输和频分复用的概念。

OFDM的发展历史 1957年，美国军方KinePlex HF Modem 最早采用多载波调制(MCM)

1966年，Bell Labs 的Chang 在美国申请第一个OFDM专利（专利号US3488445）

1971年，Weinstein & Ebert 提出采用 FFT /IFFT实现 OFDM，并引入保护间隙

1985年，Cimini 提出将 OFDM 用于移动通信

1987年，Alard & Lasalle提出将 OFDM 用于数字广播

1995年，ETSI 提出 DAB 标准——第一个 OFDM 应用系统

1997年，ETSI 提出 DVB-T 标准

1998年，ETSI Magic WAND 计划演示 WLAN OFDM Modem

1999年，WLAN标准——IEEE 802.11a 和 HIPERLAN-Ⅱ

2000年，OFDM无线本地接入(Fixed Wireless Access)应用——V-OFDM

2001年，新的 IEEE 802.11 与 802.16（UWB）标准采用 OFDM，2006年802.16e

2005年 LTE ， 2012年 4G标准

Magic WAND

FDM与OFDM的区别

FDM的频谱

OFDM的频谱

OFDM中的一个载波的频谱 OFDM中的多个载波的频谱

MCM的基本思想

Channel bandwidth is divided into multiple subchannels to reduce ISI and frequency-selective fading.

Multicarrier transmission : Subcarriers are orthogonal each other in frequency domain.

For a large number of subchannels, the arrays of sinusoidal generators and coherent demodulators required in a parallel system become unreasonably expensive and complex. The receiver needs precise phasing of the demodulating carriers and sampling times. Weinstein and Ebert applied the discrete Fourier transform (DFT) to parallel data transmission system as part of the modulation and demodulation process.

OFDM Modem

P/S QAM decoder

invert channel = frequency domain equalizer

S/P

quadrature amplitude modulation (QAM) encoder

N-IFFT add cyclic prefix

P/S D/A + transmit filter

N-FFT S/P remove cyclic prefix

TRANSMITTER RECEIVER

N subchannels N complex samples

N complex samples N subchannels

Receive filter + A/D

multipath channel

Bits

00110

OFDM DEFINITION OFDM = Orthogonal FDM

Carrier centers are put on orthogonal frequencies

ORTHOGONALITY – indicates that there is a precise mathematical relationship between the frequencies of the carriers in the system.

Subcarriers are spaced by 1/Ts

The baseband OFDM signals can be written as

Where fm=m/T is the central frequency of the mth sub-channel and Xm is the corresponding transmitted symbol.

The signals exp(j2πmt/T) are orthogonal over [0, T ] as illustrated below:

OFDM THEORY

1

0( ) exp 2 , 0

N

mm

mx t X j t t TT

π−

=

= ≤ ≤

∑

0

1 exp( 2 ).exp( 2 )T

mnm nj t j t dt

T T Tπ π δ− =∫

Cyclic Prefix (Guard time) Guard time is inserted between consecutive OFDM symbils

Helps to combat against ISI Guard time is larger than delay spread

PAPR的定义及产生的原因

12

0

1( ) , 0i

Nj f t

ii

x t X e t NTN

π−

=

= ≤ ≤∑

OFDM Advantages OFDM is spectrally efficient

IFFT/FFT operation ensures that sub-carriers do not interfere with each other.

OFDM has an inherent robustness against narrowband interference. Narrowband interference will affect at most a couple of subchannels. Information from the affected subchannels can be erased and

recovered via the forward error correction (FEC) codes. Equalization is very simple compared to Single-Carrier systems. OFDM has excellent robustness in multi-path environments.

Cyclic prefix preserves orthogonality between sub- carriers. Cyclic prefix allows the receiver to capture multi- path energy more efficiently.

OFDM Drawbacks

The OFDM time-domain signal has a relatively large peak-to-average ratio tends to reduce the power efficiency of the RF amplifier non-linear amplification destroys the orthogonality of the OFDM

signal and introduced out-of-band radiation OFDM is sensitive to frequency, clock and phase offset.

More sensitive to Doppler spreads (Df=f0×v/c) than single-carrier modulated system.

Phase noise caused by the imperfections of the transmitter and receiver oscillators influence the system performance.

Accurate frequency and time synchronization is required.

OFDMA it is possible to use OFDM for multiple-access. This technique is called

OFDMA and is implemented by providing each user with a small number of sub-carriers. Even though this technique is similar to FDMA, it avoids the use of large guard bands that are used to prevent adjacent channel interference.

IEEE 802.11a Wireless LAN Physical parameters

TFFT TGI

CP s y m b o l i

OFDM training structure

SIGNAL field, which contains the RATE and the LENGTH fields of the TXVECTOR. The RATE field conveys information about the type of modulation and the coding rate as used in the rest of the packet.

BPSK, QPSK, 16-QAM constellation bit encoding

64-QAM constellation bit encoding

发送过程

接收过程

Synchronization

*

0( ) ( ) ( )GT

x t r t r t T dτ τ τ= − − −∫

OFDM 参数选择 通常需要考虑三个因素：带宽、bit速率和多径时延扩展。

时延扩展直接决定了保护间隔，通常保护间隔应是时延扩展的均

方根值的2～4倍（其实还要考虑编码和QAM调制的类型，高阶调

制如64QAM就比QPSK对ICI和ISI更敏感，同时较低编码速率可

以明显减少对这类干扰的敏感度）。

保护时间确定了，信元周期可确定。为了最大限度地减少由于保

护时间所造成的SNR的损失，我们希望信元周期比保护间隔大的

多，但也不能任意大，因为信元周期太大，就意味着需要更多的

子载波，子载波之间的间隔越小，实现复杂度越大，对相位噪声

和频偏的敏感度越大，同时还加重了PAPR的问题。因此，实际

设计时使信元周期至少是保护间隔的5倍。

0 0.1 0.2 0.3 0.40.01

0.1

1

10

循环前缀的相对长度

信噪

比的

损失

量(

dB)

1010 log (1 )lossSNR γ= − −

/CPT Tγ =

信元周期和保护时隙确定后，子载波数就是3dB带宽除以子载波

间隔（1/T）；或者，子载波数也可以通过系统bit速率除以每个

子载波的bit速率（由调制类型、编码速率和信元速率决定）。 例如：设计一个系统，满足下列要求：

Bit速率：20Mbps 可容忍的时延扩展：200ns 带宽：<15MHz

200ns的时延扩展确保安全，保护间隔800ns； OFDM信元周期是6倍的保护间隔，4.8us; 子载波间隔是1/(4.8-0.8)=250kHz; 为了确定子载波数，我们看所需比特速率和OFDM信元速率的比值。

为了实现 20Mbps ，每个 OFDM 信元必须携带 96 比特的信息

（96/4.8us=20Mbps）。为此，有几个选择：1）16QAM+1/2编码，

每个子载波每个信元携带2bit，此时48个子载波即可。2）QPSK+3/4编码，每个子载波每个信元1.5bit，此时需要64个子载波。但64个子

载波意味着带宽为64*250kHz=16MHz，超过了目标带宽，而第一种

情况满足条件。