OFDM的原理

1.

In

modern

society

more

high

dependence

and

the

requirements

of

communication,

communication system and the design and development of high efficiency has become

the

constant

pursuit

of

communication

engineering.

The

efficiency

of

the

communication

system,

in

the

final

analysis

is

the

spectrum

utilization

and

power

efficiency. Especially in wireless communication scenarios, the requirements of these two

indicators

more

often,

especially

in

spectrumefficiency.

Because

of

the

space

available

spectrum resources are limited, and wireless applications are more and more, making use

of wireless spectrum of strict management by governments and unified planning. Thus, a

wide variety of communication technology has high spectrum efficiency continues to be

developed, OFDM

(Orthogonal

Frequency

Division

Multiplexing)

is

knownspectral

efficiency

of

a

communication

system

is

the

highest,

the

digital

modulation,

digital

signal

processing,

multi carrier transmission technology combine together, make it in the system spectrum

utilization rate, power utilization, systemcomplexities has very strong competitive power,

is support for future mobile communication especially is one of the main technology of

mobile multimedia communications.

OFDM is a multi carrier transmission technology, the N sub carrier channel is divided

into

N

sub

channel,

N

sub

channel

parallel

system

has

many

remarkable advantages. First, OFDM has very high spectrum utilization. The common

FDM system to signal from each sub channel, need to set the protection interval in the

adjacent channel (band), so that the receiver can use the band-pass filter to isolate signals

corresponding

to

sub

channels,

which

not

only

protect

the

sub

band

system

spectrum

resources

between

channels,

and

between

adjacent

channels

The

mainlobe signal spectrum is overlapping (see Figure 1.5), but the spectrum of each sub

channel signal is orthogonal to each other in the frequency

domain, each subcarrier is

orthogonal in time domain, separating each sub channel signals of the OFDM system

(demodulation) by the orthogonality to complete. In addition, sub channel OFDM can

also

be

used

M-ary

modulation

(such

as

high

spectrum

efficiency,

QAM)

to

further

improve the spectrum efficiency of OFDM system. Second, relatively simple to achieve.

When the channel using QAM or MPSK modulation, modulation demodulation process

can be completed by IFFT. The process can be completed by FFT, without oscillation

source

group

without

band-pass

filter

group

signal

separation.

Third,

anti

multipath

interference

and

anti

fading

ability.

Because

of

the

general

OFDM

system

with

cyclic

prefix (Cyclic Prefix, CP), so that it can completely eliminate the multipath propagation

caused by code interference under certain conditions, completely eliminate the damage

of multipath on the inter carrier orthogonality of subcarriers, so OFDM system has good

ability

of

anti

multipath

the

whole

channel

into

many

narrow

channel, although the channel is available It can be a very flat fading channel, but the

fading

on

each

subchannel

is

approximately

flat

(see

Figure

1.6),

which

makes

the

equalization of subchannels in OFDM system very simple, and usually requires only one

tap equalizer

Of course, with the single carrier system, OFDM also has some difficult problems to

be

solved.

These

problems

are

mainly:

first,

synchronization

problem.

Theoretical

analysis

and

practice

show

that

the

OFDM

system

of

synchronous

system

requires

higher

accuracy,

synchronization

error

not

only

caused

the

output

SNR

drop,

will

destroy the orthogonality of the sub the inter carrier, causing inter carrier interference,

which greatly affect the performance of the system, and even make the system does not

work. Second, the peak to average power ratio of OFDM signal (Peak-to- Average Power,

Ratio, PAPR) are often large, making it The linear range of amplifier requirements, but

also

reduces

the

efficiency

of

the

amplifier

in

the

future

application

in

communication system, especially mobile applications in multimedia communication in

the future will depend on the degree to solve the above problems.

OFDM

technology

has

been

or

is

gaining

some

applications,

for

example,

ETSI

(European) in broadcast applications in Europe

Telecommunication Standard Institute, the European Telecommunications Standards

Institute, has developed the number of OFDM technologies Digital Audio Broadcasting

(DVB) standard, digital video broadcasting (Digital Video

Broadcast ing

，

DVB

）

The standards are being developed; in broadband wireless access

applications, IEEE 802.11a and IEEE 802.16 are based on the advice of ETSI OFDM

technology, HiperLAN II is a OFDM technology based on the standard; used in digital

cellular mobile communication, OFDM technology is one of the hot research at present;

in the wired broadband access technology for example, xDSL (high speed digital

subscriber line) technology, a special form of OFDM (Discrete Multito - DMT NE) to get

widely used in these applications and so on;.OFDM has shown strong vitality, with

solving some key problems which restrict the application of OFDM, I believe OFDM will

play an increasingly important role in future communication applications.

2.

OFDM

发展简史

OFDM

OFDM is a multi carrier transmission

3.

Multicarrier modulation and FFT

OFDM is a multi carrier transmission technology. Let

FK (k = 1,2),

technology. Let FK (k = 1,2),

The carrier modulated signal can be expressed in

the interval of I symbols

N

?

1

（

1.2.1

）

s

i

(

t

)

=

∑

X

i

(

k

,

t

) exp(

j

2

π

f

k< /p>

t

)

k

=0

Among them, X I (k, t) is carried by the signal in the first I symbol interval information, it

determines the Si (T) amplitude and phase, generally they are only with the symbol label I

related complex constant, they carry the information to be transmitted; for example, if the

K is carrier using QPSK modulation, set by pi / 4 way sign, when the I code is

according to the mapping between the symbols and signs can know, X I (k, t) = 22 (1 + J).

For simplicity, in just a When the symbol of multi carrier signal, often omit the symbol

label I; and when the subcarrier with ordinary (without using waveform formation) QAM

or MPSK modulation, X I (k, t) has nothing to do with the T, which will X I (k, t) or X (k),

according to the context of such ambiguity not. According to the above agreement, (1.2.1)

can be written as

N

?

1

（

1.2.2

）

s

(

t

)

=

∑

X

(

k

) exp(

j

2

π

f

k

t

)

k

=0

We hope that the spectrum utilization of this multi carrier transmission method is

high, that is to say, the subcarrier interval should be as small as possible, and the system is

easy to implement

In order to realize the multi carrier transmission system, the general need N oscillator and

the corresponding bandpass filters, the complex structure of the system, does not embody

the advantages of multi carrier transmission. However, after careful analysis can be found,

the modulation and demodulation of multi carrier transmission system can use the

discrete Fourier transform (Discrete Fourier Transform. DFT), due to DFT

A fast algorithm of FFT (Fast Fourier Transform) famous, the multi carrier transmission

system implementation is greatly simplified, especially the OFDM system using FFT to

achieve, with its simple structure, high spectrum efficiency and attention

paper analyzes the conditions that multicarrier transmission systems can be

implemented with DFT In order to determine the frequency interval between

subcarriers, we consider how the receiver for signal demodulation of the received

signal. We (not to consider the influence of noise and distortion) f s sampling to

sampling rate, sampling to demodulate the signal by DFT. Using the N point DFT

can calculate the signal frequency spectrum component for k

N

?

1

S

(< /p>

k

?

f

)

=

∑

s

(

n

/

f

s

) exp(

?

j

2

π

nk

/

N

)

（

1.2.3

）

n

=0

Here, S (the K F) is the first k frequency; s (n / f s) (n = 0,1,2, N - 1) is the sampling

signal; F = FS / N

It is the resolution of DFT. In order to make DFT correctly calculate the spectrum, the

signal must be periodically repeated outside the N point sampling, when the signal is

repeated

When the number contains only the harmonic component of the DFT, the condition can

be satisfied. The T = n / Fs substitution formula (1.2.2) is obtained

N

?

1

s

(

n

/

f

s

)

=

∑

X

(

l

) exp(

j

2

π

f

l

n

/

f

s

)

L

0

（

1.2.4

）

将式（

1.2.4

）代入式（

1.2.3

）得

N

?

1

N

?

1

S

(

k

?

f

)

=

∑∑

X

(

l

) exp(

j

2

π

f

l

n

/

f

s

) exp(

?

j

2

π

nk

/

N

)

n

=

0

l

=0

N

N

?

?

1

1

=

∑

X

(

l

)

∑

exp(

j

2

π

f

l

n

/

f

s

) exp(

?

j

2

π

nk

/

N

)

L

0

n

=0

?

1

f

l

k

=

∑

X

(

l

)

δ

(

?

)

N

（< /p>

1.2.5

）

（

1.2.6

）

l

=0

其中

0,

f

s

N

m

≠

n

m

=

n

δ

(

m

,

n

) =

1,

观察上式可以发现，当多载波已调信号的频率

kf

s

f

k

=

N

时，

There is S (the K F) = CX (k), where C is a constant, that is when each subcarrier

frequency demodulation with DFT

K can be demodulated by DFT in the case of integer multiples of the discrimination rate.

From the above analysis, it is shown that in order to ensure correct demodulation, X (a) is

in the process of demodulation

One symbol interval is constant is necessary, if the QAM or MPSK subcarrier modulation

uses a waveform shaping technology, such as the use of cosine waveform, but also

specifically by DFT demodulation.

From the above analysis, when the frequency of each subcarrier is integer multiples of the

DFT resolution for demodulation, the DFT can be used to carry multiple loads

Wave modulated signal sampling demodulation. In particular, the frequency interval of the

subcarrier is f s / N, by type (1.2.4) is

N

?

1

s

(

n

/

f

s

)

=

∑

X

(

k

) exp[

j

2

π

(

kf

s

/

N

)

n

/

f

s

]

k

=0

N

?

1

=

∑

X

(

k

) exp[

j

2

π

n

/

N

]

（

1.2.7

）

k

=0

Type is X (k) (k = 0,1,2, N - 1) sequence (the sequence we denoted as X (N)) IDFT

(Inverse Discrete Fourier Transform), namely the subcarrier frequency spacing of F S / N,

multi carrier modulated signal time domain sampling sequence can be calculated by IDFT.

The sequence of X carrying information (N) is a multi carrier modulated signal sampling

sequence DFT, so we say that the modulation multi carrier modulation system based on

FFT is carried out in the frequency domain.

From the above analysis, the modulation of multi carrier modulation system can be

completed by IDFT, demodulation can be completed by DFT, by the knowledge of

digital signal processing, we can know that IDFT and DFT can be implemented by

efficient FFT

ition of OFDM system

The block diagram of the OFDM system is shown in Figure 1.1

After the input bit sequence is completed and transformed, the corresponding modulation

mapping is completed according to the modulation mode adopted, and the modulation is

formed

The information sequence X (N) is used to carry out IDFT on X (N), and the time

domain sampling sequence of OFDM modulated signal is calculated

CP (cyclic prefix cyclic prefix can enable the OFDM system to completely eliminate

multipath propagation caused by intersymbol interference (ISI) and inter carrier

interference (ICI) analysis on 1.5 section 1.4 and section), and then D/A transform,

OFDM modulated signal waveform. The receiving end of received signal in A/D remove

the CP transform, cyclic prefix, OFDM modulated signal

The sampling sequence is DFT, and the original modulation information sequence X (N)

is obtained

输入信号

串

符

...

...

IFF

...

加入

号

并

T

数

/

模

射频

映

变

射

换

CP

转换

调制

并串

输出信

号

并

串

变

换

符

号

判

..

决

...

均

衡

...

FF

T

信道

...

去

CP

模

/

数

射频

串并

转换

解调

图

1.1 OFDM

系统的结构

The

introduction

of

CP

[PR

1]

cyclic

prefix,

the

OFDM

transmission

can

be

completely eliminated due to intersymbol interference caused by multipath propagation

under certain conditions (ISI) and inter channel interference (ICI) effect, greatly promote

the practical use of OFDM technology in the process. Figure 1.2 is a schematic diagram

of the cyclic prefix.

4

图

1.2 CP

示意图

OFDM

literature, OFDM

and X (N) of each component (i.e. on each sub carrier modulation information) also

used the

with a cyclic prefix called OFDM

called X (N) component of the

symbol interference (ISI)

Refers to the inter symbol interference frame, in particular to remove the interference

between

the

cyclic

prefix

symbol

frame,

but

also

refers

to

the

same

symbol

synchronization

symbol

synchronization.

This

frame

is

consistent

with

the

name

of

OFDM in literature, and will not cause misunderstanding.

5. Time continuous system model of OFDM

There

are

some

different

forms

of

OFDM

system.

We

first

establish

the

corresponding mathematical model [ESBL 1]. on the most popular OFDM system using

cyclic prefix

The original OFDM system using digital modulation and demodulation technology,

so the OFDM model can be regarded as the ideal model of OFDM system, of course, is

generally achieved by digital synthesis technology. Figure 1.3 is a continuous time model

of OFDM baseband system.

。

图

1.3 OFDM

连续系统基带模型

z

z

transmitter

The OFDM system has a N subcarrier, the system bandwidth is W Hz, the symbol

length is Ts, and the length of the cyclic prefix CP is Tcp, that is, the transmission

time of a OFDM frame symbol is T = Ts + Tcp, considering the influence of the

cyclic prefix, the K carrier wave waveform emitted by the transmitter is as follows

φ

k

(

t

) =

0,

1

exp[

j

2

π

W

k

(

t

?

T

)]

t

∈

[0,

T

]

T

s

N

c

p

t

?

[0,

T

]

（

1.4.1

）

Note that when the T, [0, Tcp], a diameter of K (T) = K (T + N = /W) with K (T + Ts),

which is the cyclic prefix, which makes the signal within a certain period of time. This

article looks with periodic I OFDM frames have symbols adjustable waveform

N

?

1

（

1. 4.2

）

s

i

(

t

)

=

∑

X

i

(

k

)

φ

k

(

t

?

iT

)

k

=0

When the transmission is an infinite OFDM symbol sequence, the OFDM modulated

signal waveform can be expressed as

∞

∞

N

?

1

s

(< /p>

t

)

=

∑

s

i

(

t

)

< /p>

（

1.4.3

i

=

）

=

∑∑

X

i

(

k

)

φ

k

(

t

?

iT

)

i

=

k

=0

z

channel

We assume that the channel impulse response g (tau; t) the support of less than the

cyclic prefix CP, namely r e [0, Tcp], the signal is received by the receiver for

T

cp

~

（

1.4.4

）

r

(

t

)

=

(

g

?

s

)(

t

)

=

∫

g< /p>

(

τ

;

t

)

s

(

t

?

τ

)

d

τ

+

n

(

t

)

0

Here,

n

~

(

t

) is the additive white noise (complex form) of the channel Gauss.

z

receiver

The OFDM receiver consists of a filter bank, where the first k filter is matched with

the back part [Tcp, T] of the carrier wave waveform K (T)

?

ψ

k

(

t

) =

φ

k

(

T

?

t

),

t

∈

[0,

T

s

]

（

1.4.5

）

0,

t

?

[0,

T

s

]

That is to say, the cyclic prefix CP is deleted. Because the CP contains all the symbols in

front of the inter symbol interference (ISI), so the output sampling receiver filter group

will not contain ISI. therefore, we in the calculation of the K sampling the output of the

matched filter

We can ignore the time label I, the use of formula (1.4.3), (1.4.4), (1.4.5), and we obtain

y

k

=

(

r

?

ψ

k

)(

t

)

t

=

T

=

∫

?

∞

∞

r

(

t

)

ψ

k

(

T

?

t

)

dt

T T

cp

=

∫

T

A channel impulse response invariant in an OFDM symbol interval, the G (tau), so you

get

T

N

c

?

1

T

T

p

~

?

?

′

∫

0

cp

?

T

~

?

′

(

t

)

dt

+

∫

T

n

(

T

?

t

)

φ

k

g