-
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
p>
,
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
p>
)
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
p>
)
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
)
p>
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
=
∫
?
p>
∞
∞
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
)
p>
dt
+
∫
T
n
(
T
?
t
)
p>
φ
k
g
(
τ
;
t
)
∑
X
(
k
)
φ<
/p>
k
′
(
t
?
τ
)
d
τ
φ
k
(
t
)
dt<
/p>
.
k
=0
cp
N
?
1
X
y
=
(
k
)
∫
g
(
p>
τ
)
φ
(
t
?
τ
)
p>
d
τ
φ
(
p>
t
)
dt
+
n
φ
(
T
?
t
)
(
t<
/p>
)
dt
.
∫
k
k
∑
k
k
T
cp
0
′
∫
T
cp
k
=0
6
Tcp T < < T integral interval and 0 < <
0 < R Tcp contains T and T. In the integral r <
type can be written as
T
T
c
c
′
p
p
exp[
j
2
π
k
(
t
?
τ
?
T
)
W
/
N
]
cp
∫
g<
/p>
(
τ
)
φ
k
′
(
t
?
<
/p>
τ
)
d
τ
=
∫
0
g
(
τ
)
T
c
′
exp[
j
2
π
k
(
t
?
T
)
W
/
N
]
p
0
d
τ
T
s
′
cp
The integral part behind the upper part
is the sampling of the channel impulse response
in the frequency domain. The sampling
frequency is f = k 'W / N, that is, at the K'
carrier frequency
T
W
Here is the G (f) g (tau) Fourier
transform. Using these mark, the output filter can
be
reduced to the receiver
′
T
~
T
exp(
j
2
π
k
(
t
?
T
cp
)
W
/
N
?
?
N
?
1
′<
/p>
)
h
∫
k
′
φ
k
(
t
)
dt
+
∫
y
k
=
∑
X
(
k
Tcp
n
(
T
?
t
)
φ
k
(
t
)
dt
Tcp
k
=0
T
s
?
1
=
∑
x
k
p>
′
h
k
′
=
T
s
T
cp
<
t
<
0
g
(
τ
)
exp[
?
j
2
π
k
τ
W
/
N
]
d
τ
,
T
∫
h
k
′
=
G
(
k
′
N
)
=
∫
0
cp
g
(
τ
)
exp(
?
j
2
π
k
′τ
W
/
N
)
d
τ
,
N
p>
(
1.4.6
)
∫
T
T
φ
k
′
(<
/p>
t
)
φ
?
k
(
t
)
dt
+
n
k
,
c
k
p
=0
T
~
?
这里
n
k
=
∫
n
(
T
?
t
)
φ
k
(
t
)
dt
。根据滤波器组的正交性
T
cp
φ
k
′
(<
/p>
t
)
φ
?
k
(
t
)
dt
′
T
=
T
exp(
j
2
π
k
(
t
?
T
cp
)
W
/
N
exp(
< br>j
2
π
k
(
t
?
T
cp
)
W
/
N
dt
T
s
T
s
∫
T
cp
∫
T
cp
=
δ
(
k
?
k
′
),
这里
δ
(
k
)
是
Kronecker
δ
函数。这样式(
< br>1.4.6
)可以简化为
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