Transcript TECNICHE DI TRASMISSIONE-DATI DIGITALE BASATE SUL …
Corso di Comunicazioni Mobili
Data Transmission By OFDM Modulation
Prof. Carlo Regazzoni
1
References
[1] M.L. Doelz, E.T. Heald, D. Martin, “Binary Data Transmission for Linear Systems”,
Proceedings of IRE
, Maggio 1957, pp. 656-661.
Techniques [2] B. Hirosaki, Fourier Transform”, “An Orthogonally Multiplexed QAM System Using the Discrete
IEEE Trans on Comm
, Vol. 29, No. 7, Luglio 1981, pp. 982-989.
[3] J.A.C. Bingham, Whose Time Has Come”, “Multicarrier Modulation for Data Transmission:
IEEE Comm. Magazine
, Maggio 1990, pp. 5- 14.
An Idea [4] T. De Cousanon, R. Monnier, J.B. Rault, “OFDM for digital TV broadcasting”;
Signal Processing
, Vol. 39 (1994), pp. 1-32.
[5] B. Le Floch, M. Alard, C. Berrou, “Coded Orthogonal Frequency Division Multiplex”,
Proceedings of IEEE
, Vol. 83, No.6, Giugno 1995, pp. 982-996.
[6] E. Ayanoglu, et al, “VOFDM Broadband Wireless Transmission Advantages over Single Carrier Modulation”,
Proc of ICC 2001 Conference
and Its , Helsinki (SF) 11-14 Giugno 2001, Vol. 6, pp. 1660 1664.
2
Introduction
The
OFDM modulation
(Orthogonal Frequency Division Multiplexing) is the basic technique among the multi-carrier modulations a clear example of multi carrier modulation is the DMT that is employed in the ADSL standard for transmissions on twisted pair with high bit-rate.
Another example is comprised by the MC-CDMA techniques (Multi-carrier CDMA) which are the spread-spectrum version of the OFDM modulation.
The basic concept of multi-carrier modulation is the transmission in diversity, i.e. the transmission of information on sub-channels with different bandwidth, where the distortion effects of the channel are different.
As contrary to the single-carrier techniques, transmitted message will suffer, in a different measure, of the frequency selective effects of the channel. But a substantial improvement of performances in terms of BER is possible.
3
Historical Mentions
Multi-carrier modulation techniques are considered the
fourth generation (4G)
communication systems used for fixed and mobile digital transmission.
The idea of multi-carrier modulation dates at
the end of fifties
(Doelz, Heald, Martin, Procedings of IRE, May 1957, pp. 656-661).
This work showed a
practical implementation
of a digital transmission system (called
KINEPLEX
) with bit multiplexing on orthogonal carriers, which is the basis principles of the OFDM.
KINEPLEX demodulator KINEPLEX S/P converter
4
Historical Mentions
The main problem of KINEPLEX lies in the totally analogical implementation of multiplexer (RLC resonance oscillators) which involves the huge dimension of the equipments.
The theoretical evolution, which allowed the practical implementation of an OFDM system, was studied by B. Hirosaki
in 1981
(IEEE Trans on Comm, July 1981, pp. 982-989), i.e. the multiplexing mapping in frequency on a
structure like Fast Fourier Transform (FFT)
.
An FFT structure can be implemented in a
totally digital and software
way.
Ten years
after the evolution of digital processing technology (such as DSP) allowed the practical implementation of an OFDM system (see J.C. Bingham, IEEE Comm. Magazine, May 1990, pp. 5-14).
The first commercial prototypes of OFDM systems were announced in
2001
(Cisco’s
VOFDM
presented in the conference ICC2001) and their commercialization is expected for
2005
5
OFDM Modulation: Introduction
The
OFDM
is a
multi-carrier modulation
in which carriers are
frequency spaced
by a multiple of characterized by an
1/T
, where
T is the modulation period overlap of the spectrum
, and it is of the signals transmitted on different carriers.
A possible OFDM modulator could be the following: 6
OFDM Modulation: Introduction
The previous figure shows a symbol stream, codified in-phase and in quadrature components (
a n , b n
) is cyclically multiplexed on
N
branches containing a QAM digital modulator.
The output of the
k
-th modulation branch is an
M-QAM signal
, modulated on carrier frequency
f k
which is orthogonal to each other.
In this way it is possible, at the receiver, to recover the symbol streams transmitted in every branch and to rebuild, after a de-multiplexing operation, the original symbol stream.
7
OFDM Modulation: Transmitted Signal
Every QAM modulator has an assigned constellation that can be equal in every branch.
Given
r jk
and
jk
, polar coordinates of the transmitted symbol in the QAM constellation relative to the
k
-th carrier in the interval [(
j -
1)
T
,
jT
], the transmitted signal can be written as:
s k
(
t
)
j
r jk
cos( 2
f k
(
t
jT
)
jk
) (
t
jT
)
s
(
t
)
k
1
N
0
s k
(
t
) Signal transmitted by the
k
-th carrier Signal transmitted on the channel where
f k
f
0
k T
Fundamental frequency (
t
) 1 , 0
t
T
0 , altrimenti Rectangular Pulse
N
: number of sinusoidal carriers 8
OFDM Modulation: Transmitted Signal
The signal transmitted on the channel is a summation of a
huge number of sinusoidal carriers, modulated with arbitrary phase and amplitude
.
The result, in the time domain, is a
noise-like
signal: 9
OFDM Modulation: Transmitted Signal
The duration
T
of an OFDM modulation impulse is fixed and it’s equal to:
T
Na
NT s D
where •
D
is the source bit-rate; •
a
is the number of bit for each transmitted symbol; •
T s
is the duration time of a symbol (
N
multiplexed symbols are transmitted in the duration time of an OFDM modulation pulse); 10
OFDM Modulation: Transmitted Signal
The spectrum of the signal transmitted by every carrier the shape of the function
sin
(
f
)
f S k
(
f
) and zero crossing every 1/
T
Hz.
assumes The spectrum of the overall transmitted signal functions
sin
(
f
)
f
spaced by 1/
T
Hz.
S
(
f
) is a succession of The spectral components given by the single carriers are overlapped, as shown in figure: 11
OFDM Modulation: Bandwidth Occupation
The spectrum of the OFDM signal has
theoretically unlimited bandwidth
.
But it needs a truncation to compute the significant bandwidth occupied by the signal.
The truncation is performed
spectrum
which are
to remove all the components of the power at least 20 dB under the amplitude of main lobe
.
In this case only figure:
two side lobes
are conserved, as shown in the following 12
OFDM Modulation: Bandwidth Occupation
The
bandwidth
occupied by the
N
carriers of the OFMD signal is equal to:
W
N T
1 3 2
T
N T
5 It can be interesting to compute the
spectral efficiency of the QAM modulation
, given by the ratio (source bit-rate)/(occupied bandwidth).
Supposing to have an M-QAM constellation (or M-PSK) in two dimensions with
2 a
points (where
a
is the
number of bits for every transmitted symbol
); since in
T
are transmitted
N
symbols,
source bit-rate
can be expressed as:
D
Na T
Bit/sec .
W
(
N
5 )
D Na
Hz .
Now it’s easy to compute the
spectral efficiency
of the QAM modulation, that is given by:
D W
N N
5
a
13
OFDM Modulation: Bandwidth Occupation
In the following figure the
power spectral density
an
OFDM
of
modulated signal
with
T
= 125 nsec,
f0
= 8 MHz, number of carriers
N
= 32, 128, 512 is shown.
Signal spectrum is inclined to become ideal (without using spectral shaping filters, like Nyquist filter with low roll-off) when
N
is high.
In this case the spectral efficiency can be written as:
N
lim
a
The figure points out that
a
(ideal value, difficult to reach with a QAM modulation, even using Nyquist filters) for high values (but finite) of
N
.
14
OFDM Demodulation
In the following figure a possible
modulator/demodulator
schematic is shown.
The demodulator is based on the
orthogonality
of the carriers. It is composed by a
bench of demodulators with matched filter
used both for in-phase and in-quadrature components.
Modulator Demodulator
15
OFDM Demodulation
These
orthogonality conditions on the carriers
, both for in-phase and in quadrature components, allow to demodulate the signal, as pointed out in the following formulas: To have a correct demodulation process,
other two conditions
, which are considered guaranteed for simplicity,
are necessary
: 0
T
r k
cos
(
2
f k t
k )
cos
(
2
f h t)dt
0
k
h
T
2
r k
cos
(
k )
T
2
a k k
h
• strict
carrier synchronization on the
(coherent demodulation); 0
T
r k
cos
(
2
f k t
k )sin(
2
f h t)dt
0
k
h
•
strict synchronization of the clock
on the (clock recovery) receiver side
T
2
r k sin(
k )
T
2
b k k
h
16
OFDM Modulation
A modulation/demodulation schematic, such as the previous one, cannot be implemented
via hardware
with analog oscillators: it would be too much expensive and the imperfections of the oscillators (frequency drift, phase noise) would cause critical malfunctions.
But it can easily implemented
FFT (Fast Fourier Transform)
.
via software
, in a totally digital way, using the In fact, if the
k
-th symbol (
k
= 1, …,
N
, where
N
is the number of transmitted symbols in a modulation period), mapped in the chosen M-QAM constellation, is written as:
S k
r k e j
k
a k
S
0
,.....,
S N
1
Set of symbols transmitted in T sec.
jb k
17
OFDM Modulation
The OFDM signal transmitted on the channel can be obtained by the following steps: 1.
computing the
Inverse FFT (IFFT
) on a set of symbols transmitted in a modulation period
T
2.
performing the
digital-to-analog conversion
obtained in the previous step.
(D/A) of the signal In fact a
sequence s(n)
is generated by using an
IFFT operation
performed on the set of symbols transmitted in the modulation period
T
, with a number of samples
N FFT
(generally it is a power of 2).
18
OFDM Modulation
The operation, previous described, is the following:
s
(
n
) 1
N FFT
1
N FFT N k
1 0
S
W N
kn NFFT N k
1 0
S
e
2
j N FFT kn
1
N FFT
1
N FFT N k
1 0
N k
1 0
S
*
W N
kn NFFT
*
S
*
e
2
j N FFT
(
N FFT
k
)
n
1
N FFT N k
1 0
r k
cos 2
N FFT kn
k
n
0 ,..,
N FFT
1 This result is obtained remembering one of the
fundamental properties
W
coefficients of the FFT, i.e. :
W k
(
N
n
) of the Since the set of
N
symbols has to be transmitted every
T
sampling frequency
has to be:
f s
1
T
1
N FFT
seconds, the 19
OFDM Modulation
Then, the
s(n)
sequence is sent to a D/A converter which works with a smaplig frequency equal to
f s
.
The
s(t)
signal, which is the output of the converter, can be written as:
s
(
t
) 1
N FFT N k
1 0
r k
cos 2
N FFT kf s t
k
t
0 ,....,
N FFT f s
but it can also rewritten as:
s
(
t
) 1
N FFT N k
1 0
r k
cos 2
f k t
k
t
0 ,....,
T f k
T k
This is the base band OFDM signal!
T
N FFT f s
20
OFDM Modulation
The following figure shows the complete schematic of and OFDM modulator/demodulator system which uses the FFT
modulator demodulator
k 0
=0 for simplicity 21
OFDM Modulation
This schematic can be implemented in a totally software way on a DSP architecture because an FFT (or IFFT) structure can be mapped on this signal processing architecture with well known algorithms.
With the actual technology a full-digital implementation is impossible; only the base band stage and intermediate frequency stage are developed. The radio frequency stage is still implemented with analogical components.
22
OFDM: performances on AWGN channel
The performances of the OFDM modulation/demodulation systems on a noisy channel depend on the chosen M-QAM constellation.
Supposing to transmit data on an AWGN channel, the signal received by the matched filter associated to the
a
'
k
a k
n i k b k
'
b k
n k q k
-th carrier, is the following: (in-phase component) (in-quadrature component) An error occurs when the noise components are greater than the half of the distance
d
between two points of the constellation. Then the
error probability on the symbol
in an OFDM system has the following expression:
P
p n k i
d
2 1 2
erfc
d
2 8
k
2
d
depends on the chosen constellation and can be expressed as a function of the average energy
E c
of the constellation.
23
OFDM: performances on AWGN channel
Practically the error probability of an OFDM system is the same of an M-QAM system on a single carrier.
16 points QAM Constellation 32 points QAM Constellation 64 points QAM Constellation 128 points QAM Constellation
d
2 8
E c
2 10
d
2 8
E c
2 20
d
2 8
E c
2 42
d
2 8
E c
2 82 where
E c
1 2
k
2
c
1 0
a k
2 2
c b k
2 2
c
Number of points in the constellation 24
OFDM: performances with pulse noise
The OFDM modulation offers remarkable robustness properties against
impulsive noises
, where impulsive noise is defined as a
rectangular pulse
with limited amplitude and duration (generally inferior than the symbol time).
Hence it is a
wide band disturb
.
Since the information is coded in the frequency domain, the energy of the noise pulse is distributed on the
entire bandwidth
its effect on the signal sub-carriers.
of the spectrum. This fact reduce The following figure shows the error probability
versus
to-noise ratio.
the impulsive signal 25
OFDM: performances with jamming noise
OFDM is much vulnerable respect to the
narrow band interferences
like jamming ones, composed by
sinusoidal tones
which interfere with the signal (man-made noise, ingress-noise); it offers worse performances than a normal QAM (see the following figure with
N
=512 carriers).
The power of the OFDM signal is concentrated in a
reduced portion of the spectrum
; a noisy pulse which hits in the bandwidth of the signal is able to alter the bits transmitted by various sub carriers.
26
OFDM: performances with jamming noise
A possible solution consist in
switching off the sub-carriers corrupted by the jamming pulse
. This solution succeed if the position of the interfering tone in the frequency domain is fixed and known. It can be implemented without any additional hardware, by using the IFFT properties.
If the position of the interfering tone is
not fixed known
, a FEC coding has to be introduced before the modulator (called Coded-OFDM or COFDM) 27
OFDM: behave on multipath channel
After a multipath channel, a series of desired signal are received.
delayed and out of phase
replica of the Hence, sampling the signal on a certain instant, a linear combination of the
previous symbol
of the
current symbol
, and of the obtained (ISI); then the channel behaves like a
following symbol linear filter
.
is Theoretically, it could be possible to use the
digital filters
whose the coefficients are
inverse equalizers dynamically updated
, which are by proper algorithms.
The coefficients updating is a computationally heavy operation and substantially inefficient if the
modulation period delay spread
of the channel is greater than the (this condition is equivalent to the
frequency selectivity for the multipath fading
) The OFDM techniques allow to
increase the modulation period
generate a modulated signal for which the channel is and to
not frequency selective
; but the bit-rate remain the same.
28
OFDM: behave on multipath channel
Supposing to introduce a multipath channel with discreet paths, it can be represented by the following impulse response:
h
(
t
)
p
p P
0
A p
t
Without losing generality, an channel can be assumed:
extremely simplified
h
(
t
)
t
model of the multipath The signal received by every single carrier can be written as a summation of the LoS signal and its delayed echo.
s
' (
t
)
s
t
It is impossible to insulate (see figure) an interval of
T
seconds which contains only one symbol: ISI appears.
29
OFDM: behave on multipath channel
A possible solution to remove this kind of interference consists in increasing the duration of the OFDM symbol to ( Sampling properly the
T
+τ) where τ is called
cyclic prefix
.
received signal between the instants
T 1
and
T 2
it’s possible to extract a , portion of the signal, with duration which
T
seconds, contains information the
j
only about -th symbol, which is the desired;
ISI is removed
.
To realize this mechanism, keeping the orthogonality, an expansion of the duration of the modulated carriers
left
(as shown in the figure) of τ
on the
seconds is needed.
30
OFDM: behave on multipath channel
To use the OFDM on a channel where the delay spread is equal to τ p process has to be applied to every single sub-carrier with a cyclic prefix of , this τ p .
The
ISI-free
demodulation is possible if the received signal is processed in an interval comprised between τ p and (
T
+ τ p ), where
T
is the modulation period.
The cyclic prefix can be inserted by modulating quickly the modulation period:
T
'
T
p N
carriers during a before inserting, afterwards, the cyclic prefix.
To keep orthogonality,
N
carriers spaced by
f k
'
T k
'
T k
should be used, before inserting, afterwards, the cyclic prefix.
p
k
0 ,..,
N
1 The transmitted signal will be the following:
s
(
t
)
j
N
k
1 0
r jk
cos( 2
f k
'
t
jk
2
f k
'
p
) (
t
jT
) The demodulation will be performed during the period
T’.
31
OFDM: behave on multipath channel
The use of the cyclic prefix can limit the spectral efficiency of the modulation. It can be shown that the spectral efficiency of an OFDM system with cyclic prefix τ p is equal to:
D W
'
N N
T
5
T
p
6
p a
Where
T
is fixed and it’s equal to:
T
Na D
The following figure shows the required bandwidth as a function of the number of the orthogonal carriers,
a
=3,4,5,6 e
τ p
with
D
= 8msec.
=34Mb/s, 32