OFDM Orthogonal Frequency Division Multiplexing

OFDM
ORTHOGONAL
FREQUENCY DIVISION
MULTIPLEXING
Presented by : Abdullaziz Altagawy
Course : Digital Communication

Objectives Description
 Concepts
 Basic idea
 Introduction to OFDM
 Implementation
 Advantages and Drawbacks.
 FDMA

Concepts
 Consider N-periodic signal:
 And its frequency-domain representation, which
is also N-periodic:
 The “~” will indicate a periodic signal or
spectrum.
Discrete Time Signal

Concepts
 and are related by the discrete Fourier
series:

Concepts
 Recall the DTFT:
 DTFT is not suitable for DSP applications
because
o In DSP, we are able to compute the spectrum
only at specific discrete values of !,
o Any signal in any DSP application can be
measured only in a finite number of points.

Concepts
 The discrete Fourier transform relates x[n] and
X[k]:
Discrete Fourier Transform
DFT

Concepts
 CIRCULAR
CONVOLUTIO
N
 The usual convolution (or
linear convolution) is defined
as:
 But when x[n] and g[n] are
defined as N-point signals
DFT

Concepts
 CIRCULAR
CONVOLUTIO
N
 then the term g[n - m] will fall outside
the range. The definition of circular
convolution evaluates the index
modulo N:
 For example:
 >> x = [2 4 3 1 5];
 >> g = [7 3 5 2 4];
 >> y = cconv(x,g)
 y =
 56 73 57 60 69
DFT

Basic idea
 Multipath transmission :
 Most broad band systems are
subjects to Multipath transmission .
 More than one transmission path
between transmitter and receiver .
 Received signal is SUM of many
versions of the transmitted with
varying delay and attenuation .

Basic idea
 inter-symbol interference (ISI) and fading
caused by multipath propagation.
 Delayed version of one symbol from an
indirect path interference with a different
symbol causing Inter Symbol Interference
(ISI) .
 High data rate requires smaller symbol
period .
 if symbol period is less than delay spread
then we have ISI.
 Possible solutions to resolve ISI in single
carrier – Expensive channel equalizers or
low data rate .

Basic idea
 Equalization Complexity
• Let’s compare equalization complexity of a
single carrier (SC) system with the same total
bandwidth as an OFDM system subject to
similar channel conditions
 Frequency domain equalization (via
FFT) for OFDM Rx
 Decision feedback equalization for SC
Rx
• OFDM complexity grows slightly greater
than linear with BW*Delay Spread product
• Single carrier complexity grows
quadratically with BW*Delay Spread product

Basic idea
• Single Carrier Case
 GMSK or OQPSK 24 Mbps
 Delay Spread = 250 nsec
 Requires 20 FF, 20 FB taps
• OFDM Case
 QAM 52-OFDM 24 Mbps (QAM 16)
 Delay Spread = 250 nsec
 64 Point FFT
 52 Subcarriers
 Guard Interval = 800 nsec
 Rsym = 250 kHz
• GMSK Eq (LMS) = 2*20*24*106 (960E6)
rmult/sec
• OFDM (radix 4)= 96*106 = (96E6)
cmult/4msec
 = 96E6 rmult/sec
 Single Carrier DFE is 10 times as
complex
Equalization Complexity
+XX
m4
Adj Proc.
Cmplex
Data In
D D D D
Tap 0 Tap 1 Tap 2 Tap 3
[ . ]*
X
+
From other Taps FFF
+
D(k) {Training,
Demod Decisions}
-
+
+
Error
Slicer
D
1 SPS
Tap 4
Decisions
D D D
X + X X
mLMS
Error
[ . ]*
From FBF Taps
Tap FB0Tap FB1Tap FB2
Tap FB3
D
+
FEEDFORWARD FILTER (FFF)
FEEDBACK FILTER (FBF)
Eq. Output
Peamble Sequence

Introduction to OFDM
 Why Use OFDM?
•The problem is that the signal bandwidth needs to be as
narrow as possible to
mitigate multipath (the symbol period needs to be as long
as possible), Unless…
 The signal is made bandwidth-inefficient in order to
perform combining of
dispersed rays (e.g., RAKE combining)
 The optimal signal would be one which has high
bandwidth efficiency and
immunity to channel variations due to multipath
• Lower complexity equalization for given delay spread than
single-carrier modulation
OFDM allows tightly packed carriers to convey information
orthogonally and with high bandwidth efficiency

 Why Use OFDM?
 Efficient implementation using Fast Fourier
Transform (FFT).
 Low sensitivity to time synchronization
 on errors.

 What is an OFDM System :
 Data is transmitted in parallel :on multiple
carriers that overlap in frequency and also
are orthogonal to each other .

 What is an OFDM System :
 OFDM = Orthogonal FDM
 Carrier centers are put on orthogonal frequencies
 ORTHOGONALITY - The peak of each signal
coincides with trough of other signals
 Subcarriers are spaced by 1/Ts

 Two conditions must be considered for the
orthogonality between the subcarriers.
o Each subcarrier has exactly an integer number
of cycles in the FFT interval.
o The number of cycles between adjacent
subcarriers differs by exactly one.

 Guard Interval and Cyclic
Extension :
 Two different sources of
interference can be identified in
the OFDM system.
 Intersymbol interference (ISI) is
defined as the crosstalk between
signals within the same sub-
channel of consecutive FFT frames,
which are separated in time by the
signaling interval T.
 Inter-carrier interference (ICI) is the
crosstalk between adjacent

 Guard Interval and Cyclic Extension :
 For the purpose to eliminate the effect of ISI, the
guard interval could consist of no signals at all.
 Guard interval (or cyclic extension) is used in
OFDM systems to combat against multipath
fading.
 Tg :guard interval
 Tdelay-spread : multi path delay spread
 Tg > Tdelay-spread
 In that case, however, the problem of inter-carrier
interference (ICI) would arise.
 The reason is that there is no integer number of
cycles difference between subcarriers within the
FFT interval.

 Guard Interval and Cyclic
Extension :

Implementation of OFDM
 Computational speed of FFT:

 Practical considerations :
 If N is not a power of 2 , there are 2
strategies available to complete an
N-point FFT.
1. take advantage of such factors as
N possesses. For example, if N is
divisible by ‰(e.g. N = 48™), the final
decimation stage would include a ‰-
3 point transform.

 Practical considerations :
 If N is not a power of 2 , there are 2
strategies available to complete an N-
point FFT.
2. pack the data with zeroes; e.g. include
16 zeroes with the 48 data points (for N
=48™) and compute a 64Œ-point FFT.
(However, you should again be wary of
abrupt transitions between the trailing
(or leading) edge of the data and the
following (or preceding) zeroes; a better
approach might be to pack the data with
more realistic “dummy values”).

 CFO
 The carrier frequency offset (CFO) is caused by Doppler frequency shift fd .
 We intend to generate exactly the same carrier frequencies in the
transmitter and receiver, but ,there may be an unavoidable difference
between them due to the physically inherent nature of the oscillators. Let fc
and f ’c denote the carrier frequencies in the transmitter and receiver,
respectively. Let foffset denote their difference (i.e., foffset = fc - f ’c).
 Doppler frequency fd is determined by the carrier frequency fc and the
velocity v of the terminal (receiver) as
fd = (v.fc)/c
where c is the speed of light. Let us define the normalized CFO, Ɛ, as a ratio of
the CFO to subcarrier spacing Δf , shown as
Ɛ=(Foffset / Δf)
Let Ɛi and Ɛf denote the integer part and fractional part of Ɛ, respectively,
and therefore,
Ɛ=Ɛi+Ɛf, where Ɛi= |Ɛ|.

 EFFECT OF INTEGER CARRIER FREQUENCY
OFFSET(IFO):
 Due to the IFO, the transmit signal X(k) is
cyclic shifted by Ɛi in the receiver, and
thus producing X(k-Ɛi) in the kth subcarrier.
Unless the cyclic shift is compensated, it
will incur a significant degradation in the
BER performance. However, we note that
the orthogonality among the subcarrier
frequency components is not destroyed
and thus, ICI does not occur.

 EFFECT OF INTEGER CARRIER
FREQUENCY OFFSET(IFO):

 CFO ESTIMATION
TECHNIQUES:
 CFO can be estimated in time
domain and frequency domain.
There are different techniques for
both cases. The most popular being
Moose for frequency domain and
Schmidl for time domain.

 CFO ESTIMATION TECHNIQUES:
 Moose’s Method
Using this relationship CFO can be
estimated as:
This is the well known Moose’s method.
Although the range of CFO estimated
is |ε|≤0.5

 Schmidl’s and the Improvement
method is different in terms of the
Pilot arrangement.
 In Schmidl method we use two
repeated N/2 length long pilot
sequences.
 While in the Improvement method
we use four repeated N/4 length
long pilot sequences.

 CFO ESTIMATION
TECHNIQUES:

 CFO ESTIMATION
TECHNIQUES:
Schmidl Method
Here CFO estimation is done with a single step. We use the
correlation between the two PN sequences to determine
an intermediate variable.

 CFO ESTIMATION
TECHNIQUES:
Schmidl Method
In is the sum of all noise, which can be regarded as AWGN
when N is larger enough.
CFO estimated by taking the phase of ϕ.

 Improvement Method
This estimation is done in two steps.
First we do a coarse estimation to get
the coarse CFO value.
Then after correcting for this rough
value we do a fine estimation on the
corrected signal to get a better
approximation to the true value.
 Coarse Estimation
This estimation is done by the
following iteration to get the
intermediate value.

 Improvement Method
Essentially we are correlating the first and fourth N/4
length pilot symbols.
Coarse estimate is obtained by taking the phase of
φ1.

 CFO ESTIMATION
TECHNIQUES:
 Correction
The received signal is corrected
by accounting for the CFO
estimated.

 CFO ESTIMATION
TECHNIQUES:
 Fine Estimation
This estimation is done by the
following iteration to get a
second intermediate value.

 CFO ESTIMATION
TECHNIQUES:
 Fine Estimation
Here we are correlating the second and third N/4
length pilot symbols. Where ε2=ε-ε1 the residual
CFO.
Fine estimate is obtained by taking the phase of φ2.
The total CFO is the sum of the fine and coarse
estimates.

Advantages and Drawbacks
 Advantages:
 OFDM can easily adapt to severe channel conditions without the need
for complex channel equalisation algorithms being employed
 It is robust when combatting narrow-band co-channel interference. As
only some of the channels will be affected, not all data is lost and
error coding can combat this.
 Intersymbol interference, ISI is less of a problem with OFDM because
low data rates are carried by each carrier.
 Provides high levels of spectral efficiency.
 Relatively insensitive to timing errors
 Allows single frequency networks to be used - particularly important
for broadcasters where this facility gives a significant improvement in
spectral usage.

Advantages and Drawbacks
Drawbacks :
 High peak-to average-power ratio
(PAPR) This put high demand on
linearity in amplifiers.
 Phase noise error cause degradation
to OFDM system
 Very sensitive time frequency
synchronization

FDMA
 The available bandwidth is divided
into frequency bands.
 Each station is allocated a band to
send its data.
 each band is reserved for a specific
station, and it belongs to the station
all the time.
 Each station also uses a bandpass
filter to confine the transmitter
frequencies.

FDMA
 To prevent station interferences, the
allocated bands are separated from
one another by small guard bands.

FDMA
 We need to emphasize that although
FDMA and frequency-division
multiplexing (FDM) conceptually seem
similar, there are differences between
them. FDM is a physical layer
technique that combines the loads
from low bandwidth
 channels and transmits them by using
a high-bandwidth channel.
 The multiplexer modulates the signals,
combines them, and creates a
bandpass signal. The bandwidth of
each channel is shifted by the
multiplexer.

FDMA
 FDMA, on the other hand, is an access method
in the data-link layer. The datalink
 layer in each station tells its physical layer to
make a bandpass signal from the data passed
to it.
 The signal must be created in the allocated
band.
 There is no physical multiplexer at the physical
layer.
 The signals created at each station are
automatically bandpass-filtered.
 They are mixed when they are sent to the
common channel.

OFDM Orthogonal Frequency Division Multiplexing

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