Multiplexing generally refers to independent signals, those produced by different sources. SO it is a question of how to share the spectrum with these users. In OFDM the question of multiplexing is applied to independent signals but these independent signals are a sub-set of the one main signal. In OFDM the signal itself is first split into independent channels, modulated by data and then re-multiplexed to create the OFDM carrier. OFDM is a combination of modulation and multiplexing.

1. OFDM(Tutorial)
SUBMITTED BY:-
GOPAL RAKECHA
2011BTECHECE011
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2. ORTHOGONALITY
A
B
C
In a Vector space
 A, B and C vectors in space are
orthogonal to each other
 A.B=B.C=C.A=0
 (A+B+C).A=(mod A)^2
 (A+B+C).B=(mod B)^2
 (A+B+C).C=(mod C)^2
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3. ORTHOGONALITY…
 The main concept in OFDM is orthogonality of the sub-carriers. Since the
carriers are all sine/cosine wave, we know that area under one period of a
sine or a cosine wave is zero. This is easily shown:
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4. ORTHOGONALITY…
 Let's take a sine wave of frequency m and multiply it with a sinusoid (sine
or a cosine) of a frequency n, where both m and n are integers. The
integral or the area under this product is given by
f(t)= sin mwt X sin nwt
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5. OFDM
 Orthogonal Frequency Division Multiplexing
 OFDM is a combination of modulation and multiplexing.
 Multiplexing generally refers to independent signals, those produced by
different sources. SO it is a question of how to share the spectrum with
these users. In OFDM the question of multiplexing is applied to
independent signals but these independent signals are a sub-set of the
one main signal.
 In OFDM the signal itself is first split into independent channels,
modulated by data and then re-multiplexed to create the OFDM carrier.
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6. OFDM….
 OFDM is a special case of Frequency Division Multiplex (FDM). As an
analogy, a FDM channel is like water flow out of a Tap, in contrast the
OFDM signal is like a Shower. In a tap all water comes in one big stream
and cannot be sub-divided. OFDM shower is made up of a lot of little
streams.
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7. An example of OFDM using 4 sub-
carriers
 In OFDM we may have N carriers, N can be anywhere from 16 to 1024 in
present technology and depends on the environment in which the system
will be used.
 Let's examine the following bit sequence we wish to transmit and show the
development of the OFDM signal using 4 sub-carriers. The signal has a
symbol rate of 1 and sampling frequency is 1 sample per symbol, so each
transition is a bit
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8. An example of OFDM using 4 sub-
carriers…
 First few bits are 1,1,-1,-1,1,1,1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1....
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9. An example of OFDM using 4 sub-
carriers…
 Modulate each column with corresponding sub-carrier using BPSK
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10. An example of OFDM using 4 sub-
carriers…
 Now we have modulated all the bits using four independent carriers of
orthogonal frequencies 1 to 4Hz. What we have done is taken the bit
stream, distributed the bits, one bit at a time to the four sub-carries as
shown in figure below
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11. An example of OFDM using 4 sub-
carriers…
 Now add all four of these modulated carriers to create the OFDM signal,
often produced by a block called the IFFT.
The generated OFDM signal
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12. The block diagram
• The functional block diagram of how the signal is modulated/demodulated is
given below:
FFT:
IFFT:
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13. Defining Fading
 If the path from the transmitter to the receiver either has reflections or
obstructions, we can get fading effects. In this case, the signal reaches the
receiver from many different routes, each a copy of the original. Each of
these rays has a slightly different delay and slightly different gain. the time
delays result in phase shifts which added to main signal component
(assuming there is one.) cause the signal to be degraded.
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14. Defining Fading… 14

15. Dealing with Fading
 To improve the ability of OFDM signal to deal with fading and interference,
we just add the "Cyclic Prefix" after taking the IFFT. And then at receiver
end, we remove the cyclic prefix before taking the FFT of received signal.
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16. Advantages
 Multi-user Diversity
 broadband signals experience frequency selective fading
 OFDMA allows different users to transmit over different portions of
the broadband spectrum (traffic channel)
 Different users perceive different channel qualities, a deep faded
channel for one user may still be favorable to others
 Receiver Simplicity
 It eliminates the intra-cell interference avoiding CDMA type of multi-
user detection
 Orthogonality of code destroyed by selective fading
 Only FFT processor is required
 Bit Error Rate performance is better only in Fading environment
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17. Disadvantages
 Synchronization
 Tight Synchronization between users are required for FFT in receiver
 Pilot signals are used for synchronizations
 Co-channel interference
 Dealing with this is more complex in OFDM than in CDMA
 Dynamic channel allocation with advanced coordination among
adjacent base stations
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18. References..
 www.complextoreal.com
 www.wiki.en/OFDM
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19. Thank You
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