# OFDM with pulse shaping

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```							    OFDM with pulse shaping

Gang LIN
Department of Electronics and telecommunications
August 26, 2004

1
Multiplex (FDM)
• Sub-channels are completely separated in
frequency

2
Orthogonal Frequency Division
Multiplex (OFDM)
• There exists intersection between sub-channels but
sub-channels are orthogonal to each other.

3
Why we use OFDM in wireless channel?

• OFDM is much more robust in wireless fading
channel than single carrier system

4
Two main categories of OFDM

• OFDM/QAM with guard interval:
- The most common type of OFDM
- Used in ADSL, DVB, IEEE 802.11, etc.
• OFDM/OQAM with pulse shaping:
- Improved power and bandwidth efficiency
- Lower side lobes in frequency domain

5
OFDM/QAM with guard interval

6
Guard interval to eliminate ISI in
OFDM/QAM

If the maximum delay of multi-path channel is less
than the guard interval , there will be no inter-
symbol interference (ISI) and inter-channel
interference (ICI); The guard interval can be
7
implemented by inserting cyclic prefix or suffix.
Efficient scheme for OFDM/QAM
based on DFT

8
Some characteristics of OFDM/QAM

• The DFT based scheme has low complexity;
• The receiver pulse is not matched with transmitter
pulse. SNR loss:
∆
SNRloss   = 10 log(1 + )
T
• The guard interval will reduce the information rate:

BWloss = 1 (1 + ∆ T )

• Usually, ∆ = 0.2T
9
Basic block diagram of OFDM/OQAM

10
Pulse design for OFDM/OQAM
Principles for the design of pulse:
- Zero ISI and ICI
- Concentrated in time and/or frequency
Example:
(1) Square root raised cosine pulse with a roll off factor less
than 1, which is strictly band limited to [-1/T,1/T];
(2) Optimal finite duration pulses with maximum energy
concentration in [-1/T,1/T].

11
Modulator of OFDM/OQAM based on DFT

12
Demodulator of OFDM/OQAM based on DFT

13
Equalization for OFDM/OQAM
• OFDM/OQAM need equalizer in multi-path
channel;
• If the equalizer eliminates ISI, then ICI is also
eliminated;
• If the number of sub-channel is large enough, the
channel can be viewed as flat fading. Then a one-
tap equalizer is sufficient.

14
A rough Comparison of OFDM/QAM
and OFDM/OQAM

OFDM/QAM            OFDM/OQAM

Total computations        5 N (log 2 N − 1)   4 P + 5 N (log 2 N − 1)
per complex
s
(Cariolano’ scheme)
symbol period
Equalizer               One-tap equalizer              Yes
Information rate                                  No reduction
1 (1 + ∆ T )
reduction
SNR loss (dB)                           ∆
10 log(1 +     )              0
T
P : the length of shaping pulse with respect to
15
an over sampling interval T/N
Work done so far

• Implementation of OFDM/OQAM;
• Equalization for OFDM/OQAM over multi-path
• Design of pulses robust to carrier frequency offset.

16
Future research

• Synchronization;
- Timing and frequency offset estimation
- Joint timing and frequency offset and channel estimation

• A comparison of OFDM/QAM and
OFDM/OQAM;
• Wireless MIMO system based on OFDM/OQAM.

17

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