EE 132A, Spring 2009
Communication Systems
Prof. John Villasenor
Handout # 18
TA:
Pooya Monajemi, Yuxing Han
Computer Assignment 4
Assigned: Wednesday, May 20, 2009
Due: Monday, June 1, 2009
This computer assignment addresses Orthogonal Frequency Division Multiplexing (OFDM). OFDM is a
popular technique used in several current and emerging technologies such as IEEE 802.11a/g (WiFi),
UWB, and LTE. We will explore OFDM generation and detection, its ability to reduce ISI, and its
performance in noise.
We will start by generating a binary PAM signal and sending it through a channel that introduces ISI. Then
we will send the same information using OFDM with 4 subcarriers and an appropriate cyclic prefix, and
observe how ISI is eliminated. Finally we will send information using OFDM through a noisy channel and
compute bit error probabilities.
What to turn in:
•
Answers to questions and required plots.
•
Source file for programs (.m files).
Suggestions:
•
Start working on this assignment early. Do not wait until the last moment.
•
Make your code parametric. You will be required to design an OFDM modulator and
demodulator, and then change the different parameters to observe different situations. It is easier
to do this if you define your modules in terms of these parameters.
Introduction to OFDM
The basic principle of OFDM is to split a highrate data stream into a number of lower rate streams that are
transmitted simultaneously over a number of subcarriers. Because the symbol duration increases for lower
rate parallel subcarriers, the relative amount of dispersion in time caused by multipath delay spread is
decreased. Inter Symbol Interference (ISI) is addressed by introducing a guard time at the beginning of
every OFDM symbol.
The frequency spacing between these subcarriers is chosen to be equal to the inverse of the OFDM symbol
interval. When no cyclic prefix is added, this causes the subcarriers to be orthogonal over the symbol
interval, and the spectrum of each of the subcarrier signals to be zero at the peak frequency of all signals in
the other subcarrier frequencies, thus eliminating Inter Carrier Interference (ICI).
The basic diagram of the OFDM system is shown in Figure 1.
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View Full DocumentFigure 1: OFDM system
In an OFDM system with
N
subcarriers, input (information) symbols are grouped in blocks of
N
information symbols
each. Each one of these blocks of N symbols are transmitted using what we will call
an
OFDM symbol
. If there are a total of
M
blocks transmitted, this corresponds to
MN
input symbols. For
the
m
th block, the transmitted symbols are {
x
0,
m
,
x
1,
m
,
…
,
x
N1,
m
}, as shown in Figure 1.
We wish to transmit a total (across all N subcarriers) of 1/
T
s
information symbols per second. Since every
OFDM symbol can transmit the outcome of N information symbols, the duration of each OFDM symbol is
T=NT
s
. This corresponds to the OFDM symbol interval. In principle we could make the subcarriers
orthogonal by choosing a spacing of 1/
T
Hz between them. However, since the first portion of the OFDM
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 Spring '09
 IzhakRubin
 Frequency, cyclic prefix, OFDM symbol

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