This document describes a project comparing single carrier and multi-carrier transmission schemes in a wireless multipath channel. A group of electrical engineering students - Asghar Hasnain, Anantakrishna Varanasi, and Pavan Venugopal - worked on the project under professor Dr. Pao Lo Liu and teaching assistant Saurav Bandyopadhyay. The project involved using MATLAB to simulate both transmission schemes and measure their bit error rates in the presence of inter-symbol interference caused by multipath delay spread. The results showed that multi-carrier transmission via OFDM outperformed single carrier transmission for a given channel and equal forward error correction.

1. • Electrical Engineering
Group Members:
Asghar Hasnain
Anantakrishna Varanasi
Pavan Venugopal
Professor : Dr. Pao Lo Liu
Teaching Assistant: Saurav Bandyopadhyay
Comparison of Single Carrier and Multi-carrier (OFDM) PSK
transmission schemes in Multi-path Wireless channel

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Presentation Outline
•Understanding Multipath Wireless channel and ISI
•OFDM and OFDM Block Diagram
•Our approach
•MATLAB Implementation – Block by Block explanation
•Simulation Results
•Conclusion

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Characteristics of a Multipath Wireless Channel
– Delay Spread – It is the interval for which a symbol remains
inside the multi path channel.
– Channel can be modeled as a FIR filter with one line of sight
path and several multipaths , the signals from the multipaths
being delayed and attenuated version of the signal from the
line of sight path.

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Inter Symbol Interference and its Solution
• High Data rate requires smaller symbol period
• If symbol period < delay spread then we have ISI.
• Effect of Modulation Scheme and Symbol period on ISI.
• BER BER

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Solution to ISI
• Having multiple carriers and making the symbol period on each
carrier higher than the delay spread of the channel .
• Effective rate will be high because we are using multiple carriers
(serial to parallel conversion).
• This is similar to FDM where we use different carriers in non-
overlapping frequency bands – NOT BANDWIDTH EFFICIENT
• In OFDM due to the orthogonality property of the carriers we place
them as close as possible ensuring bandwidth efficiency.

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A Qualitative Description of OFDM
OFDM stands for Orthogonal Frequency Division
Multiplexing.
• OFDM is based on a parallel data transmission
scheme that reduces the effect of multipath fading and
makes the use of complex equalizers unnecessary.
•OFDM is derived from the fact that the digital data is
sent using many carriers, each of a different frequency
and these carriers are orthogonal to each other, hence
Orthogonal Frequency Division Multiplexing . The
frequency spacing of the carriers is chosen in such a
way that the modulated carriers are orthogonal and do
not interfere with one another.

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Our approach
– To use MATLAB to simulate a multi path (frequency selective
fading) channel for a given number of Multi Paths. We will
explain and use the FIR filter model of a Frequency Selecting
Fading Channel.
– Simulate Modulator and Demodulator Structures for the Single
and Multi Carrier PSK Transmission System along with proper
“Symbol Generation” system to simulate Frequency Selective
Fading in the Wireless Channel
– Employ equal degree of FEC or forward error correction such as
Rate Punctured Convolution Encoder/Decoder (RCPC) and
compare the BER performance of both the Single and Multi
Carrier Transmission systems against symbol period and SNR .
– Compare the Results and give a justification if the use of Multi-
Carrier Transmission is sensible.

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OFDM BLOCK DIAGRAM

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Source Encoder / Decoder
ENCODER
 The data is usually image, wav or text which is
converted into binary data bits.
 These bits are then padded with zeros such as
to form group of bits to create the symbols
based on the modulation scheme.
DECODER
 At the decoder the recovered bits are put back
to get back the original source data.

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Channel Encoder/Decoder
ENCODER
 The data is then encoded for the channel
based on the channel rate.
 We use RCPC ( Rate Compatible
Punctured Convolution Codes).
 RCPC is used to give different level of
protection for the data bits. The channel
rates used are (1/3 , 1/2 and 2/3).

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Channel Encoder/Decoder...contd.
DECODER
• The data recovered is in the form of + 1 and
-1 (bipolar form).
• The bits recovered from demodulator
inserted with zeros at the punctured places-
-- this is the UNQUANT MODE.
• These bits are then decoded using VITERBI
Decoder. We use the standard vitdec ( )
function in MATLAB.

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Mapping /Recovering Symbols
MAPPING of SYMBOLS
 We group the bits based on the
modulation method selected by the user
to form symbols ready for modulation.
 For Multicarrier transmission signal we
pad the bits with zeros to make it a
multiple of sub- carriers .
RECOVERING of SYMBOLS
 The bits are recovered from the symbols
by unpacking the symbols.

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Modulation / Demodulation
The symbols are then modulated and demodulated
using the different modulation schemes
1. BPSK Modulation
2. QPSK Modulation
3. 8PSK Modulation
4. 16PSK Modulation
5. 8QAM Modulation
6. 16QAM Modulation
7. 32QAM Modulation
8. 64QAM Modulation

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Generation of FIR filter model to
simulate a multipath fading channel
• The function takes in the number of
multipaths and the delay spread.
• It returns a vector ( our channel ) whose length
is equal to the delay spread and the number
of non zero coeffcients is the given number of
multipaths.
• We try to implement a Rician Fading Channel
which has a LOS path.
• Technically, we should choose our Channel
Coefficients from a Rician PDF, but we
approximated it using a Raleigh PDF.

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Single carrier Transmission Scheme
• After the Modulator, we employ the following for
Single Carrier Transmission Scheme.
• The Modulated Data is Delayed and Multiplied
with the associated channel coefficient and added
to get the channel output.
• This signal is corrupted with noise based on the
modulation scheme, with BPSK getting Real
Noise and Complex Noise for Other Schemes.

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Simulation of a multi-carrier system -
Transmitter
• Using the Spectrum of a Particular symbol we locate the
carrier positions in the frequency domain.
• We proceed to perform a serial to parallel conversion on the
stream of symbols and placing them at the positions of the
carriers along with pilot symbols next to them.
• We take an IFFT to get the OFDM time signal per block of
symbols. We concatenate all the blocks to get the total OFDM
time signal
• We insert guard time(cyclic prefix) to prevent inter-block
interference.
• We filter this time signal through an FIR filter and add noise to
obtain our received signal

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Simulation of a multi-carrier system -
Receiver
• We remove the Guard Band and divide the time signal
into the OFDM blocks.
• For Each Block we take the FFT and locate the symbols
on interest and also pilot symbols as per the carrier
locations.
• We try to Estimate the Channel Frequency Response
using the Pilot Symbols and use the same to
approximately correct the distortion in the desired
symbol.

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Pilot Signal Transmission Technique
The channel is frequency selective and in order to
reconstruct the symbols at the receiver we need the
channel response at the position of the symbol.
We insert known pilot symbols very next to our symbols
and send them through the same channel filter.
At the receiver we estimate the channel response by
using the pilot symbols and take the frequency response
of the channel to be the same at the position of the
symbol
 We correct the distortion in the symbols of interest using
the approximate channel response obtained using pilot
symbols.

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Insertion of Guard Time – Cyclic Prefixes

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Insertion of guard time (cyclic prefixing)
Our function inserts the Cyclic Prefix to serve
as a Guard time for the OFDM time signal. The
length of the Guard Time (M) is chosen to be the
length of the filter. We basically copy the last M
samples of the previous block and attach it to
the beginning of the current block.

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SIMULATION RESULTS
SINGLE CARRIER
MULTI CARRIER
SINGLE CARRIER
MULTI CARRIER

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SINGLE CARRIER
MULTI CARRIER
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
10
-4
10
-3
10
-2
10
-1
10
0
COMPARISON OF SINGLE CARRIER AND MULTI CARRIER PSK SYSTEM FOR BER VS USER SNR
BIT
ERROR
RATE
USER SNR
SINGLE CARRIER
MULTI CARRIER

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COMPARISON TABLES

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Conclusions and Future Work
• Conclusions:
 Multi Carrier Outperforms Single Carrier Transmission
Schemes for a Given Channel and Equal Degree of
FEC at a particular high data rate.
• Future Work:
 Implementation of the same with Time Varying
Channel and Rician Fading Coefficients.
 Addressing the Problem of Peak to Average Power
Problem in OFDM.

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Questions?
?

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THANK YOU