Meixia Tao @ SJTU

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Principles and Experiments of Communications

Weiyao Lin

Dept. of Electronic EngineeringShanghai Jiao Tong University

Textbook: Chapter 11

Lecture 06: Multicarrier modulation and OFDM

Meixia Tao @ SJTU

Multicarrier Modulation

§ Multipath channels cause intersymbol interference (ISI) when the reciprocal of the symbol rate is smaller than the dispersion of the nonideal channel.

§ A solution:§ Subdivide the available channel bandwidth into a

number of equal-bandwidth subchannels;§ The frequency response characteristics of each

subchannel are nearly ideal.

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Subdivision of Channel Bandwidth

where T is the symbol interval3

1fT

D =

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Orthogonal Frequency Division Multiplexing (1/2)

§ Each subchannel associate a carrier

§ Orthogonal Frequency Division Multiplexing (OFDM)§ The subcarriers are orthogonal over the symbol

interval;§ Independently of the relative phase relationship

between subcarriers.

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( ) cos 2 , 0,1, , 1k kx t f t k Np= = -!

( ) ( )0cos 2 cos 2 0

T

i i j jf t f t dtp f p f+ + =ò

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Orthogonal Frequency Division Multiplexing (2/2)

§

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Modulation

§ Each OFDM symbol is the sum of signals modulated by subcarriers.

§ OFDM symbol can express as

equivalent baseband signal

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( ) ( )2 1

22

0.5Re exp 22

N

N c s s sii N

is t d j f t t t t t Tp-

+=-

ì üé + ùæ ö= - - £ £ +í ýç ÷ê úè øë ûî þå

( ) ( )2 1

22exp 2

N

N s s sii N

is t d j t t t t t TT

p-

+=-

é ù= - £ £ +ê úë ûå

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Demodulation

§ For the k th signal

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( ) ( )

( )

2 1^

22

2 1

22

1 2exp 2 exp 2

1 2exp 2

s

s

s

s

Nt Tk s N sit

i N

N t T

N si ti N

k

k N id j t t d j t t dtT T T

i k Nd j t t dtT Td

p p

p

-+

+=-

- +

+=-

-é ù é ù= - - -ê ú ê úë û ë û

- +é ù= -ê úë û=

åò

å ò

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Modulation and Demodulation of OFDM System

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FFT and IFFT

§ Inverse DFT and IDFT are critical in the implementation of an OFDM system

§ IFFT and FFT algorithms are the fast implementation for the IDFT and DFT

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21

021

0

1IDFT x[n]= [ ]

x[k]= [ ]

N j knN

n

N j knN

n

x k eN

DFT x n e

p

p

- -

=

-

=

å

å

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Modulation Using IDFT

§ OFDM equivalent baseband signal can implement with IDFT.

let ,

is IDFT of

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( ) ( )2 1

22exp 2

N

N s s sii N

is t d j t t t t t TT

p-

+=-

é ù= - £ £ +ê úë ûå

0st = , 0,1, , 1kTt k NN= = -!

( )1

0

2exp 0 1N

ii

kT kis k s d j k NN N

p-

=

æ ö æ ö= = £ £ -ç ÷ ç ÷è ø è ø

å

( )s kid

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Demodulation Using DFT

§ At the receiver

§ Modulating the transmitted signal and demodulating the received signal is equivalent to the computation of the IDFT and its inverse.

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( )1

0

2exp 0 1N

ik

kid s k j i NNp-

=

æ ö= - £ £ -ç ÷è ø

å

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OFDM via the FFT Algorithm

§ Algorithm complexity§ DFT/IDFT:§ FFT/IFFT:

§ Implement the OFDM system via the FFT algorithm instead of DFT algorithm can be achieved more easily.

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( )2O N

( )2log2NO Næ ö

ç ÷è ø

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Eliminate ISI (1/2)

§ To eliminate ISI, we need to insert guard interval between OFDM symbols.

§ If the guard interval is larger than the delay spread, the multipath component of a symbol does not interfere with adjacent symbols.

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Eliminate ISI (2/2)

§ An alternative approach is to append cyclic prefix to each OFDM symbol

§ Since the ISI in any pair of successive signal transmission block only affects the cyclic prefix, we discard the affected samples of received signal to eliminate ISI

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Cyclic Prefix and Delay Spread

§ 3 cases:§ (a) Delay Spread < Cyclic Prefix § (b) Delay Spread is 3% over Cyclic Prefix§ (c) Delay Spread is 10% over Cyclic Prefix

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Multicarrier OFDM Comunication System

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The AWGN Channel Model

§ The channel is assumed to corrupt the signal by the addition of white Gaussian noise as shown in the following figure.

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OFDM System Performance over AWGN Channel (1/3)

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OFDM System Performance over AWGN Channel (2/3)

§ QAM

§ M-ary PSK

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( ) ( ) ( ) ( ) ( )

( )

( )

( )

( )

2

,2

22

0

2 2

0 0

22

0

1 1p 1 2 | 4 2 | 4 |log

32 1

2| 1 2

2 2| 1 2 1

2| 1

e M QAM

s

M p c I M p c II p c IIIM M

EaM

ap c I QN

a ap c II Q QN N

ap c III QN

-ì üé ù= - - + - +í ýê úë ûî þ

=-

é ùæ öê ú= - ç ÷ç ÷ê úè øë ûé ù é ùæ ö æ öê ú ê ú= - -ç ÷ ç ÷ç ÷ ç ÷ê ú ê úè ø è øë û ë û

é ùæ öê ú= - ç ÷ç ÷ê úè øë û

!

0

p erfc sinse

EN M

pæ öæ ö» ç ÷ç ÷ç ÷è øè ø

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OFDM System Performance over AWGN Channel (3/3)

§ BER versus SNR curves for the OFDM system in AWGN

channel using BPSK/QPSK, 16QAM, 64QAM, 256QAM

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SNR per subchannel

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§ The SNR per subchannel can be defined as:

§ In subchannels with high SNR, we transmit more bits/symbol. Thus, the bit rate on each subchannel can be optimized

2

2SNR k kk

nk

TP Cs

=

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Spectra of OFDM Signal (1/2)

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§ OFDM signals are orthogonal in the time domain but have significant overlap in frequency domain.

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Spectra of OFDM Signal (2/2)

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§ The large spectral overlap of the OFDM signals causes intersubchannel interference (ICI) when the communication channel is a fading channel

§ OFDM may not be as robust as a single carrier system in radio communications where the receiving terminal is moving at high speed

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Peak-to-Average Power Ratio

§ Major problem: high PAPR§ Large peaks occurs when the signals in the K

subchannels add constructively in phase.§ Such large signal peaks may saturate the power

amplifier at the transmission, thus, causing intermodulation distortion in the transmitted signal.

§ Solution:§ Insert different phase shifts in each of the subcarriers;§ Modulate a small subset of the subcarriers with dummy

symbol.

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Applications of OFDM

§ Digital audio broadcasting (DAB)§ Digital video broadcasting (DVB)§ Digital subscriber lines (DSL)§ Wireless local area networks (LANs)

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Advantages and disadvantages of OFDM

§ Advantages:§ High data rate§ Immunity to delay spread§ Efficient bandwidth

§ Disadvantages:§ The problem of Synchronization§ Need FFT units at transmitter, reciver§ The problem of high peak to average power ratio

(PAPR)

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