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Presented by

Md. Imdadul Islam

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Orthogonal Frequency Division Multiplexing (OFDM) is a multi-carrier modulation scheme that transmits data over a number of orthogonal subcarriers. A conventional transmission uses only a single carrier modulated with all the data to be sent. OFDM breaks the data to be sent into small chunks, allocating each sub-data stream to a sub-carrier and the data is sent in parallel orthogonal sub-carriers. As illustrated in Figure 1, this can be compared with a transport company utilizing several smaller trucks (multi-carrier) instead of one large truck (single carrier).

Fig.1 Single carrier vs. multi-carrier transmission

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OFDM is actually a special case of Frequency Division Multiplexing (FDM). In general, for FDM, there is no special relationship between the carrier frequencies, f1, f2 and f3. Guard bands have to be inserted to avoid Adjacent Channel Interference (ACI). For OFDM on the other hand, there must be a strict relation between the frequency of the sub-carriers, i.e. fn = f1 + n Δ⋅ f where Δf = 1/TU and TU is the symbol time. Carriers are orthogonal to each other and can be packed tight as shown in Figure 2.

Splitting the channel into narrowband channels enables significant simplification of equalizer design in multipath environments. Flexible bandwidths are enabled through scalable number of sub-carriers. Effective implementation is further possible by applying the Fast Fourier Transform (FFT). Dividing the channel into parallel narrowband sub-channels makes coding over the frequency band possible (COFDM). Moreover, it is possible to exploit both time and frequency domain variations, i.e. time and frequency domain adaptation.

Fig.2

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A baseband OFDM transmission model is shown in Figure 3. It basically consists of a transmitter (modulator, multiplexer and transmitter), the wireless channel, and a receiver (demodulator).

tfje 02

U

U

Tm

mT

)1(

...mNca 1

ˆ

S/PΣ x(t)

x0(t)

x1(t)

xNc-1(t)

Channel

r(t)

mN

mmC

aaa 110 ,...,,

ma0

ma1

mNca 1

tfje 12

tfj Nce 12

tfje 02

tfje 12

tfj Nce 12

………

U

U

Tm

mT

)1(

...

U

U

Tm

mT

)1(

...

ma0ˆ

ma1ˆ

Fig.3

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In Figure 3, a bank of modulators and correlators is used to describe the basic principles of OFDM modulation and demodulation. This is not practically feasible, and the specific choice of sub-carrier spacing being equal to the per carrier symbol rate 1/TU makes a simple and low complexity implementation using Fast Fourier Transform (FFT) processing possible as shown in Figure 4. For more details on the FFT implementation

tfjtfjtfjtfj Nco eeee 121 2222 ,,,

is a set of complex orthogonal waveforms

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S/P IDFT

0

0

……

A0

A1

AN-1

P/S

mN

mmC

aaa 110 ,...,,

ma0

ma1

mNca 1

………

………………

D/A Channel

DFTA/D P/S

r0

r1

rN-1

……………… …

…

………

ma0ˆ

ma1ˆ

ma0ˆ

mNC

a 1ˆ

Useless

P/S

mN

mmC

aaa 110 ˆ,...,ˆ,ˆ

Fig.4 Transmitter and receiver by using FFT processing

r(t)

x(t)

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Orthogonal Frequency Division Multiplexing (OFDM) shows better spectral efficiency than that of Frequency Division Multiplexing (FDM) technique due to orthogonal relationship between sub-carriers. Orthogonal frequency division multiplexing (OFDM) introduces the concept of allocating more traffic channel within limited spectral width compared to Frequency Division Multiplexing (FDM). Here spectrums of adjacent channels are overlapped which resembles to adjacent channel interferences but interferences are avoided maintaining orthogonal relation between sub-carriers.

Practical Implementation

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First of all high speed serial data is converted to low speed parallel data based. Output of each parallel line is modulated; two widely used modulation schemes are QPSK and 16-QAM. Parallel waves are again converted to an instantaneous serial waves prior transmission. This phenomenon resembles to Inverse First Fourier Transform (IFFT) mentioned. At receiving end signals are detected by coherent or envelope detection. Entire communication system is shown in fig.1.

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Serial data input m(t)

OFDM signal v(t)

Im(g(t))

Re(g(t))

………………………

………………………

S/P converter

IFFT P/S converter

Re(ej2πfct)

Im(ej2πfct)

Σ

Modulator

Serial data output m(t)

ChannelAWGN

n(t)

D-ModulatorS/P converter…

…

FFT……

P/S converter

Fig. 1: OFDM communication system

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Kth sub carrier signal is defined as

],0[0

],0[)(~

2

s

sftkj

kTtwhen

Ttwhenetg

]T,T[twhen0

]T,T[twhene)t(g

sg

sgftk2j

k

K=0,1,2……..Nc-1; Nc is the number of sub carrier

Δf is the frequency separation between carriers

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mth OFDM block

1

0

)(1

)(cN

kk

mkm mTtga

NtS

Total Continuous-time signal of OFDM

0

1

0

)(1

)(m

N

kk

mk

c

mTtgaN

tS

Where amk are the constellation vector

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OFDM is a block modulation scheme. Let Ts be the symbol intervals of the input source sequence. A block of N serial symbols is converted into a block of N parallel modulation symbols, each of duration T = NTs.

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1

0

0 )(1

)(cN

kkk tga

NtS

],0[0

],0[)(;/

2

12

Tt

TtetgTt

Nkj

k

For simplicity, m=0,

The set of complex orthogonal waveform,

s

N

k

TtN

kj

k NTteaN

tSc

0;

1)(

1

0

;/2

12

0

1

0

;/2

12

;/201)(

cN

k

TtN

jTktj

k eeaN

tS

Now,

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1

0

;/2

12

;/201)(

cN

k

NlN

jNklj

k eeaN

lTsS

NlN

j

e/

2

12

tfj ce 2

Sampling S(t) at t = lTs,

The term is independent of k and can be combined

with carrier

Therefore the complex envelope can be written as,

)(.1

)( 001

0

/20kl

N

k

Nkljk aIDFTKAea

NlTsS

c

Where, l = 0, 1, 2 ,…, N-1

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The samples 01

02

01

000 ,,, NAAAAA

are then passed through a D/A converter and are used to modulate the carrier which produce the OFDM signal,

tetStx sc nT

Nfj

2

12

)(Re)(

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IDFT

D/A Carrier MOD

OFDM signal x(t)

ak0 ak

1 … … … akN-1

Ak0 Ak

1 … … … AkN-1

aK

Received OFDM signal r(t) = x(t) + n(t)

A/DCarrier DMOD

DFT

rk0 rk

1 … … … rkN-1

Rk0 Rk

1 … … … RkN-1

Decision device

rK

Transmitter

Transmitter

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Modulation symbol amk is recovered by correlation

dt)t(g)t(gg,g lklk

)(),( nTtgtST

Na km

Sk

m

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Received signal

)(),( nTtgtrT

NR km

S

mk

)()()( tntStr mm and n(t) is AWGN of environment and

A maximum likelihood sequence estimator would have to choose one out of all possibly transmitted symbol sequence μ. The sequence estimator determines an estimated <Sm,k> according to the following criterion,

Where μ is the types of possible modulation symbols and Hmk is

the transfer function of channel during mth block

k

mk

mk

mk

mk SHRa 2|)(|min