COFDM Kenneth Welling

CodedOrthogonal Frequency Division

Multiplexing (COFDM)

Kenneth WellingJune 23, 1999

COFDM Kenneth Welling

OFDM Overview• Spectrum of normal

time domain sequence

• Spectrum of classicalfrequency divisionmultiplexing (FDM)

• Spectrum ofOrthogonal FrequencyDivision Multiplexing

COFDM Kenneth Welling

OFDM Overview

Each of the series of carriers is multiplied by a(complex) scalar from the input data.

xN-1,m

x0,m

x1,m

Inpu

t con

stel

latio

n po

ints

(co

mpl

ex)

φ0(t)

φ1(t)

φN-1(t)

0 1 2 3 . . . N-1

B

Spectrum of the composite signal

One OFDM Symbol

COFDM Kenneth Welling

SYSTEM REQUIREMENTS• Orthogonal carriers• Guard band• Error Control Coding

BENEFITS• Performs well in the presence of

frequency selective fading• No ISI, ICI

COFDM Kenneth Welling

Carrier Orthogonality

• Whole number ofcycles in a symbolperiod (τ)

• Example: basisfunctions of theFourier transformΨk(t) = e jωt

COFDM Kenneth Welling

Guard band

COFDM Kenneth Welling

Guard band

guard active symbolCyclic extension in the time domain

Tg Ts = N/WT

• Guard band is the last Tg seconds of theactive symbol period prefixed to thewaveform, making it a cyclic prefix

• Must be kept short, a fraction of T, yet longerthan the channel impulse response– Completely eliminates ISI, ICI

– Maintains subcarrier orthogonality

– Time waveform appears periodic to the receiver

COFDM Kenneth Welling

h(t) = δ(t) + Γδ (t-τ)

H(f) = 1 + Γej2πfτ

2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0-1

-0 . 5

0

0 . 5

1

1 . 5

2

magnitude

phase

frequency

Multipath Fading• Two-ray model allows for a main component and

a single reflection with magnitude and phase

COFDM Kenneth Welling

Multipath Fading

x

COFDM Kenneth Welling

• Spectrum is multiplied by the frequencyresponse of the channel

Multipath Fading

• Some frequency bins are attenuated, others are amplified

COFDM Kenneth Welling

• Interleaving in frequency• Convolutional coding• Equalization

Resolved through:

Multipath Fading

COFDM Kenneth Welling

OFDM System using DFT/FFT

h(t)

n(k)

Channel

• The IFFT creates a time domain waveform with the exactfrequency content specified by the basis functions of theDFT and the complex constellation points xn,m.

Input

data

Fre

quen

cyIn

terle

aver

Serial toParallel

x0,m

x1,m

xN-1,m

s (k)

Transmitter

IDFT(IFFT)

cyclic prefix

QPSK

map

Conv

Conv

COFDM Kenneth Welling

OFDM System using DFT/FFT

Input

data

Fre

quen

cyIn

terle

aver

Serial toParallel

x0,m

x1,m

xN-1,m

s (k)

Transmitter

IDFT(IFFT)

cyclic prefix

QPSK

map

Conv

Conv

h(t)

n(k)

Channel

Receiver

r(k)

y0,m

y1,m

yN-1,m

SignalMapping(detector)

Parallel to Serial

Output cyclic prefix

DFT(FFT)

De-

Inte

rleav

erConv

Conv

• In the Reciever, the FFT acts as a bank of filters, wherethe values of the resulting frequency bins become thesignal constellation points.

)(1fH

COFDM Kenneth Welling

Simulation Results

0 0.5 1 1.5 210

-8

10-6

10-4

10-2

100

QP SK mapped OFDM, N=256 carriers

Pro

ba

bili

ty o

f B

it E

rro

r

Phase of Null (radians/p)

Actual (with null) Theoretic (no null)

-5 0 5 10 1510

-8

10-6

10-4

10-2

100

QPS K with 50 ns delay (G= 0.7ej0.5p)

Uncoded Eb/N

0 (dB )

Pro

ba

bili

ty o

f B

it E

rro

r

256 carriers , K =3

1024 carriers , K = 3

Theoret ic al, K =3

256 carriers , K =4

1024 carriers , K = 4

Theoret ic al, K =4

COFDM Kenneth Welling

Simulation Results

0 0.5 1 1.5 210

-8

10-6

10-4

10-2

100

QP SK mapped OFDM, N=256 carriers

Pro

ba

bili

ty o

f B

it E

rro

r

Phase of Null (radians/p)

Actual (with null) Theoretic (no null)

-5 0 5 10 1510

-8

10-6

10-4

10-2

100

QPS K with 50 ns delay (G=0.7ej0.75p)

Uncoded Eb/N

0 (dB)

Pro

ba

bili

ty o

f B

it E

rro

r

256 carriers , K =3 1024 carriers , K=3Theoretical, K =3 256 carriers , K =4 1024 carriers , K=4Theoretical, K =4

COFDM Kenneth Welling

Simulation Results

0 0.5 1 1.5 210

-8

10-6

10-4

10-2

100

QP SK mapped OFDM, N=256 carriers

Pro

ba

bili

ty o

f B

it E

rro

r

Phase of Null (radians/p)

Actual (with null) Theoretic (no null)

-5 0 5 10 1510

-8

10-6

10-4

10-2

100

QPSK with 50 ns delay (G=0.7ej1p)

Uncoded Eb/N

0 (dB )

Pro

ba

bili

ty o

f B

it E

rro

r

256 carriers , K= 3 1024 carriers , K=3Theoretical, K=3 256 carriers , K= 4 1024 carriers , K=4Theoretical, K=4

COFDM Kenneth Welling

• Performs better than a single modulatedcarrier in multipath fading

• With a properly implemented guardinterval:– Time waveform appears periodic– orthogonality of subcarriers is ensured– ISI and ICI are eliminated

Conclusion