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