Ncc2004 ofdm tutorial part i-rvr

OFDM (Part – I)
Theory and Performance
Dr. R. V. Raja Kumar
Professor, Dept. of E & ECE,
Indian Institute of Technology,
Kharagpur – 721302
deanac@hijli.iitkgp.ernet.in
rkumar@ece.iitkgp.ernet.in
A Tutorial presentation at NCC2004

© Prof. R. V. Raja Kumar Dept. of E & ECE
Contents of Part - I
IIT
Kharagpur
1. Introduction to Multi-carrier, DMT and
Orthogonal frequency division modulation
(OFDM)
2. OFDM by IDFT
3. OFDM demodulation by DFT
4. Multipath channel, its model and its effect on a
signal.
5. Need for cyclic prefixing in OFDM
6. Block schematic of an OFDM system
7. Bit error performance of an OFDM system

Variations of Multicarrier
SystemsIIT
Kharagpur
Frequency Division
Multiplexing
MC-CDMA
MC-DS-CDMA
MT-CDMA
Multicarrier Modulation
Multicarrier
Modulation
OFDM Discrete Multi-
tone (DMT)

Advantages and Disadvantages
IIT
Kharagpur
• Robust in noisy environments:
Impulse noise, RF noise, channel distortion,
crosstalk, . . . . .
• Simplified channel equalization
• Suitability for efficient implementation
• Good spectral efficiency
• Sensitive to receiver synchronization
imperfections.

APPLICATIONS
IIT
Kharagpur
• Wideband communication over mobile radio:
Mobile radio FM, Dig. Cellular telephony, WLAN,
WMAN, UWB, . . . . .
• Digital subscriber lines:
ADSL, HDSL, VHDSL, . . . . . .
• Digital audio broadcasting
• Digital video broadcasting
• HDTV broadcasting
• Optical communication – HFC
• Underwater communications

QAM
IIT
Kharagpur
x x x x
x x x x
x x x x
x x x x
Re {x} = α
Im {x} = β
Constellation
16 QAM: s0, s1 , . . s15
Baseband signal,
x = Re{(α + j β) e j ω
0
t
}
= Re{ r e j θ
. e j ω
0
t
}
= αcos(ω0t) - βsin(ω0t)
α = amplitude of the in-phase comp. of the carrier
β = amplitude of the quadrature -phase comp. of
the carrier
r = amplitude of the carrier
θ = phase of the carrier

Single Carrier QAM Modulator
IIT
Kharagpur
HT(f)
HT(f)
M-ary symbol
to quadrature
Signal
encoding
×
×
+
cos(ω0t)
- sin(ω0t)
{d0, d1, d2, d3, . . . . }
{α0 , α1 , α2 , α3 , . . . }
{β0 , β1 , β2 , β3 , . . . }
α0
α1 α2
β0
β1 β2
O/P

QAM Demodulator
IIT
Kharagpur
Carrier
Recovery
Subsytem
HR(f)
HR(f)×
×
Quadrature
signal
to symbol
Decoding
Demodulated
output
os(ω0t)
sin(ω0t)
Comparator
chain

Complex Equivalent
IIT
Kharagpur
HT(f) ×
X(t)
exp(j ω0 t )
X(t) exp(j ω0 t )(α + j
β) δ(t)
H*T(f)×
exp(-j ω0 t )
(α + j β)
QAM
decision
QAM Symbol
Mapping

Multi-Carrier Comm. System
IIT
Kharagpur
Modulator
Modulator
Modulator
De-
MUX
+
{. . ,d1
i
, d2
i
, . . dM
i
, d1
i+1
, d2
i+1
, . . dM
i+1
, . . }
Mr bps
. . ,d1
i
, d1
i+1
, d2
i+2
, . .
r bps
. ,d3
i
, d3
i+1
, . .
. ,dM
i
, dM
i+1
, . .
f0
f0+B f0+2B f0+(M-!)B
Signal spectrum
p(t)
p(t)
p(t)
f0
f0+B
f0+(M-1)B
Subcarrier
MC signal

Receiver of a Multi-Carrier
SystemIIT
Kharagpur
MUX
p(t)
p(t)
p(t)
X
X
X
QAM
decision
QAM
decision
QAM
decision
f0
f0+B
f0+(M-1)B
Rx.
data
I/P
signal

Baseband Equivalent System
IIT
Kharagpur
Modulator
Modulator
Modulator
De-
MUX
+
{. . ,d1
i
, d2
i
, . . dM
i
, d1
i+1
, d2
i+1
, . . dM
i+1
, . . }
Mr bps
. . ,d1
i
, d1
i+1
, d2
i+2
, . .
r bps
. ,d3
i
, d3
i+1
, . .
. ,dM
i
, dM
i+1
, . .
0 B 2B (M-1)B
Baseband
Signal spectrum
p(t)
p(t)
p(t)
0
B
(M-1)B f0
f0+B f0+2B f0+(M-!)B
RF Signal spectrum
X
exp(j ω0 t )
Re

Multicarrier Signal Spectrum
IIT
Kharagpur
f0
f0+B f0+2B f0+(M-!)B
f0
f0+B f0+2B f0+(M-!)B
• Negligible interference
from adj. Subcarriers.
• Spectrally inefficient.
• Interference from
adjacent subcarriers
• Spectrally efficient.
When the baseband carrier spacing = n/T, the
baseband carriers are orthogonal.
• No interference from
adjacent subcarriers
• Spectrally efficient.

Orthogonal Carriers
IIT
Kharagpur
T
T
T
T
Carrier-0: x(t) = A
Carrier-1: x(t) = Acos(2πt/T)
When the baseband carrier spacing = n/T, the
baseband carriers are orthogonal.

Spectrum of the Carriers
IIT
Kharagpur
f0 = B = 1/T
f00 2f0 3f0 4f0
f
xi(t) xj(t) dt = 0, i = j
T
0 = 1, i = j
Orthogonal

OFDM Signal
IIT
Kharagpur
An M = N/2 – carrier OFDM signal for the QAM
mapped symbol sequence, { d0, d1, d2,. . ., dN/2-1}
is given by,
x(t) =Re{ Σ dk ej2πkt/T
}
k=0
N/2-1
for 0 < t < T
When this OFDM signal is sampled at t = nTs, the
discrete time OFDM signal/symbol becomes,
x(n) = Σ dk ej2πkn/N
k=0
N-1
for 0 < n < N-1
N – pt. IDFT of { d0, d1, d2,. . ., dN-1}
= Σ dk ej2πkt/T
k=0
N-1
when dN-k = d*k

Mapping of Symbols
IIT
Kharagpur
d0 = α0
d1 = α1 + j β1
d2 = α2 + j β2
.
.
dN/2-1 = αN/2-1 + j βN/2-1
dN/2 = j β0
d N/2+1 = αN/2-1 - j βN/2-1
.
.
dN-2 = α2 - j β2
dN-1 = α1 - j β1
d0
d1 d*
1
d*
2d2
dN/2
Even/odd
symmetry yields a
real IFFT output
IEEE 802.11a:
N=64

OFDM Reception
IIT
Kharagpur
An N – carrier OFDM signal yields the
detection statistic for the QAM mapped
symbol sequences as,
dk = x(t) e-j2πkt/T
dt for 0 < k < N-1
The QAM mapped symbols can be obtained by comparing
{ d0, d1, d2,. . ., dN-1} against the appropriate thresholds.
When the OFDM signal is sampled at t = nTs,
dk = Σ x(n) e-j2πkn/N
k=0
N-1
for 0 < k < N-1
N – pt. DFT of { x(0), x(1),. . ., x(N-1)}
T
0

OFDM Signal in Time-
Frequency PlaneIIT
Kharagpur
time
frequency
T One OFDM symbol
One carrier
f0
Data
subsymbol

OFDM Transceiver
IIT
Kharagpur
Mappi-
ng of
Symb-
ols
IFFT TDM
cyclic
Pre-
fixing
ADC
Compa-
rison FFT DeMUX
cyclic
Prefix
Remo-
val
DAC
Demap-
ping
of
Symb-
ols
Data
I/P
Data
O/P
Rx.
I/P
Tx.
O/P
Mix.
FS
Mix.
FS
fc

Features of OFDM
IIT
Kharagpur
• No intercarrier guard bands
• Orthogonal carriers and controlled overlapping
of bands
• Maximum spectral efficiency (Nyquist rate)
• Robustness against frequency selective fading
• Immunity to inter-symbol-interference
• Simplified equalization
• Very sensitive to time-freq. synchronization
• Easy and efficient implementation using IFFT

CP
Cyclic Prefixing
IIT
Kharagpur
Guard time or Cyclic prefixing is needed for discarding
ISI from the previous symbol. Avoids transients.
CP
T
CP CP
ISIISI
Only consider
this part
Only consider
this part
Tg
IEEE 802.11a:
T=3.2µS
Tg=0.8µS
Channel O/P:

IEEE 802.11a Example
IIT
Kharagpur
Data rate for each 20 Mhz channel:
20 Msamples per second.
250 K OFDM symbols per second.
48 data carriers per symbol.
Rate 1/2 or 3/4 convolutional code.
1 bit/carrier (BPSK) to 6 bits/carrier (64 QAM)
Only 52 of the 64 carriers are used.
4 of the 52 carriers are used for pilot carriers
(no data).
Data rate = 48 * 6 * 3/4 * 250K = 54 Mbps..

One OFDM Symbol of 802.11a
IIT
Kharagpur
Cyclic prefix

A Typical OFDM Signal
IIT
Kharagpur

Discrete Multi-tone Modulation
IIT
Kharagpur
Same as OFDM. But, it uses adaptive loading
of the subcarriers by data based on the sub-
band SNR.
Signal and noise
power spectral
densities on a
telephone channel.
4 5 8 8 8 5 4 3 2 1Loading example:

Multipath Propagation
EnvironmentIIT
Kharagpur
M
r(t) = Σ ai s(t-
τi)
i = 0
a3
(τ3)
a0 (τo)
a1
(τ1)
a2(τ2)
The received signal when the tx. signal is s(t) 

IIT
Kharagpur
• Reflection, diffraction and scattering takes place.
• Received signal varies with location
• Shadowing takes place
Effect of Motion  Fading
• Rx. signal fluctuates (rapidly) with time also
• Motion can be due to mobile or movement of surroundings
• Slow motion  less variation
Fading  Long term and short term
Signal spreads in time  ISI  limits the symbol rate
Multipath Propagation
Environment

Delay Spread
IIT
Kharagpur
-30
-25
-20
-15
-10
-5
0
0 50 100 150 200
|h(t)indB->
tinnsec.->
"channel.dat"
•Multipath propagation causes delay spread
•Mean delay < t > =
T= max. delay spread
P(t) = Rx. power at delay, t
•MS delay
Impulse response  h(t)
τ
P(τ)
Powerdelayprofile(dB)
Excess delay (μ sec)0
a1
2
a2
2
a3
2a0
2
a4
2
a5
2
t P(t) dt
T
0
P(t) dt
T
0
t2
P(t)dt
T
0
P(t) dt
T
0

Typical Delay Spreads
IIT
Kharagpur
Frequency response of the channel, | H(f) | = | FT of {h(t) }|
Coherence Bandwidth
Stationary range of frequencies over which the frequency response is flat
3dB coh. Bandwidth, Bc ≈ 1/(5 στ ).
Flat or frequency selective nature depends on Bc
Environment Frequency (MHz) typ. rms delay spread(στ ) worst case
Suburban 910 200 – 300 nSec 1.96 –2.11µSec
Indoor 850 < 270 nsec.
Indoor 1500 about 25 nSec.
Indoor 1900 < t> = 70 – 90 nSec.
Urban 890 – 910 600 nSec 25µSec

Outdoor Propagation
IIT
Kharagpur
Free space propagation  proportional to d -2
,
where d = distance
Faded signal  proportional to d -n
, 3 < n <4 (typically)
Distance, d
Signal
strength
dB
free space
open area
suburbanindoor
Indoor Propagation:
Rms delay spread = 30 to 60 nSec
15 dB and 6 to 10 dB for the first and the next 4 floors respectively.

Effect of Motion
IIT
Kharagpur
The received unmodulated signal r(t) can be expressed
as,
s(t) = cos(ωct+Ψ)
Let the n-th reflected wave with amplitude
cn and phase Φn arrive from an angle αn
relative to the direction of the motion of the
antenna. The Doppler shift of this wave is
where v is the speed of the antenna, λ is the wavelength.
In case of an unmodulated carrier, the transmitted signal has
the form

Doppler Shift
IIT
Kharagpur
Coherence time ( and Doppler Spread ):
As the vehicle moves or the surroundings move, h(t) varies. H(f)
also varies at certain rate.
Coherence time : time interval over which the channel response is
nearly the same
Doppler spread : the amount of spectral broadening which
depends on the vehicle speed  Doppler frequency
Tc ≈ 9/(16π f m) , fm = max. doppler frequency
Ex : when velocity = 50 m/sec.
at 1900 MHz , Tc = 1.336 msec. , fm = 316.66 Hz.
The given fading is fast or slow depends on Tc

Types of Fading
IIT
Kharagpur
Small Scale Fading
Flat Fading
Bs < Bc
Ts > στ
Freq. selective fading
Bs > Bc
Ts < στ
Slow fading
Ts < Tc
Bs > BD
Fast fading
Ts > Tc
Bs < BD
Based on multipath Based on Doppler
time delay spread spread
Bc - Coherence Bandwidth Ts - Symbol Period
BD - Doppler Spread Tc - Coherence Time
Bs - Symbol Bandwidth στ - Rms Delay Spread

Model of a Multipath Channel
IIT
Kharagpur
x(t) =Re{c(t)exp(jωct)}
y(t) =Re{r(t)exp(jωct)}
y(t) = x(t) * h(t)
h(t,τ) =
Re{hb(t,τ)exp(jωct)}
x(t) y(t)
Bandpass channel model
(1/2)hb(t,τ)c(t) r(t)
Baseband channel model
(1/2) r(t) = (1/2) c(t) * (1/2) hb(t)
• c(t) and r(t) are complex baseband equivalent signals
• h(t,τ) is the impulse response of the time varying multipath radio
channel.
The variable t represents the time variation due to motion,
whereas τ is the
channel multipath delay for a fixed value of t.
• hb(t,τ) is the complex baseband impulse response.

Rayleigh Fading
IIT
Kharagpur
• Rayleigh fading is caused by multipath reception. The
mobile antenna receives a large number of reflected
and scattered waves.
• Because of wave cancellation effects, the
instantaneous received power seen by a moving
antenna becomes a random variable, dependent on the
location of the antenna.
• Signal amplitude (in dB) versus time for an antenna moving at
constant velocity.Notice the deep fades that occur occasionally.
• Although fading is a random process, deep fades have a
tendency to occur approx. every half a wavelength of motion.)

IIT
Kharagpur
TIME (ms)
-35
-30
-25
-20
-15
-10
-5
0
5SIGNALSTRENGTHINdB
0 25050
Coherence time(Tc) = 10 ms
Simulated Rayleigh fading envelope at 900MHz & receiver
speed:120km/hr
Rayleigh Fading

.
Model to Generate Rayleigh
FadingIIT
Kharagpur
Baseband quadrature channel impulse response
Gaussian
noise source
g1(t)
Gaussian
noise source
g2(t)
θ(t) = tan-1
[hq(t)/ hi(t)]
hi(t)
hq(t)
hi(t)
hq(t)
ci(t)
cq(t) +
+
+ -
ri(t)
rq(t)
Complex lowpass equivalent of a bandpass system
hb(t)
hi(t)
Doppler filter
hq(t)
.
2
.
2
Doppler filter
exp{jθ(t)}

Model to Generate Multipath
FadingIIT
Kharagpur
r(t)
….τ1
Rayleigh fading
simulator
a0
…..
τn
Transmitted Signal
s(t)
Rayleigh fading
simulator
a1
Rayleigh fading
simulator
aN
ai=0.5938, 0.7305, 0.3175, 0.1137,
and , τi = 0.1, 0.5, 1 s, respectively.
Applicable for a wide range of channel conditions.
Both flat and frequency selective fading conditions may
be simulated, depending on gain (a’s) and time delay (τ’s) settings

Effect of Channel
IIT
Kharagpur
where,
Y(k) = FT of y(t) and
H(k) = FT of h(t)
dk = Σ x(n) e-j2πkn/N
n=0
N-1
y(t) = h(t)*d(t) = Σ h(k) d t-k
k=0
N-1
Y(k) = H(k). x(n)
Here H(k) can be estimated using a measured Y(k) for given
x(n). This can be done by finding a pilot response.

Need for Pilot Transmission
IIT
Kharagpur
• Channel estimation and equalization
• Carrier frequency offset estimation
• Clock time offset estimation
• Blind estimation methods are slow convergent.
• Small overhead for pilot transmission

Pilot Transmission
IIT
Kharagpur
Time
Frequency
0 1 2 3 4 5 7
Pilot symbols
0
1
2
3
4
5
6
7
Time
0 1 2 3 4 5 7
Pilot carriers
0
1
2
3
4
5
6
7
Frequency
IEEE 802.11a/g pilot carriers: 7, 21, 42, 56

Distributed Pilot
TransmissionIIT
Kharagpur
Time
0 1 2 3 4 5 7
0
1
2
3
4
5
6
7
Frequency
Pilot subsymbol

Performance Analysis
IIT
Kharagpur
• The channel estimation is by Linear MMSE
method.
• Interference from orthogonal carriers is
negligible.
• Channel equalization is by interpolation of the
channel estimates in the Time-frequency
plane.
• Channel impulse response 
• { 0.5938, 0.7305, 0.3175, 0.1137}
• Excess delays = { 0, 0.1, 0.35, 1.0 µSec}

BER Performance of BPSK and
DQPSKIIT
Kharagpur

Performance of 16-QAM
IIT
Kharagpur

IIT
Kharagpur
BER performance of
OFDM over time variant
Ricean fading channels
(bit rate f = 128 kbits/s, f
= 100 Hz, = 1).
Courtesy: Lei Wan and V. K. Dubey
Performance of OFDM Over
Ricean Channels

Multicarrier CDMA Systems
IIT
Kharagpur
• Higher capacity over TDMA
• Immune to frequency selective fading
• Supports variable data rate transmission.
• Frequency diversity in MC-CDMA
• Less sensitive to receiver synchronization
imperfections.
MC-CDMA,
MC-DS-CDMA,
MT-CDMA

MC - CDMA System
IIT
Kharagpur
Modulator
Modulator
Modulator
+
{. . ,d1, d2, . . dM, . . }
r bps
c1
j
. ,d1, . . (r bps)
0 r 2r (M-1)r
MC-CDMA
Signal spectrum0
r
(M-1)r
X
exp(j ω0 t )
Re
X
X
X
. ,d1, . .
. ,d1, . .
(r cps)
• M fold Frequency diversity.
• Signal generation for the jth user.
c2
j
cM
j

MC - DS - CDMA System
IIT
Kharagpur
Modulator
Modulator
Modulator
De-
MUX
+
{. . ,d1
i
, d2
i
, . . dM
i
, d1
i+1
, d2
i+1
, . . dM
i+1
, . . }
Mr bps
c1, c2, c3, . .
. ,d1, . . (r bps)
0 p 2p (M-1)p
MC-DS-CDMA
Signal spectrum0
p
(M-1)p
X
exp(j ω0 t )
Re
X
X
X
c1, c2, c3, . .
c1, c2, c3, . .
. ,d2, . .
. ,dM-1, . .
(p cps)
(p/r: spreading gain)

Multi-tone CDMA System
IIT
Kharagpur
Modulator
Modulator
Modulator
De-
MUX
+
{. . ,d1
i
, d2
i
, . . dM
i
, d1
i+1
, d2
i+1
, . . dM
i+1
, . . }
Mr bps
c1, c2, c3, . .
. ,d1, . . (r bps)
0 r 2r (M-1)r
OFDM
Signal spectrum0
r
(M-1)r
X
exp(j ω0 t )
Re
X
X
X
c1, c2, c3, . .
c1, c2, c3, . .
. ,d2, . .
. ,dM-1, . .
(rN cps)
0 r 2r (M-1)r
MT-CDMA
Signal spectrum
(N: spreading gain)

Extensions of OFDM
IIT
Kharagpur
• Pre-coded OFDM
• Polynomial Cancellation Coding (PCC) –
OFDM
• Synchronous time domain (STD)-OFDM
• Transformed (WHT) OFDM
• Pulse shaping OFDM/OQAM

Current Research in OFDM
IIT
Kharagpur
• Improved forms of OFDM (ex.: coded OFDM)
Turbo coded, space time coded,
• Performance evaluation
Higher modulation schemes, ST codes,
nonlinear channels
• Channel equalization
Pre-FFT eq., reduced complexity eq.,
• PAPR analysis and PAPR reduction methods.
• Timing synchronization: blind methods
• Diversity: space-frequency diversity, transmit
antenna diversity
• Adaptive modulation, power allocation and
control

References
IIT
Kharagpur
1. J.A.C. Bingham, “Multicarrier Modulation for Data
Transmission: An Idea Whose Time Has Come,” IEEE
Communications Magazine, 28, 5, pp. 5-14, 1990.
2. J.K. Cavers, “An Analysis of Pilot-Symbol Assisted
Modulation for Rayleigh-Fading Channels,” IEEE Transactions
on Vehicular Technology, 40, 4, pp. 686-693, 1991.
3. L.J. Cimini, “Analysis and Simulation of a Digital Mobile
Channel Using Orthogonal Frequency-Division Multiplexing,”
IEEE Transactions on Communications, 33, 7, pp. 665-675,
1985.
4. S. Hara, and R. Prasad, “Overview of Multicarrier CDMA,”
IEEE Communications Magazine, 35, 12, pp. 126-133, 1997.
5. S.D. Sandberg, and M.A. Tzannes, “Overlapped Discrete
Multitone Modulation for High Speed Copper Wire
Communications,” IEEE Journal on Selected Areas in
Communications, 13, 9, pp. 1571-1585, 1995.

Ncc2004 ofdm tutorial part i-rvr

More Related Content

What's hot (20)

Similar to Ncc2004 ofdm tutorial part i-rvr (20)

More from Arpan Pal (20)

Ncc2004 ofdm tutorial part i-rvr