Chap2 ofdm basics

Darmstadt
University of
Technology
OFDM Basics for
Wireless
Communications
Institute of
Microelectronic
Systems

2VLSI_Comms WS03-04/Generalities L.D. Kabulepa
Single Carrier vs. Multicarrier
Single Carrier
MODMOD
e.g., QAM
TX
Filter
TX
Filter h(t, τ)h(t, τ)
+ RX
Filter
RX
Filter DEMODDEMOD
Noise
Wireless Channel
Data
bits
Data
bits
Multicarrier
MODMOD TX
Filter
TX
Filter
RX
Filter
RX
Filter DEMODDEMOD
Data
bits
Data
bits
MODMOD TX
Filter
TX
Filter
RX
Filter
RX
Filter DEMODDEMOD
Σ h(t, τ)h(t, τ)
+
Noise
Wireless Channel
1
N

Multicarrier Transmission
FSC
tTsymb, SC
f
|h(f)|2
τ
| h(τ) |2
Single Carrier (SC)
Multicarrier
FSC
t
f
|h(f)|2
F = N
TS = N Tsymb, SC
Basic principle:
• Split the transmision bandwidth
into many narrow subchannels
which are transmitted in parallel
• (Ideally) Each subchannel is
narrow enough so that it
experiences a flat fading
although the overall radio
propagation environment is
frequency-selective.
The time dispersion effects
are less significant as the
symbol duration increases

Benefit of Multicarrier Transmission
The multicarrier transmission allows to achieve high data rate
in frequency-selective radio propagation environment
By assuming the same data rate:
• Single-Carrier
⇒> C
SCsymb,
B
T
1
Distortion, interference (ISI)
Large amount of signal processing
required in the equalizer
• Multicarrier
⇒< C
SCsymb,
B
TN
1
No interference
- Data rate can be increased by using
a larger number of subcarriers
- Less equalization effort (as ISI is reduced
by a factor N)
(BC = Coherence bandwidth)

Benefit of Multicarrier Transmission: Example
• A data rate of 10 Mbit/s is targeted in a multipath radio environment by
using the BPSK modulation. Maximum spread delay = 5 µs
5 Mbit/s with BPSK ⇒ Bandwidth = 5 MHz
• Single Carrier Scenario
Tsymb,SC = 0.2 µs ⇒ τmax = 25 Tsymb,SC
• Multicarrier Scenario
Number of subcarriers: 128
Symbol duration = N Tsymb,SC ⇒ τmax = 0.039 NTsymb,SC
⇒ ISI significantly reduced
⇒ Intersymbol-Interference (ISI) is extended over 25 symbols

Orthogonal Multicarrier
Frequency
Orthogonality between the sub
-carriers allows their overlapping
while disabling the occurrence of
crosstalks.
Thus, a significant power saving
can be achieved by using an
orthogonal multicarrier technique
Frequency
Bandwidth saving

Orthogonal Multicarrier (cont‘d)
The orthogonality between the subcarriers can be achieved by letting the
transmit filters gi(t) and the receive filters ri(t) fulfill the following conditions
(i ∈ {1, ... , N})
1. Matched filter condition
2. Convolution condition
( ) ( )tTgKtr 0ii −⋅= ∗
( ) ( ) ( )dττthτg0tc n
τ
jnj, −⋅== ∫
+∞
−∞=
( ) ( )
⎩
⎨
⎧
≠
=
==−⋅= ∗
∞+
−∞=∫ nj,0
nj,1
δdττtgτg nj,n
τ
j
(Assumption: Perfect synchronization, T0 = 0, K = 1)

Conventional OFDM
OFDM = Orthogonal Frequency Division Multiplexing
• In a conventional OFDM system, the orthogonality between the subcarriers
is achieved by means of the discrete Fourier transform (DFT)
• Baseband OFDM signal
• Passband OFDM signal
∑
−
=
=
1N
0k
t∆fkj2π
kas(t)
( )
⎭
⎬
⎫
⎩
⎨
⎧
= ∑
−
=
+
1N
0k
t∆fkfj2π
k
C
aRes(t)
ak = complex-valued modulated symbols (e.g., QAM)
N = number of subcarriers
fC = carrier frequency
Ts = sampling period, f = subcarrier spacing
The inverse DFT is used at the transmitter side
Tt0, ≤≤
Tt0, ≤≤
STN
1
T
1
∆f ==

Conventional OFDM(cont‘d)
1 subcarrier
• The receiver is expected to compute the spectra values at those points
corresponding to the maxima of individual subcarriers
• As a maximum of a subcarrier corresponds to zeros of other subcarrier,
each subcarrier can demolutated independently of the others (by assuming
a perfect synchronization)
6 subcarriers

Impact of a Wireless Channel
OFDM Symbol OFDM Symbol OFDM Symbol OFDM Symbol
t
ii-1 i+1 i+2
|h(τ)|2
Symbol (i-1)
Symbol (i)
Interference
Channel Power
Delay Profile

Cyclic Extension
OFDM Symbol OFDM Symbol OFDM Symbol
t
ii-1 i+1
|h(τ)|2
Symbol (i-1)
Symbol (i)
Channel Power
Delay Profile
Cyclic Extension
Tg T
Interference induced by
the channel are canceled
by inserting a cylic extension
with Tg > τmax
(at the expense of the data
Rate)
GGG G

Circular Convolution
• In the presence of interference induced by the channel
• The cyclic extension (with Tg > τmax) allows to apply the circular
convolution
{ } { } { }NNN
s(k)DFTh(k)DFTs(k)h(k)DFT ∗≠∗
{ } { } { }NNN
s(k)DFTh(k)DFTs(k)h(k)DFT ∗=∗ ˆˆ
∗ˆ= Circular Convolution
This property allows the use of a simple equalization scheme in the
receiver
Relationship between transmitted
and detected symbol
y(n)H(n)(n)y ⋅=ˆ⇒

OFDM Transceiver
P/S
S/P
DFT
S/P
P/S
IDFT
Receive
Filter
Receive
Filter
Transmit
Filter
Transmit
Filter
Multipath
Propagation
Environment
+
AWGN
η
Transmitter
Receiver
Channel
xk
sk
rkyn
s‘k
Remove CP{

OFDM Drawbacks
1. High sensitivity to synchronization errors
Synchronization errors ⇒ Interference, loss of orthogonality
( ) ( ) tf2j
efFttf
δπ
δ −
⋅−
Timing Errors
tf2 C
δπ∆Φ =
I
Q
FFT Window
Frequency
Time
tδ
FFT Window
Frequency
Time
ff ∆ζ
( ) ( ) ( )fffFetf f
ft2j f
∆ξδ∆ξπ
−∗⋅ −
Frequency OffsetErrors
∆f
f-1 f1 f2f0
ff ∆ζ
fC
Frequency

OFDM Drawbacks(cont‘d)
2. Occurrence of very high peak values
A reduction of
the PAPR is highly
desirable. The higher
the PAPR, the lower
The efficiency of circuits
such as power amplifiers
and analog-to-digital
converters
Peak amplitude
RMS amplitude
time
Amplitude
Peak amplitude
RMS amplitude
PAPR = CR2 =
Peak power
Average power
CR =
CR: Crest Factor PAPR: Peak-to-Average Power Ratio

OFDM Drawbacks(cont‘d)
MPX
Tx Analog
DAC
Shaping
Filter
Inter-
polation
DLC
(MAC)
DLC
(MAC)
Scrambling
Encoding
Interleaving
Mapping
IFFT
Append
Cyclic
Prefix
S/P
P/S
Inter-
polation
Shaping
Filter
DAC
Tx Analog
MPX
Append
Preambles
I/Q
Mod.
DAC
DACDAC
DAC
I/Q
Mod.
LO1 LO2
PA
Transmit
Filter
Nonlinear effects generated
by the power amplifier
may introduce intercarrier-
interfrence and thus destroy
the orthogonality

Chap2 ofdm basics

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