ELEC 7073 Digital Communications III, Dept. of E.E.E., HKUp. 1
Part 5. Orthogonal Frequency Division Multiplexing
ELEC 7073 Digital Communications III, Dept. of E.E.E., HKUp. 2
Introduction
OFDM is a multi-carrier transmission scheme– transform high-speed serial transmission to low-speed
parallel transmission– increase symbol duration, robust to multipath interference
serial transmission
1 second 10 bits transmitted in 1 second, data rate: 10bits/s, bit duration: 1/10s
parallel transmission
bit duration: 1/10s
10 bits transmitted in parallel, bit
duration: 1s, total data rate: 10bits/s,
data rate per channel: 1bit/s
different bit duration,
same data rate
ELEC 7073 Digital Communications III, Dept. of E.E.E., HKUp. 3
Introduction (2)
Realization of parallel transmission
Multicarrier Transmission
serial to parallel converter
p. 4 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Multipath Channels (1)
Terrestrial Mobile Radio Communication– Multipath
channels– Transmitted
signals arrive at the receiver in various paths
Illustration of multipath transmission
p. 5 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Multipath Channels (2)
Measurement of multipath channel
time
impulse signal
MultipathChannel
Channel impulse response– τmax is the maximum delay spread– T is the data symbol duration– When T< τmax, frequency selective fading channel– Multipath interference
Desired signal interfered by τmax/ T previous signals
Transmitter
ReceiverT
1/T
T→0
p. 6 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Multipath Channels (3)
Illustration of multipath interference
Transmitter
Receiver
Multipath channel
p. 7 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Multipath Channels (4)
Example: Broadband transmission, 100MHz– Single carrier systems: DS-CDMA, chip duration (T) about
10ns– Urban area, Microcell (<1km): τmax =1us
0path 0
path 10
path 100(1us/10ns)
0
100
–Each chip influenced by 100 previous chips–Serious multipath interference and complex to recover the desired signal at the receiver
�τmax =1us
T=10ns
p. 8 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
f
Signal Bandwidth ~100MHz
frequency selective fading channel
the signal experiences a frequency selective fading channel
Multipath Channels (5)
Interpretation of multipath interference in freq. domain
Multipath channel
time freq.
f
p. 9 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Multipath Channels (6)
Example: Broadband transmission, 100MHz– Parallel processing– Multicarrier system with 1000 subcarriers, T about 10us– Urban area, Microcell (<1km): τmax 1us
no delay
–Each data influenced by approximately 0.1 previous data symbol: overcoming multipath interference
1000
delayed version 1000
T=10us
τmax=1us
p. 10 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Multicarrier Transmission
frequency selective fading channel
f
flat fading channel
Multipath Channels (7)
Interpretation in freq. domain
p. 11 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
OFDM Basics (1)
Conventional Frequency Division Multiplexing
f2/T ∆f >=2/T
filter at the receiver
Orthogonal Frequency Division Multiplexing (OFDM)
f2/T
∆f=1/T
Better spectrum efficiency
Data symbolT
time
2/Tf
freq.
p. 12 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
OFDM Basics (2)Why could sub-carrier spacing be ∆f=1/T?– Received signal:
– Sub-carrier down-conversion:
22
00 for can be obtained as long as is an integerji
T j f tj f te e dt i j f Tππ − = ≠ ∆ ⋅∫
( )1
2
0
i
Mj f t
ii
y t d e π−
=
= ∑
( ) ( )
( )( )
( )
1 12 22 2
0 00 0
21
0
12
12
j ji
M MT Tj f t j f tj f t j f i j Tj i i
i i
j i j fTM
j iii j
T i jr y t e dt d e e dt d e i j
j f i j
ed T dj f i j
π ππ π
π
π
π
− −− − ∆ −
= =
− ∆−
=≠
=⎧⎪= = = ⋅ −⎨ ≠⎪ ∆ −⎩
−= ⋅ + ⋅
∆ −
∑ ∑∫ ∫
∑
– The minimum sub-carrier spacing ∆f=1/T!
M is the total number of sub-carriers, di is the data signal transmitted on the ith sub-carrier
Interference from other sub-carriers
p. 13 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
OFDM Basics (3)Basic structure of OFDM systems
0
T
∫
0
T
∫
0
T
∫
Oscillators are analog devices: expensiveM up- and down- conversion: complicated
p. 14 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
OFDM Basics (4)
IFFT and FFT can be employed to realize the M sub-carrier up- and down-conversion– Digitalize the analog signal by sampling – Sample rate: fs=Mx∆f, duration: Ts=1/fs
( )1
2
0
i
Mj f t
ii
s t d e π−
=
= ∑ t=nTs
( ) ( )( )
1 1 122 2
10 0 0
ii s
s
M M Mj i fn M ff i fj f nT j in M
s i i iT M fi i i
s nT d e d e d eππ π− − −
∆ ⋅∆= ∆= ⋅∆
= = =
= ⎯⎯⎯⎯⎯→ =∑ ∑ ∑
IFFT of di
M sub-carrier up-conversion
( )1
2
0
i
Mj f t
ii
s t d e π−
=
= ∑
M-point IFFT of di
( )1
2
0
Mj in M
ii
s n d e π−
=
= ∑
p. 15 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
( )( )
( ) ( )( )
( )
12
0
12
0
21 1 12
20 0 0
101
Mj in M
ii
s n d eMj mn M
nn
j i mM M Mj i m n M m
i i j i m Mi n i
y m s e
Md i mey m d e di me
π
π
ππ
π
−
=
=−−
=
−− − −−
−= = =
∑= ⎯⎯⎯⎯⎯⎯→
=⎧−⎛ ⎞= = = ⇒⎨⎜ ⎟ ≠−⎝ ⎠ ⎩
∑
∑ ∑ ∑ FFT
OFDM Basics (5)
Receiver
M-point FFT of s(n)
( ) ( )1
2
0
Mj mn M
my m s n e π
−−
=
= ∑
M sub-carrier down-conversion
( ) ( ) 2
0m
T j f ty m s t e dtπ−= ∫
Proof:
p. 17 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Cyclic Prefix of OFDM (1)OFDM symbol
interference from the previous symbol
OFDM symbol
received symbol
received symbolno interference
from the previous symbol
p. 18 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Cyclic Prefix of OFDM (2)
• Cyclic prefix is introduced to combat the inter-OFDM symbol interference (ISI) caused by the multipath channel.
ISI due to the previous symbol falls into the cyclic prefix; OFDM data symbols not affected by ISI. ⇒ Adverse effects of ISI are removed.
p. 19 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Cyclic Prefix of OFDM (3)
( )1
2
0, 0, , 1
Mj in M
ii
s n d e n Mπ−
=
= = −∑
Transmitted signal:
( ) ( )1
0
L
ll
H n h n lδ−
=
= −∑
How does CP help to avoid ISI?
( ) ( )12
0, 0, , 1, , 1g
Mj i n L M
i g gi
s n d e n L M Lπ−
−
=
= = − + −∑
⎯⎯⎯⎯⎯→add cyclic prefix
Multipath Channel
( ) ( ) ( ) ( )( )
( ) ( ) ( )
0 1 1
1
0
1 1L
L
ll
y n h s n h s n h s n L
h s n l s n H n
−
−
=
= + − + + − −
= − = ⊗∑
Received signal:
p. 20 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
( ) ( ) ( )1 1
2 2
0
gg
g
m
M L Lj n L m M j ml M
m ln L l
H
r m y n e Md h eπ π+ − −
− − −
= =
⎛ ⎞= = ⎜ ⎟
⎝ ⎠∑ ∑
FFT after discarding cyclic prefix:
Channel response on the mth sub-carrier
Cyclic Prefix of OFDM (4)
( ) ( )Recovered data symbol on the mth sub-carrier:
m m md r m MH d= = One-step equalization in frequency domain
p. 21 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Cyclic Prefix of OFDM (5)
Power efficiency–total transmission power fixed–the cyclic prefix: no new data information–the system power efficiency is degraded
Definition of power efficiency: g
g
LM L
γ =+
How to improve power efficiency– reduce Lg: if Lg is shorter than the maximum channel
delay, there will be ISI– increase M: the bandwidth is fixed, larger M, narrower
sub-bands, the system is vulnerable to inter-carrier interference caused by fast fading or frequency synchronization error
p. 22 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Cyclic Prefix of OFDM (6)Summary of CP
–As long as the length of CP is no less than the maximum channel delay, there is no ISI in OFDM and data symbols can be recovered by using a simple one-step equalization in frequency domain
–Since the CP reduces the power efficiency of the system, the length of cyclic prefix is generally set to about 20% of the whole OFDM symbol length.
• Example: IEEE 802.11a & HIPERLAN/2• Data symbol length =3.2µs• Cyclic prefix = 800ns [can absorb a channel dispersion of
800ns]• Total length =4µs
p. 24 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Flexibility of OFDM (2)
Easy to adapt to channel conditions
Assume the channel condition is known at the transmitter (realized by feedback)
sub-channel in good condition
1.0
high-level modulations
such as 64QAM
sub-channel in deep fading
(bad condition)
low-level modulations
such as QPSK
p. 25 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Flexibility of OFDM (3)
Multiuser Diversity
A combination of the former two: channel conditions of all users are known to the transmitter
user3
user2
user1
for user3 for user2 for user1
p. 26 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Advantages of OFDM
Solves the multipath-propagation problem–Simple equalization at receiver
Computationally efficient–Main parts: IFFT/FFT; for broadband systems more efficient than SC
Supports various modulation schemes–Adaptability to SNR of sub-carriers is possible
Elegant framework for MIMO-systems–MIMO system works well in flat fading channels–All interference among symbols is removed
p. 27 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Problems of OFDM
Synchronization issues–Time synchronization: Find start of symbols–Frequency sync.: Find sub-carrier positions
Non-constant power envelope–large peak to average power ratio (PAPR), amplifiers with large linear range needed
*Channel estimation–to retrieve data, channel is time-variant, frequency-variant
p. 28 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Time SynchronizationWhy is time synchronization needed?
– frame synchronization
effective OFDM symbolCPeffective OFDM symbolCP
effective OFDM symbolCPeffective OFDM symbolCP
channel delayISI from the previous symbol
for FFT
Received signal
start of a symbol?
wrong timingwrong decision
find the start of a symbol
Frame synchronization
of OFDM
p. 29 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Time Synchronization (2)Why is time synchronization needed?
–sampling timing
Ts effective OFDM symbolCP
M samples
effective OFDM symbolCP CPT's
different
M samples
Ts≠T's
Transmitter:
Receiver:
In practical systems, difference between Ts and T's is very small, e.g., ±0.3ppm. For one OFDM symbol, the influence of sampling timing drifting is negligible, however, if a long sequence of OFDM symbols are considered, this timing difference must be considered.
start of a symbol
end of a symbol
p. 30 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Time Synchronization (3)Why is time synchronization needed?
–Example: effect of timing error
Original QPSK
constellation
correct timing
effective OFDM symbolCP
erroneous timingerroneous timingerroneous timing
constellation with timing
error: within CP
constellation with timing
error: out of CP
p. 31 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
ReviewWhat is OFDM?
–Basic idea
–What is special about OFDM: IFFT/FFT, Cyclic Prefix
–Advantages: Computationally efficient, flexible: a multiple access scheme, adapt to channel conditions, multiuserdiversity
–Problems: Synchronization, Non-constant power envelope, channel estimation
–Time synchronization: frame sync., sampling timing
p. 32 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
0
T
∫
Carrier frequency offset: |f0-f0'|
different oscillators at the transmitter
and receiver
f0≠f0'
Frequency SynchronizationWhy is freq. synchronization needed?
–Carrier freq. offset
p. 33 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Frequency Synchronization (2)Why is freq. synchronization needed?
–Carrier freq. synchronization
Inter-carrier interference (ICI)
Source: www.cm.chu.edu.tw/teacher/Chen/OFDM/Handout/CHAP11-SYNC.PDF
f1' f1
p. 34 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Frequency Synchronization (3)Why is synchronization needed?
–Effect of carrier freq. offset: QPSK, M=64, CP: 25%, perfect time synchronization
–normalized offset: the carrier freq. offset divided by the sub-carrier spacing
offset=0 offset=0.1
Source: www.cm.chu.edu.tw/teacher/Chen/OFDM/Handout/CHAP11-SYNC.PDF
p. 35 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Frequency Synchronization (4)Why is synchronization needed?
–Effect of carrier freq. offset (con't)
offset=0.2 offset=0.5
Source: www.cm.chu.edu.tw/teacher/Chen/OFDM/Handout/CHAP11-SYNC.PDF
p. 36 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Frequency Synchronization (5)Why is synchronization needed?
–Effect of carrier freq. offset (con't)
offset=1 offset=2
Source: www.cm.chu.edu.tw/teacher/Chen/OFDM/Handout/CHAP11-SYNC.PDF
p. 37 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Frequency Synchronization (6)Why is synchronization needed?
–Effect of carrier freq. offset (con't)
offset=1
offset=0When offset is
integer, there is no ICI. But the
detected symbol is not the original one transmitted
on the sub-carrier
offset=-1
Source: www.cm.chu.edu.tw/teacher/Chen/OFDM/Handout/CHAP11-SYNC.PDF
p. 38 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Synchronization AlgorithmsSynchronization algorithms
–based on training symbols: design a training sequence with a special structure to carry out synchronization
–based on CP: exploiting the redundancy introduced by the CP
Adv.: better performance, suitable for burst modeDisadv.: efficiency reduced, acquisition time is long, complexity is higher
OFDM Symbol
Adv.: no loss in efficiency, complexity is low, suitable for continuous modeDisadv.: limited performance
p. 39 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Synchronization Algorithms (2)Example: based on training symbols
– IEEE 802.11a: packet structure
–Possible frequency offset: Carrier Freq. Offset (CFO) deviation of the center freq. at transmitter and receiver: ±20ppm (part per million); operating freq.: 5G
frequency offset: 5Gx40ppm=200kHz, normalized: 0.64
–Bandwidth: 20M, no. of subcarriers: 64, sub-carrier spacing: 312.5kHz
p. 42 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Synchronization Algorithms (5)Frequency synchronization (CFO)
–coarse synchronization: auto-correlation of received signals, short training symbols
r(n) r(n+Ns)
t8 t9 t10received
signal: r(n)
( ) ( ) ( )2 s sj f N Tsr n N r n e π∆+ =
Since all 10 short training symbols are repetition of one symbol, t9 is similar to t8 except the phase shift caused by CFO (slow fading channel)
( ) ( ) ( ) ( )2 2* s sj f N Tsr n N r n r n e π∆+ =
( ) ( ) ( )( )*12 s
s s
f angle r n N r nN Tπ
∆ = +
r(n+1) r(n+Ns+1)r(n+Ns-1) r(n+2Ns-1)
p. 43 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Synchronization Algorithms (6)Frequency synchronization (CFO)
–coarse synchronization: averaging over multiple symbols to reduce the noise effect
( ) ( ) ( )1
*
0
12
sN
sms s
f angle r n m N r n mN Tπ
−
=
⎛ ⎞∆ = + + +⎜ ⎟
⎝ ⎠∑
Estimation Range: ( )2 s sf N Tπ π π− ≤ ∆ ≤
( ) ( )1 1
2 2s s s s
fN T N T
− ≤ ∆ ≤
Ts=1/20M, Ns=16[ ]625 625f∆ ∈ − +kHz, kHz
CFO frequency offset: 5Gx40ppm=200kHz
CFO can be estimated by the
coarse sync.
p. 44 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Synchronization Algorithms (7)Frequency synchronization (CFO)
– fine synchronization: same algorithm, using long training symbols
T1:Nl=64 T2
GI
r(n) r(n+Nl)
( ) ( ) ( )1
*
0
12
lN
lml s
f angle r n m N r n mN Tπ
−
=
⎛ ⎞∆ = + + +⎜ ⎟
⎝ ⎠∑
Estimation Range:( ) ( )
1 12 2l s l s
fN T N T
− ≤ ∆ ≤
Ts=1/20M, Nl=64[ ]156.25 156.25f∆ ∈ − +kHz, kHz
[ ]625 625f∆ ∈ − +kHz, kHzCoarse freq. sync.:
further correction
of the residual
freq. offset after the
coarse freq. sync.
received signal after coarse freq. sync.
p. 45 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Synchronization Algorithms (8)Frequency synchronization (CFO)
–Performance: 64QAM
Constellation before freq. sync.
Constellation after freq. sync.
p. 46 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Peak to Average Power Ratio (PAPR)
Power envelope of OFDM–OFDM symbol is a sum of sinusoids. When the number of sub-carriers M is large, power envelope varies significantly
p. 47 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
PAPR (2)OFDM Signal Amplitude Statistics
Pro
babi
lity
Amplitude Histogram
p. 48 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
PAPR (3)OFDM Signal Amplitude Statistics
Distribution of measured amplitude which the value is larger than threshold
p. 49 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
PAPR (4)
( )( ){ }
2
2
maxPAPR=
s n
E s n
PAPR: Peak-to-Average Power Ratio–Definition:
Signal Power in one OFDM symbol
duration
copied from http://www.ece.uvic.ca/~agullive/defence.pdf
p. 50 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
PAPR (5)PAPR: Peak-to-Average Power Ratio
–What is the problem of a large PAPR?
p. 51 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
PAPR (6)PAPR: Peak-to-Average Power Ratio
–RF amplifiers: limited linear range, distort OFDM signals
Input
Output
linear range
Input: Output:
p. 52 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
PAPR (7)How to reduce PAPR: Clipping
–Clipping: Simplest way to reduce PAPR–The peak amplitude becomes limited to some desired level
p. 53 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
PAPR (8)Clipping
–By distorting the OFDM signal amplitude, a kind of self-interference is introduced that degrades the BER
Symbol error rate versus SNR in
AWGN channel, OFDM signal is
clipped to PAPR of (a) no distortion(b) 5 (c) 3 (d) 1 dB
p. 54 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
PAPR (9)Clipping
–Nonlinear distortion increases out-of-band radiation
ELEC 7073 Digital Communications III, Dept. of E.E.E., HKUp. 55
Channel EstimationWhy is channel estimation needed?– Digital communication systems: channel estimation is not
necessary: noncoherent detection – Compare to coherent detection, 3dB performance loss
Example of noncoherent detection
BPSK modulation: 0→-1, 1→+1
di=2bi-1
Information bits stream: bi : 0, 1, 1, 0, 1, 0, 0, 0, 1
di: -1, +1, +1, -1, +1, -1, -1, -1, +1
DBPSK modulation: 1. Differential encoding of info. bits: ai=ai-1+bi in binary, a1=12. BPSK modulation: di=2bi-1
bi: 0, 1, 1, 0, 1, 0, 0, 0, 1
ai: 1, 1, 0, 1, 1, 0, 0, 0, 0, 1
di: +1, +1, -1, +1, +1, -1, -1, -1, -1, +1
ELEC 7073 Digital Communications III, Dept. of E.E.E., HKUp. 56
Channel Estimation (2)Example of noncoherent detection
Received signal: dixh
Fading channel: h
Transmitted signal seq.: didi: -1, +1, +1, ....
BPSK
ri: -h, +h, +h, ....
DBPSK
di: +1, +1, -1, +1...
ri: +h, +h, -h, +h ....
h must be known to correctly detect the BPSK signals
Coherent detection
same
b1=0
diff.
b2=1
diff.
b3=1
No need to know h to detect DBPSK signals Noncoherent detection
ELEC 7073 Digital Communications III, Dept. of E.E.E., HKUp. 57
Channel Estimation (3)
0 5 10 15 20 25 30 35 4010
-5
10-4
10-3
10-2
10-1
100
Eb/N0 (dB)
Bit
Erro
r Pro
babi
lity
Coherentdetection
Noncoherentdetection
Performances for BPSK and DBPSK using coherentand noncoherent detection techniques, respectively
Rayleigh fading channel
A 3dB loss in Eb/N0 is incurred by using noncoherent detection over coherent detection.
An evidence showing that coherent detection is preferred for mobile radio communications.
ELEC 7073 Digital Communications III, Dept. of E.E.E., HKUp. 60
Channel Estimation (5)Channel Estimation Techniques– Pilot-aided
Inserting pilot tones into each OFDM symbol on certain sub-carriers or inserting pilot tones into all of the subcarriers of OFDM symbols with a specific periodUse one dimensional (1-D), and two dimensional (2-D) filtering algorithms
ELEC 7073 Digital Communications III, Dept. of E.E.E., HKUp. 61
Channel Estimation (5)Channel Estimation Techniques– Decision directed: Symbol decisions are remodulated and
then employed as "pilot symbols"Used for coherent detection, co-channel interference suppression, and transmitter diversity
– Blind methods: Based on the second and higher order statistics; Determines the channel transfer function without the need for pilot symbols
ELEC 7073 Digital Communications III, Dept. of E.E.E., HKUp. 62
Channel Estimation (6)
frequency
mag
nitu
de
Pilot tones
Pilot-aided Channel Estimation– Pilot tone: known symbols– More pilot tones: better noise resistance
lower throughput or efficiency (pilot carries no information)– Limited no. of pilot tones: filtering or interpolation
y(m)=p(m)*Hm+ηm
Data tonesy(n)=d(n)*Hn+ηn
ELEC 7073 Digital Communications III, Dept. of E.E.E., HKUp. 63
Channel Estimation (7)Channel Estimation via Interpolation– For each pilot tone ki, find Hki = y(ki) / p(ki )– Interpolate unknown values using interpolation filter– Hn = an,1 Hk1 + an,2 Hk2 + … the weighting factors, an,1 an,2... ,
depend on the interpolation filter– Longer interpolation filter: more computation, timing
sensitivity – Simplest interpolation: linear interpolation
frequency
mag
nitu
de
ELEC 7073 Digital Communications III, Dept. of E.E.E., HKUp. 64
Channel Estimation (8)Channel Estimation via Interpolation– Interpolation in both time and freq. domains
freq.
time
p. 65 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Summary of OFDM
• Advantages– Easy to mitigate the adverse effects of channel dispersion by the use
of cyclic prefix.– Low-complexity implementation based on FFT/IFFT.– Support high-rate transmission at a low implementation cost.
• Disadvantages– High peak-to-average power ratios, so that highly linearly power
amplifiers are required at the transmitters in order to avoid intermodulation interference.
– The use of cyclic prefix reduces transmission efficiency. Some power is wasted by transmitting cyclic prefixes, which are redundant.
• Good reference: R. van Nee and R. Prasad, OFDM for Wireless Multimedia Communications, Boston: Artech-House, 2000.
p. 66 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU
Applications of OFDM
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