Part 5. Orthogonal Frequency Division Multiplexingsdma/elec7073_2008/Part5-OFDM...Part 5. Orthogonal...

ELEC 7073 Digital Communications III, Dept. of E.E.E., HKUp. 1

Part 5. Orthogonal Frequency Division Multiplexing

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

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

Measurement of multipath channel

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

Illustration of multipath interference

Transmitter

Receiver

Multipath channel

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)

–Each chip influenced by 100 previous chips–Serious multipath interference and complex to recover the desired signal at the receiver

�τmax =1us

T=10ns

Signal Bandwidth ~100MHz

frequency selective fading channel

the signal experiences a frequency selective fading channel

Interpretation of multipath interference in freq. domain

Multipath channel

time freq.

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

delayed version 1000

T=10us

τmax=1us

Multicarrier Transmission

frequency selective fading channel

flat fading channel

Interpretation in freq. domain

OFDM Basics (1)

Conventional Frequency Division Multiplexing

f2/T ∆f >=2/T

filter at the receiver

Orthogonal Frequency Division Multiplexing (OFDM)

∆f=1/T

Better spectrum efficiency

Data symbolT

OFDM Basics (2)Why could sub-carrier spacing be ∆f=1/T?– Received signal:

– Sub-carrier down-conversion:

00 for can be obtained as long as is an integerji

T j f tj f te e dt i j f Tππ − = ≠ ∆ ⋅∫

Mj f t

y t d e π−

( ) ( )

( )( )

1 12 22 2

0 00 0

M MT Tj f t j f tj f t j f i j Tj 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

− −− − ∆ −

− ∆−

=⎧⎪= = = ⋅ −⎨ ≠⎪ ∆ −⎩

−= ⋅ + ⋅

∆ −

∑ ∑∫ ∫

– 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

OFDM Basics (3)Basic structure of OFDM systems

Oscillators are analog devices: expensiveM up- and down- conversion: complicated

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

Mj f t

s t d e π−

= ∑ t=nTs

( ) ( )( )

1 1 122 2

10 0 0

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

Mj f t

s t d e π−

M-point IFFT of di

Mj in M

s n d e π−

( )( )

( ) ( )( )

21 1 12

20 0 0

Mj in M

s n d eMj mn M

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

=−−

−− − −−

−= = =

∑= ⎯⎯⎯⎯⎯⎯→

=⎧−⎛ ⎞= = = ⇒⎨⎜ ⎟ ≠−⎝ ⎠ ⎩

∑ ∑ ∑ FFT

OFDM Basics (5)

Receiver

M-point FFT of s(n)

( ) ( )1

Mj mn M

my m s n e π

−−

M sub-carrier down-conversion

( ) ( ) 2

T j f ty m s t e dtπ−= ∫

Proof:

Cyclic Prefix of OFDM (1)OFDM symbol

interference from the previous symbol

OFDM symbol

received symbol

received symbolno interference

from the previous symbol

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.

0, 0, , 1

Mj in M

s n d e n Mπ−

= = −∑

Transmitted signal:

( ) ( )1

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

( ) ( ) ( ) ( )( )

( ) ( ) ( )

y n h s n h s n h s n L

h s n l s n H n

= + − + + − −

= − = ⊗∑

Received signal:

( ) ( ) ( )1 1

M L Lj n L m M j ml M

m ln L l

r m y n e Md h eπ π+ − −

− − −

⎛ ⎞= = ⎜ ⎟

⎝ ⎠∑ ∑

FFT after discarding cyclic prefix:

Channel response on the mth sub-carrier

( ) ( )Recovered data symbol on the mth sub-carrier:

m m md r m MH d= = One-step equalization in frequency domain

Power efficiency–total transmission power fixed–the cyclic prefix: no new data information–the system power efficiency is degraded

Definition of power efficiency: g

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

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

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

high-level modulations

such as 64QAM

sub-channel in deep fading

(bad condition)

low-level modulations

such as QPSK

Flexibility of OFDM (3)

Multiuser Diversity

A combination of the former two: channel conditions of all users are known to the transmitter

for user3 for user2 for user1

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

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

Time SynchronizationWhy is time synchronization needed?

– frame synchronization

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

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

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

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

Carrier frequency offset: |f0-f0'|

different oscillators at the transmitter

and receiver

f0≠f0'

Frequency SynchronizationWhy is freq. synchronization needed?

–Carrier freq. offset

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

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

–Effect of carrier freq. offset (con't)

offset=0.2 offset=0.5

offset=1 offset=2

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

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

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

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

f angle r n N r nN Tπ

∆ = +

r(n+1) r(n+Ns+1)r(n+Ns-1) r(n+2Ns-1)

–coarse synchronization: averaging over multiple symbols to reduce the noise effect

( ) ( ) ( )1

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.

– fine synchronization: same algorithm, using long training symbols

T1:Nl=64 T2

r(n) r(n+Nl)

( ) ( ) ( )1

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.

–Performance: 64QAM

Constellation before freq. sync.

Constellation after freq. sync.

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

PAPR (2)OFDM Signal Amplitude Statistics

Amplitude Histogram

PAPR (3)OFDM Signal Amplitude Statistics

Distribution of measured amplitude which the value is larger than threshold

PAPR (4)

( )( ){ }

maxPAPR=

PAPR: Peak-to-Average Power Ratio–Definition:

Signal Power in one OFDM symbol

duration

copied from http://www.ece.uvic.ca/~agullive/defence.pdf

PAPR (5)PAPR: Peak-to-Average Power Ratio

–What is the problem of a large PAPR?

PAPR (6)PAPR: Peak-to-Average Power Ratio

–RF amplifiers: limited linear range, distort OFDM signals

Output

linear range

Input: Output:

PAPR (7)How to reduce PAPR: Clipping

–Clipping: Simplest way to reduce PAPR–The peak amplitude becomes limited to some desired level

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

PAPR (9)Clipping

–Nonlinear distortion increases out-of-band radiation

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

Channel Estimation (2)Example of noncoherent detection

Received signal: dixh

Fading channel: h

Transmitted signal seq.: didi: -1, +1, +1, ....

ri: -h, +h, +h, ....

di: +1, +1, -1, +1...

ri: +h, +h, -h, +h ....

h must be known to correctly detect the BPSK signals

Coherent detection

No need to know h to detect DBPSK signals Noncoherent detection

Channel Estimation (3)

0 5 10 15 20 25 30 35 4010

Eb/N0 (dB)

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.

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

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

Channel Estimation (6)

frequency

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

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

Channel Estimation (8)Channel Estimation via Interpolation– Interpolation in both time and freq. domains

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.

Applications of OFDM

Part 5. Orthogonal Frequency Division Multiplexingsdma/elec7073_2008/Part5-OFDM...Part 5. Orthogonal...

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