Intro Ofdm

E225C – Lecture 16 OFDM Introduction EE225C

Introduction to OFDM l

Basic idea » Using a large number of parallel narrow-band subcarriers instead of a single wide-band carrier to transport information

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Advantages » Very easy and efficient in dealing with multi-path » Robust again narrow-band interference

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Disadvantages » Sensitive to frequency offset and phase noise » Peak-to-average problem reduces the power efficiency of RF amplifier at the transmitter

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Adopted for various standards – DSL, 802.11a, DAB, DVB

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Multipath can be described in two domains: time and frequency Time domain: Impulse response

time

time

time Impulse response

Frequency domain: Frequency response time

time

time Sinusoidal signal as input

f

time

Frequency response

Sinusoidal signal as output

Modulation techniques: monocarrier vs. multicarrier Channel N carriers

Channelization

Similar to FDM technique

Guard bands

B Pulse length ~1/B – Data are transmited over only one carrier

Drawbacks

B Pulse length ~ N/B – Data are shared among several carriers and simultaneously transmitted Advantages

– Selective Fading

Furthermore – Flat Fading per carrier

– Very short pulses

– N long pulses

– ISI is compartively long

– ISI is comparatively short

– EQs are then very long

– N short EQs needed

– Poor spectral efficiency because of band guards

– Poor spectral efficiency because of band guards

– It is easy to exploit Frequency diversity – It allows to deploy 2D coding techniques – Dynamic signalling

To improve the spectral efficiency: Eliminate band guards between carriers To use orthogonal carriers (allowing overlapping)

2

Orthogonal Frequency Division Modulation N carriers Symbol: 2 periods of f0

Transmit

+

f

Symbol: 4 periods of f0

f B Symbol: 8 periods of f0

Channel frequency response

Data coded in frequency domain Transformation to time domain: each frequency is a sine wave in time, all added up.

Decode each frequency bin separately Receive time

f B

Time-domain signal

Frequency-domain signal

OFDM uses multiple carriers to modulate the data N carriers

Frequency

Time-frequency grid

B

Data

Carrier

f0

B Features – No intercarrier guard bands – Controlled overlapping of bands – Maximum spectral efficiency (Nyquist rate) – Easy implementation using IFFTs – Very sensitive to freq. synchronization

T=1/f0

One OFDM symbol Time

Intercarrier Separation = 1/(symbol duration)

Modulation technique A user utilizes all carriers to transmit its data as coded quantity at each frequency carrier, which can be quadrature-amplitude modulated (QAM).

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OFDM Modulation and Demodulation using FFTs d0 b0 d1 P/S IFFT b1 d2 d0, d1, d2, …., dN-1 b2 Inverse fast d3 Parallel to . Fourier transform . serial converter . Transmit time-domain . f . samples of one symbol . . . time bN-1 dN-1 Data coded in Data in time domain: frequency domain: one symbol at a time one symbol at a time

d0’ d1’ d2’ . . . . dN-1’

S/P

d0’, d1’, …., dN-1’

Receive time-domain samples of one symbol

Serial to parallel converter

time

Decode each b0’ frequency bin b1’ independently b2’ . . f . . bN-1’

FFT Fast Fourier transform

Loss of orthogonality (by frequency offset) ψ k (t) = exp( jk 2π t / T ) y ψ k +m ( t) = exp ( j2π (k + m )t / T )

Transmission pulses

ψ k+ m (t) = exp ( j2π (k + m + δ ) / T ) con δ ≤ 1 / 2 δ

Reception pulse with offset δ

Interference between channels k and k+m

I m (δ) =

Summing up ∀m

π m+δ

∑I m

N −1

2 m

(δ ) ≈ (Tδ)2 ∑ m =1

1 23 ≈ (Tδ )2 14 m2

-10

m=1

-20

m=3 m=5 m=7

-50

Asymetric

-70 -0.4

-0.3

-0.2

0

-0.1 0.1 Frequency offset: ∂

j 2π(m + δ )

N >> 1 (N > 5

Is enough )

Total ICI due to loss of orthogonality

-40

-60

for

T (1 − exp(− j2πδ ))

-10 -15 δ =0.05 -20 -25 δ =0.02 -30 δ =0.01 -35 δ =0.005 -40 Practical -45 δ =0.002 δ assumed r.v. -50 δ =0.001 Gaussian σ=δ -55 -60 2 4 6 8 10 12 14 16 Carrier position within the band (N=16) ICI in dB

Interference: Im(? )/T en dB

T

0

Loss for 8 carriers

0

-30

T sin πδ

I m (δ ) = ∫ exp( jk2πt / T ) exp(− j(k + m + δ )2πt / T )dt =

0.2

0.3

0.4

limit

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Loss of orthogonality (time) Let us assume a misadjustment τ

Then if m=k-l

Xi = c 0 ∫

− T /2+ τ −T /2

ψ k (t )ψ l (t − τ )dt + c 1 ∫ *

τ  senmπ 2 T T , c ≠c 0 1 Xi =  mπ  0, c0 = c1 

In average, the interfering power in any carrier is

X 2 E i2  T

T/ 2

independent on m

τ  2  , τ << T  T Per carrier

ICI ≈ 20log

2 2  1 τ 1 τ  = 4 T  2 + 0 2 = 2 T  

ICI due to loss of orthogonaliy 45

Doubling N means 3 dB more ICI

40

m=1

35 ICI in dB

Interference en dB

τ Xi 2mπ T τ ≈ =2 T T mπ

Or approximately, when τ<
Loss for 16 carriers 0 -5 -10 -15 -20 -25 -30 -35 -40 -45 -50 0

2 consecutive symbols

ψ k (t )ψ l (t − τ )dt *

−T / 2+τ

m=5 m=10

τ assumed an Uniform r.v.

30 25

Max. practical limit

N=8

20 15

0.1

0.2

Zone of interest

0.3 0.4 0.5 0.6 0.7 Relative misadjustment τ

0.8

0.9

1

10 0

N=64

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Typical deviation for the relative misadjustment

Including a “cyclic prefix” To combat the time dispersion: including ‘special’ time guards in the symbol transitions co p y

Furthemore it converts Linear conv. = Cyclic conv.

CP τ

(Method: overlap-save)

T Tc

Without the Cyclic Prefix

Including the Cyclic Prefix

Symbol: 8 periods of fi

Initial transient

Channel:h(n )=(1 ) – n / n

n =0 , …,2 3

≠Ψ i(t)

Loss of orthogonality

Decaying transient

Symbol: 8 periods of fi

Passing the channel h(n)

Passing the channel h(n)

CP Ψi(t)

Ψi(t)

Initial transient remains within the CP

The inclusion of a CP maintains the orthogonality

Ψj (t)

Ψ j(t)

Symbol: 4 periods of fi

Final transient remains within the CP

Symbol: 4 periods of fi

CP functions: – It acomodates the decaying transient of the previous symbol – It avoids the initial transient reachs the current symbol

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Cyclic Prefix

Tg

T

Multi-path components

τmax Tx

T

Sampling start

802.11a System Specification t1 t2 t3 t4 t5 t6 t7 t8 t9 t10

GI2

Short training sequence: AGC and frequency offset l l l l l

T1

T2

GI

OFDM Symbol

GI

OFDM Symbol

Long training sequence: Channel estimation

Sampling (chip) rate: 20MHz Chip duration: 50ns Number of FFT points: 64 FFT symbol period: 3.2µs Cyclic prefix period: 16 chips or 0.8µs » Typical maximum indoor delay spread < 400ns » OFDM frame length: 80 chips or 4µs » FFT symbol length / OFDM frame length = 4/5

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Modulation scheme » QPSK: 2bits/sample » 16QAM: 4bits/sample » 64QAM: 6bits/sample

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Coding: rate ½ convolutional code with constraint length 7

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Frequency diversity using coding Random errors: primarily introduced by thermal and circuit noise. Channel-selected errors: introduced by magnitude distortion in channel frequency response. Data bits

Frequency

Time-frequency grid

B

Bad carriers

f0

f Frequency response

T=1/f0

Time

Errors are no longer random. Interleaving is often used to scramble the data bits so that standard error correcting codes can be applied.

Spectrum Mask Power Spectral Density

-20 dB -28 dB

-40 dB

-30

-20

-11 -9

f carrier

9 11

20

30 Frequency (MHz)

• Requires extremely linear power amplifier design.

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Adjacent Channel and Alternate Channel Rejection Date rate 6 Mbps

M inimum Sensibility -82 d B m

Adjacent Channel Rejection 16 dB

Alternate Channel rejection 32 dB

12Mbps

-79 d B m

13 dB

29 dB

24Mbps

-74 d B m

8 dB

24 dB

36Mbps

-70 d B m

4 dB

20 dB

54Mbps

-65 d B m

0 dB

15 dB

32 dB blocker

16 dB blocker

Signal

Frequency

• Requires joint design of the anti-aliasing filter and ADC.

OFDM Receiver Design Yun Chiu, Dejan Markovic, Haiyun Tang, Ning Zhang EE225C Final Project Report, 12 December 2000

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OFDM System Block Diagram

Synchronization l

Frame detection

Frame start

Tg

T

l

Frequency offset compensation

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Sampling error » Usually less 100ppm and can be ignored – 100ppm = off 1% of a sample every 100 samples

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System Pilot Structure

IEEE 802.11a OFDM Txer Short Preamble Gen.

Long Preamble Gen.

OFDM Data Path 10 x 0.8 = 8 uS 1 2

3

4

5 6

7

2 x 0.8 + 2 x 3.2 = 8 uS 8

9 10

GI2

T1

T2

Signal Detection, AGC, Channel & Fine Freq. Diversity Selection Offset Estimation Coarse Freq. Offset Est.,Timing Sync.

0.8 + 3.2 = 8 uS 0.8 + 3.2 = 8 uS 0.8 + 3.2 = 8 uS GI

Signal

Rate, Length

GI

Data

Data

GI

Data

Data

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Short & Long Preambles 1+j

-24

-20 -12 -16

-1-j

f

Short Preamble Period = 16 Chips

+1

-26

-24 -16

-12

f

-1

Long Preamble Period = 64 Chips

Correlation of Short Preamble Correlation Fine Timing

AutoCorrelation Coarse Timing

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Synchronization From AGC

16Td

Td

Td

* Td

Td

* Td

Td

... T ... * * d

...

Σ

Moving AutoCorr. Unit

Td From AGC

Td

Moving SP Corr. Unit

Td

*

Td

*

... T ... * * d

Σ

... Short Preamble (LUT)

Impairments: Multi-Path Channel Tc 0

0

2T T

T

0 2T

t

0

T

T

2T

3T

4T

0

0

T

t c

Ch. Impulse Response

2T

t

T

3T

3T

t

4T

4T

T

t

t

5T

0 2T

3T

4T

t

c

t

T

2T

3T

5T

4T

t 5T

Auto-Correlation w/ Multi-Path Channel Response.

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Impairments: Frequency Offset

0

0

T

T

2T

2T

3T

3T

4T

4T

t

t

t

0

T

2T

3T

4T

t

Fine Frequency Offset Est.

Accumulator

Complex Multiplier

Sync. Signal

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0

Coarse-Fine Joint Estimation & Decision Alignment Error Correction π

π 3 4

1

5

8 6

0

π

Average over 64 chips

π B A C D

−π

7

0

π

π

Average over 16 chips

2

0

0

Coarse

Fine

Folding Signal

π 0

Vin

Folding ADC

±100ppm ∆fc @ 5.8GHz

0

π

0

π

Frequency Offset Compensation

Decision Alignment

Channel

Joint CoarseFine Est. Offset Corr.

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Performance Summary Parameters

Metrics

Number of sub-carriers

48 data +4 pilot

OFDM symbol freq.

4 µs

Modulation Scheme

BPSK up to 64-QAM

Sampling clock freq.

20 MHz

Sync. Frame Start Accuracy Freq. Offset Est. Range

≤ 8 chips (CP = 16 chips) ± 5π = ± 100ppm @ 5.8 GHz

Freq. Offset Est. Accuracy

1% (@ 15dB SNR)

Critical path delay

12.7 ns

Silicon area

397,080 µm2

Total power consumption

3.4 mW @ 20 MHz

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