e225c – lecture 16 ofdm introduction ee225c. multipath can be described in two domains: time and...

E225C – Lecture 16OFDM Introduction

EE225CEE225C

Multipath can be described in two domains: time and frequency

time

time

Sinusoidal signal as input

time

time

Sinusoidal signal as output

f

Frequency response

Time domain: Impulse response

Frequency domain: Frequency response

time

Impulse response

timetime

Modulation techniques: monocarrier vs. multicarrier

To improve the spectral efficiency:

To use orthogonal carriers (allowing overlapping)Eliminate band guards between carriers

– Selective Fading

– Very short pulses

– ISI is compartively long

– EQs are then very long

– Poor spectral efficiency because of band guards

Drawbacks

– It is easy to exploitFrequency diversity

– Flat Fading per carrier

– N long pulses

– ISI is comparatively short

– N short EQs needed

– Poor spectral efficiency because of band guards

Advantages

Furthermore

– It allows to deploy2D coding techniques

– Dynamic signalling

N carriers

B

Pulse length ~ N/B

Similar toFDM technique

– Data are shared among several carriers and simultaneously transmitted

B

Pulse length ~1/B

– Data are transmited over only one carrier

Channel

Guard bands

Channelization

Orthogonal Frequency Division Modulation

Data coded in frequency domain

N carriers

B

Transformation to time domain:each frequency is a sine wavein time, all added up.

f

Transmit

Symbol: 8 periods of f0



+

Receivetime

B

Decode each frequencybin separately

Channel frequencyresponse

f

f

Time-domain signal Frequency-domain signal

OFDM uses multiple carriersto modulate the data

N carriers

B

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).

Intercarrier Separation = 1/(symbol duration)

– No intercarrier guard bands– Controlled overlapping of bands– Maximum spectral efficiency (Nyquist rate)

– Very sensitive to freq. synchronization– Easy implementation using IFFTs

Features

Data

Carrier

T=1/f0Time

f0B

Fre

quen

cy

One OFDM symbol

Time-frequency grid

OFDM Modulation and Demodulation using FFTs

b0b1b2....bN-1

Data coded infrequency domain:one symbol at a time

IFFT

Inverse fastFourier transform

Data in time domain:one symbol at a time

d0d1d2d3....dN-1

time

f

P/S

Parallel toserial converter

Transmit time-domainsamples of one symbol

d0, d1, d2, …., dN-1

Receive time-domainsamples of one symbol

d0’, d1’, …., dN-1’ S/P

Serial toparallel converter

d0’d1’d2’....dN-1’

time

FFTFast Fouriertransform

b0’b1’b2’....bN-1’

f

Decode eachfrequency binindependently

Loss of orthogonality (by frequency offset)

k (t) exp( jk2t /T ) y km( t)exp j2 (k m)t /T

km (t) exp j2 (k m ) / T con 1/ 2

Transmission pulses

Reception pulse with offset

2 4 6 8 10 12 14 16-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

Total ICI due to loss of orthogonality

Carrier position within the band (N=16)

ICI

in d

B =0.05

=0.02

=0.01

=0.005

=0.002

=0.001

Practical limit assumed r.v.Gaussian =

0-0.4 -0.3 -0.2 -0.1 0.1 0.2 0.3 0.4

Frequency offset:

Inte

rfe

renc

e:

Im(Ž

)/T

en

dB

Loss for 8 carriers

m=1

m=3m=5m=7

-70

-60

-50

-40

-30

-20

-10

0

Im( ) exp jk2t /T exp j(k m )2t / T dt0

T

T 1 exp( j2 )

j2(m )

Im () T sin m

Im2 ()

m T 2 1

m 2m1

N 1

T 2 2314

for N 1 (N 5 Is enough)

Interference betweenchannels k and k+m

Summing upm

Asymetric

Loss of orthogonality (time)

X i c0 k (t) l* ( t )dt

T / 2

T / 2

c1 k (t) l* (t )dt

T / 2

T / 2

Let us assumea misadjustment

2 consecutivesymbols

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.0810

15

20

25

30

35

40

45

Typical deviation for the relative misadjustment

ICI

in d

B

N=8

N=64

ICI due to loss of orthogonaliy

assumed an Uniform r.v.

Max. practical limit

Doubling N means 3 dB more ICI

EXi

2

T 2

4

T

2 1

2 0

1

22

T

2 ICI 20log 2T

, T

Per carrier

In average, the interferingpower in any carrier is

XiT

2m

Tm

2T

Or approximately,when <<T

independenton m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Relative misadjustment

Inte

rfe

ren

ce

en

dB

Loss for 16 carriers

m=1

m=5

m=10

Then Xi 2T

senmT

m, c0 c1

0, c0 c1

Zone of interest

if m=k-l

Including a “cyclic prefix”

CP

Pas

sin

g t

he

chan

nel

h(n

)

i(t)

j(t)

h(n)=(1)–n/n n=0,…,23

j(t)

i(t)

i(t)

To combat the time dispersion: including ‘special’ time guards in the symbol transitions

CP

TTc

copyFurthemore it converts Linear conv. = Cyclic conv.

(Method: overlap-save)

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

Including the Cyclic Prefix

Symbol: 8 periods of fi


Initial transientremains within

the CP

Final transientremains within

the CP

The inclusion of a CPmaintains the orthogonality

Pas

sin

g t

he

chan

nel

h(n

)

Initial transient Decaying transient

Channel:



Without the Cyclic Prefix

Loss of orthogonality

802.11a System Specification

Sampling (chip) rate: 20MHz Chip duration: 50ns Number of FFT points: 64 FFT symbol period: 3.2s Cyclic prefix period: 16 chips or 0.8s

» Typical maximum indoor delay spread < 400ns» OFDM frame length: 80 chips or 4s» FFT symbol length / OFDM frame length = 4/5

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

Coding: rate ½ convolutional code with constraint length 7

GI2 T1 GI OFDM Symbol GI OFDM SymbolT2t1 t2 t3 t4 t5 t6 t7 t8 t9 t10

Short training sequence:AGC and frequency offset

Long training sequence:Channel estimation

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

Bad carriers

T=1/f0Time

f0

B

Fre

qu

en

cy

Time-frequency grid

Frequency response

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

f

Spectrum Mask

Frequency (MHz)f carrier

Power Spectral Density

9 11 20 30-9-11-20-30

-20 dB

-28 dB

-40 dB

• Requires extremely linear power amplifier design.

Adjacent Channel and Alternate Channel Rejection

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

Daterate

MinimumSensibility

Adjacent ChannelRejection

AlternateChannel rejection

6 Mbps -82 dBm 16 dB 32 dB

12Mbps -79 dBm 13 dB 29 dB




16 dB blocker

32 dB blocker

Signal Frequency

OFDM Receiver Design

Yun Chiu, Dejan Marković, Haiyun Tang, Ning Zhang

EE225C Final Project Report, 12 December

2000

Introduction to OFDM Basic idea

» Using a large number of parallel narrow-band sub-carriers instead of a single wide-band carrier to transport information

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

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

amplifier at the transmitter Adopted for various standards

– DSL, 802.11a, DAB, DVB

Data set to be encoded on sub-carriers

IFFT at transmitter

FFT at receiver

OFDM Signal Representation

Cyclic Prefix

Tg T

max

Tx

Multi-path components

TSampling start

OFDM System Block Diagram

Synchronization

Frame detection

Frequency offset compensation

Sampling error » Usually less 100ppm and can be ignored

– 100ppm = off 1% of a sample every 100 samples

Tg TFrame start

Channel Estimation

0 20 40 60 80 100 1200

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Multipath propagation distance

A

Simulated multipath components on 3rd floor of Soda Hallfrom transmitter (26, 18) to receiver (9, 22.5)

Channel Estimation

0 20 40 60 80 100 1200

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Multipath propagation distance

A

Simulated multipath components on 3rd floor of Soda Hallfrom transmitter (26, 18) to receiver (9, 22.5)

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

x 107

0

0.005

0.01

0.015

0.02

0.025

0.03

Hz

Simulated channel frequency response from (26, 18) to (9, 22.5)

System Pilot Structure

Synchronization, Frequency

Offset Compensation

Outline

• IEEE 802.11a OFDM Transmitter Model

• Receiver Synchronization Module A Robust Double Correlation (Correlation & Auto-

Correlation) Based Algorithm

• Receiver Frequency Offset Estimation Module A Coarse-Fine Joint Estimation Algorithm with Decision-

Alignment Error Correction

• Receiver Frequency Offset Compensation Module

• Performance Summary

IEEE 802.11a OFDM Txer

Short Preamble Gen.Long Preamble Gen.

OFDM Data Path

Signal Data Data21 4 73 5 986 T1GI2 GIGI GI10

Signal Detection, AGC,Diversity Selection

10 x 0.8 = 8 uS

T2

2 x 0.8 + 2 x 3.2 = 8 uS

Channel & Fine Freq.Offset Estimation

Coarse Freq. OffsetEst.,Timing Sync.

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

Rate, Length Data Data

Short & Long Preambles

f-24

1+j

-20

-16-12

-1-j

f-1

-16

-26

+1

-24

-12

Short Preamble

Long Preamble

Period = 16 Chips

Period = 64 Chips

Correlation of Short Preamble

Correlation

Coarse Timing

Fine Timing

Auto-Correlation

Synchronization

16Td

* S

Td Td Td...

* * *...

Td Td Td Td...

Td

From AGC

* S

Td Td Td...

* * *...

Short Preamble (LUT)

...

Td

From AGC

Moving Auto-Corr. Unit

Moving SP Corr. Unit

Impairments: Multi-Path Channel

tT

0 2T

t

0

t

0T

2T3T

4T

Tc

Tc

Ch. Impulse Response

t

0

t

0T

2T3T

4T Tc

t5T

T2T

3T4T

t

0T

2T3T

4T5T

t

t

0T

2T3T

4T5T

Auto-Correlation w/ Multi-Path Channel Response.

Impairments: Frequency Offset

t

0T

2T3T

4T

t

0T 2T

3T4T

t

t

0T

2T3T

4T

Fine Frequency Offset Est.

Complex Multiplier

Sync. Signal

Accumulator

Coarse-Fine Joint Estimation & Decision Alignment Error Correction

00

0

0

1

23

76

4

85

0

AD

BC

Vin

Folding Signal

0

0 0 Folding ADC

Coarse Fine ±100ppm fc @ 5.8GHz

Average over 16 chips

Average over 64 chips

Frequency Offset Compensation

Joint Coarse-Fine Est.

Offset Corr.

Decision Alignment

Channel

Performance Summary

Parameters MetricsNumber of sub-carriers 48 data +4 pilot

OFDM symbol freq. 4 s

Modulation Scheme BPSK up to 64-QAM

Sampling clock freq. 20 MHz

Sync. Frame Start Accuracy 8 chips (CP = 16 chips)

Freq. Offset Est. Range ± 5 = ± 100ppm @ 5.8 GHz

Freq. Offset Est. Accuracy 1% (@ 15dB SNR)

Critical path delay 12.7 ns

Silicon area 397,080 m2

Total power consumption 3.4 mW @ 20 MHz

e225c – lecture 16 ofdm introduction ee225c. multipath can be described in two domains: time and...

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