Synchronization and Channel Synchronization and Channel Estimation in Cyclic Postfix Estimation in Cyclic Postfix

based OFDM Systembased OFDM System

Xian-Xu, Jongkyung-Kim, Sangjin-Lee, and Jongsoo-Seo

Digital Transmission Lab.Digital Transmission Lab.

School of Electrical & Electronics Eng.School of Electrical & Electronics Eng.

YONSEI Univ., Seoul, KOREAYONSEI Univ., Seoul, KOREA

2/13

Contents

Introduction

Cyclic Postfix based OFDM system System model

Generation of cyclic postfix based OFDM symbol

Timing synchronization Coarse synchronization

Fine synchronization

Channel estimation Least square channel estimation in time domain

Frequency domain channel estimation using postfix

Simulation Results

Conclusions

3/13

Introduction (1/2)

Cyclic prefix (CP) OFDM systemFFT size NG

CP symbol k symbol k+1

copy copy

FFT size NG

Contaminated CP by Inter-Block Interference (IBI)

• Converting multi-path fading to circular convolution in OFDM block

• Simple channel estimation by pilot in frequency domain and timing synchronization using CP

CP

Pseudo random postfix OFDM system

• Channel estimation with IBI suppression using pseudo random sequence (postfix) in time domain

FFT size N

symbol k symbol k+1 FFT size N

postfix postfix

G G

IBI from channel delay spread

4/13

Introduction (2/2)

Cyclic postfix based OFDM system

symbol k symbol k+1 postfix postfix

G GFFT size NFFT size N

• FFT(IFFT) operation including postfix

• No inter-block interference due to the guard interval (GI) effect of previous postfix

• Making multi-path fading to cyclic convolution in OFDM block

• Channel estimation both in frequency and/or time domain

• Timing synchronization using postfix

No IBI due to GI effect of previous postfix

5/13

Cyclic postfix based OFDM system

Transmitter of cyclic postfix based OFDM system

Map

pin

gM

app

ing

P/S

P/SS/P

S/P

IFF

TIF

FT

Cyclic PostfixGenerator

Cyclic PostfixGenerator

.

.

.

dX xX

N : FFT sizeG : postfix lengthM : pilot spacing

: frequency domain data symbol [N 1]d X

: frequency domain pilot symbol [G 1]P

: extended pilot symbol [N 1]P X

= : time domain transmit signal [N 1]H x F X

: FFT matrix [N N]F

: IFFT matrix [N N] H F

: input to IFFT [N 1]d p X = X + X

IFFT

···P1 P2 PG ··· p1 p2 pG

time domain OFDM symbolfrequency domain

d pX = X + X = Hx F XM

: time domain postfix [G 1]p

6/13

Cyclic postfix based OFDM system

Cyclic postfix generation

Hd p = F X VP -1 H

dP = V (p - F X )

where

1

2 ,

N G

N GH

N

f

fF

f

1

2H

N

f

fF

f

⇒

2 ( 1)( 1) 2 ( 1)(2 1) 2 ( 1)(( 1) 1) 2 ( 1)( 1)

2 ( 2))( 1) 2 ( 2))(2 1) 2 ( 2))(( 1) 1) 2 ( 2))( 1)

2 ( 1)( 1) 2 ( 1)(2 1) 2

j N G M j N G M j N G G M j N G GM

N N N N

j N G M j N G M j N G G M j N G GM

N N N N

j N M j N M j

N N

e e e e

e e e e

e e e

V

( 1)(( 1) 1) 2 ( 1)( 1)

2 ( )( 1) 2 ( )(2 1) 2 ( )(( 1) 1) 2 ( )( 1)

N G M j N GM

N N

j N M j N M j N G M j N GM

N N N N

e

e e e e

⇒

Frame structure

symbol 1 postfix symbol 2 postfix G

FFT size N

postfix symbol I postfix

7/13

Timing synchronization

Coarse time Fine time

symbol 1 postfix symbol 2 postfix symbol I postfix postfix

auto-correlation

auto-correlation

2

2

( )( )

( )

Ac

A

R nM n

E n

ˆ arg max ( )c cn M n

: normalized auto- correlation metric

: auto-correlation metric

: rx. signal power

1

2 2

1

( ) ( ) ( 1)

1( ) ( ) ( 1)

2

IH

A n ni

I

A n ni

R n i i

E n i i

r r

r r

Estimated coarse time

2

2

( )( )

( )

Cf

C

R nM n

E n

ˆ arg max ( )f fn M n

: normalized cross- correlation metric

: cross-correlation metric

: rx. signal power

0

2

0

( ) ( )

( ) ( )

IH

C n ni

I

C ni

R n i

E n i

p r

r

Estimated fine time

cross-correlation

postfix postfix

cross-correlation

postfix

cross-correlation

postfix

cross-correlation

: i’th received OFDM postfix part( )

[ ] Hi

r

: conjugate transpose

8/13

G G

Channel estimation (1/3)

Postfix design for channel estimation

symbol i symbol i+1

FFT size NFFT size N

… … postfix postfix

Time domain least square channel estimation• 2nd part of received postfix

t circq = p h + w ⇒ 1ˆt

circh = p q

where T0 1 L-1=[ h h h 0 0]

[ ]t

circ

h

a

w

: channel impulse response

: circular matrix of vector a

: AWGN

• Postfix is designed such that exists (rank G/2)

• Performance improvement by noise averaging within a frame

p 1circp

• Instead of IBI cancellation, postfix of length G/2 is repeated twice

– 1st part of postfix as guard interval role

– 2nd part of postfix as a training sequence for channel estimation

9/13

Channel estimation (2/3)

Frequency domain channel estimation using postfix Postfix design

IFFT

···P’1 0 ··· 0P’20 P’3 P’G/20···0 ··· 0 P’G/2-1

2M

FFT sizeN

p1 p2 p3 ···pG/2 p1 p2 p3 pG/2 ··· p1 p2 p3 ···pG/2

2M identical part

G/2

postfix

• P is designed such as frequency domain pilot symbols for channel estimation

FFT

10/13

Channel estimation (3/3)

FFT based channel estimation 2nd part of received postfix : q

circ circ

q p

q pq h + w h p + w

q p

FFT

After 2M repetition of

( ) ( )diag circFq F h p + w H P w

q

1 2where =[ ]TNH H H H Fh

• P’ is treated as a pilot symbols

• H can be obtained by simple pilot based channel estimation

• Comparable performance as conventional pilot based channel estimation

• Hybrid channel estimation using pilot symbols and cyclic known postfix

⇒ P (for postfix generation) + Pi (for pilot symbol based channel estimation)

p1 p2 p3 ···pG/2 p1 p2 p3 pG/2

G/2

··· q

: frequency domain channel response

···P1 0 ··· 0Pi0 P2 PG/20···0 ··· 0 Pi

2M

FFT size N

11/13

Simulation results (1/2)

System configurationCarrier Frequency 2.0 ㎓

System Bandwidth 2.5 ㎒

FFT size 256

Sub-frame duration 0.5 ㎳

Sampling frequency 3.84 ㎒

Number of OFDM symbol per sub-frame 6

GI / postfix length 16,32

Tap

Pedestrian Channel A Pedestrian Channel B Vehicular Channel C

Doppler SpectrumRelative delay

(ns)Average power

(dB)Relative delay

(ns)Average

power (dB)Relative delay

(ns)Average power

(dB)

1 0 0.0 0.0 0.0 0 0.0 Classic

2 110 -9.7 200 -0.9 310 -1.0 Classic

3 190 -19.2 800 -4.9 710 -9.0 Classic

4 410 -22.8 1200 -8.0 1090 -10.0 Classic

5 - - 2300 -7.8 1730 -15.0 Classic

6 - - 3700 -23.9 2510 -20.0 Classic

Channel model

12/13

Simulation results (2/2)

Time synchronization Channel estimation

0 1 2 3 4 5 6 7 8 9 1010

-4

10-3

10-2

10-1

average SNR[dB]

Syn

chro

niza

ton

Err

or R

ate

(SY

ER

)

Cyclic Prefix basedpostfix based coarse timepostfix based fine timepostfix based coarse time - averagingpostfix based fine time - averaging

averaging

• Mobile speed : 60km/h

• Improved performance due to the cross-correlation effect of the postfix and received signal

• N=256, CP length : 16, postfix length : 32

• Similar spectral efficiency

10 15 20 25 30

10-3

10-2

10-1

average SNR[dB]

Bit

Err

or R

ate

(BE

R)

perfect channel estimationfreq. domain - repeated postfix basedfreq. domain - repeated postfix & pilot based (hybrid)time domain - postfix averaging (60km/h)time domain - postfix averaging (5km/h)CP-OFDM pilot based M=8CP-OFDM pilot based M=16

13/13

Conclusions

A new Cyclic Postfix based OFDM system Cyclic postfix at the end of OFDM symbol to prevent inter-block

interference

A simple frequency domain channel estimation by permitting the cyclic convolution of the channel

More precise timing synchronization by exploiting the cross- and auto-correlation of the postfix

Future works Extension to the channel estimation and synchronization in multi-antenna

system by designing different postfix in each antenna

Cell search techniques in multi-cell environment by assigning different postfix to cell

Back up slidesBack up slides

15/13

System model

Channel modeling L’th order FIR filter (L≤G)

circreceived signal hy = x + w

1

1

2

3

4

5

6

1

1 0 1 2 1

2 1 0 1 2

3 2 1 0 1

4 2 1 0

5

6

7

8

2

2

1 1

L

L

L

L

N

N

N G

N G

G

GN

y

r

r

y

y

y

y

y

y

y

h h h h

y h h h h

y h h h h

y h h h h

y

y

y

y

y

r

y

r

y

y

1

1 2 1 0

1 2 1 0

1 2 1 0

1 2 1 0

1 2 1 0

1 2 1 0

1 2 1 0

1 2 1 0

1

2

1

2

3

4

5

6

1 2 1 0

1 2 1

1

0

1

L

L

L

L

L

L

L

L

L

L

N G

N G

G

G

h h h h

h h h h

h h h h

h h h h

h h h h

h h h h

h h h h

h h h h

h h h h

h

x

x

x

x

x

p

p

h h

x

x

x

h

p

p

1

2

3

4

5

6

7

8

2

1

N

N

N

w

w

w

w

w

w

w

w

w

w

w

T0 1 L-1 circ=[ h h h 0 0] , h ( )circh h

is a circular matrix of : linear convolution cyclic convolution⇒

Frequency domain equalization is possible circh h

16/13

Least square channel estimation

0 1 2 1

1 0 1 2

2 1 0 1

2 1 0 1

1 2

1 1

2 2

3 3

4 4

/ 2 2

/ 2 1

/

1 0

1 2 1 0

1 2 1 0

1 2 1 0 2

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

G

G

G

L

L

L

L

L

L

L

L

p w

p

h h h h

h h h h

h h h h

h h h h

h h h h

h h h h

h h h h

h h

w

p w

p w

p

p

ph h

q

/ 2 2

/ 2 1

/ 2

1 / 2 / 2 1 5 4 3 2

2 1 / 2 / 2 1 5 4 3

3 2 1 / 2 / 2 1 5 4

4 3 2 1 / 2 / 2 1 5

5 4 3 2 1 / 2 / 2 1

5 4 3 2 1 / 2 / 2 1

/ 2 1 5 4 3 2 1

circ

G

G

G

G G

G G

G G

G G

G G

G G

G G

w

w

w

p p p p p p p

p p p p p p p

p p p p p p p

p p p p p p p

p p p p p p p

p p p p p p p

p p p p p p p

h p w

1

2

3

4

/ 2 2

/ 2 / 2 1

/ 2 / 2 1 5 4 3

0

2

1

1

2

1

/ 2

0

0

circ t

G

G

G G G

L

L

w

w

w

w

w

w

p p p p p w

h

h

p p

h

h

p h w

17/13

Bandwidth efficiency

N = 256

CP-OFDM

G = 16, Freq. pilot Spacing (Δf)

5 6 8 10 12

0.7529 0.7843 0.8235 0.8471 0.8624

Cyclic postfix based

OFDM

Postfix length (G) Postfix & pilot (hybrid)

16 32 64G = 32

Δf = 8

G = 32

Δf = 16

0.9375 0.875 0.75 0.75 0.8125

18/13

Simulation Environment

System comparison

CP based OFDM (3GPP LTE) Cyclic Postfix based OFDM

Sampling frequency 3.84 ㎒

Sampling time 0.2604 ㎲

FFT signal duration 0.2604 * 256 = 66 ㎲

GI length 64 samples, 16.67 ㎲ (long CP)16 samples, 4.17 ㎲

32 samples, 8.3 ㎲

OFDM symbol length 66 + 16.37 = 83.336 ㎲66 + 4.17 = 70.82 ㎲

66 + 8.3 = 75 ㎲

Sub-frame duration 83.336 ⅹ 6 = 0.5 ㎳ 70.82 ⅹ 6 + 4.17 = 0.43 ㎳

75 ⅹ 6 + 8.3 = 0.458 ㎳

Doppler frequency (fm) 150km/h ⇒ 277.7㎐

Coherence time 0.423 / fm = 1.522 ㎳