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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 ㎳
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