Adaptive Channel Estimator Design for OFDM-Based Wireless Communication Systems

klapdorothypondMobile - Wireless

Nov 23, 2013 (3 years and 8 months ago)

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Adaptive Channel Estimator Design for


OFDM
-
Based Wireless Communication Systems




Reporter
: Yen
-
Ming
Huang


Date
: 2012 .
11
.
22


Outline


Motivation


Introduction


Interpolation Criterion in Frequency Domain


Interpolation Criterion in Time Domain


Adaptive Channel Estimator Design


Conclusions


Reference


2

Motivation


The
goal
is to develop an adaptive channel estimator in light
of practical
concerns according to wireless channel
characteristics.







3

Wireless
Channel

RX

TX


Multipath Propagation Delay


Doppler Shift

Introduction

4

Outline


Motivation


Introduction


Interpolation Criterion in Frequency Domain


Linear Interpolation Criterion


DFT
-
Based Interpolation with Virtual Subcarriers


Time Domain Threshold Selection


Edge Effect Mitigation


Interpolation Criterion in Time Domain


Adaptive Channel Estimator Design


Conclusions


Reference


5

Linear Interpolation Criterion

6

[ ] , 1~
LS CP
h n n N


Based on the estimated
CIR within CP length


SNR

1
0
( ) ( ) .........CIR
L
i l
l
h a
  


 

1
2
0
( ).........CFR
l
L
j f
i
l
H f a e
 






2 3
1
0
1 1 1
0 0 0
(2 ) (2 )
( ) 1 2
2!3!
1 2 2 ( )
L
l l
l l
l
L L L
l l l l l
l l l
f f
H f a j f j
a j f a j a f
 

  


  
  
 
    
 
 
   

  
2
( 2 )
2
arg max
2!
l
l
l
f
j
a C
 


1 1 1
2
0 0 0
( 2 ) 2
2!2 2
L L L
l
l l l l
l l l
a
f f
j a j a C
   
  
  
 
 
  
High SNR


Edge Effect


Complexity Increasing

Linear Interpolation Criterion

7

Path

1

Path

2


Path

3


Path

4


Path

5


Path

6


Path

7


Path

8


Path

9


EPA



0

0.0188



0.0814

0.1069

0.0505

0.0181

0.0368

EVA

0

0.0000

0.0004

0.0010

0.0027

0.0014

0.0054


0.0043

0.0030


ETU

0

0.0000

0.0002

0.0007

0.0009

0.0043

0.0223

0.0291

0.0867

Ratio

EPA

0.0001524

EVA

0.0076

ETU

0.0512

0
2
4
6
8
10
12
14
16
18
20
10
-3
10
-2
10
-1
10
0
Eb / No [ dB ]
MSE of Channel Estimation
Linear Interpolation in Frequency Domain (QPSK)


EPA
EVA
ETU
2
( 2 )
2
arg max 0.02
2!
l
l
l
f
j
a C
 

 
1 1 1
2
0 0 0
( 2 ) 2 0.02
2!2 2
L L L
l
l l l l
l l l
a
f f
j a j a C
   
  
  
 
  
  
10
3


10
3


10
3


10
3


10
3


10
3


DFT
-
Based Interpolation with Virtual Subcarriers

8

λ

In practical, the temperature and the bandwidth are
known to receiver. Therefore, we may have the
information of noise in advance.

2
~ (0,)
AWGN Nm

0
0 0
1 1
S
SNR N
N N SNR
   
2
1
0
1
, 0,1,,1
P
P
j ki
N
N
i k P
k
P
z Z e i N
N



  

1
2
2 2
2
2
0
1 1 1
P
N
p i k
k
P P P
E z Z
N N N SNR




 
    
 

2 2
1 1
0 0
1 1
, 0,1,,1
P P
P P
j ki j ki
cN N
cN cN
i k k P
k k
P P
z Z e Z e i cN
cN cN
 
 
 
   
 
1
2
2 2
2
2 2 2 2
0
1 1 1
P
N
p i k
k
P P P
E z Z
c N c N c N SNR




 
    
 

Noise Power

P
N
P
cN
Time Domain Threshold Selection



9

Method 1

The real and the imaginary part of noise
follow Gaussian probability distribution.









ˆ
ˆ
Re ( ) , for Re ( )
Re ( )
ˆ
0 , for Re ( )
h n h n
h n
h n


















ˆ
ˆ
Im ( ) , for Im ( )
Im ( )
ˆ
0 , for Im ( )
h n h n
h n
h n










Method 2

Rayleigh probability derived from complex
Gaussian variables is exploited.

2
2
2
( ) 1 , 0...........
x
F x e x CDF


  
2
2
2
( )........... The probability outside th
e threshold.
p
out
P P x e




  
ˆ
ˆ
( ) , for ( )
( )
ˆ
0 , for ( )
h n h n
h n
h n










2
p
 

Although the larger value of threshold can achieve more complete noise reduction, the taps
with slight channel energy will be removed possibly.

2
ln( ) 2
out p
P
 
  
P

0.01

0.02

0.03

0.04

0.05

Out%

5.7%

9.97%

13.71%

17.1%

20.24%

Edge Effect Mitigation

ˆ
( ) , for 1,2,,
2
ˆ
( )
ˆ
( ) , for ,1,,1
2 2
VC
R R R R
P
P P P P P
P
VC VC
L L L L
P P
P P P P P
N
H k k k k k
H k
N N
H k k k k k

 
   

 
  


   

    
   

   

1
ˆ
ˆ
ˆ
ˆ
( ) ( ) ( ) ( ) ,
1
for 1,2,,1
R L R
P P P P P P P
VC
P
R R L
P P P
H k H k H k H k
N
k k k k
 
  
 

   
10

0
500
1000
1500
2000
2500
0
0.5
1
1.5
2
2.5
Subcarrier Index
Amplitude
CFR (EPA)


LI
DFT-Based
DFT-Based+Rep [18]
DFT-Based+LF [21]
Repetition[18]

Linear Fashion[21]

0
2
4
6
8
10
12
14
16
18
20
10
-3
10
-2
10
-1
10
0
Eb / No [ dB ]
MSE of Channel Estimation
Band Edge Subcarriers (EPA)


LI
DFT-Based
DFT-Based+Rep [18]
DFT-Based+LF [21]
Outline


Motivation


Introduction


Interpolation Criterion in Frequency Domain


Interpolation Criterion in Time Domain


Analysis of Time Varying Channel


Approaches to CFO Estimation


Linear Interpolation Criterion


Adaptive Channel Estimator Design


Conclusions


Reference


11

Analysis of Time Varying Channel

12

0
1
2
3
4
5
6
x 10
-4
-16
-14
-12
-10
-8
-6
-4
-2
0
2
Time [Second]
Amplitude [dB]
WINNER D2a Channel with 350km/hr,K=7dB
0
1
2
3
4
5
6
x 10
-4
-1.5
-1
-0.5
0
0.5
1
1.5
2
Time in Second
Phase (rad)
WINNER D2a Channel with 350km/hr,K=7dB
1
( ) ( ) ( )
1 1
LOS Rayleigh
K
h t h t h t
K K
   
 
-60
-40
-20
0
20
40
60
5
10
15
20
25
30
35
Frequency [Hz]
Power Spectrum [dB]
Doppler Spectrum


Jakes Rayleigh Theory
Simulation
0
2
4
6
8
10
12
14
16
18
20
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Eb / No [dB]
BER
Linear Interpolation in Time Domain , Velocity = 300 km/hr


QPSK , Rayleigh
QPSK , Rician Factor = 10dB
16QAM , Rayleigh
16QAM , Rician Factor = 10dB
64QAM , Rayleigh
64QAM , Rician Factor = 10dB
Approaches to CFO Estimation

13

1
*
1
ˆ
arg
2
cp
F n n N
n N
y y





 
 

 
 
 

1
*
0
ˆ
ˆ
ˆ
arg ( [ ]) ( [ ])
2 ( )
P
N
F m D m
j
cp
N
H p j H p j
D N N





 

 
 
 



*
ˆ
ˆ
ˆ
arg ( ) ( )
2 ( )
F LOS LOS
cp
N
h m D h m
D N N


 

offset
I F
f
f
  
  

CP
-
Based Estimator [26]:

Pilot
-
Based Estimator[27]:

LOS
-
Based Estimator [28]:

There are two main causes of distortion associated with the carrier frequency. One is the non
-
coherent up and down frequency conversion accompanied with an unavoidable difference
due to physically inherent nature of the transceiver
oscillators
. The other is caused by
Doppler
shift

due to the transceiver mobility.

Linear Interpolation Criterion

14

0
5
10
15
20
25
30
10
-2
10
-1
10
0
Eb / No [ dB ]
BER
D2a Channel with 350km/hr , K=10dB (64QAM)


No CFO Compensation
CP-Based [26]
Pilot-Based [27]
LOS-Based [28]
0
5
10
15
20
25
30
10
-2
10
-1
10
0
Eb / No [ dB ]
BER
D2a Channel with 200km/hr, K=7dB, OSC=0.02 (64QAM)


No CFO Compensation
CP-Based [26]
Pilot-Based [27]
LOS-Based [28]
2
( ) 1 2
d
j f t
LOS d
h t e j f t


  
2
2
2
(1 2 ) (1 2 )
2
d
d
t
j f
j f t
d d
t
e j f t e j f C


 


     
2
0
( )
l
L
j f t
LOS l
l
h t a e




Most of the maximum Doppler offset can be compensated with the proper schemes in the
Rician

fading
channel. Broadly speaking, the LOS component usually emerges on the first arrival propagation path, and
the
Rician

factor enlarges its weight diminishing the affection of scattered components.

ˆ
2 ( )
2
ˆ
1 2 ( )
2
d d
t
j f f
d d
t
e j f f C





 
   
 
 
Outline


Motivation


Introduction


Interpolation Criterion in Frequency Domain


Interpolation Criterion in Time Domain


Adaptive Channel Estimator Design


Moving Average


DFT
-
Based Transition


Strategies for Large Delay Spread Channel


Conclusions


Reference


15

Moving Average

16

Owing to the performance of linear interpolation highly depends on pilots,
noise reduction on them makes an improvement as expected.

0
1
1
window
slot
N
m i N
m
P P
i
window
N
 




H H
,max
1
min,4
20
window
d slot
N
f T
 
 
 

 
 
 
 
 
 
 
0
5
10
15
20
25
30
10
-4
10
-3
10
-2
10
-1
10
0
Eb / No [ dB ]
MSE
Noise Reduction on Pilots, EPA, 2km/hr, 700MHz


Original
1 Window
2 Windows
3 Windows
4 Windows
Although more MAWs mitigate the effect of noise
evidently, it means the requirement of constant in several
time
-
slots must to be satisfied.

Moving Average

17

0
5
10
15
20
25
30
10
-4
10
-3
10
-2
10
-1
10
0
Eb / No [ dB ]
MSE
Noise Reduction on Pilots, EVA, 30km/hr, 700MHz


Original
1 Window
2 Windows
3 Windows
4 Windows
0
5
10
15
20
25
30
10
-4
10
-3
10
-2
10
-1
10
0
Eb / No [ dB ]
MSE
Noise Reduction on Pilots, EVA, 30km/hr, 2.6GHz


Original
1 Window
2 Windows
3 Windows
4 Windows
0
5
10
15
20
25
30
10
-4
10
-3
10
-2
10
-1
10
0
Eb / No [ dB ]
MSE
Noise Reduction on Pilots, ETU, 120km/hr, 700MHz


Original
1 Window
2 Windows
3 Windows
4 Windows
0
5
10
15
20
25
30
10
-4
10
-3
10
-2
10
-1
10
0
Eb / No [ dB ]
MSE
Noise Reduction on Pilots, ETU, 120km/hr, 2.6GHz


Original
1 Window
2 Windows
3 Windows
4 Windows
DFT
-
Based Transition

18

0
20
40
60
80
100
120
140
160
180
200
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time Index
Amplitude of CIR
Time Domain Processing


LS
Processed
Threshold
0
20
40
60
80
100
120
140
160
180
200
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Pilot Index
Amplitude of CFR
Noise Reduction on Pilots


LS
DFT-Based Transition
Real
When the rise of velocity such that the technique of
Moving Average is unsuitable to use especially at high
SNR, DFT
-
based transition is an alternative way. By
inherent time domain processing, the goal of noise
reduction on pilots can be achieved.

,max
1
min,4 0
20
window
d slot
N
f T
 
 
 
 
 
 
 
 
 
 
 
1
2
2 2
2
2
0
1 1 1
P
N
p i k
k
P P P
E z Z
N N N SNR




 
    
 

0
20
40
60
80
100
120
0
1
2
3
4
5
6
Maximum Doppler Frequency (Hz)
Moving Average Windows
DFT
-
Based Transition

19

0
5
10
15
20
25
30
10
-4
10
-3
10
-2
10
-1
10
0
Eb / No [ dB ]
MSE
Noise Reduction on Pilots, ETU, 120km/hr, 2.6GHz


Original
1 MAW
2 MAWs
DFT-Based Transition
0
5
10
15
20
25
30
10
-4
10
-3
10
-2
10
-1
10
0
Eb / No [ dB ]
MSE
Noise Reduction on Pilots, EVA, 30km/hr, 2.6GHz


Original
1 MAW
2 MAWs
DFT-Based Transition
Strategies for Large Delay Spread Channel

20

In order to make the frequency domain interpolation more robust to such large
delay spread scenario, the time domain interpolation may be performed prior to
the frequency domain interpolation.

0
20
40
60
80
100
120
10
-3
10
-2
10
-1
10
0
Velocity in km/hr
BER
ETU Channel, Noise Free (64QAM)


Freq & Time LI
Time & Freq LI
Mirrored [30]
Merged [31]
Channel Information Acquirement

21

Adaptive Channel Estimator Design

22

Outline


Motivation


Introduction


Interpolation Criterion in Frequency Domain


Interpolation Criterion in Time Domain


Adaptive Channel Estimator Design


Conclusions


Reference


23

Conclusions


In order to accomplish the intention desired, the first and the second term
of Taylor expansion are used as a
criterion of linearity
.



Compared with many proposed methods of time domain processing based
on the information of channel delay length, the proper
threshold selection
according to the known noise power is more rational.



In this study, inspired from
the statistical characteristics of Gaussian noise
,
two schemes of threshold selection have been proposed.



By the reasonable assumptions of time
-
varying channel and the techniques of CFO
compensation, the effect of
Doppler shift
due to mobility can be mitigated
evidently in the
Rician

fading channel. Accordingly, the feasibility of time domain
linear interpolation can be firmly confirmed.


24

Conclusions



To enlarge the usability of linear interpolation, two techniques of
Moving
Average
and
DFT
-
based transition
for noise reduction on pilots have been
proposed.



There
are benefits to adaptability for a low power mobile terminal
due to
the restricted quantity of available processing power.



Given the practical positions taken for the study and the status of the field
as completely introduced above, the goal to provide an adaptive channel
estimator design based on
channel understanding
is achieved.


25

Reference

26

[13] J. J. van de Beek, 0. Edfors, M. Sandell. S. K. Wilson and P. 0.
Borjesson
, “On channel
estimation in OFDM systems,” Proc. IEEE Vehicular Technology Conf. vol. 2, Jul. 1995, pp.
815
-
819.

[18] X.
Hou
, Z. Zhang, and H. Kayama, “Low
-
Complexity Enhanced DFT
-
based Channel Estimation
for OFDM Systems with Virtual Subcarriers,” in Proc. IEEE PIMRC’07, Sep. 2007.

[21]
Szu
-
Lin Su, Yung
-
Chuan Lin,
Chieh
-
Chih

Hsu, and Gene C. H. Chuang, “A DFT
-
based Channel
Estimation Scheme for IEEE 802.16e OFDMA
Systems,”International

Conference on
Advanced Communication Technology, (ICACT10), IEEE Press, 2010, pp.775
-
779.


[26] J. van de
Beek
, M.
Sandell
, and P.
Börjesson
, “ML estimation of timing and frequency offset
in OFDM systems,” IEEE Trans. Signal Processing, vol. 45, no. 7, pp. 1800

1805, Jul. 1997.


[27] F.
Classen

and H.
Meyr
, “Frequency synchronization algorithms for OFDM systems suitable
for communication over frequency selective fading channels,” in Proc. IEEE VTC’94,
Stockholm, Sweden, Jun. 1994, pp. 1655

1659.

[28] L. Yang, G.
Ren
, and Z.
Qiu
, “A novel Doppler frequency offset estimation method for DVB
-
T
system in HST environment,” IEEE Trans. Broadcasting, vol. 58, no. 1, pp. 139

143, Mar. 2012.

[30] F.
Foroughi
, J. Lofgren, and O.
Edfors
, "Channel estimation for a mobile terminal in a multi
-
standard environment (LTE and DVB
-
H)," in Signal Processing and Communication Systems,
2009. ICSPCS 2009. 3rd International Conference, pp. 1
-
9, 2009.


[31] F.
Foroughi
, F.
Sharifabad
, and O.
Edfors
, “Low complexity channel estimation for LTE in fast
fading environments for implementation on Multi
-
Standard platforms,” in proc. IEEE
Vehicular Tech. Conf., Ottawa, September 2010.



27