Channel Estimation in
Filter Bank-based Multicarrier Systems:
Fundamentals and Recent Advances
Eleftherios Kofidis
Computer Technology Institute, Greece
University of Piraeus, Greece
31 Aug. 2015 CentraleSupelec, Rennes 2
Future mobile networks – Vision and
needs
High
data rate
reliability
QoS
in demanding transmission scenarios
Increased flexibility
Efficient use of fragmented spectrum
Robustness to asynchronism
Co-existence of different systems (HetNets)
…
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Toward a new PHY – Modulation Is OFDM an adequate solution?
Poor spectral containment
Bandwidth/power inefficiency
Challenging synch in multi-access
Sensitivity to severe dispersions
…
FBMC: an attractive alternative Good spectral (/time) containment
High spectral (/power) efficiency
Flexibility (e.g., for multi-mode comms)
Relaxed synch requirements
Able to cope with severe multipath (e.g., large cells) and high mobility
…
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FBMC research and applications
Filter bank-based multi-carrier modulation:
• FBMC/OQAM
• FMT
• GFDM
• UFMC
• …
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FBMC research and applications
Filter bank-based multi-carrier modulation:
• FBMC/OQAM
• FMT
• GFDM
• UFMC
• …
• Max. spectral efficiency
• Time-freq. localization
• Robust to lack of synch
• But: Intrinsic interference
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FBMC/OQAM challenges - Solutions
Intrinsic ISI/ICI
Frequency / time selective subchannels
Challenges in Channel Estimation (CE)
Classical assumption: channel of low freq./time selectivity CE analogous (similar) to OFDM Preamble/pilots design for increased accuracy
However: in many realistic scenarios Severe performance error floors outperformed by OFDM at higher SNRs
More recently: CE training and techniques for demanding channels
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Outline Fundamentals of FBMC/OQAM
System model
Intrinsic interference effect
FBMC/OQAM CE fundamentals
Preamble-based
Pilot-based
Preamble-based CE
Low frequency selective channels
Highly frequency selective channels
Simulation examples
Additional results - on-going/future work
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FBMC/OQAM vs. OFDM/QAM
1 2F
complex QAM
real
imaginary
F=1/T: sub-carrier spacing
T: OFDM/QAM symbol
duration
T-F density:
OFDM/QAM (without CP): 1/(TF)=1
OFDM/OQAM:
Spectral efficiency (e.g., (O)QPSK):
OFDM/QAM (without CP): 2/(TF)=2
OFDM/OQAM:
1 2F
1/ 2F
Phase space
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Offset-QAM Modulation (staggering)
Re
Im
2
2 z-1
+d2k,n
c2k,m
Im
Re
2
2 z-1
+d2k+1,n
c2k+1,m
even sub-carriers
odd sub-carriers
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FBMC/OQAM Transmitter
IFFT
2
0 ( )A z
2
1( )A z
2
1( )MA z
2M
2M
2M
1z
1z
0,n
0,n
1,n
1,M n
1,M n
1,n
0,nd
1,nd
1,M nd
C2R
C2R
C2R
OQAM modulation Transform blockPolyphase
filtering
P/S
conversion
SFB:
P. Siohan et al., “Analysis and design of OFDM/OQAM systems based on filterbank theory,”
IEEE Trans. SP, May 2002.
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FBMC/OQAM Receiver
2
0 ( )B z
2
1( )B z
2
1( )MB z
FFT
1z
1z
2M
2M
2M
Subchannel
processing
Subchannel
processing
Subchannel
processing
*
0,n
*
1,n
*
1,M n
*
0,n
*
1,n
Re
*
1,M n
0,nd
1,nd
1,M nd
Re
Re
R2C
R2C
R2C
S/P
conversion
Polyphase
filteringTransform block OQAM demodulation
AFB:
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System model (1)
M: #subcarriers
K: overlapping factor
g: prototype filter (length )
C2R SFB h + AFB
Intrinsic interference:
13 March 2014 Patras (ENDECON) 15
Intrinsic interference in FBMC/OQAM
1,1,11,1
1,1,11,1
1,,1,
1,1,11,1
1,0,01,0
nMnMnM
nknknk
nknknk
nknknk
nnn
ddd
ddd
ddd
ddd
ddd
13 March 2014 Patras (ENDECON) 16
Intrinsic interference in FBMC/OQAM
With good TF localization,contributions to intrinsicinterference only come from thefirst-order neighboring TFpoints
1,1,11,1
1,1,11,1
1,,1,
1,1,11,1
1,0,01,0
nMnMnM
nknknk
nknknk
nknknk
nnn
ddd
ddd
ddd
ddd
ddd
13 March 2014 Patras (ENDECON) 17
Intrinsic interference in FBMC/OQAM
With good TF localization,contributions to intrinsicinterference only come from thefirst-order neighboring TFpoints
1,1,11,1
1,1,11,1
1,,1,
1,1,11,1
1,0,01,0
nMnMnM
nknknk
nknknk
nknknk
nnn
ddd
ddd
ddd
ddd
ddd
13 March 2014 Patras (ENDECON) 18
Example – “PHYDYAS filter”
FBMC/OQAM TMUX transfer function (interference function):
( - Even k
- after “de-phasing” ( ) to bring into the form
- before that: green real, brown imaginary OQAM ! )
time
freq.
n-4 n-3 n-2 n-1 n n+1 n+2 n+3 n+4
k-1 j0.005 -j 0.043 j0.125 -j0.206 j0.239 -j 0.206 j0.125 -j0.043 j0.005
k 0 j0.067 0 j0.5644 1 -j0.5644 0 -j0.067 0
k+1 -j0.005 -j0.043 -j0.125 -j 0.206 - j0.239 -j0.206 -j0.125 -j 0.043 -j0.005
*
, k n
k n j
, , , k n k nd ju k
• N. J. Fliege, “DFT polyphase transmultiplexer filter banks with effective reconstruction,” EUSIPCO 1992.
• C. S. Lee and K. Y. Yoo, “Polyphase filter-based OFDM transmission system,” VTC-2004 (Fall).
13 March 2014 Patras (ENDECON) 19
More examples
IOTA filter
Bregović-Saramäki filter
P. Siohan and C. Roche, IEEE Trans. SP, Dec. 2000.
M. G. Bellanger, ICASSP-2001.
R. Bregović and T. Saramäki, IEEE Trans. SP, Aug. 2005
PHYDYAS filter
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System model (2) Common assumptions (locally freq./time-invariant channel):
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System model (2) Common assumptions (locally freq./time-invariant channel):
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System model (2) Common assumptions (locally freq./time-invariant channel):
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System model (2) Common assumptions (locally freq./time-invariant channel):
OFDM-like
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System model (2) Common assumptions (locally freq./time-invariant channel):
OFDM-like
colored
virtual Tx symbol
(pseudo-symbol)
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Preamble-based channel estimation (1)
Control / Data
Pre
am
ble
Frame: SFB
non-z
ero
part
0 0
prevents interference
from previous frame
(often unnecessary!)
prevents interference
from control/data
channel time invariant
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Preamble-based channel estimation (2)
Control/Data
Pre
am
ble
Full
(block-type):
Control/DataSparse
(comb-type):
0
0
protect from ICI
Scattered pilot-based channel estimation Help (auxiliary) pilot
31 Aug. 2015 CentraleSupelec, Rennes 28
J.-P. Javaudin, D. Lacroix, and A. Rouxel, VTC-2003 (Spring).
1,1,11,1
1,1,11,1
1,,1,
1,1,11,1
1,0,01,0
nMnMnM
nknknk
nknknk
nknknk
nnn
ddd
ddd
ddd
ddd
ddd
Interference Approximation Method (IAM):
Interference in a positive role!
Known input interference approximation possible
pseudo-pilots
Choose input so as to maximize pseudo-pilot magnitude
Compute channel estimate (as in OFDM):
31 Aug. 2015 CentraleSupelec, Rennes 30
0,0 0,1 0,2
1,0 1,1 1,2
2,0 2,1 2,2
1,0 1,1 1,2M M M
d d d
d d d
d d d
d d d
C. Lélé et al., “Channel estimation methods for preamble-based OFDM/OQAM modulations,”
European.Trans. Telecomm., 2008.
estimation error
Example: IAM-R
Null side symbols ( base design on middle
symbol only)
Carefully choose signs so as to maximize
pseudo-pilots’ magnitude
31 Aug. 2015 CentraleSupelec, Rennes 31
010
010
010
010
010
010
010
010
31
d
d
d
Idea:
Example:
M=8, OQPSK
More IAM variants – Using imaginary pilots
Idea: Use Imaginary pilots to generate imaginary- or real-valued
pseudo-pilots (of even larger magnitude)
Not a strictly OQAM input!
31 Aug. 2015 CentraleSupelec, Rennes 32
• C. Lélé et al., ICC-2008.
• J. Du and S. Signell, ICC-2009.
• PHYDYAS deliverable D3.1
• E. Kofidis and D. Katselis, EUSIPCO-2011.
00
00
00
00
00
00
00
00
0
0
1
1
1
0
0
0
jd
d
d
jd
d
d
jd
d
00
010
00
010
00
010
00
010
j
j
j
j
11
1
11
1
11
1
11
1
j
jj
j
jj
j
jj
j
jj
IAM-I IAM-C E-IAM-C
1/3 of the subcarriers:
Price for good performance: high PAPR!
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SFB-modulated preambles (magnitudes squared)
Sample no.
• M=256, K=4
• OQPSK
Interf. from data part
Optimal preambles (1)
Preamble optimization:
Minimize MSE subject to transmit power/energy constraint
For low frequency selective channels:
FBMC/OQAM
Block-type: equal pilot tones
Comb-type: equispaced & equipowered
OFDM/QAM (no account for CP energy):
Block-type: DFT matrix column
Comb-type: equispaced & equipowered
31 Aug. 2015 CentraleSupelec, Rennes 34
• D. Katselis et al., IEEE Trans. SP, May 2010.
• E. Kofidis et al., Signal Processing, July 2013.
• C. Mavrokefalidis et al., EURASIP JASP, May 2014 (for relaying networks).
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Highly frequency selective channels
No simplifying assumptions:
D. Kong et al., IEEE TSP, Jan. 2014
E. Kofidis, ICASSP-2014.
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Optimal preambles (2)
Optimization problem:
Problem structure:
E. Kofidis, ICASSP-2014
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Optimal preambles (3)
Block-type preamble:
Complex-valued:
Real-valued:
Simple estimation procedure (for real preamble):
Take the first terms of
Divide them by
31 Aug. 2015 CentraleSupelec, Rennes 38
Optimal preambles (4)
Comb-type preamble ( pilot tones):
Equipowered and equispaced
Estimation procedure:
Prototype filter autocorrelation:
Compute the “weighted” freq. response first:
Compute the “weighted” impulse response via IFFT and
divide by the weights to arrive at the impulse response
estimate:E. Kofidis, ISCCSP-2014
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Simulation example: Comb-type
ITU-VehA channel model error floor
31 Aug. 2015 CentraleSupelec, Rennes 41
More and on-going
Preamble-based CE:
POP etc. [1,3]
MIMO case [2,3,4]
Multiuser case [7]
Longer preambles [5,8]
LMMSE channel estimation [10]
Scattered pilot-based CE:
Extend help pilot idea to highly selective channels
Take into account
virtual (edge) subcarriers [6]
interference from data [6]
1. C. Lélé et al., EW-2007.
2. E. Kofidis and D. Katselis, ICSIPA-2011.
3. E. Kofidis et al., Signal Process., July 2013.
4. E. Kofidis, EW-2015.
5. M. Newinger et al., VTC-2013 (Spring).
6. L. Baltar et al., EUSIPCO-2014.
7. F. Rottenberg et al., ISWCS-2015.
8. E. Kofidis, ISWCS-2015.
9. EMPhAtiC deliverable D3.1
10. L. Caro et al., VTC-2015 (Spring).
…