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Frequency-Domain Channel Estimation for Single-Carrier Transmission in Fast Fading Channels
Tetsuya Yamamoto
Department of Communications Engineering,
Graduate School of Engineering, Tohoku University
Wireless Signal Processing & Networking Workshop
Advanced Wireless Technologies II @Tohoku University 18 February, 2013
Outline
Introduction
Transmission System Model
Frequency-Domain Channel Estimation Schemes
Simulation Results
Conclusion
2
Introduction
Broadband single-carrier (SC) transmissions
– must deal with inter-symbol interference (ISI) arising from the severe
frequency-selectivity of the channel.
Frequency-domain equalization (FDE) [A, B]
– is simple, but effective to combat frequency-selective fading channel.
3
Frequency Channel gain
f
Received signal spectrum
FDE
[A] D. Falconer, et. al., “Frequency domain equalization for single-carrier broadband wireless systems,” IEEE Commun. Mag., Apr. 2002.
[B] F. Adachi, et. al., “Introduction of frequency-domain signal processing to broadband single-carrier transmissions in a wireless channel,”
IEICE Trans. Commun., Sept. 2009.
f
Transmitted signal spectrum FDE weight
f
Equalized signal spectrum
Introduction
SC-FDE is a block transmission and DFT is used at the receiver.
– Cyclic prefix (CP) is often inserted in front of each data block.
» to avoid the inter-block interference (IBI)
» to make the received signal to be a circular convolution of the
transmit signal block and the channel impulse response
4
Time
CP Data CP Data
CP Data CP Data
… …
… …
Direct path
CP-SC
Delayed path
FDE
DFT
Introduction
Instead of CP insertion, a known training sequence (TS) insertion
[C, D] can be used.
– Identical TS is used for all blocks.
– The TS in the previous block acts as the CP in the present block.
– The TS can be utilized for channel estimation.
» No pilot block is needed unlike CP-SC transmission.
5
Time
TS Data TS Data
TS Data TS Data
… …
… …
TS-SC
FDE
DFT
CP Pilot CP Data … … CP-SC CP Pilot CP Data …
TS Data TS Data … … TS-SC TS Data TS Data … TS
[C] L. Deneire, et. al., “Training sequence versus cyclic prefix - a new look on single carrier communication,” IEEE Commun. Lett., July, 2001.
[D] F. Adachi, et. al., “Capacity and BER performance considerations on single-carrier frequency-domain equalization,” Proc. ICICS 2011, Dec. 2011.
Introduction
Conventional channel estimation for TS-SC transmission [E, F]
– TS of 2L-symbol length, which is constructed from a TS of L-symbol
length, is used.
» Interference from the data block can be avoided.
» The channel can be estimated in frequency-domain by exploiting
the circular property of the TS.
We introduce frequency-domain channel estimation schemes
which require a TS of L-symbol length.
6
•L: Channel length
Transmission efficiency reduces.
[E] J. Coon, et. al., “Channel and noise variance estimation and tracking algorithms for unique-word based single-carrier systems,”
IEEE Trans. Wireless Commun., June 2006.
[F] Y. Hou et. al., “Improvement on the channel estimation of pilot cyclic prefixed single carrier (PCP-SC) system,” IEEE Signal Processing Lett., Aug. 2009.
Time
TS Data TS Data
TS Data TS
… …
…
Channel estimation
TS TS
TS TS Data …
Conv. CE
Time
Data TS Data … …
Prop. CE
Channel estimation
TS
Data TS Data … … TS
L symbols L symbols
Transmission System Model
Transmitter and receiver structure
Block structure
– TS can be viewed as a CP of an Nc+Ng-symbol block.
» The received signal is decomposed into Nc+Ng orthogonal
frequency components by applying (Nc+Ng)-point DFT.
» Simple one-tap FDE can be applied as in CP-SC. 7
Nc+
Ng-
poin
t D
FT
FD
E Data
+TS
Data
m
odula
tion
Nc+
Ng-
poin
t ID
FT
Data
de-
modula
tion
Received data
Channel estimates
Data symbols(0) TS
Nc symbols
Data symbols(1) TS
Time Ng (≥L)symbols
DFT block
TS is identical for all blocks.
TS … … TS Data symbols(n) …
TS-Based Frequency-Domain Channel Estimation - Basic concept -
TS based frequency-domain channel estimation
– Obtaining the instantaneous channel estimate using Ng-symbol TS.
» The received TS having cyclic property is constructed for the
frequency-domain channel estimation.
8
Time
(3) Instantaneous frequency-domain channel estimation
TS Data(n) … … TS
L-1 symbols Ng symbols
(1) Add
TS Data(n) … … TS
Frequency 0 1 Ng-1 q … …
Instantaneous channel estimates
(2) Ng-point DFT
TS
TS TS
Cyclic property of TS is constructed.
The received TS is decomposed into
Ng orthogonal frequency components
by applying Ng-point DFT.
TS-Based Frequency-Domain Channel Estimation - Basic concept -
TS based frequency-domain channel estimation
– Delay time-domain windowing technique [G] is used for interpolation.
9 [G] J. J. de Beek, et. al., “On channel estimation in OFDM systems,” Proc. VTC, July 1995.
(1) Ng-point IDFT
Delay time 0 Ng-1 …
(2) Zero padding
(3) Nc+Ng-point DFT
Frequency 0 1 k Nc+Ng-1 … …
Impulse response
Channel estimates
Frequency 0 1 Ng-1 q … …
Instantaneous channel estimates
Ng-symbol TS only has the frequency components
at k=q(Nc+Ng)/Ng, q=0~Ng-1.
1~0 ,ˆ )(
g
g
gcn NqqN
NNH
1~0 ),(ˆ )( g
n Nh
1
0
)()( 2exp)(~
)(~ gN
gc
nn
NNkjhkH
Nc+Ng channel gains are obtained for performing
FDE by interpolation with DFT/IDFT.
TS-Based Frequency-Domain Channel Estimation
Channel estimation accuracy is poor due to the interference from
the data block.
We consider three schemes to obtain the improved channel
estimate.
I. Simple averaging and iterative channel estimation
II. Recursive least square (RLS) algorithm based channel estimation
III. RLS-based channel estimation with polynomial prediction
10
TS Data(n) … … TS
L-1 symbols Ng symbols
Add
TS Data(n) … … TS
TS-Based Frequency-Domain Channel Estimation I. Simple averaging and iterative channel estimation
Improved channel estimate is obtained by simply averaging the
instantaneous channel estimates over several (NB) blocks.
At the iteration stage, both the estimated data blocks and the TSs
are used.
Tracking ability is a problem in a fast fading environment.
– The channel gains are assumed to stay constant over NB blocks. 11
Instantaneous channel estimate
1
0
)(
)(
)(~
~ BN
n
n
g
gc
qU
qYq
N
NNH Frequency-domain representation for TS
Received TS having the cyclic property (q=0~Ng-1)
1
0
2)(
1
0
*)()(
|)(ˆ|
)}(ˆ){(
)(~
B
B
N
n
n
N
n
nn
kS
kSkY
kH k-th frequency component of the transmit symbol replica block
k-th frequency component of n-th received signal block (k=0~Nc+Ng-1)
TS-Based Frequency-Domain Channel Estimation II. RLS algorithm based channel estimation
The interference to TS from the data block is canceled by utilizing
the channel estimates of the previous block.
Channel estimates are obtained based on RLS algorithm.
– Updates at the n-th block
12
TS Data(n) … … TS
(2) Add
TS Data(n) … … TS
(1) Cancel (1) Cancel
TS
TS TS Time
It is benefit of sequential channel
estimation.
Replica of the interference from the data
block is generated by pre-equalization
using previous channel estimates.
2)()1()(
*)()()1()(
|)(ˆ|)()(
)}(ˆ){()()(
kSkk
kSkYkZkZ
nnn
nnnn
otherwise )(/)(
1~0 , if
|)(|
)()(~
)(~
)1()1(
)1(2
)1(*)(
)(
kkZ
NqqN
NNk
qN
NNqU
qN
NNZqUqY
kH
nn
g
g
gc
g
gcn
g
gcnn
n
• : Received TS having the cyclic property
(q=0~Ng-1)
•U(q): Frequency-domain representation for TS
•Y(n)(k): Frequency-domain received signal block
(k=0~Nc+Ng-1)
• : Frequency-domain symbol replica block
(q)(n)Y~
(k)(n)S
Forgetting factor(0<<1)
TS-Based Frequency-Domain Channel Estimation III. RLS-CE with polynomial prediction
RLS algorithm based channel estimation (RLS-CE)
– Replica of the interference from the data block is generated by pre-
equalization using previous channel estimates.
» The tracking ability against a very fast fading is limited.
13
Block n n-1 n-MB …
Actual channel
RLS-CE
)(~ )1( kH n
Block … n n-1 n-MB
)(~ )1( kH n
RLS-CE
)(~ )( kH n
Utilized for pre-equalization
RLS-CE Interference cancellation from the
data block does not work effectively.
The previous channel estimates
may be old at the present block in
very fast fading channels.
TS-Based Frequency-Domain Channel Estimation III. RLS-CE with polynomial prediction
RLS algorithm based channel estimation (RLS-CE)
– Replica of the interference from the data block is generated by pre-
equalization using previous channel estimates.
» The tracking ability against a very fast fading is limited.
Polynomial prediction is introduced.
– Predicted channel gains are utilized for the replica generation.
14
Block n n-1 n-MB …
Actual channel
RLS-CE
)(~ )1( kH n
Block … n n-1 n-MB
)(ˆ )( kH n
RLS-CE
)(~ )( kH n
Utilized for pre-equalization
RLS-CE with polynomial prediction Polynomial prediction using MB past
channel estimates are applied.
)(~ )(
kH BMn
RLS-CE
…
Polynomial prediction
Simulation Result I. Simple averaging and iterative channel estimation
Normalized Doppler frequency fDTs vs Average BER
15
Data modulation QPSK
Data symbol block length Nc=64
TS length Ng=16
TS Chu sequence [H]
Fading type Frequency-selective
Rayleigh
Power delay profile L=16 path uniform
power delay profile
Equalization MMSE-FDE
Av
erag
e B
ER
Normalized Doppler frequency, fDTs
QPSK
Nc64, Ng=16
L=16-path uniform
Eb/N0=14dB
106
101
102
103
104
105 104
NB=32, I=1
NB=16, I=2
NB=8, I=3
Ideal channel estimation
Travelling speed (km/h)
5.4 54 540
•10MHz signal bandwidth at the carrier frequency 2GHz is assumed.
Tracking ability against the fading variations
tends to be lost as NB increases.
With the increase in the number I of iterations,
smaller NB can be used and tracking ability is
improved.
Simulation Results II&II. RLS-CE & RLS-CE with prediction
Normalized Doppler frequency fDTs vs Average BER
16
Av
erag
e B
ER
101
102
103
104
Normalized Doppler frequency, fDTs
104 105
QPSK
Nc64, Ng=16
L=16-path uniform
Eb/N0=14dB
Simple averaging (NB=8, I=3)
RLS-CE
RLS-CE w/ prediction
Ideal CE
Travelling speed (km/h)
54 540
•10MHz signal bandwidth at the carrier frequency 2GHz is assumed.
RLS-CE
• Forgetting factor is optimized for each fDTs.
RLS-CE with polynomial prediction
• Second-order polynomial is used.
• Forgetting factor and the number MB of
blocks to be used for the prediction are
optimized for each fDTs.
RLS-CE provides better BER performance
than simple averaging in a fast fading channels.
RLS-CE with polynomial prediction further
improves the BER performance in very fast
fading channels.
Conclusion
We presented frequency-domain channel estimation schemes
suitable for TS-SC block transmission with FDE.
– The received TS having cyclic property is constructed to perform
frequency-domain channel estimation with a TS of L-symbol length.
– Improved channel estimate is obtained by
» Simple averaging and iterative channel estimation
» RLS-based channel estimation
» RLS-based channel estimation with polynomial prediction
RLS-CE with polynomial prediction
– has the best tracking ability against fast fading channel.
– achieves a BER performance close to the perfect channel estimation
case even in a fast fading environment.
17
18
Thank you very much for your kind attention.