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.