Channel Estimation Techniques Based on Pilot Arrangement in O

FDM SystemsSinem Colet, Mustafa Ergen, Anuj Puri, and Ah

mad BahaiIEEE TRANSACTIONS ON BROADCASTING, VOL.48, NO.

3,SEPTEMBER 2002

老師：高永安學生：蔡育修

Outline

• Introduction• System description• Channel Estimation Based on Block-Type Pilot

Arrangement• Channel Estimation at Pilot Frequencies in

Comb-Type Pilot Arrangement• Interpolation Techniques in Comb-Type Pilot

Arrangement• Simulation• Conclusion

Introduction

• A dynamic estimation of channel is necessary before the demodulation of OFDM signals since the radio channel is frequency selective and time–varying for wideband mobile communication systems.

• The channel estimation： Block-type： by inserting pilots into all of the subcarriers

of OFDM symbols with a specific period.-Slow fading channel. Least Square (LS) or MMSE.

• Comb-type ： by inserting pilots into each OFDM symbol.

when the channel changes even in one OFDM block.

LS, MMSE or Least Mean-Square (LMS).

System description

-1

2

0

0, 1, 2, ..., -1

: the DFT length.

Nj kn N

k

x n IDFT X k n N

X k e

N

Specific period or uniformly

1/N?

, - , - 1, ..., -1

, 0, 1 , ..., -1

: the length of the guard intervel

g gf

g

x N n n N Nx n

x n n N

N

fx n

: Additive White Gaussian Noise

: channel impulse response

f fy n x n h n w n

w n

h n

• Guard interval

• will pass through the frequency selective time varying fading channel with additive noise.

1

2

0

0 -1

: total number of propagation paths

: complex impulse response of the th path

: the th path Doppler frequency shift

: delay spread index

: sample period

: the th

Di

i

rj N f Tn

i ii

i

D

i

h n h e n N

r

h i

f i

T

i

path delay normalized by T

• The impulse response h：

for - 1

0, 1, 2, ..., -1

f g

f g

y n N n N

y n y n N n N

-1

- 2

0

0, 1, 2, ..., -1

1

Nj kn N

n

Y k DFT y n k N

y n eN

• At the receiver,

• Sent to DFT block,

12

0

21 12

20 0

0, 1, ..., -1

sin

1

1

iD ii

i

Di

i

Di

rDj f T j N k

ii D

j f T k Kr Nj N Ki

j N f T k Ki K

K k

Y k X k H k I k W k k N

f TH k h e e

f T

h X K eI k e

N e

• Assuming there is no ISI, I(k) that is ICI because of Doppler frequency.

0, 1, ..., -1ee

Y kX k k N

H k

• Following DFT block, the estimated channel He(k) is obtained in channel estimation block.

• Then the transmitted data is estimated by：

Channel Estimation Based on Block-Type Pilot Arrangement• OFDM channel estimation symbols are transmitted

periodically , in which all sub-carriers are used as pilots.• The estimation can be performed by using either LS or

MMSE.

• In matrix notation

0 100

2

1 0 1 1

0 , 1 ,..., 1

0 1 ... 1

0 1 ... 1

0 1 ... 1

...1

,

...

T

T

T

N

NN N

j n N knkN

N N NN N

Y XFh W

X diag X X X N

Y Y Y Y N

W W W W N

H H H H N DFT h

W W

F W eN

W W

1

2

22

: the auto-covariance matrix of h.

: the noise variance E W k

MMSE hy YY

H H HhY hh

H H HYY hh N

hh

H FR R Y

R E hY R F X

R E YY XFR F X I

R

• If the time domain channel vector h is Gaussian and uncorrelated with channel noise W, the frequency domain MMSE estimate of h is：

1

which minimizes

LS

H

H X Y

Y XFh Y XFh

• The LS estimate

• When the channel is slow fading, the channel estimation inside the block can be updated using the decision feedback equalizer at each sub-carrier.

0, 1, ..., -1ee

Y kX k k N

H k

0, 1, ..., -1epure

Y kH k k N

X k

• Decision feedback equalizer for the kth subcarrier： 1)The channel response at the kth subcarrier estimated

from the previous symbol {He(k)}.

2){Xe(k)} is mapped to the binary data through “demapper”and then obtained back through “mapper”as {Xpure(k)}.

3)update

• The fast fading channel will cause the complete loss of estimated channel parameters.

• For fast fading channel , as will be shown in simulations, the comb-type based channel estimation performs much better.

Channel Estimation at Pilot Frequencies in Comb-Type Pilot Arrangement

, 0

inf . , 1, ..., -1

number of carriers

: the th pilot carrier value.

P

P

P

X k X mL l

x m l

data l L

L N

x m m

• The NP pilot signals are uniformly inserted into X(k).

• We define {HP(k) k = 0, 1, …, NP-1} as the frequency response of the channel at pilot sub-carriers.

• The estimate of the channel at pilot sub-carriers based on LS estimation.

0, 1, ..., -1

: output at the th pilot sub-carrier.

: intput at the th pilot sub-carrier.

Pe P

P

P

P

YH k N

X

Y k k

X k k

Interpolation Techniques in Comb-Type Pilot Arrangement

0

1

e e

P P P

H k H mL l l L

lH m H m H m

L

• An efficient interpolation technique is necessary in order to estimate channel at data sub-carriers by using the channel information at pilot sub-carriers.

• The channel estimation at the data-carrier k, mL<k<(m+1)L, using linear interpolation：

1 0 1

1

0

1

1 1

1,

2

where 1 1 ,

1,

2

e e

P P P

H k H mL l

c H m c H m c H m

c

lc

N

c

• The second-order interpolation is to fit better than linear interpolation.

• The low-pass interpolation is performed by inserting zeros into the original sequence and then applying a lowpass FIR filter that allows the original data to pass through unchanged and interpolates between such that the mean-square error between the interpolated points and their ideal values is minimized.

• The spline cubic interpolation produces a smooth and continuous polynomial fitted to given data points.

1

2 /

0

, 0, 1, ..., 1P

P

Nj kn N

P Pk

G n H e n N

P

12

, 0 - 2

N0,

22 1 , - - -1

P

P

N

P

NM

G n M

G N M

G n N M M n N

• The time domain interpolation is a high-resolution interpolation based on zero-padding and DFT/IDFT.

1)convert pilot channel HP(k) to time domain by IDFT.

2)by using the basic multi-rate signal processing, NP N

3)

1

2

0

, 0 -1N

j N nkN

n

H k G n e k N

Simulation

• A. Description of Simulation

1)System Parameters： perfect synchronization

0.3162 2 0.1995 17

0.1296 36 0.1 75 0.1 137

h n n n n

n n n

2)Channel Model： 1.ATTC and the Grande Alliance DTV laboratory’s ens

emble E model static case

2.DVB-T channel model

1

: fading factor

: AWGN noise

h n ah n w n

a

w n

• In the simulation, we have used Rayleigh fading channel.• In order to see the effect of fading on block type and LM

S channel estimation, we have also modeled channel that is time-varying according to autoregressive (AR).

• a is chosen to be close to 1 in order to satisfy the assumption don’t change within one OFDM symbol duration.

• a changes from 0.9 to 1.

3) Channel Estimation Based on Block-Type Pilot Arrangement ：

1.Each block consists of 30 symbols.

2.Pilots are sent in all the sub-carriers of the first symbol of each block.

3.channel estimation is performed by using LS estimation.

4) Channel Estimation at Pilot Frequencies in Comb-Type Pilot Arrangement ：

1.We have used both LS and LMS.

2.The LMS estimator uses one tap LMS adaptive filter at each pilot frequency.

• B. Simulation Results

• The block type estimation and decision feedback BER is 10-15dB higher than the comb type estimation.

channel changes so fast there are even changes for adjacent OFDM symbols.

• The comb type channel estimation with low pass interpolation achieves the best performance.

low pass time domain second order linear• DQPSK shows almost the same performance for all cha

nnel estimation techniques except decision feedback.

in demapper eliminates the time varying fading channel effect.

• Fig.9• a increase from 0.9 to 0.999, the performance improves.• When channel is fast, the estimation don’t improves as

SNR increases.• For slow fading, the decision feedback much better

compared to the other two schemes.

• BER increases as the Doppler spread increases.

Doppler shifts cause severe ICI.• Time domain interpolation performance improves as

Doppler freq. increase.?

Conclusion

• The comb type channel estimation with low pass interpolation performs the best among other techniques.

allows the tracking of fast fading channel & low pass interpolation haves MMSE.

• For low Doppler freq., the performance of decision feedback is observed to be slightly worse than that of the best estimation.

can be tolerated for higher data bit rate for low Doppler spread channel although low pass interpolation is more robust for Doppler freq. increase.