1 Block-by-Block Blind Channel Estimation Algorithm Using Subcarrier Averaging for Multi-user OFDM Systems Presenter: Teng-Han Tsai ( 蔡騰漢 ) Institute of

1

Block-by-Block Blind Channel Estimation Algorithm Using Subcarrier Averaging for Mul

ti-user OFDM Systems

Presenter: Teng-Han Tsai ( 蔡騰漢 )

Institute of Communications Engineering &Department of Electrical Engineering

National Tsing Hua UniversityHsinchu, Taiwan 30013, R.O.C.

E-mail: [email protected]

2

Outline

1. Introduction

3. MIMO Model for Post-FFT Beamforming Structure4. Proposed Blind Channel Estimation Algorithm by Subcarrier

Averaging5. Simulation Results

6. Conclusions

MUSIC: Multiple Signal Classification

MVDR: Minimum Variance Distortionless Response

2. Review of MVDR beamformer and MUSIC algorithm

MIMO: Multiple-input Multiple-output

3

Introduction

4

Wireless Environment

: path gain of the lth path of user p,p l

: Direction of arrivals (DOA) of the lth path of user p

,p l )2/2/( , lp

: time delay of the lth path of user p

,p l

Q : number of antennas P : number of users

1[ ]x n

2[ ]x n

[ ]x nQ

1[ ]s n

[ ]Ps n

1,11,1

1,1

1,1 L1,1 L

1,1 L

1,P 1,P 1,P

PLP , PLP , PLP ,

user 1

user P

BS

: number of paths (or DOAs) associated with user p.pL

: ( ) total number of paths (or DOAs) of all the users.PLLL 21L

MS 1

MS P

L1

LP

...

..

.

...

NoiseNoise

ULA (Uniform Linear Array)

Tx signals

Rx signals

5

(A1) , are QPSK ( BPSK ) zero-mean independent identically distributed (i.i.d.) random sequences with , and is statistically independent of for .

2{| [ ]| } 1pE u k [ ]pu k

[ ] qu k pq [ ] pu k

(A4) is zero-mean white Gaussian and statistically independent of

, and . , ..., ,2 ,1 PpH 2{ [ ] [ ]]} wE n n w w IQ

[ ]nw

[ ]pu k

QI : identity matrix

Q Q

(A2) for all ,lpmq ,, ),( ),( lpmq LQ

Assumptions

BPSK : Binary phase shift keying

QPSK : Quadriphase shift keying

(A3) , ... ,2,1, gpLppp N0 . p

, and L is known.

1,2,...,p P

6

Review of MVDR Beamformer and MUSIC Algorithm

7

Beamforming (1/3) [2][3]

Interference suppression

Antenna gain enhancement

Spectral efficiency increase

Signal separation and extraction

Beamformer

(Interfering signal)

(Desired signal)

1

P

][nr

v][1 nu

][nuP

...

...

1

P

#1

#2

#Q ][][ 11 nuny

8

Beamforming (2/3)

Assumptions:(M1) , are wide-sense stationary random processes, and is statistically independent of for .

Pp ..., ,2 ,1 ][nup ][nuq ][nup

(M2) for all , ij ij

(M3) is zero-mean white Gaussian with and statistically independent of . ..., ,2 ,1 Pp

QIww 2H ]]}[][{ wnnE ][nw],[nup

. PQand

pq

Beamformer

(source P )

(source 1)

Beamformer Output

1

P

[ ]nx

v][1 nu

][nuP

...

...

1

P

#1

#2

#Q

MIMO Model

path gain

DOA (Direction of Arrival)

][ny

1

[ ] ( ) [ ] [ ]P

p P pp

n u n n

x a w

9

Beamforming (3/3)

H1 1[ ] [ ] [ ]MVy n n u n v x

Under the assumption (M1) and (M2),

as which implies the MVDR beamformer can perfectly extract

the desired signal by processing .

02 w][11 nu [ ]nx

MVDR Beamformer:

subject to

11

H 11 1

( )

( ) ( )xx

MVxx

R a

va R a

whereH{ [ ] [ ]}xx E n nR x x : correlation matrix of [ ]nx

1 : (known in advance) DOA of the path of user 1 (Desired source)

2 Hmin {| [ ] | } min xxE y n v v

v R v

1)( 1H av

Criterion:

By Lagrange multiplier

MVDR : Minimum Variance Distortionless Response

10

DOA Estimation - MUSIC Method (1/2)

EVD (Eigenvalue Decomposition) of Correlation matrix :

1 1

1

0 0

0 0

0 0

H

xx QH

Q Q

e

R e e

e

H H 2{ [ ] [ ]}xx uu wE n n R x x AR A IQ

where

H{ [ ] [ ]}uu E n nR u u ( )uurank PR

H

1xx i i i

i

R e eQ

Qeeee ,..., , ,..., 11 PP are orthonormal basis.1.2.

2

2

if 1,...,eigenvalues

otherwisei w

i w

i P

11

Signal subspace is orthogonal to noise subspace :

DOA Estimation - MUSIC Method (2/2)

Compute MUSIC spectrum :

)()(

1

)(

1)(

H2

aPaaP NN

MUSICS

and search for “infinitely high” spectral peaks.

0)(H ij ae Pi ,...,2 ,1 Q,...,2,1 PPj, ,

Construct projection matrix :NP

Q

1

H

PiiiN eeP

may be found by solving for .

P ,..., , 21 0aP )(N

12

MIMO Model for Post-FFT Beamforming Structure

13

Post-FFT Beamforming Structure (1/2)

… …A/D GI Removal

S/PN-point

FFT

GI

RemovalS/P

N-point FFT

GI Removal

S/PN-point

FFT

)0(1v

)0(2v

)0(Qv

P/S

[ ]nx[0]X

[ ]pu kA/D

A/D … ………

)0(pv

[ ]kX

[0]pu

..

beamformer

channel information at subcarchannel information at subcarrier rier 00 for user for user pp

NN beamformers beamformers

14

( ) ( )[ ] [ ] [ ]k kk k k X A u w

,2 /

, ,1 1

[ ] ( ) [ ] [ ]p

p l

LPj N

p l p l pp l

k e u k k

X a w

MIMO model for each subcarrier k:

Post-FFT Beamforming Structure (2/2)

( source vector)

( ) T1 2[ ] [ [ ], [ ] ,... , [ ]]k

Pk u k u k u ku 1P

[ ]kw ( white Gaussian noise vector)1Q

pL

l

lpN

kj

lplpk

p e1

,2

,,)( )(

aa ( vector )1Q

where ( channel matrix)

], ... ,,[ )()(2

)(1

)( kP

kkk aaaA PQ

, , ,1 1

[ ] ( ) [ ] [ ]pLP

p l p l p p lp l

n s n n

x a w

FFT

Channel response of user p at subcarrier k

15

Proposed Blind Channel Estimation Algorithm by Subcarrier Averaging

16

where ],,,[ 21 PAAAA ( DOA matrix)Q L

( source vector)L 1

MIMO Model (1/4)

MIMO Model

)](..., ),(),([ ,2,21,1 pLppp,Lpp,pp,p aaaA

T,2,1, ] ][, ... ],[],[ [][ kukukuk

pLpppp u

P

p

pL

l

lpN

kj

plplp kekuk1 1

,2

,, ][][)(][ w

aX

][][][ kkk wAuX 1 10 , ..., N, k

T21 ] ][,],[],[ [][ kkkk Puuuu

][kw ( white Gaussian noise vector )Q 1

Nlpkjplp ekuku

/,2, ][][

( )

pL 1( )full column rank by Assumption (A2)

Q pL

(component)

re-expression

17

MIMO Model (2/4)

2. Same user but different path:

1. Different users:

,0}])[]([{ *,, kukuE jqip

Source Vector : ][ku

,0}])[])([{(/),,(2*

,, Njpipkjjpip ekukuE

ji

qp

The components of the source vector are statistically correlated.

][ku

Under Assumption (A1) and Assumption (A3), check the components of the L × 1 source vector by statistical averaging :][ku

MVDR

18

MIMO Model (3/4)

Under Assumption (A1) and Assumption (A3), check the components of the L × 1 source vector by subcarrier averaging :][ku

Define the subcarrier averaging of :

1

0

][1

][N

kku

Nku

][ku

,0])[]([ P*,, kuku jqip ),(),( jqip

where denotes “convergence in probability” as N . P

Each components of can be “de-correlated” by subcarrier averaging.

][kuMVDR

19

MIMO Model (4/4)

MVDR and MUSIC methods by subcarrier averaging:

By subcarrier averaging, MVDR and MUSIC methods can be applied to post-FFT beamforming structure by processing

][][][ kkk wAuX

where ],,,[ 21 PAAAA ( DOA matrix)Q L

( source vector)L 1

)](..., ),(),([ ,2,21,1 pLppp,Lpp,pp,p aaaA

T,2,1, ] ][, ... ],[],[ [][ kukukuk

pLpppp u

T21 ] ][,],[],[ [][ kkkk Puuuu

][kw ( white Gaussian noise vector )Q 1

Nlpkjplp ekuku

/,2, ][][

( )

pL 1( )full column rank by Assumption (A2)

Q pL

(component)

20

)(ˆ l)(ˆ l

)(ˆ l

DOA Estimation

Source Extraction

Time Delay Estimation

Path Gain Estimation

Classificationand Grouping

Algorithm Procedure

1 10 ],[ , ..., N, kkX

1 10 , , ..., N, k

MUSIC

MVDR Beamformer

(estimate of channel matrix)

(received signal vector)

( )ˆ kA

Ll ..., ,2 ,1

21

Proposed Algorithm – DOA Estimation

MUSIC method :

)(ˆ)(

1)(

H

aPa NMUSICS

where

H

1

ˆ ˆ ˆN i ii L

P e eQ

: projection matrix

H H

1

ˆˆ ˆ ˆ[ ] [ ]XX i i ii

k k

R X X e eQ

: EVD of correlation matrix

EVD : eigenvalue decomposition

( MUSIC spectrum )

Q

Q

eeee ˆ , ,ˆ ,ˆ , ,ˆ

ˆˆˆˆ

11

11

LL

LL

( noise ( noise eigenvectors )eigenvectors )

( the smallest ( the smallest QQ - - LL eigenvalues ) eigenvalues )

All the DOAs can be estimated by finding the L largest local maxima of SMUSIC(θ) .

22

Proposed Algorithm – Source Extraction

By and , we have MVDR beamformer

)ˆ(ˆ)ˆ(

)ˆ(ˆ

)(1)(H

)(1)(

lXX

l

lXXl

aRa

aRv

XXR̂)(ˆ l

and MVDR beamformer outputNkjllll l

ekukky /2)()(H)()( )(

][][)(][ Xv

where )(l : path gainpath gain associated with DOA and

)(ˆ l

][)( ku l : datadata associated with DOA and

)(ˆ l

)(l : time delaytime delay associated with DOA and

)(ˆ l

},,,,,,{ ,1,1,11,1)(

PLPPLl

]}[,],[{][ 1)( kukuku P

l

},,,,,,{ ,1,1,11,1)(

PLPPLl

][][ˆ H kkXX XXR

23

Proposed Algorithm – Time Delay Estimation (1/3)

Data sequence (QPSK signals):

( ) 4( [ ]) 1lu k ( )[ ] {1, 1, , }lu k j j

Estimate time delay :)(ˆ l

where

( )QPSKˆ arg max{ ( )},l J

gN ,,1 ,0

,0

,1

)(l )(l

Estimate time delay by processing : ][)( ky l

Nkjll l

eku /2)()( )(

][

( ) 4

QPSK 22( )

8( [ ] ) exp{ }

( )

[ ]

l

l

ky k j

NJ

y k

24

2)(

2)(

BPSK

][

}4

exp{) ][ (

)(ky

Nk

jkyJ

l

l


Data sequence (BPSK signals):

( )[ ] { 1, 1}lu k

Estimate time delay :)(ˆ l

where

( )BPSKˆ arg max{ ( )},l J

gN ,,1 ,0

,0

,1

)(l )(l

Estimate time delay by processing : ][)( ky l

Nkjll l

eku /2)()( )(

][

( ) 2( [ ]) 1lu k

25


][} ˆ2

exp{][][ )()()()()( kuNk

jkyky lllllc

Time compensated beamformer output associated with : ][)( ky l

c)(ˆ l

where )(l : path gainpath gain associated with DOA and

)(ˆ l

][)( ku l: datadata associated with DOA and

)(ˆ l

},,,,,,{ ,1,1,11,1)(

PLPPLl

]}[,],[{][ 1)( kukuku P

l

26

Calculate for all the paths to be analyzed.

Select a path and set it to be .

Proposed Algorithm – Classification and Grouping

(1)[ ]cy k 1[ ]g k

Define

(Step 1)(Step 1)

Procedures of classification and grouping:

2*2)(

*)(

,

][][

][][

kgky

kgky

pl

c

pl

c

pl

,l p(Step 2)(Step 2)Extract all the paths that have and assign them as a new group. (Step 3)(Step 3) , 0.5l p

From the remaining paths, select another path and set it to be , where i = 2, …, P.(Step 4)(Step 4)( )[ ]icy k

[ ]ig kGo to Step 2 until there is no more path to group. (Step 5)(Step 5)Finally, there will be P groups where all the paths of a group belongs to the same user. (Step 6)(Step 6)

27

Proposed Algorithm – Path Gain Estimation (1/9)

After Classification and Grouping: It is obtained P groups, where in each group there are Lp sequences with the same data symbol information multiplied by different coefficient:

[ ]pu k

1

1

(1)1,1 1

1, 1

[ ] [ ]

[ ] [ ]

c

Lc L

y k u k

y k u k

(1),1

,

[ ] [ ]

[ ] [ ]P

P

c P P

Lc P L P

y k u k

y k u k

Group 1Group 1 Group PGroup P

28


Estimate path gain :)(ˆ l

( ) 4 ( ) 4( [ ] ) ( )l lQPSK cE y k

)(ˆ l ,1 ,2 ,3 ,4( ) ( ) ( ) ( ), , , l l l lj j j jl l l le e e e

The 4 solutions have the same magnitude but different phase angle. Therefore, it needs to choose one of them.

( ) 4( [ ]) 1lu k ( )[ ] {1, 1, , }lu k j j

Estimate path gain by processing : ][)( ky lc

Data sequence (QPSK signals):

][)()( ku ll

29

1,(1) (1),1[ ] [ ] [ ]ij j

rot c py k y k e u k e


Decision of the path gain phase angle:

For QPSKQPSK case:

Select its corresponding path (first path) and rotate the path by its corresponding phase angle estimate .

(1)[ ]cy k(Step 2)(Step 2)

1,i

From the 4 phase angle solutions , select an angle , for i = 1, …, 4.(Step 1)(Step 1)1,i

1,1 1,2 1,3 1,4{ , , , }

Re

Im

1,i ,l i

After rotationRe

Im

30, , ,

2 2

Ambiguity phase

30

Re

Im

Re

Im

Re

Im



For QPSKQPSK case:Select another path , where l = 2, …, Lp and rotate it by its 4 possible path gain phase angles .

( )[ ]lcy k(Step 3)(Step 3)

,l i

,1 ,2 ,3 ,4{ , , , }l l l l

,1l

Re

Im

Re

Im

,2l ,3l,4l

, ,1[ ]rot ly k

, ,2[ ]rot ly k

, ,3[ ]rot ly k

, ,4[ ]rot ly k

31



For QPSKQPSK case:Perform the inner product of the first rotated path and the four l-th rotated paths , for l= 2, …, Lp. . ,1[ ]roty k(Step 4)(Step 4)

, ,1[ ] [ ]Hrot l roty k y k

Calculate the phase angle of the four inner products , which the results will be approximated to {0, π/2, π, 3π/2}. (Step 5)(Step 5)

, [ ]rot ly k

Choose the path gain phase angle whose phase angle of inner product is closed to 0. (Step 6)(Step 6) 1,i

Re

Im

Re

Im

,1l1,i

, ,1[ ]rot ly k,1,1[ ]roty kThey are in phaseThey are in phase

32



For QPSKQPSK case:Go to the Step 2 until there is no more paths to rotate in the group. .(Step 7)(Step 7)

Finally, the path gain phase angle for each path of the group will be obtain. (Step 8)(Step 8) 1,i

Note:Note: As the proposed algorithm is a blind method, the estimated path

gain has an ambiguity scalar . This value depends on the choice of the

Phase angle solution in Step 1.

je

33


Estimate path gain :)(ˆ l

( ) 2 ( ) 2( y [ ] ) ( )l lBPSK cE k

)(ˆ l )(l)(l or

The 2 solutions have the same magnitude but different phase angle. Therefore, it needs to choose one of them.

( ) 2( [ ]) 1lu k ( )[ ] { 1, 1}lu k

Estimate path gain by processing : ][)( ky lc

Data sequence (BPSK signals):

( ) ( )[ ]l lu k

34



For BPSKBPSK case:

Select its corresponding path (first path) and rotate the path by its corresponding phase angle estimate . ,1[ ]mcy k(Step 2)(Step 2)

1,i1,

,1 ,1[ ] [ ] [ ] pi jjrot mc py k y k e u k e

From the 2 phase angle solutions , select a solution , for i = 1, 2.(Step 1)(Step 1)1,i

1,1 1,2{ , }

0,p

Select another path , where l = 2, …, Lp and rotate it by its 2 possible path gain phase angles . , [ ]mc ly k(Step 3)(Step 3)

,1 ,2{ , }l l Perform the inner product of the first rotated path and the four l-th rotated paths , for l= 2, …, Lp. . ,1[ ]roty k(Step 4)(Step 4)

, [ ]rot ly k

Ambiguity phase

35



For BPSKBPSK case:

, ,1[ ] [ ]Hrot l roty k y k

Calculate the phase angle of the four inner products , which the results will be approximated to {0, π}. (Step 5)(Step 5)

Choose the path gain phase angle whose phase angle of inner product is closed to 0. (Step 6)(Step 6) 1,i

Go to the Step 2 until there is no more paths to rotate in the group. .(Step 7)(Step 7)

Finally, the path gain phase angle for each path of the group will be obtain. (Step 8)(Step 8) 1,i

Note:Note: As the proposed algorithm is a blind method, the estimated path

gain has an ambiguity scalar . This value depends on the choice of the

Phase angle solution in Step 1.

pje

36

( )( )

where

Proposed Algorithm – Channel Recovery

Estimate of channel matrix :)(ˆ kA

PA )(k

],...,,[ )()(2

)(1

)( kP

kkk aaaAP is P × P unknown permutation matrix.

PIPP H

]ˆ,,ˆ,ˆ[ˆ )()(2

)(1

)( kP

kkk aaa A

group group indexindex

user indexuser index

With the estimated DOA, time delay and path gain of each path,

the channel matrix can be obtain:)(ˆ kA

Note: Note: The permutation matrix P can be obtained using the information

of the transmitted sources after the data sequence detection.

37

Data Sequence Detection

Once the channel information and the noise power (from MUSIC) are obtained. A MMSE beamformer can be applied:

( ) 2 1 ( ) ( ) ( ) 2 1 ( )( ) ( )k k k k kMMSE n n

H

xxV R I A A A I A

)(ˆ kA

( )ˆ [ ] ( ) [ ] [ ] pjk Hp MMSE pu k k u k e V X

Then the estimated data sequence for a user p will be:

30, , ,

2 2p

for 1,...,p P

2n

0,p

For QPSK

For BPSK

Ambiguity phase

38

Simulation Results

39

Performance Index

Definition of Normalized Mean Square Error (NMSE):

1

02)(

2)()( ~1

NMSEN

kF

k

F

kk

N A

AA

where H)()( ˆ~PAA kk : estimate of channel matrix )(kA

: Frobenius normF

40

Parameters Used

: i.i.d. zero-mean Gaussian with . ][nw QIww 2H ]}[][{ wnnE

A two-user (P =2) OFDM system

Q = 10.

Ng= 20

N = 1024.

DOA randomly generated for all the users . Time delay randomly generated for all the users . Path gain randomly generated for all the users .

/ 2 : / 2

,p l gN 2

, 1| | = 1pL

p ll

Input SNR: 2

, ,1

2

E ( ) [ ]

SNRE{|| [ ] || }

pL

p,l p l p p ll

s n

n

a

w

L = 6 . 1 2( 3, 3)L L

41

NMSE of A

42

Symbol Error Ratio

43

Conclusions

We have presented blind channel estimation algorithm by sublind channel estimation algorithm by subcarrier averagingbcarrier averaging for the post-FFT beamforming structure opost-FFT beamforming structure over one OFDM blockver one OFDM block. This proposed algorithm basically includes DOA estimation using MUSIC method, source extraction using MVDR beamformer, time delay estimation and compensation, classification and grouping, path gain estimation and channel recovery.

Some simulation results were provided to support the blind beamformer designed by the proposed channel estimation algorithm, and its performance is very closed to the performance of the MMSE beamforming using perfect channel.

The proposed channel estimation algorithm only needs one one OFDM blockOFDM block to estimate channel with good performancegood performance..

44

References (1/3)

[1] R. V. Nee and R. Prasad, OFDM for Wireless Multimedia Communications . Boston: Artech House, 1999.

[2] J. C. Liberti and T. S. Rappaport, Smart Antennas for Wireless Communications: IS- 95 and Third Generation CDMA Applications. New Jersey: Prentice Hall, 1999.

[4] Ralph O. Schmidt, “Multiple emitter location and signal parameter,” Proc. IEEE Trans.

Antennas and Propagation, vol. AP-34, No. 3, pp. 3381-3391, Dec. 1999. [5] Shinsuke Hara, Montree Budsabathon, and Yoshitaka Hara, “A pre-FFT OFDM adaptive antenna array with eigenvector combining,” Proc. IEEE International Conference on Communication., vol. 4, pp. 2412-2416, June. 2004.

[3] L. C. Godara, “ Application of antenna arrays to mobile communications, Part II: Beam-forming and direction-of-arrival considerations,” IEEE Proceeding, vol. 85, No. 8, pp 1195-1245, Aug. 1997.

[6] Ming LEI, Ping ZHANG, and Hiroshi HARADA, and Hiromitsu WAKANA, “LMS adaptive beamforming based on pre-FFT combining for ultra high-data-eate OFDM system,” Proc. IEEE 60th Vehicular Technology Conference, vol. 5, Los Angeles, California, USA, Sept. 26-29, 2004, pp. 3664-3668.

45

References (2/3)

[7] Fred W. Vook and Kevin L. Baum, “Adaptive antennas for OFDM,” Proc. IEEE 48th Vehicular Technology Conference, vol. 1, Ottawa, Ont., May 18-21, 1998, pp. 606-610. [8] Chan Kyu Kim, Kwangchun Lee, and Yong Soo Cho, “Adaptive Beamforming Algorithm for OFDM Systems with Antenna Arrays,” IEEE Trans. Consumer Electronics, vol. 46, No. 4, pp. 1052-1058, Nov. 2000. [9] Hidehiro Matsuoka and Hiroki Shoki, “Comparison of pre-FFT and post-FFT processing adaptive arrays for OFDM systems in the presence of co-channel interference,” Proc. IEEE 14th International Symposium on Personal, Indoor and Mobile Radio Communications, vol. 2, Beijing, China, Sept. 7-10, 2003, pp. 1603-1607. . [10] Zhongding Lei and Francois P.S. Chin, “Post and pre-FFT beamforming in an OFDM system,” Proc. IEEE 59th Vehicular Technology Conference, vol. 1, Milan, Italy, May 17-19, 2004, pp. 39-43. . [11] Matthias Munster and Lajos Hanzo, “Performance of SDMA multi-user detection techniques for Walsh-Hadamard-Spread OFDM Schemes,” Proc. IEEE 54th Vehicular Technology Conference, vol. 4, Atlantic City, NJ, USA, Oct. 7-11, 2001, pp. 2219-2323.

46

References (3/3)

[12] Samir Kapoor, Daniel J. Marchok, and Yih-Fang Huang, “Adaptive interference suppression in multiuser wireless OFDM systems using antenna arrays,” IEEE Trans. Signal Processing, vol. 47, No. 12, pp. 3381-3391, Dec. 1999. [13] Shenghao Yang and Yuping Zhao, “Channel estimation method for 802.11a WLAN with multiple-antenna,” Proc. 5th International Symposium on Multi-Dimensional Mobile Communications, 29 Aug.-1 Sept, 2004, pp. 297-300. [14] Bassem R. Mahafza and Atef Z. Elsherbeni, Matlab Simulations for Radar Systems Design. Boca Raton, FL :CRC Press/Chapman & Hall, 2004. [15] Kai-Kit Wong, Roger S.-K. Cheng, Khaled Ben Letaief, and Ross D. Murch, “Adaptive antennas at the mobile and base stations in an OFDM/TDMA system,” IEEE Trans. Signal Processing, vol. 49, No. 1, pp. 195-206, Jan. 2001. [16] Shiann-Shiun Jeng, Garret Toshio Okamoto, Guanghan Xu, Hsin-Piao Lin, and Wolfhard J. Vogel, “Experimental evaluation of smart antenna system performance for wireless communications,” IEEE Trans. Antennas and Propagation, vol. 46, No. 6, pp. 749-757, June 1998.

47

Thank you very muchThank you very much

48

Transmitter of OFDM Systems

],[ mkup : data sequence of userp

: number of subcarriers

N

1

0

/2][1

][N

k

Nknjpp eku

Nns

gN : length of GI )2/( N

D/A & Up Converter

GI Insertion

S/PN-point

IFFT

… …],[ mkupP/S

],[ mns p

User p

1 ..., ,1 , NNNn ggP,p ..., ,2 1 ,,

gN

n : time-domain sample index

k : frequency-domain sample index

49

Symbol Error Ratio (QPSK)

50

Symbol Error Ratio (BPSK)

Documents

1 Block-by-Block Blind Channel Estimation Algorithm Using Subcarrier Averaging for Multi-user OFDM Systems Presenter: Teng-Han Tsai ( 蔡騰漢 ) Institute of