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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: g945614@oz.nthu.edu.tw
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
Proposed Algorithm – Time Delay Estimation (2/3)
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
Proposed Algorithm – Time Delay Estimation (3/3)
][} 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
Proposed Algorithm – Path Gain Estimation (2/9)
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
Proposed Algorithm – Path Gain Estimation (3/9)
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
Proposed Algorithm – Path Gain Estimation (4/9)
Decision of the path gain phase angle:
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
Proposed Algorithm – Path Gain Estimation (5/9)
Decision of the path gain phase angle:
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
Proposed Algorithm – Path Gain Estimation (6/9)
Decision of the path gain phase angle:
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
Proposed Algorithm – Path Gain Estimation (7/9)
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
Proposed Algorithm – Path Gain Estimation (8/9)
Decision of the path gain phase angle:
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
Proposed Algorithm – Path Gain Estimation (9/9)
Decision of the path gain phase angle:
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)
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