124-250-1-PB

Cc cng trnh nghin cu, pht trin v ng dng CNTT-TT Tp V-1, S 10 (30), thng 12/2013

- 14 -

Abstract: Network coding at the physical layer - (Physical layer Network Coding: PNC) is a promising technique to increase transmission throughput over two-way relay wireless networks. In a relay network, selecting a most capable intermediate node to serve as the relay help to increase transmission performance. This paper applies the selection to the MIMO-PNC network and proposes three relay selection algorithms based on the eigenvalue, harmonic mean (harmmean) and norm of the channel matrix. It is shown that the eigenvalue based algorithm has the best BER performance.

Key words: PNC, selected relay, wireless network, network coding.

I. GII THIU

M ha mng- Network Coding (NC) ln u tin c xut trong [2] l mt k thut ha hn t c dung lng max-flow min-cut trong truyn dn a ng. M ha mng tuyn tnh c bit nh l mt bin php hiu qu tng thng lng mng [3]. M ha mng thng thng c p dng cho cc mng khng dy. Truyn thng khng dy t im - im n phng thc a chng c cc nt chuyn tip. ng dng ca m ha mng vi cc mng khng dy l phng php tip cn t nhin tng thng lng ca mng.

H thng MIMO c bit n nh mt gii php quan trng tng dung lng knh truyn trong mi trng pha inh. S kt hp MIMO v m ha mng cho php t c thng lng ca mng tt.

T vn nu trn cn lm r mt s ni dung sau: Mt l s khc bit ca m ha mng cho cc mng c dy v khng dy; Hai l lm th no thc hin m ha mng lp vt l (PNC) cho mng khng dy; Ba l lm th no t c m ha trong mng khng dy MIMO; Bn l hng m c th thc hin PNC.

c nhiu cng trnh nghin cu v truyn thng hp tc MIMO hai chiu. Timo Unger v Anja Klein trong cng trnh [4] nghin cu phn tch phm cht h thng chuyn tip hai chiu vi trm chuyn tip a ng-ten. MIMO chuyn tip hai chiu ch yu cu thng tin trng thi knh truyn CSI (Channel state information) cc trm chuyn tip qua lm gim ng k tip u thng tin CSI (CSI signaling overhead). So snh vi cc giao thc khc, hiu sut t c xt v tc tng ca xut giao thc chuyn tip hai chiu MIMO l tt hn. Trong cng trnh nghin cu [5] Shengli Zhang cng cng s ch ra rng p dng trc tip ca m ha mng NC lp vt l trong mng chuyn tip khng dy c th tng gp i dung lng ca hai hng truyn thng im-im.

Cng trnh nghin cu [6] phn tch v so snh cc m hnh PNC vi 2,3,4 time slot. Kt qu ch ra rng i vi m hnh PNC 2 time slot cho tc tng cc i tt hn cc m hnh cn li. Sungsoo Kim cng cng s trong cng trnh nghin cu [7] kt hp NC cho cc h thng chuyn tip MIMO vi b cn bng trc tuyn tnh trong knh hai chiu. M hnh xut ny lm tng li ghp knh 2 ln v cng bc phn tp so vi chuyn tip mt chiu. Cng trnh

Kt hp m ha mng lp vt l v la chn nt chuyn tip cho knh v tuyn chuyn tip hai chiu

Combined Relay Selection and Physical Layer Network Coding for Wireless Two-Way Relay Network

V c Hip v Trn Xun Nam


- 15 -

[8] xem xt m hnh m ha mng (NC) trong nt chuyn tip c lng tng tn hiu

1x v

2x t hai

nt u cui 1 v 2, sau thc hin chuyn tip phin bn m ha mng dng

1 2x x ti hai nt u

cui. Trong cng trnh [1] Zhang v Liew xut m hnh m ha mng lp vt l PNC (Physical Layer Network Coding) vi nhiu ng-ten c gi l MIMO-PNC. Trong m hnh PNC, nt Chuyn tip khng c lng cc tn hiu

1x v

2x ring bit m

c lng cc phin bn kt hp 1 2x x+ v

1 2x x

v chuyn tip cc phin bn ny n 2 u cui. u im ca phng php PNC so vi NC nh ch ra [1] l mang li hiu sut BER tt hn do khng chu nh hng ca hin tng lan truyn li (error propagation) do tch nhm tn hiu mt cch ring r trc khi chuyn tip cho cc nt ch.

Trong bi bo ny, da trn tng [1] i vi m hnh MIMO-PNC, chng ti xut s dng kt hp la chn nt vi PNC tng cht lng truyn. Chng ti s dng 3 thut ton la chn nt Chuyn tip, c th l da trn gi tr ring (eigenvalue), trung bnh hi ha (harmmean) v chun ca ma trn knh truyn (channel norm). Ba thut ton xut ny cho phm cht BER tt hn so vi m hnh khng s dng la chn nt xut trong [1].

Bi bo ny c t chc nh sau: M hnh ca h thng MIMO PNC c trnh by trong mc II. Mc III trnh by cc phng php la chn nt Chuyn tip. Cc kt qu m phng c ch ra trong mc IV v cui cng mc V l kt lun ca bi bo.

II. M HNH H THNG II.1. M hnh h thng

Chng ti xem xt knh Chuyn tip hai chiu tng t [1], nh minh ha trong Hnh 1. Mt h thng mng bao gm hai nt Cui

1N v

2N trao i

thng tin qua nt Chuyn tip 3

N . Khng c ng kt ni trc tip gia hai nt Cui. n gin gi s

cc nt Cui c trang b 1 ng-ten, v nt Chuyn tip c trang b 2 ng-ten.

T m hnh v gi thit trn chng ta c th v li m hnh Chuyn tip th K vi 1,2...k K= hai chiu nh Hnh 2.

Vic truyn dn PNC bao gm hai pha. Pha u tin c hai nt Cui u truyn cng mt lc n nt Chuyn tip. Gi thit tn hiu hai nt Cui n nt Chuyn tip vi cc symbol ng b. Tn hiu thu ti nt Chuyn tip biu din nh sau:

1 11 1 12 2 1

2 21 1 22 2 2

r h x h x n

r h x h x n

= + +

= + + (1)

trong ir k hiu tn hiu thu c ti ng-ten th i

ca nt Chuyn tip, ijh l h s knh Gaussian phc t

nt j

N n ng-ten th i ca nt Chuyn tip, ix l tn

hiu pht ca nt i

N v j

n l tp m Gaussian phc ti ng-ten th j ca nt Chuyn tip vi trung bnh bng 0 v phng sai 2 cho c hai chiu.

Gi thit cc nt c iu ch BPSK. Trong pha u tin, gi thit bit thng tin v knh y ti nt Chuyn tip (nt nhn) v khng c thng tin v knh ti hai nt Cui (nt pht). S nh hng ca cng sut pht

1N

3N

2N

Hnh 1. M hnh knh chuyn tip hai chiu

H

1x

2x

1r

2r

k

11h

12h21h

22h

Hnh 2. M hnh h thng chuyn tip hai chiu tng ng


- 16 -

v pha sng mang c th hin trong h s knh phc. Cng thc (1) c vit di dng vc t nh sau:

R= HX+N (2) trong k hiu H l ma trn knh, X l vc t tn hiu pht, N l vc t tp m, R l vc t tn hiu thu. Nt Chuyn tip c gng c lng dng m ha mng ca tn hiu hai nt Cui ngha l

1 2x x . Trong k

hiu l php XOR. Trong pha hai, nt Chuyn tip pht cc c lng gi d liu c m ha mng cho c hai nt Cui. Mi nt Cui sau gii m gi d liu nhn c bng cch thc hin php XOR gia tn hiu thu c vi thng tin chnh n.

II.2. M hnh tch tn hiu MIMO-PNC Cng trnh [1] xut m hnh PNC da trn

tch tuyn tnh MIMO. Trong m hnh ny nt Chuyn tip c lng

1 2x x+ v

1 2x x ch khng

ring l 1x v

2x t tn hiu thu c. Sau n pht

c 1 2x x+ v

1 2x x n cc nt Cui, tn hiu

1 2x x vi php nh x PNC. Tn hiu thu c trong (2) c th c vit nh sau [1]:

1

=

== -R HX+N

(HD )(DX)+N HX+N (3)

11 1

21 1

=

D= D

i vi tch tuyn tnh, cn phi tm ma trn cn bng G tng ng vi H tnh c lng ca X . c lng ca thng tin pht c tnh [1]:

Y =GR=GHX+GN (4) Trng hp tch ZF (Zero-Forcing),

H -1 HG =(H H) H , cn i vi trng hp tch MMSE (Minimum mean square error),

2 1 ( )H H= +G I H H H .

Tn hiu c lng ca X nh sau:

1 1 2

2 1 2

x x x

x x x

+ = = X (5)

Theo [1] s dng Log Likelihood Ratio (LLR) ca 1 2x x t

1y v

2y nh sau:

1 2 1 2

1 2 1 2

1 2 1 2

2 2 2 2

2 1 1 1 2 2

( 1)( )

( 1)

exp(2 / 2 / )cosh(2 / )/ cosh(2 / )

P y y x xL x x y y

P y y x x

y y

= =

=

=

(6) trong { }2 2

,

H

ii i

= G G l phng sai tp m ca

dng th i sau kt hp tuyn tnh. Nguyn tc quyt nh nh sau [1]:

1 2 1 21 2

1 2 1 2

1 khi ( ) 1

1 khi ( ) 1

L x x y yx x

L x x y y

=


- 17 -

Eigenvalue, MSE, Harmonic mean v cui cng l Norm. Cc thut ton ny u c xut s dng cho m hnh MIMO-SDM (phn chia theo khng gian) s dng b tch tn hiu a ng-ten ZF hoc MMSE ti nt ch nn vic p dng vo m hnh MIMO-PNC l cha kh thi. V vy bo m tnh kh thi, chng ti ch xut s dng 3 phng php la chn nt da trn chun ma trn knh, la chn nt da trn trung bnh hi ha v la chn nt da trn gi tr ring vo m hnh MIMO-PNC.

iu ny c ngha rng cc nt Chuyn tip 1,2,...,k K= s hp tc vi nhau chn mt nt c

kh nng nht lm nt Chuyn tip. m lm c nh vy, cc nt Chuyn tip s s dng thng tin v knh c sn n chng qua cc lin kt cc b. Gi thit mi nt Chuyn tip u bit knh thun t cc nt Cui n n k hiu l Hxk. Mi nt k s tnh ch s cht lng knh truyn (CQI: channel quality index) ca cc nt Cui n chnh n. Nt c CQI ln nht c k hiu l s c la chn lm nt Chuyn tip. Trong phn tip theo trnh by cc phng php la chn nt Chuyn tip cho knh v tuyn Chuyn tip hai chiu MIMO-PNC. III.1. La chn nt chuyn tip da trn gi tr ring (Eigenvalue) ca knh

tng ca la chn nt Chuyn tip ny da trn gi tr ring xut pht t thc t rng trong cc h thng MIMO tr ring ca ma trn knh l c xem nh l li nng lng ca knh [11,12]. Kt qu l knh m c gi tr ring ln hn s c li nng lng hn. Gi tr ring ca knh abH l gii phng trnh c trng sau y

det( ) 0,ab =H I (9) Trong I l mt ma trn dng N N v det()

l a thc c trng ca ma trn c hnh thnh bi ab H I . Ma trn abH l mt ma trn phc

( )N N s c N gi tr ring khc nhau. Ma trn abH xem xt y c dng (2 2) s c 2 gi tr

ring c cho bi:

2

11 22 11 22 11 22 12 21

1,2

( ) ( ) 4( )

2

ab ab ab ab ab ab ab ab

abh h h h h h h h+ +

=

(10) c c CQI th mi nt Chuyn tip k u

tin s la chn ( )1,2mink xk = v sau tnh

CQIk k= . Thut ton la chn max-min da trn gi tr ring c tm tt dng pseudocode (m gi) nh trong bng 1. iu ch rng vi trng hp s ng-ten ln ( 2)N > , vic tnh ton gi tr ring nh trong cng thc (10) l khng cn chnh xc v v vy phi s dng cc thut ton tnh gi tr ring ca ma trn bc cao.

III.2. La chn nt chuyn tip theo chun ca vc-t knh (channel norm)

tng chnh ca thut ton ny l nh gi li knh MIMO cho Chuyn tip hai chiu. Tiu ch s dng nh gi li knh MIMO l chun (norm) ca ma trn knh [9,10]. Thut ton ny cng c m rng cho trng hp knh Chuyn tip hai chiu, ch s CQI tng ng vi nt Chuyn tip k c cho bi cng thc sau:

{ }22CQI min xkk = H (11) arg max{CQI }

kk= (12)

trong 2

2H biu din chun Frobenious ca H .

Bng 1. Thut ton la chn nt Chuyn tip da trn gi tr ring (eigen value) ca knh

Input: K , xkH for 1 to k K=

Tnh 1,2

xk theo (10) La chn { }1,2mink xk =

tnh CQI kk=

La chn arg max{CQI }kk

=

end for Output: nt l chuyn tip r


- 18 -

Nt Chuyn tip tt nht s c la chn theo cng thc (12). Chi tit thut ton la chn nt Chuyn tip theo chun ca vc-t knh dng pseudocode (m gi) c trnh by Bng 2 .

III.3. La chn nt chuyn tip theo tiu chun trung bnh hi ho (harmonic mean)

Trong trng hp ny cc nt Chuyn tip s s dng trung bnh hi ha (harmonic mean) thnh phn bin ca knh lm tiu ch la chn [9,10]. Thut ton la chn da trn cc i ha trung bnh hi ha cng c th c m rng cho trng hp knh Chuyn tip hai chiu. Mi nt Chuyn tip tn ti mt lin kt nh Hnh 2. Knh MIMO trn mt lin kt c cha 2x2

knh thnh phn. V vy, trung bnh hi ha ca li knh trong trng hp ny s c tnh nh sau:

2 2

21 1

2CQI

1k

xki jijh= =

=

(13)

Da trn ch s cht lng knh truyn ny v cng thc (12), c th biu din thut ton la chn nt Chuyn tip theo tiu chun trung bnh hi ho dng pseudocode nh Bng 3 .

IV. KT QU M PHNG IV.1. M hnh m phng

chng minh li th ca cc thut ton trn i vi m hnh knh Chuyn tip hai chiu MIMO-PNC, chng ti c thc hin khc nhau m phng Monte-Carlo c c BER trung bnh. Trong kch bn m phng u tin, chng ti s dng mt m hnh n gin vi ba nt, tc l 2 nt Cui v 1 nt Chuyn tip. la chn nt Chuyn tip, chng ti gi nh rng c hai nt Chuyn tip trong vng ph sng ca 2 nt Cui. Cc thut ton la chn nt s c s dng chn nt tt nht lm nt Chuyn tip. Cc knh gia 2 nt Cui n cc nt Chuyn tip c gi nh chu nh hng ca pha-inh Rayleigh khng tng quan. Cc nt Cui c trang b mt ng-ten, nt Chuyn tip c trang b hai ng-ten v truyn tn hiu BPSK trn hai nhnh song song. Nng lng symbol trung bnh ca mi nt c chun ha l

sE .

Nt Chuyn tip s dng b kt hp ZF, MMSE trong phn II (0) c lng tn hiu pht. T tn hiu c lng ny s c m ha theo php nh x modul-2 (XOR) bng phng php LLR hoc Selective pht qung b ti hai nt Cui. Trong m phng th hai, chng ti s dng mt m hnh tng t nhng t s

0/

bE N l c nh, trong khi s lng cc nt Chuyn tip tng ln phn tch hiu qu ca vic la chn mt nt Chuyn tip t mt s lng ln cc nt. Trong tt c cc m phng, BER ca trng hp khng la chn nt [1] cng c v ln so snh. IV.2. Phn tch hiu sut

Hnh 3 v Hnh 4 so snh hiu sut BER trung bnh thu c ca cc thut ton xut so vi trng hp khng la chn nt m [1] xut trong m hnh MIMO-PNC s dng tch ZF (LLR v Selective).

T Hnh 3 v Hnh 4 chng ta thy r rng ba thut ton c xut c hiu sut BER tt hn trong trng hp khng la chn nt m [1] xut, ti tt c khu vc

0/

bE N thp, v

0/

bE N cao. C th, ti

3BER 10= thut ton xut la chn nt Chuyn tip da trn gi tr ring ca ma trn knh c t s

Bng 3. Thut ton la chn nt Chuyn tip theo tiu chun trung bnh hi ha


tnh CQIk

theo (13) La chn arg max{CQI }

kk=


Bng 2. Thut ton la chn nt Chuyn tip theo chun ca vc-t knh (channel norm)


tnh CQIk

theo (11) La chn arg max{CQI }

kk=



- 19 -

0/

bE N tt hn 5dB (s dng tch ZF-LLR) v 6dB (s dng tch ZF-Selective) trong khi thut ton xut da trn chun ca vc-t knh v trung bnh hi ha ci thin t c 1dB. R rng khong cch gia thut ton xut la chn nt da trn Eigenvalue l ln hn nhiu so vi cc thut ton xut cn li.

Hnh 5 v Hnh 6 so snh hiu sut BER trung bnh thu c ca cc thut ton xut so vi trng hp khng la chn nt m [1] xut trong m hnh MIMO-PNC s dng tch MMSE (LLR v Selective). Hnh 5 v Hnh 6 chng ta thy r rng ba thut ton c xut (Eigenvalue, norm, Harmmean) c hiu

sut BER tt hn trong trng hp khng la chn nt m [1] xut, ti tt c khu vc

0/

bE N thp, v

0/

bE N cao. C th, ti 3BER 10= thut ton xut la chn nt Chuyn tip da trn gi tr ring ca ma trn knh c t s

0/

bE N tt hn 2dB (s

dng tch MMSE -LLR) v khong 3, 3 dB (s dng tch MMSE-Selective) trong khi thut ton xut da trn trung bnh hi ha (Harmmean) ci thin c 1 dB (s dng tch MMSE-LLR, Selective). Thut ton xut da trn chun (norm) ci thin ln lt l 0,5 dB (s dng tch MMSE-LLR) v 0, 8 dB (s dng tch MMSE-Selective).

Hnh 3. Phm cht BER ca m hnh MIMO-PNC da trn ZF (LLR) cho cc trng hp la chn nt khc

nhau v khng la chn nt, 2 nt chn 1

Hnh 4. Phm cht BER ca m hnh MIMO-PNC da trn ZF (Selecttive) cho cc trng hp la chn nt

khc nhau v khng la chn nt, 2 nt chn 1

Hnh 6. Phm cht BER ca m hnh MIMO-PNC da trn MMSE (Selective) cho cc trng hp la chn nt khc nhau v khng la chn nt, 2 nt chn 1

Hnh 5. Phm cht BER ca m hnh MIMO-PNC da trn MMSE (LLR) cho cc trng hp la chn nt khc

nhau v khng la chn nt, 2 nt chn 1


- 20 -

Trong hai phng php tch tn hiu (ZF, MMSE) chng ta thy phng php tch MMSE cho phm cht BER tt hn so vi phng php tch ZF khi s dng thut ton la chn nt Chuyn tip da vo chun (norm) hay trung bnh hi ha (harmmean), cn thut ton la chn nt Chuyn tip da vo gi tr ring ca ma trn knh cho phm cht BER gn nh ging nhau cho c hai phng php tch ZF hay MMSE, c th xt

0/

bE N = 30 dB t cc Hnh 3, Hnh

4, Hnh 5 v Hnh 6 phm cht BER = 41, 5 10 . iu ny kh th v khi s dng phng php tch ZF chng ta ch cn bit thng tin trng thi v knh truyn, trong khi phng php tch MMSE ngoi thng tin trng thi knh truyn chng ta cn phi bit phng sai ca tp m.

Hnh 7, Hnh 8, Hnh 9 v Hnh 11 chng ti minh ha hiu sut BER ca ba thut ton thu c ti

0/

bE N = 10 dB, 20 dB i vi trng hp s nt

trung gian ng c ln lt bng 2, 3, 4, 5, 6 . C th thy rng trong ba thut ton xut th thut ton la chn nt da trn gi tr ring ca ma trn knh l tt nht, k n l thut ton la chn nt da trn trung bnh hi ha (harmmean) ca knh v cui cng l thut ton la chn nt da trn chun ca ma trn knh (channel norm). Tuy nhin, tng t nh [10,11] iu th v l vic tng s lng cc nt Chuyn tip khng t c ci thin tt hn, iu ny c gii thch trong [10]. Bn cnh , iu ny cng c th l do thc t suy hao ng truyn khng c tch hp vo m hnh knh. iu ny vn cn c nhng kho st thm nh gi.

T cc kt qu m phng c th thy rng thut ton la chn nt da trn gi tr ring mang li hiu qu tt nht, k n l thut ton da trn trung bnh hi ha, v cui cng l thut ton da trn chun ca ma trn knh. iu ny c th c gii thch thng qua ngha li knh ca gi tr ring knh truyn. La chn knh vi tr ring ln nht tng tng vi knh c li ln nht v v vy mang li phm cht BER tt nht. Thut ton trung bnh hi ha vt tri so vi chun ma trn do trnh c trng hp mt trong hai chng b nh hng ln ca pha-inh.

Hnh 7. Phm cht BER ca cc thut ton chn nt theo s nt ng c trong trng hp tch ZF (LLR)

Hnh 8. Phm cht BER ca cc thut ton chn nt theo s nt ng c trong trng hp tch ZF (Selective)

Hnh 10. Phm cht BER ca cc thut ton chn nt theo s nt ng c trong trng hp tch MMSE (LLR)


- 21 -

V. KT LUN Trong bi bo ny, chng ti xut s dng kt

hp la chn nt Chuyn tip vi PNC tng cht lng truyn. Chng ti s dng ba thut ton la chn nt Chuyn tip cho mng Chuyn tip hai chiu MIMO-PNC. Tt c cc thut ton u t c ci thin phm cht BER so vi khng la chn nt Chuyn tip m [1] xut. Thut ton la chn nt Chuyn tip da trn gi tr ring ca ma trn knh c th hin l ng vin tt nht v mt phm cht BER. Cc thut ton nu trn u da trn m hnh la chn nt phn tn (distributed) v v vy rt thch hp cho mng Ad-hoc, mng thng tin di ng t bo.

LI CM N

Cng trnh c thc hin trong khun kh ti Ngh nh th m s 39/2012/H/NT do B Khoa hc v Cng ngh ti tr.

TI LIU THAM KHO [1] S. ZHANG AND S. C. LIEW, Physical layer network

coding with multiple antennas, in The 2010 IEEE Wireless Communications and Networking Conference (WCNC10), April 2010.

[2] R. AHLSWEDE, N. CAI, S. Y. R. LI, R. W. YEUNG, Network information flow, IEEE Trans. Inform. Theory, vol.46, No.4, 2000, pp. 1204-1216.

[3] S. Y. R. LI, R. W. YEUNG AND N. CAI, Linear network coding, IEEE Trans. Inform. Theory, vol.49, No.2, pp. 1204-1216, Feb. 2003.

[4] T. UNGER AND A. KLEIN, On the Performance of Two-Way Relaying with Multiple-Antenna Relay Stations, in Proc. of 16th IST Mobile and Wireless Communications Summit, Budapest, Hungary, July 2007.

[5] S. ZHANG, S. C. LIEW AND P. P. LAM, Hot topic: Physical layer network coding, ACM MobiCom 06, Sept. 2006, pp. 358-365.

[6] R. H. Y. LOUIE, Y. LI AND B. VUCETIC, Practical Physical Layer Network Coding for Two-Way Relay Channels: Performance Analysis and Comparison, IEEE Trans. Wireless Communication, vol.9, No.2, February 2010, pp. 764-777.

[7] S. KIM AND J. CHUN, Network Coding with Linear MIMO Pre-equalizer using modulo In Two-way channel, in The 2008 IEEE Wireless Communications and Networking Conference (WCNC08), 2008.

[8] Y. LI, R. H. Y. LOUIE, Relay Selection with Network Coding in Two-Way Relay Channels, IEEE Transactions on Communications, vol.59, No. 9, Nov. 2010, pp. 4489-4499.

[9] BLETSAS, A., A simple cooperative diversity method based on network path selection, IEEE Journal on Selected Areas in Communications, vol.24, No.3, March 2003, pp. 659-672.

[10] TRAN, X. N., NGUYEN, V. H., BUI, T. T., DINH, T. C., Distributed relay selection for MIMO-SDM cooperative networks, IEICE Transactions on Communications, vol.E95-B, March 2012, pp. 1170-1179.

[11] D. H. VU, Q. T. DO, X. N. TRAN AND V. N. Q. BAO, Improved Relay Selection for MIMO-SDM Cooperative Communications Lecture Notes in Electrical Engineering (LNEE), Springer, vol. 240, 2013, pp. 919-926.

[12] ANDERSEN, J. B., Array gain and capacity for known random channels with multiple element arrays

Hnh 11. Phm cht BER ca cc thut ton chn nt theo s nt ng c trong trng hp tch MMSE (Selective)


- 22 -

at both ends, IEEE Journal on Selected Areas in Communications, vol.18, No.11, 2000, pp. 2172-2178.

Nhn bi ngy: 25/05/2013

S LC V TC GI V C HIP

Sinh nm 1976 ti Nam nh. Tt nghip C nhn Thng tin Qun s, Khoa V tuyn in, Trng s quan CHKT Thng tin nm 1999; K s ngnh in-in t ti Hc vin K thut Qun s nm 2006; Thc s K thut in t ti Hc vin K thut Qun s nm 2009.

Hin l Nghin cu sinh ti khoa V tuyn in t, Hc vin K thut Qun s. Hng nghin cu chnh bao gm: K thut truyn dn MIMO, cc phng php tch tn hiu MIMO, truyn thng hp tc. T: 0979.365.045 Email: [email protected]

TRN XUN NAM Sinh nm 1971 ti Thanh Ha. Tt nghip th khoa chuyn ngnh K s Thng tin, Khoa V tuyn in t, Hc vin K thut Qun s nm 1993; Thc s K thut vin thng ca Trng i hc K thut Sydney, Australia nm 1998; Tin s K thut

in t ca Trng i hc in-Thng tin, Nht Bn nm 2003; Nhn chc danh Ph Gio s nm 2009. Hin l Ph Ch nhim Khoa V tuyn in t, Hc vin K thut Qun s. Hng nghin cu chnh bao gm: K thut truyn dn MIMO, cc phng php tch tn hiu MIMO, k thut x l khng gian thi gian, m khng gian-thi gian, truyn thng hp tc. T: 069-515384 Email: [email protected]

Documents

124-250-1-PB