MIMO III: CN BNG PHN TP GHP KNH V CC M KHNG GIAN THI GIAN

VN NNG

NHM 8 CHNG 9Vn Quang DngTrn Vit HngNguyn Nam PhongNguyn Hng Sn

NHM 8 CHNG 9

H NI 9/20141

Ni dung Chng 1: Gii thiu chung

1. Gii thiu v cc h thng truyn thng khng dy

2. Tm tt ni dung cc chng ca cun sch

Chng 2: Cn bng phn tp ghp knh v cc m khng gian thi gian vn nng

2

khng gian thi gian vn nng1. Xc nh cn bng ghp knh phn tp cho trng

hp knh fading chm c SNR cao

2. Xy dng cc m vn nng cho trng hp cc knhMIMO v MISO

Chng 1 Gii thiu chung

Gii thiu s hnh thnh, pht trin ca truyn thngkhng dy: 1897: h thng in bo u tin ca Marconi

S pht trin mng di ng: AMPS GSM, TDMA (IS-36), CDMA (IS-95) 3G 4G;

3

36), CDMA (IS-95) 3G 4G;

H thng cc mng WLAN, Bluetooth, Adhoc

Chng 1 Gii thiu chung Ni dung cc chng, ch yu lin quan n knh

fading khng dy: Chng 2: m hnh knh fading a ng

Chng 3: truyn thng qua knh fading im im

Chng 4: a truy nhp v qun l nhiu

Chng 5: dung lng knh khng dy

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Chng 5: dung lng knh khng dy

Chng 6: dung lng a ngi dng v truyn thng c hi

Chng 7: MIMO I: M hnh knh v ghp knh khng gian

Chng 8: MIMO II: Dung lng v kin trc ghp knh

Chng 9: MIMO III: Cn bng phn tp ghp knh v cc mkhng gian thi gian vn nng

Chng 10: MIMO IV: Truyn thng a ngi dng

Chng 2 Cn bng phn tp ghp knh Cng thc

Knh Rayleigh v hng

Knh Rayleigh song song

Knh Rayleigh MISO

Knh 2 x 2 Rayleigh MIMO

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Knh 2 x 2 Rayleigh MIMO

Knh i.i.d Rayleigh MIMO tng qut

Cng thc li phn tp :

Hiu nng quan trng d* c o cho knh fading chm ( tc c nh R, tc cao nht ph thuc vo s r rng knh truyn, xc sut dng)

V d knh i.i.d MIMO

Xc sut dng Xc sut dng

li ghp knh Cc knh MIMO fading nhanh : dung lng ghp knh ( M

ha trn rt nhiu s r rng knh, dung lng trung bnh)

Vi knh i.i.d MIMO

t li phn tp ti a, tc phi c c nh

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Cng thc (tip) Cn bng ghp knh phn tp

li phn tp d*(r) l t c vi li ghp knh nu

v

logR r SNR=*( )(R) SNR d routP

*logp (rlogSNR)lim ( )out d r=

ng cong d*(r) l cn bng phn tp ghp knh caknh fading chm

Vi m hnh m ha khng gian thi gian : thay th Poutbng Pe (v bng d

* )

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*logp (rlogSNR)lim ( )outSNR

d rlogSNR

=

Knh Rayleigh v hng - PAM

M hnh knh v hng Nhiu Gauss trng cng H s fading Cng sut hn ch SNR Xc sut li PAM

Vi SNR cao Ta gi s khong cch cc chm t n Khong cch nh nht t c

Vi ta c

Cn bng phn tp ghp knh cho PAM

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Knh Rayleigh v hng - QAM

QAM : c 2R/2 im chm sao trn mi kch thc thc o

Khong cch nh nht v xc sut li QAM ( SNR cao)

Cn bng phn tp ghp knh cho QAM Cn bng phn tp ghp knh cho QAM

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Knh Rayleigh v hng PAM&QAM

Phn tch trng hp 1: dmax :=d(0) li phn tp c in cho mt m hnh c tc c nh

M t xc sut li R = const c th c gim vi SNR cho mt tc c nh

V d : Tng SNR 6dB vi tc c nh

pe gim do tng Dmincng vi tng SNR

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Knh Rayleigh v hng PAM&QAM

Phn tch trng hp 2 : rmax = arg d(r) = 0

S cc bc t do

M t s nhanh ca tc c th tng vi SNR cho mt xc sut li c nh: pe = const

V d : Tng SNR ln 6dB V d : Tng SNR ln 6dB

Vi pe = const hay

(Dmin = const) th li SNR

c th tn dng tng s

lng bit

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Knh Rayleigh v hng cn bng ti u

Xc sut dng v SNR cao xp x

(Bc cui : cho Rayleigh fading v s nh

QAM khng m ha l ti u DMT

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Knh Rayleigh song song M hnh knh : cc knh song song

Nhiu cng Cng sut gii hn SNR trn tng knh ph li phn tp ti a

Gi s tc mc tiu cho tng knh ph Xc sut dng Xc sut dng

Xc sut dng xy ra nu tng knh ph l dng

Knh bng phn tp ghp knh ti u

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Knh Rayleigh song song

M ha lp li : truyn k t xc nh QAM cho tng knh song song

M ha lp li t c phn tp ton b

Tc c gim bi nhn t 1/

So snh

So snh

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Knh Rayleigh MISO M hnh knh : nt anten truyn Vi:

Nhiu cng Cng sut truyn ton b gii hn SNR li phn tp ti a

Gi s tc mc tiu Xc sut dng Xc sut dng

l mt gi tr bt k vi bc t do 2nt v do

Cn bng phn tp ghp knh ti u

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Knh Rayleigh MISO

Alamouti chuyn mt knh MISO thnh 1 knh v hngvi im dng ging

Alamouti vi QAM l ti u cn bng phn tp ghp knh

M ha lp : truyn cng 1 k t qua 2 anten vo cng 1thi im, ng cn bng phn tp ghp knh vi nt =2thi im, ng cn bng phn tp ghp knh vi nt =2l

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Knh Rayleigh MIMO 2x2

So snh 4 trng hp : M ha lp, Alamouti, V-BLAST

Chng trnh chuyn cc knh thnh knh v hng DFT c th thu c trong cc trng hp v hng

V-BLAST vi b gii m kh nng ti a (ML) Xc sut li cp (PEP) vi 2 t m (vi nng lng truyn trung bnh

chun ha v 1)Xc sut li cp (PEP) vi 2 t m (vi nng lng truyn trung bnhchun ha v 1)

Trng hp xu nht PEP

DMT : ()=2 Ti u DMT : ng tuyn tnh tng phn ni nhau (0,4) , (1,1) v

(2,0)

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Knh Rayleigh MIMO 2x2

So snh 4 m hnh m ha

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Knh i.i.d Rayleigh MIMO tng qut

M hnh knh : (nt x nr) knh MIMO vi i.i.d Rayleigh fading

Xc sut dng vi: R = r logSNR

chin lc truyn K ph thuc vo SNR chin lc truyn Kx ph thuc vo SNR Gi s

DMT cho knh MIMO vi i.i.d Rayleigh fading c th c chia thnh cc on vi cc im ni

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Knh i.i.d Rayleigh MIMO tng qut

Bn tri: ng DMT ti u cho knh MIMO vi i.i.d Rayleigh fading

Bn phi: thm 1 anten pht 1 anten nhn dch ton bng DMT thm 1

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Chng 2 Thit k m ti u ngcn bng phn tp ghp knh

M hnh m vn nng xp x

Knh v hng

Knh song song

Knh MISO

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Knh MISO

Knh MIMO

M hnh m vn nng xp x

Xc sut dng v cc m vn nng t c xc sut nh ty khi knh khng mt lin lc

(chiu di m khi ln, m mnh)

Hin tng fading su nh hng ti hiu sut li SNRcao; n ph thuc vo m hnh v knh truyncao; n ph thuc vo m hnh v knh truyn

Cc m hnh m vn nng xp x Hin tng fading su ch ph thuc vo knh, khng

ph thuc vo m hnh

M xp x l iu kin t c ti u DMT caknh

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Knh v hng

Xc sut li c iu kin h s fading knh l h :

vi dmin 1/2R/2

Xt 2 trng hp Khi khong cch gia cc im chm sao

l ln hn nhiu so vi lch chun ca nhiu Gausian

2 2min| |2

SNRQ h d

minSNR d 1h l ln hn nhiu so vi lch chun ca nhiu Gausian

Khi khong cch gia cc im chm saol nh nhau v mt ln so vi lch chun

Hin tng suy gim su: |h|2< 2R/SNR

iu kin dng ca knhlog ( 1 + |h|2SNR )

Knh v hng

Phn tch trn ch ng vi iu kin knh c h sfading l h nhng khng ng cho h s phn b P(h)

QAM t c DMT ti u di bt k loi knhthng k (khng ch Rayleigh), do n l vn nng

iu kin vn nng xp x ca QAM l: d2min> 1/2Riu kin vn nng xp x ca QAM l: d min> 1/2

Bt c chm sao no vi thuc tnh trn th u l mvn nng xp x

Tm li: Mt m hnh gi l xp x nu n suy gim su ch khi

knh trng thi dng (mt lin lc) M xp x l iu kin t c cn bng DMT

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Knh song song Tiu ch thit k m

Gi s c L knh song song, c m hnh:

yl=hlxl + wl vi iu kin:

M ha: Chiu di t m l L theo L knh con

Tc mi knh con: R bit/s/Hz

Knh i.i.d AWGN nhiu wi CN(0,1)Cng sut truyn mi knh con P = SNR

Tc mi knh con: R bit/s/Hz

iu kin dng ca knh:

iu kin xc sut li cp cho t m xA , xB

Vi sai lch t m chun ha knh th l l:

2

1log(1 | | )

L

ll

h SNR LR=

+

Knh song song Tiu ch thit k m

Mc ch thit k: Tm xc sut li trong trng hp xu nhttrn tt c cc knh m khng mt lin lc:

tng ng

Bi ton ti u

Cng thc thay th, vi ta c:

1

2 2

..... 1min | | | d |

2L

L

l lh h l

SNR h=

2

1log(1 | | )

L

ll

h SNR LR=

+

2 2:Q SNR h d= Cng thc thay th, vi ta c:

tng ng

Cch gii quyt nh Waterfiling

Knh cht lng km nht:

Vi l b nhn Lagrange tha mn iu kin rng buckhng mt lin lc

2 2:l l lQ SNR h d=

1 0.....Q 0 1

1min

2L

L

lQ lQ

=

21

log 1 | |L

l

l l

Q LRd

=

+

22

1 1| | 1| d |l lh

SNR

+

=

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Knh song song Tiu ch thit k m

Xc sut li trng hp xu nht

Vi tha mn

Tiu ch thit k m vn nng

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Knh song song V d M hnh khng m:

L chm sao c lp (QAM) vi mi chm 2R im c pht tch bit c lp trn mi knh con

Trong trng hp xu nht: 2 t m xA , xB ch khc nhau 1 k t, hay ni cch khc ch c 1 t m non-zero dl

Tiu ch thit k c nh gi

M hnh m lp

2 0ld = M hnh m lp

Cng mt k t c truyn trn tt c cc knh con

V d: L = 2 knh con, tc R = 2 bits/s/Hz

Tnh c:

Tiu chun thit k

m l: 8/3

2min 4 / 9d =

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Knh song song V d

M hon v Cng mt chm sao s dng chung cho cc knh con nhng

khc th t k t

Cc k t gn nhau trong chm sao ny th xa nhau trong chm sao kia

V d: L = 2 knh con, R = 2 bits/s/Hz V d: L = 2 knh con, R = 2 bits/s/Hz

Tham s thit k

m l 44/9

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Knh MISO

Ti s kin mt lin lc cho knh MISO nt x 1

Trng hp c bit nt = 2. M hnh Alamouti chuyn knhMISO thnh knh v hng vi li cng sut gimtheo h s 2 xc sut dng thay i nh nhau

h

2log 1 SNRh Rn

+ 2 th sao?

Gii php: chuyn knh MISO thnh knh song song S dng mt anten ti 1 thi im vi 1 m song song ti u

Thu c li cao nht nt cho knh i.i.d Rayleigh fading

t c ti u cn bng cho cc knh vi h s i.i.d fadingnhng khng tng qut

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Knh MISO So snh 2 m hnh: Alamouti v hon v trong trng hp

QAM khng m

li hn km nhau 1.5 dB

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Knh MISO Tiu ch thit k m Xc sut li cp cho 2 ma trn t m b xo trn XA , XB

Trng hp xu nht trn tt c cc knh khng mt lin lc

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vi gi tr ring nh nht 1 ca sai lch t m chun ha:

N t sp xp theo ng cht lng km nht ca ma trn sai lch t m

Tiu ch thit k:Ti a ha gi tr ring nh nht ca khong cch t m

m bo rng tt c cc cp t m tha mn

Knh MIMO M ha m hnh D-BLAST

M hnh knh MIMO fading chm

S kin mt lin lc ma trn hip phng sai phn pht Kx

M hnh D-BLAST vi MMSE-SIC chuyn i knh MIMO thnh nt knh con song song

Vi SINR1 , , SINRnt l tng quan

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Knh MIMO M ha m hnh D-BLAST Xc sut mt lin lc (D-BLAST v MMSE-SIC tc R=rlogSNR

bits/s/Hz)

Xc sut mt lin lc coi nh l suy hao khi to cho n dng bitghp xen

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So snh vi xc sut mt lin lc MIMO

t ng cong cn bng n , n l iu kin bt buc gn ti ucho n xc nh

Ci thin hiu sut cn bng bng b gii m ML chung cho cc dng bit

Knh MIMO V d V d knh fading MIMO 2 x 2

n = 2 vi cc t m con

v

Truyn pht phn chia theo anten v thi gian

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D-BLAST vi b gii m ML l DMT ti u vi 0 r 1

Knh MIMO Tiu ch thit k m

Tng t nh trng hp knh MISO: knh trong trng hpxu nht t sp xp theo hng yu nht c cho bi ma trnsai lch t m i mt

Knh MIMO: c nmin hng

Tiu ch thit k: ti a ha vi nmin l gi tr nhnht ca cc ma trn sai lch t m chun ha

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nht ca cc ma trn sai lch t m chun ha

Vi nt nr , n tng ng vi tiu ch quan trng

Nh cho cc knh song song, m xp x vn nng c c tnh:

Tiu ch lng hn:

vi c l hng s >0

Knh MIMO Tiu ch thit k m

Mt m m tha mn tiu ch lng nu trn cho knhMIMO kch thc nt x nt th cng l m xp x cho knhMIMO kch thc nt x nr vi mi gi tr ca s lnganten thu nr .

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anten thu nr .

KT LUN i vi mt knh fading chm c SNR cao, s cn bng

gia tc d liu v xc sut li c xc nh bi s cnbng gia li ghp knh v phn tp;

li phn tp ti u d*(r) c xc nh bi xc sut mtlin lc ca knh tc d liu r logSNR bits/s/Hz;

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M vn nng cung cp mt tiu chun thit k m mi;thay v trung bnh ha trn s liu thng k ca knh,chng ta xem xt n hiu sut ca mt m qua knh xunht m n khng mt lin lc;

KT LUN i vi mt knh song song, tiu ch thit k m vn nng

l ti a tch ca cc sai lch t m; n cng tng tnh tiu chun xy ra bi trung bnh ha qua knhRayleigh thng k

i vi knh MISO, tiu chun thit k m vn nng l ti a ha gi tr n nh nht ca ma trn sai lch t m.

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ti a ha gi tr n nh nht ca ma trn sai lch t m.

i vi knh MIMO kch thc nt x nr , tiu ch thit k mvn nng l ti a ha tch ca nmin cc gi tr n nhnht ca ma trn sai lch t m. i vi nr nt , tiu chunny tng t nh tiu chun trung bnh ha qua knhthng k i.i.d Rayleigh.

Nhm 8 Truyn thng s nng cao40