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
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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
=
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log 1 | |L
l
l l
Q LRd
=
+
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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