SIC_K18D_11021083

I HC QUC GIA H NI

TRNG I HC CNG NGH

---------------- ----------

HONG HU THNH

DUNG NNG A NGI DNG V K

THUT SIC

Ngnh : Cng ngh in t - Vin thng

Chuyn ngnh : K thut in t

M s : 60.52.0203

LUN VN THC S CNG NGH IN T - VIN THNG

NGI HNG DN KHOA HC:

PGS.TS. TRNH ANH V

H Ni-2013

LI CAM OAN

Ti xin cam oan Lun vn: "Dung nng a ngi dng v k thut SIC" l

cng trnh nghin cu ca ring ti. Cc s liu, kt qu trnh by trong Lun vn l

trung thc, mt phn c cng b trn cc tp ch khoa hc chuyn ngnh, k yu

hi ngh khoa hc trong nc v quc t. Phn cn li cha c cng b trong bt k

cng trnh nghin cu no. Nhng kt qu tnh ton m phng t c trong Lun

vn khng sao chp t bt c ti liu no di mi hnh thc. Nhng kt qu l

nhng g ti nghin cu, tch ly trong sut thi gian lm Lun vn.

H Ni, ngy 28 thng 9 nm 2013

HC VIN

LI CM N

Ti xin by t lng bit n su sc ti PGS.TS. Trnh Anh V ngi tn tnh

hng dn ti trong sut qu trnh thc hin v hon thnh Lun vn. c bit, Thy

nh hng v c nhng s ch bo tn tnh, to iu kin thun li trong khi xy

dng cng nghin cu, cng nh trong qu trnh thc hin Lun vn. S ch bo

tn tm ca Thy c ngha v cng to ln ti c th hon thnh Lun vn ny.

Xin trn trng cm n s ch bo, gip tn tnh ca cc thy c gio khoa

in t - Vin thng trong qu trnh hc tp v nghin cu ti Khoa.

Xin chn thnh cm n Trng i hc Cng Ngh - HQGHN h tr,

gip ti c iu kin v thi gian hc tp, nghin cu.

Cui cng ti xin cm n gia nh, bn b, ng nghip v ngi thn gip

, chia s, khch l, ng vin ti c th hon thnh lun vn ny.

H Ni, ngy 28 thng 09 nm 2013

HC VIN

MC LC

LI CAM OAN ................................................................................................ 2

LI CM N ..................................................................................................... 3

MC LC ........................................................................................................... 4

DANH MC CC K HIU, CH VIT TT ............................................... 6

DANH MC CC HNH V, TH, BNG BIU .................................... 10

GII THIU ............................................................................................................ 11

Mc tiu nghin cu ca Lun vn .................................................................. 12

i tng nghin cu: ...................................................................................... 12

Phng php nghin cu:................................................................................. 12

Cu trc ca Lun vn: .................................................................................... 13

CHNG I. M HNH KNH MIMO ................................................................... 14

1.1. Gii thiu h thng MIMO ................................................................................ 14

1.2. Knh MIMO tng qut ....................................................................................... 15

1.3. M hnh knh ly mu ....................................................................................... 17

1.3.1. Tng quan khng gian fading................................................................ 17

1.3.2. Mng anten nhn thy nhau (Line-of-sigh) LOS ..................................... 19

1.3.3. Mng anten i cc (Cross-polarized) ..................................................... 20

1.4. M hnh tn hiu vo ra ..................................................................................... 20

1.5. Kt lun chng ................................................................................................ 23

CHNG II: DUNG NNG KNH MIMO A NGI DNG (MU-MIMO) ..... 24

2.1. Dung nng knh SU-MIMO .............................................................................. 25

2.2. Vng dung nng knh MAC .............................................................................. 26

2.3. Vng dung nng knh qung b (BC) ............................................................... 29

2.3.1. Dung nng tng BC c th t c v i ngu UL/DL ........................ 31

2.4. T MIMO n ngi dng n MIMO a ngi dng .................................... 36

2.4.1. Nhc li khi nim ng ln, ng xung. .......................................... 36

2.4.2. Cc c im ni bt ca MU-MIMO so vi SU-MIMO. ........................ 37

2.4.3. Nhng kt qu t c v vn tn ti h MU-MIMO so vi SU-

MIMO ................................................................................................................ 38

2.5. Kt lun chng ................................................................................................ 40

CHNG III: K THUT SIC VI MU-MIMO UPLINK .................................... 42

3.1. Ghp knh khng gian ....................................................................................... 43

3.1.1. Nguyn l c bn ...................................................................................... 43

3.1.2. Ghp knh da trn m trc .................................................................. 46

3.1.3. X l b thu phi tuyn .............................................................................. 48

3.2. M trc SMMSE .............................................................................................. 49

3.3. Gii m vi b thu SMMSE-SIC ....................................................................... 52

3.4. Kt lun chng ................................................................................................ 55

CHNG IV: M PHNG NH GI H THNG ............................................ 56

4.1. nh gi hiu sut b thu qua dung nng tng t c ca b thu ............... 56

4.2. nh gi hiu sut qua t l li bt BER ........................................................... 58

4.3. Kt lun chng ................................................................................................ 60

KT LUN V HNG PHT TRIN .................................................................. 61

1. Kt lun ca ti ................................................................................................ 61

2. xut hng pht trin ca ti ..................................................................... 61

TI LIU THAM KHO ......................................................................................... 63

DANH MC CC K HIU, CH VIT TT

()+ - (x)+:= max(0, x)

||X || - Chun Frobenius ca mt ma trn

X* - Ma trn lin hp

XH - Chuyn v ca ma trn lin hp

XT - Ma trn chuyn v

1 - Ma trn vi tt c cc phn t l 1 (ma trn n v)

A - Ma trn iu hng mng

- H s xc nh t xch c s dng t gii hn cng sut pht

B - Ma trn phn hi THP kch thc r r

CN (a, b) - Bin ngu nhin Gauss phc vi k vng a v phng sai b

CBC - Dung nng Shannon ca knh qung b

CMAC - Dung nng Shannon ca a truy cp

CSU - Dung nng Shannon n ngi dng

D - Ma trn gii m kt hp cho tt c ngi dng trn ng ln kch thc r x MT Di - Ma trn gii m ca ngi dng th i on the trn ng ln kch thc ri x MT

Da - Ma trn gii m kt hp kh MUI cho tt tt c ngi dng trn ng ln

Db - Ma trn gii m kt hp d liu gii m cho tt c ngi dng trn ng ln

Dai - Ma trn gii m ca ngi dng th i kh MUI trn ng ln

Dbi - Ma trn gii m ca ngi dng th i cho gii m d liu trn ng ln

E {} - Hm trung bnh

- Ma trn ti cng sut

i - Ma trn ti cng sut ca ngi dng th i

impD - Ma trn ti cng sut phn tp ci tin

MMSE - Ma trn ti cng sut MMSE

i,i - Phn t trn ng cho chnh ca ma trn ti cng sut

f0 - Khong cch sng mang con

Fa - Ma trn m trc kt hp kh MUI cho tt c ngi dng trn ng xung

Fb - Ma trn m trc kt hp d liu m trc cho tt c ngi dng trn ng xung

Fai - Ma trn m trc ca ngi dng th i kh MUI trn ng xung

Fbi - Ma trn m trc ca ngi dng th i cho d liu m trc trn ng xung

F - Ma trn m trc kt hp cho tt c ngi dng trn ng xung kch thc MT xr

Fi - Ma trn m trc ca ngi dng th i trn ng xung vi kch thc MT ri

GCSI - li c lng knh

G - Ma trn gii m kt hp tt c cc ngi dng trn ng xung kch thc r x MR

Gi - Ma trn gii m ngi dng th i trn ng xung vi kch thc ri MR

H - Ma trn knh mng MIMO kt hp kch thc MR MT

Hest - c lng ca ma trn knh

Hi - Ma trn knh MIMI ca ngi dng th i kch thc MRi MT

2

(,)

- Ma trn knh MIMI ca ngi dng th i trn mu th j ca on d liu th k

()

- Ma trn knh tng ng ca ngi dng th I trn on d liu th k

- Ma trn knh mng MIMO kt hp ca nhiu ng knh ln ngi dng th i

H (l) - Ma trn knh mng MIMO kt hp ca thnh phn ng dn knh th l

Hw - Knh khng gian MIMO trng kch thc MR MT

I - Ma trn n v

K - S ngi dng

KR - H s Ricean

MR - Tng s anten ca u cui ngi dng

MRi - S lng anten ti u cui ngi dng th i

MT - S lng anten ti trm c s

n - Vector mu tp m Gauss cng sinh ti u vo ca anten thu

- Tp m cng sin c lc trn d liu th i

N - Tng s sng mang con trong h thng OFDM

Npre - Chiu di ca k hiu tin t tun hon OFDM

Nc - S sng mang con c dng truyn mt khi d liu

Nsymb - S Number k hiu OFDM trong mt khi d liu

PT - Tng cng sut pht

Pt - Cng sut ca mt k hiu d liu phc

PAP () - Thng tin v cng sut gc ca knh

PDP ( ) - Thng tin cng sut tr ca knh

Q - Ma trn m trc kt hp ca tt c ngi dng ng ln kch thc MR x r

Qi - Ma trn m trc ngi dng th i trn ng ln kch thc MRi ri

R - Ma trn tng quan

Ri - Tc d liu ngi dng th i

- Tc d liu ngi dng th i trn ng xung

- Tc d liu ngi dng th i trn ng ln

r - Tng s lung d liu c truyn trong mt h thng a ngi dng

ri - S lung d liu c truyn ti ngi dng th i

Rr - Ma trn tng quan bn thu

Rt - Ma trn tng quan bn pht

Rx - Ma trn tng quan d liu u vo kch thc r r

Rn - Ma trn tng quan tp m

e - Phng sai ca sai s c lng knh

i - Gi tr ring th i

- Phng sai tp m cng sinh ti u vo ca mt anten

- tr RMS

- rng gc RMS

- Ma trn ng cho vi cc gi tr ring trn ng cho chnh khng tng

U - Cc vector suy bin phi (ct)

V - Cc vector suy bin tri (hng)

x - Vector d liu u vo kt hp tt c ngi dng kch thc r 1

xi - Vector d liu u vo ca ngi dng th i kch thc ri 1

y - Vector thu kt hp ca tt c ngi dng kch thc r 1

yi - Vector thu ca ngi dng th i kch thc ri 1

zi - D liu m ha ngi dng th i

ADC - Analog digital converter

AP - Access point

BC - Broadcast channel

BER - Bit error rate

BD - Block diagonalization

BS - Base station

CCDF - Cumulative complementary distribution function

CQI - Channel quality indicator

CSI - Channel state information

DET - Dominant eigenmode transmission

DFE - Decision feedback equalizer

DFT - Discrete Fourier transform

DL - Downlink

DPC - Dirty-paper coding/Dirty-paper code

FDD - Frequency division duplex

FDMA - Frequency division multiple access

IQ - In-phase /Quadrature

IRBD - Iterative regularized block diagonalization

JRBD - Joint regularized block diagonalization

LDC - Linear Dispersion Code

LNA - Low-noise amplifier

LOS - Line of sight

MAC - Multiple access channel

MIMO - Multiple-input multiple-output

MMSE - Minimum mean square error

MSE - Mean square error

MU - Multi-user

MUI - Multi-user interference

NLOS - Non-line-of sight

OFDM - Orthogonal frequency division multiplex

OFDMA - Orthogonal frequency division multiple access

OSTBC - Orthogonal space-time block code

PA - Power amplifier

PAP - Power angle profile

PDP - Power delay profile

QAM - Quadrature amplitude modulation

QoS - Quality of service

RF - Radio frequency

RMS - root-mean-squared

RBD - Regularized block diagonalization

RSO THP - Regularized successive optimization Tomlinson-Harashima-precoding

QOSTBC - Quasi-orthogonal space time block coding

SDMA - Spatial division multiple access

SIC - Successive interference cancellation

SINR - Signal to interference plus noise ratio

SISO - Single-input single-output

SNR - Signal to noise ratio

SMMSE - Successive minimum mean square error

SMUX - Spatial Muliplexing

SO THP - Successive optimization Tomlinson-Harashima-precoding

STC - Space Time Coding

SU - Single user

SVD - Singular value decomposition

TDD - Time division duplex

TDMA - Time division multiple access

THP - Tomlinson-Harashima-precoding

UL - Uplink

ULA - Uniform Linear Array

UT - User Terminal

V-BLAST - Vertical Bell Labs Layered SpaceTime

VS - Very simple

WINNER - Wireless World Initiative New Radio

ZF - Zero forcing

DANH MC CC HNH V, TH, BNG BIU

Hnh 1.1: M hnh h thng MIMO............................................................................ 14

Hnh 1.2: M hnh knh MIMO vi MT anten pht v MR anten thu ........................... 15

Hnh 1.3: M hnh mng anten nhn thy ................................................................... 19

Hnh 1.4: S khi h thng MU-MIMO downlink .................................................. 21

Hnh 1.5: S khi tn hiu vo ra h thng MU-MIMO ng uplink.................... 22

Hnh 2.1: Vng dung nng MAC vi k thut thu SIC h thng SISO ((2,1),1) ........... 28

Hnh 2.2: Hnh bn tri l hai vng dung nng s dng cho mt BC suy bin vi M=1.

Hnh ph bn phi l hai vng dung nng s dng cho mt BC khng suy

bin vi M>1. Khu vc ny l phn li ca s kt hp t l dung nng ca

hai ngi dng. ......................................................................................... 31

Hnh 2.3: Gii hn cn trn ca BC, dung nng tiu hao 10%. Trng hp MR < MT .................................................................................................................. 35

Hnh 2.4: Gii hn cn trn ca BC, dung nng tiu hao 10%. Trng hp MR > MT .................................................................................................................. 36

Hnh 3.1: Kin trc b thu MIMO ti u .................................................................... 42

Hnh 3.2: H thng MIMO cu hnh anten 2x2 .......................................................... 45

Hnh 3.3: Thu tuyn tnh/Gii ghp knh cc tnh hiu c ghp khng gian ........... 45

Hnh 3.4: Ghp knh khng gian da trn m trc .................................................. 46

Hnh 3.5: Trc giao ha tn hiu ghp khng gian thng qua m trc. l gi tr eigen

th i ca ma trn HHH .............................................................................. 47

Hnh 3.6: Truyn dn mt t m (a) v a t m (b) .................................................. 48

Hnh 3.7: Gii ghp knh/gii m tn hiu ghp khng gian da trn SIC .................. 49

Hnh 4.1: Dung nng cc b thu tuyn tnh v phi tuyn (4x4) ................................... 56

Hnh 4.2: T l tng i ca dung nng cc b thu (4x4) ......................................... 57

Hnh 4.3: Dung nng cc b thu tuyn tnh v phi tuyn (12x12) ............................... 58

Hnh 4.4: M hnh m phng nh gi t l li bt BER ............................................. 58

Hnh 4.5: Hiu sut BER ca ZF, MMSE, ZF-SIC, MMSE-SIC vi iu ch BPSK trn

knh truyn Rayleigh MIMO (4x4) ng uplink. ...................................... 59

Hnh 4.6: Hiu sut BER ca ZF, MMSE, ZF-SIC, MMSE-SIC vi iu ch BPSK trn

knh truyn Rayleigh MIMO (12x12) ng uplink. .................................. 60

GII THIU

Trong thi i pht trin bng n ca cc h thng thng tin v tuyn, nhu cu

v cht lng, dung lng, cc dch v a phng tin v tnh a dng trong cc h

thng thng tin khng dy nh thng tin di ng, internet ang tng ln mt cch

nhanh chng trn phm vi ton th gii. Tuy nhin, ph tn s v tuyn l hu hn,

mun tng dung lng bt buc phi tng hiu qu s dng ph tn s. V vy, vic

nghin cu, ng dng cc cng ngh v k thut tin tin p ng nhu cu ny lun

l mt i hi cp thit. Mt trong nhng k thut c th gip ci thin ng k ch

tiu, dung lng, tc d liu nh v phm vi lin lc ca h thng c tp trung

nghin cu trn th gii trong thi gian gn y chnh l k thut a u vo a u

ra MIMO (Multiple Input Multiple Output) hay k thut s dng nhiu anten pht v

nhiu anten thu. H thng MIMO c th xem nh mt h thng ghp nhiu knh con

mt u vo mt u ra SISO (Single Input Single Output) hay h thng n anten.

Dung lng knh ca h thng MIMO l tng hp dung lng ca cc knh con thnh

phn. Dung lng knh MIMO b nh hng bi s thay i phn b tng ch c

trng ca cc knh con SISO. Gii php s dng nhiu phn t anten ti c my thu v

my pht cho php khi phc d liu pht tt hn, ci thin qu trnh tch d liu ca

ngi s dng. Hai m hnh MIMO c bn l m ha khng gian thi gian STC

(Space Time Coding) v ghp knh phn chia khng gian SM (Spatial Multiplexing).

M ha khng gian thi gian c dng lm ti a phn tp khng gian trong cc

knh MIMO. MIMO s dng nhiu anten pht v nhiu anten thu m thm cc

knh truyn trong min khng gian. Do cc knh song song c m ra cng thi

gian, cng tn s, nn t c tc d liu cao m khng cn bng thng ln. Ni

mt cch khc l nh s dng nhiu phn t anten c pha pht v pha thu, cng vi

cc k thut x l tn hiu bn pht v bn thu, m k thut ny cho php s dng hiu

qu ph tn s cho h thng thng tin v tuyn, ci thin tc d liu, dung lng

knh truyn cng nh tin cy hn so vi cc h thng truyn thng n anten bng

cch x l theo c hai min khng gian v thi gian.

Trong thi gian gn y, cc nghin cu trn th gii ngy cng quan tm nhiu

n cc h thng thng tin v tuyn MIMO. Trong c nhiu hng nghin cu gii

quyt cc vn khc nhau nh bi ton dung lng knh a ngi dng MIMO, cc

bi ton tch sng, bi ton c lng knh truyn, bi ton m ha khng gian thi

gian, x l tn hiu khng gian thi gian,... Mt kh khn gp phi trong vic gii

quyt bi ton tch sng l cht lng h thng ny b nh hng mnh bi can nhiu

a truy cp MAI (Multiple Access Interference), hiu ng xa gn (near-far effect) v

giao thoa lin k t ISI (InterSymbol Access Interference), c bit l khi s lng

anten tng ln. Do nhng hn ch trn, nhiu hng nghin cu khc nhau c

xut trit can nhiu MAI, trong ng ch l phng php tch sng a truy

cp MUD (MultiUser Detection). tng c bn ca phng php ny l khai thc

cu trc ca can nhiu MAI trit n. my thu, thng tin ca tt c cc user c

s dng thc hin vic tch sng cho tng user. Do tnh phc tp qu cao ca

phng php tch sng ti u nn cc nghin cu v MUD tp trung vo cc b

tch sng cn ti u. Cc b tch sng ny c hiu nng gn bng b tch sng ti u

nhng n gin, thc t hn, chng c chia lm hai loi tuyn tnh v khng tuyn

tnh. Cc b tch sng tuyn tnh p dng php bin i tuyn tnh i vi ng ra ca

b lc phi hp nh b tch sng gii tng quan, b tch sng MMSE (Minimum

Mean-Square Error). Trong khi , cc phng php khng tuyn tnh thc hin lp

li vic ti to v tr can nhiu MAI, chng hn nh b trit nhiu ni tip SIC

(Successive Interference Cancellation), b trit nhiu song song PIC (Parallel

Interference Cancellation ), vv

Lun vn nghin cu v Dung nng a ngi dng v k thut SIC trong h

thng MIMO, i vo nghin cu k thut x l, tnh ton thc hin lp li vic ti

to v kh nhiu ni tip t tn hiu thu c ti b thu ca h a ngi dng nhm

t c dung nng tng mong mun. Hot ng ca cc h thng c xy dng trn

c s ton hc v kt qu m phng so snh gia m hnh tch sng SIC mi t

c dung nng so vi cc m hnh tch sng khc thc hin bng MATLAB. MIMO

a ngi dng c p dng cho c ng ln v ng xung nhng lun vn ch

trnh by su v ng ln v b thu p dng k thut SIC ti trm c s.

Mc tiu nghin cu ca Lun vn

- C s l thuyt dung nng a ngi dng so vi dung nng n ngi dng.

- K thut SIC t dung nng so vi k thut khc.

- M phng v nh gi h thng.

i tng nghin cu:

- H thng thng tin v tuyn MIMO.

- X l tn hiu min khng gian, thi gian v tn s trong h thng thng tin v

tuyn tin tin.

- K thut kh nhiu ni tip SIC ca b thu trong h thng MU-MIMO p dng

cho ng uplink ti trm c s.

Phng php nghin cu:

Phng php nghin cu ca lun vn bao gm vic nghin cu l thuyt, xy

dng m hnh, xut, ci tin cc thut ton kt hp vi m phng trn my tnh.

Cu trc ca Lun vn:

Lun vn gm 4 chng vi ni dung tm tt nh sau:

Chng 1: M hnh knh MIMO

Chng ny l ci nhn tng quan v m hnh knh h thng MIMO, m t cc

m hnh knh m n s c s dng trong cc m phng, v mt m hnh tn hiu vo

ra ri rc cng s c gii thiu. Biu din knh da trn m hnh ton hc, phn

tch v tm iu kin p dng k thut MIMO mt cch hiu qu.

Chng 2: Vng dung nng ca knh MU-MIMO

Trong chng ny, chng ta tp trung dung nng knh MIMO n ngi dng

v a ngi dng trong l thuyt Shannon. Dung nng Shannon ca mt knh bt

bin theo thi gian c nh ngha l thng tin tng h ln nht gia cc knh u

vo v u ra. y l tc d liu ti a c th c truyn qua cc knh vi xc

sut li nh ty . i vi ng ln chng ta s tn ton dung nng tng t c khi

s dng k thut thu MMSE kt hp vi SIC. Cui cng l s so snh, nh gi gia

dung nng knh MIMO a ngi dng v n ngi dng.

Chng 3 : K thut SIC vi MU-MIMO uplink

Chng ny chng ta s tp trung phn tch m ha v gii m trong h thng

MU-MIMO qua m t thut ton SMMSE-SIC p dng ti b thu a ngi dng

cho ng uplink (ti trm c s), mt phng php kh nhiu lin tip kt hp vi k

thut thu SMMSE trong h thng MU-MIMO.

Chng 4: M phng nh gi h thng

S dng Matlab tin hnh m phng cc k thut ZF, MMSE, ZF-SIC,

MMSE-SIC t kt qu m phng chng ta s phn tch, so snh v nh gi hiu nng

ca k thut SIC so vi k thut tch sng a ngi dng khc.

Phn kt lun v hng nghin cu tip theo ca lun vn: Trnh by tm tt cc

kt qu t c ca lun vn v nu ra hng pht trin tip theo ca ti, cng

nh nhng nghin cu d kin s thc hin trong tng lai.

CHNG I. M HNH KNH MIMO

1.1. Gii thiu h thng MIMO

MIMO l cc h thng truyn dn v tuyn s dng ng thi nhiu anten my

pht v my thu, nhm tng tc truyn. Chui tn hiu pht c m ha theo c hai

min khng gian v thi gian nh b m ha khng gian thi gian (STE: Space-Time

Encoder). Tn hiu sau khi c m ha khng gian - thi gian c pht i nh N

anten pht. My thu s dng cc k thut thu vi M anten thu. Knh tng hp gia

my pht (Tx) v my thu (Rx) c N u vo v M u ra c gi l knh MIMO

MN. Trong cc trng hp c bit khi N = 1 v M = 1, cho ta h thng MIMO n

ngi dng (tng ng SISO).

H thng MIMO c th tng ng k tc truyn d liu, gim nhiu, tng vng

bao ph h thng v tuyn m khng cn tng cng sut hay bng thng h thng. Bn

cnh vic tng dung lng, k thut truyn dn ghp knh khng gian cho php t

c tc cao nh truyn tn hiu song song t cc anten pht. Ti my thu, cc

lung d liu c tch ra thng qua cc dy k t knh khng gian khc nhau, mc

d chng c truyn i cng tn s. Ngi ta s dng cc b tch hp l cc i c

li phn tp ti a t c hiu nng ti u, song phc tp tng theo hm

m cng vi s lng anten ca my pht. dung ha gia phc tp v hiu nng

cn phi nghin cu dung ha cc gii thut vi quy tc tch sng nhm ci thin cht

lng h thng MIMO.

Hnh 1.1: M hnh h thng MIMO

1.2. Knh MIMO tng qut

Xt m hnh knh MIMO tng qut gm MT anten pht v MR anten thu c

minh ha trong hnh 1.2 vi ma trn (,):

Hnh 1.2: M hnh knh MIMO vi MT anten pht v MR anten thu

Ma trn knh (,) cho m hnh MIMO c biu din nh sau:

(;)=

,(,) ,(,)

,(,) ,(,)

(1.1)

Trong : ,(,)l p ng xung ca knh truyn gia anten truyn th n

( = 1 ) v anten thu th m ( = 1 ) nh mt hm c tr v thi

gian t.

Cc knh MIMO c xy dng theo cc gi nh mng bng tn hp. Theo ,

bng thng ca tn hiu c gi nh l nh hn nhiu so vi i ng ca thi gian

truyn ca cc tn hiu trn cc mng anten. V tr tn x, yu t m hnh, hnh hc ca

anten, v cng vi m hnh phn tn quyt nh cng sut trung bnh v mi tng

quan gia cc phn t ca (,):

Knh fading bin i theo thi gian do s tn x hay do kt qu ca s dch

chuyn b thu / pht trn khong rng Doppler trn mt bng thng quang ph hu

hn ( ), trong l tn s Doppler ti a. Knh fading chn lc thi gian

c c trng bi thi gian gn kt . cng ln, cc knh bin i cng chm.

,

,

,

,

,

.

.

.

.

.

.

My pht My thu

Trong mi trng a ng, mt s thi gian chuyn v cc kiu m rng ca

tn hiu truyn n ngi nhn, m gy ra fading chn lc tn s. tr ng truyn

ti a c gi l khong thi gian tr lan truyn max. tr root-mean-squared

(RMS) ca knh , c nh ngha nh sau:

= ( )()

()

(1.2)

Trong PDP () l gi tr tr cng sut ca cc knh, tc l cng sut trung

bnh nh mt hm tr, v

= ()

()

(1.3)

Knh fading chn lc tn s c c trng bi bng thng kt hp BC ci m

t l nghch vi s tr RMS v l thc o chn lc tn s ca mt knh. Khi bng

thng kt hp l tng ng hoc t hn so vi tn hiu bng rng, knh c cho l

chn lc tn s.

Gc m ti b pht/thu cp n gc m ti ni i/ni n ca cc thnh phn

a ng ti mng anten pht/thu. Gc m RMS, , c xc nh bng cch s

dng ph gc (PAP - power angle profile), tc l cng sut trung bnh l hm ca gc

ti, , nh sau:

=

()

()

(1.4)

y l gc trung bnh ti:

= ()

()

(1.5)

Gc m l cn nguyn ca fading chn lc khng gian, n c c trng bi

khong cch kt hp . Khong cch kt hp l s phn chia khng gian m cc h

s knh tng quan ng k, v n t l nghch vi gc m RMS. Gc m cng ln,

khong cch kt hp cng ngn.

Khong thi gian tr tng t l thun vi khong cch gia cc trm c s v

thit b u cui ngi dng (UT). Trong cc mi trng nng thn l t hn

0,07ms. Trong khu vc th thng l 0,8ms, trong khi trong a hnh i ni

ca 2-3ms c quan st. Trong khi, trong nh cc gi tr trung bnh ca t hn

200ns.

Gc m ph thuc rt nhiu vo kch bn v chiu cao anten. Ti trm c s

(BS) n thay i t mt phn s ca , trong mt kch bn nng thn bng phng ln

n 200 trong cc tnh hung i ni v th dy c. Bin thin khong cch kt

hp t 3-20c, trong c l bc sng ca sng mang. Tn x ti cc u cui ngi

dng (UT) c phn phi trong tt c cc hng ci m mang li chnh lch gc m

ln hn nhiu. Khong cch kt hp ti UT thay i t 0.25c ti 5c. Gc m

phng v trong kch bn trong nh l trong khong 200 n 400.

1.3. M hnh knh ly mu

Chng ta hy xem xt mt mt phng tn s, knh MIMO bin i chm. Ma

trn trong phng trnh (1.1) c th c vit li nh sau:

=

, ,

, ,

(1.6)

Trong , bao gm nhng hiu ng ca trng thi xung ti my pht, lc

kt hp ti b thu v cc knh vt l.

Cc thuc tnh thng k ca ph thuc vo mi trng phn tn v kiu hnh

mng anten ti my pht v my thu. Knh khng gian MIMO Gauss trng c in

c c trng bi:

, = 0;, = 1;,,

= 0, (1.7)

Trong , cc phn t ca , c m hnh ha nh cc bin ngu nhin

Gauss phc. Trong thc t, cc knh MIMO c th lch hng ng k so vi hot

ng bi nhiu l do m s c cp trong cc phn sau.

1.3.1. Tng quan khng gian fading

Tng quan khng gian fading c th c m hnh ha bi:

()= () (1.8)

Trong l knh MIMO khng gian Gauss trng v l ma trn tng

quan khng gian c nh ngha l:

= {()()} (1.9)

Hot ng ca () sp xp tt c cc phn t ca ma trn ct theo ct

trong mt vector ct. Nu SVD ca ma trn R c nh ngha l = , do

c nh ngha l = .

Trong nhiu ng dng, mt m hnh chung n gin v nh, c gi l m

hnh Kronecker, l thch hp hn v c cho bi:

=

(1.10)

Trong l ma trn tng quan pht v

l ma trn

tng quan thu. C hai v l cc ma trn thc bn xc nh. M hnh trong

phng trnh (1.10) c bc t do b hn (1.8), cc m c kh nng chp bt k hiu

ng tng quan no gia cc phn t ca .

M hnh knh MIMO chn lc tn s

Trong trng hp cc knh chn lc tn s, s tng quan anten c m hnh

ha trong phm vi thi gian tr bng cch s dng m hnh Kronecker. Cc thnh phn

ng truyn knh th l c m hnh ha nh:

()= ()

()()

(1.11)

Trong ()

l knh khng gian MIMO fading phng kch thc , c

gi tr phng sai n trng, trong khi ()= ()()/ v

()= ()()/ l cc ma trn tng quan truyn vi

() = v

() = .

Chng ta hy xem xt mt kch bn m bn thu c bao quanh bi mt mi

trng tn x phong ph v cc anten pht c ngn cch bi mt khong nh hn

khong cch ph hp. Nhng iu kin truyn sng tng ng vi mt h thng

truyn thng di ng thng c c trng bi gc m thp my pht. Mt khc,

gc m in thoi di ng thng l rt ln v mi tng quan khng gian thp nh

vy c th t c vi khong cch ly anten tng i nh. Do , chng ta c th

vit:

()= ,

()=

(()()

) ()

()

(1.12)

V thnh phn ng truyn knh th c m hnh nh sau:

()=

(()()

) ()()

(1.13)

Trong () l mt ma trn nh hng mng anten bao gm N

mng vector ca mng anten bn pht tng ng vi N hng ti, v () l

knh khng gian MIMO fading phng, vi gi tr phng sai n trng.

1.3.2. Mng anten nhn thy nhau (Line-of-sigh) LOS

Chng ta hy xt knh MIMO trong iu kin khng c phn x hay nhiu

x, cc dy anten pht v thu u c t thng hng (hnh 1.3), khong cch

gia cc anten trong mng pht v thu tng ng l tt v rc .

Hnh 1.3: M hnh mng anten nhn thy

Cc knh MIMO c th c m hnh tnh ton nh tng ca mt thnh phn

c nh v mt phn nm ri rc nh sau:

=

+ 1 +

1

+ 1 (1.14)

y {} =

l thnh phn LOS ca knh v

l thnh

phn fading gi nh khng tng quan. Cc phn t ca c gi nh l c n

v cng sut. l h s Rice v c nh ngha l mt t l cng sut ca cc thnh

phn LOS v cng sut ca cc thnh phn phn tn.

D ma trn c kch thc nhng v kch thc mng anten rt nh

so vi khong cch thu pht nn cc sng ti anten gn nh song song vi nhau. Mi

mng anten nhiu phn t t n to ra bp sng nhn. Mi tn hiu n trong phm

vi bp sng th u coi l cng mt hng. Mc d c nhiu anten pht nhng v

khong cch rt xa nhau nn cc tn hiu n mng thu khng th tch bit v

hng c th lm tng ng k dung nng ca knh truyn. Thc t ma trn vn c

hn mt gi tr n, nhng l cha . Trong trng hp ny ma trn knh ch

c mt gi tr n thc s, cn cc gi tr n khc l rt nh.

Tm li trong mi trng khng c vt cn, tc ch c tn hiu trc tip t anten

pht n anten thu, nu khong cch thu pht rt ln so vi kch thc mng anten,

knh MIMO ch lm tng li cng sut ch khng lm tng bc khng gian t do.

1.3.3. Mng anten i cc (Cross-polarized)

Cho n nay, chng ti gi nh rng cc anten ti my pht v my thu c

phn cc ging ht nhau. Vic s dng anten vi phn cc khc nhau my pht v

ngi nhn dn n li v s mt cn bng tng quan gia cc phn t ca knh

. Kt qu l cc phn t ca cho thy hot ng phc tp hn.

Gi s tng quan Rayleigh fading, knh c m hnh ha xp x nh sau :

=

(1.15)

Trong :

= 1 1

1 1 (1.16)

Hn na, * l tch Hadamard v 1 l mt ma trn vi tt c cc phn

t bng 1. Tham s 0 1 c lin quan n vic phn tch cc phn cc trc

giao. Cc gi tr ca , v ph thuc vo nhiu yu t bao gm cc anten s

dng phn cc cho khc nhau, cc anten s dng phn cc cho nh nhau v khong

cch gia cc anten. Nu anten c kh nng phn cc tch bit hon ton th = 0,

cn nu anten s dng phn cc ging nhau hoc mi trng tn x phong ph s

phn cc ca tn hiu, gn hoc bng 1.

1.4. M hnh tn hiu vo ra

Trong phn tip theo chng ta s cho rng vic truyn d liu c thc hin

bng cch s dng iu ch OFDM, m tin t chu k di hn knh thi gian tr lan

truyn v tn s Doppler ti a l nh hn nhiu so vi khong cch gia cc sng

mang con. Trong trng hp ny chng ta c th b qua s can thip ca nhiu do

sng mang bn trong gy ra bi di rng Doppler v cho rng cc knh l hng s

trong thi gian mt k hiu OFDM. Vi MIMO a ngi dng (MU- MIMO), trong

cp n mt cu hnh bao gm mt trm c s vi nhiu anten thu/pht c

tng tc vi mi ngi dng u c mt hoc nhiu anten. Cc bit thng tin c

truyn i c m ha v ghp xen k. T m xen k l nh x ti k hiu d liu

(chng hn nh BPSK, QPSK, QAM, vv) bng b s k hiu. Cc k hiu d

liu u vo cho mt m ha khng gian thi gian m kt qu u ra mt hoc nhiu

dng d liu khng gian, cc dng d liu khng gian c nh x ti anten ca khi

m trc khng gian-thi gian. Cc tn hiu a ra t cc anten pht thng qua cc

knh v n mng ng ten thu. Bn thu s thu thp cc tn hiu thu c u ra ca

tng phn t anten v o ngc cc hot ng pht gii m d liu nhn c x

l khng gian-thi gian, tip theo l gii m khng gian thi gian , gii nh x cc

k hiu, gii ghp xem v gii m. Mi quan h tn hiu u vo-u ra ri rc cho h

thng MIMO trn sng mang con th k c th c vit nh sau :

()= ()(()()()+ ()) (1.17)

trong () l vecto d liu c truyn, () vecto d liu ti u ra ca

knh v () l vector bao gm cc mu phc, gi tr trung bnh tp m Gauss trng

cng sinh ti cc u vo ca mng anten thu. Cc ma trn () v () l ma trn

m trc v gii m tng ng. Trong phn tip theo, n gin ha vn chng ta

s loi b cc ch s ca cc sng mang con , tr trng hp cn thit ch r vic

x l chung ca mt nhm cc sng mang con.

Trong mt kch bn MU-MIMO cc anten MT c t ti cc trm c s v

cc anten c t ti u cui ngi dng th , vi = 1,2,3,. C

ngi dng (hoc cc UT) trong h thng. Tng s anten ti u cui ngi dng

tng ng l:

=

(1.18)

Chng ta s s dng k hiu ,, m t cu hnh h thng

anten. Knh MIMO ca ngi dng c k hiu l .

Chng ta s s dng k hiu ny cho ma trn knh ngi dng, s anten ti

trm c s v s anten ti u cui ngi dng cho c ng uplink v downlink.

Ma trn knh MU-MIMO kt hp c cho bi:

= [

] (1.19)

S khi h thng downlink:

Hnh 1.4: S khi h thng MU-MIMO downlink

M hnh tn hiu vo ra h thng MU-MIMO ng downlink c th c m

t nh sau :

= ( + ) (1.20)

trong y, G, F, v n cho bi :

= [

]

= [

]

= [

] (1.21)

= 0 0

= [ ]

Cc vecto v

l vecto d liu c truyn v nhn c

ca ngi dng th , tng ng. () min (,) l s lung d liu

thng tin hp knh khng gian c truyn ti ngi dng th . Tng s lung d

liu c truyn l = . Mu tp m Gauss trng cng sinh ti u vo ca

mng anten ca ngi dng th cho bi . Cc ma trn

v

l ma trn m trc v gii m tng ng.

S khi m hnh d liu vo ra ri rc h thng MU-MIMO ng uplink :

Hnh 1.5: S khi tn hiu vo ra h thng MU-MIMO ng uplink

Biu din ton hc :

= ( + ) (1.22)

Tng t nh ng downlink, vecto v l vecto d liu

c truyn v nhn c ca ngi dng th , vecto l vecto ca mu

tp m Gauss trng cng sinh ti u vo ca mng anten BS. Ma trn v c

cho bi :

= [

]

= 0 0

(1.23)

Trong v

l ma trn m trc v gii m ca

ngi dng th trn ng uplink.

1.5. Kt lun chng

Chng 1 l khi qut v m hnh h thng knh MIMO, trong chng ny

chng ta gii thiu khi nim v cc m hnh knh ly mu, m t cc m hnh

knh m n s c s dng trong cc m phng, v m hnh tn hiu vo ra ri rc

ca c gii thiu. Biu din knh da trn m hnh ton hc, phn tch v tm

iu kin p dng k thut MIMO mt cch hiu qu. Chng sau chng ta s i

vo tm hiu dung nng knh MIMO n ngi dng v a ngi dng cho c ng

ln v ng xung v qua s c c mt nh gi v kh nng p ng dung

nng tng ca h MIMO a ngi dng so vi n ngi dng.

CHNG II: DUNG NNG KNH MIMO A NGI DNG (MU-MIMO)

Cc h thng MIMO n ngi dng c tm hiu rt nhiu v khng th

ph nhn nhng u im m n mang li cho h thng truyn thng khng dy. Hin

nay, cc nghin cu cng nh vic p dng MIMO ang dnh s quan tm nhiu n

h thng MIMO a ngi dng v nhng u im ca n vt tri hn hn so vi h

thng MIMO n ngi dng. Trong chng ny, chng ta tp trung nghin cu v

dung nng knh MIMO n ngi dng v a ngi dng trong l thuyt Shannon.

Dung nng Shannon ca mt knh bt bin theo thi gian c nh ngha l thng tin

tng h ti a gia cc knh u vo v u ra. y l tc d liu ti a c th

c truyn qua cc knh vi xc sut li nh ty . Khi CSI l hon ton c bit

n c my pht v my thu, my pht c th thch ng vi chin lc truyn dn

tng ng ca n v trng thi knh ngay lp tc. Nu knh l thi gian bin i, dung

nng Ergodic l thng tin tng h ti a trung bnh trn tt c cc trng thi knh

truyn. Dung nng Ergodic thng t c bng cch s dng chnh sch truyn

thch ng ni m bin thin cng sut v tc d liu lin quan ti bin thin trng

thi knh truyn.

Trong mt kch bn a ngi dng, MU-MIMO cho php ti s dng ngun ti

nguyn thi gian v tn s. Do s phn tn trong cc tnh hung khc nhau, cc dng

sng ca ngi s dng c gc m ln v k hiu ngu nhin. V vy, ngay c ngi

dng m ring bit, gc m c th c kh nng chng cho khng gian con bi cc

vector ring bn tri ca ma trn knh ca chng. S phn chia cc khng gian con ca

chng l rt kh t c.

Vi mt h thng MIMO n ngi dng lin kt l im-im cho mt dung

nng xc nh. Trong mt h thng MIMO a ngi dng, lin kt l mt knh a truy

cp trn cc ng ln v knh qung b trn ng xung. Tc t c m t

trong trng hp ny l v mt ca tc tng cng. SU-MIMO ch c mt bt li

nh trong tc thng tin ngoi CSI my pht. MU-MIMO c mt tnh th bt li

ln hn nhiu trn ng xung. Trong mt h thng SU-MIMO, m trc my

pht v gii m b thu c th c thc hin vi s hp tc tt gia cc anten c

sp xp. Trong mt h thng MU-MIMO, cc anten c th hp tc ti cc trm c s

cho m trc trn ng xung v gii m trn ng ln. Tuy nhin, ngi dng

khng th hp tc trong gii m trn ng xung hoc trong qu trnh m ha trc

trn ng ln. Trong mt h thng MU-MIMO, s hp tc gia ngi s dng c th

thc hin c v mt n nh mc cng sut cho ngi dng. Trong mt h thng

SU-MIMO, tc thng tin l ging ht nhau trn ng ln v ng xung cho

cng sut pht tng ng nu knh c bit n ti my pht v my thu.

2.1. Dung nng knh SU-MIMO

Khi m knh truyn c nh v bit trc ti b thu v b pht h thng

(closed-loop), dung lng ca h thng c nh ngha bi :

= max:(

)logdet ( +

)

det () (2.1)

Trong v l cc ma trn tng quan d liu u vo v ma trn tng

quan tp m, l cng sut pht ti a.

Chin lc ti u t c tc thng tin ti a l chuyn i cc knh

MIMO thnh song song, khng can thip vo cc knh SISO thng qua mt php phn

tch gi tr ring (SVD) ca ma trn knh. Phn tch SVD cho min(,) cc knh

song song vi li thng tin vi cc gi tr ring ca .

Gi nh rng t by gi cc thnh phn ca v trong (1.20) l bin ngu

nhin c lp phn phi u v

{} = 0,

{||

} = 1 (2.2)

{} = 0,

{||

} = (2.3)

Nu SVD ca ma trn knh l = , knh c chia ra thnh mt tp hp

cc knh con song song bng cch chn nh sau :

= (2.4)

trong l mt ma trn n v v = . Ma trn l

ma trn ti cng sut khng m. Gii php ti u cho ma trn ti cng sut c xy

dng thng qua thut ton nc :

, =

, = 1,, (2.5)

Nh vy : ,

=

y l hng s, min (,) l hng ca ma trn knh v l gi tr

ring th ca . Gi tr ca c tnh ton s dng thut ton lp. im quan

trng cn lu l phng php phn tch t c tc thng tin ti a khi CSI

c sn my pht v my thu.

Nu l ngu nhin, dung nng knh cng l mt bin ngu nhin, v c th

thay i t khng n v cng. S liu thng k ca dung nng knh ly c bi hm

phn phi tch ly ca n (CDF). % dung nng hiu dng l tc m cc knh c

th h tr vi (100 )% kh nng. Nu chng ta s dng khi (gi) kch thc

ln, v cc m t c dung nng, xc sut li c th c (BLER) s lun lun nh

phn. Khi lun lun c gii m thnh cng nu tc bng hoc thp hn dung

nng tc thi hin c, v lun lun li nu tc vt qu dung nng tc thi. Do ,

nu my pht khng bit CSI, BLER s bng xc sut tiu hao cho tc tn hiu ,

tc l dung nng tiu hao.

Nu CSI thc s khng bit ti my pht (open-loop), ti a ha tc thng

tin by gi c th c thc hin ch v mt ca dung nng tiu hao hoc Ergodic.

Dung nng Ergodic ca mt knh MIMO (1.20) c cho bi :

= max:()

{ log det ( + )} (2.6)

Cng thc cho thy tc thng tin ti a c th t c bi cc tn hiu

Gauss lin kt dc theo vector ring ca ma trn tng quan = {}, ngha l,

= trong = . Dung nng t c vi cng sut n nh l kh khn

hn tnh ton. N cng cho thy rng, ty thuc vo ma trn tng quan truyn ,

c mt di cc t l tn hiu trn nhiu (SNR) m chin lc ti u l iu khin tt

c cng sut ch trong ch ring ch o ca .

2.2. Vng dung nng knh MAC

S kt hp gia tc t c trong tt c cc chin lc truyn c gi l

vng dung nng h thng a ngi dng. N vch r cc gii hn ca giao tip khng

li cho c tnh knh nht nh v c s dng nh l dng c o c bn ca dung

nng knh.

Chng ta hy biu din tc c th l ng tin cy, v d thng tin truyn

khng li c truyn cho ngi dng th ca , (bps/Hz) v gi nh tn hiu l

Gauss cho mi ngi dng. Chng ta s xem xt ti gii m cc tn hiu ca ngi

dng. Phn gii m c ngha l gii m tt c cc tn hiu c thc hin cng mt lc.

Vng dung nng MU-MAC vi phn gii m v cc rng buc cng sut ring

,. . . , trn mi ngi dng c a ra m t.

max

log det ( + )

(2.7)

= max

log det +

Trong khi b gii m ti a kh nng xy ra (ML) l ti u, dung nng tng

MU-MAC cng c th c thc hin thng qua mt my thu MMSE vi kh nhiu

ni tip (SIC). iu ny c th c nhn thy nu chng ta vit li phng trnh (2.7)

nh sau:

log det +

+

= log det +

+ (2.8)

log det + +

Hm mc tiu (2.7) l mt hm li ca ma trn m trc ng ln v

nhng rng buc c th phn bit bi v c mt t rng buc l c bit trn mi tng

quan ma trn . Trong tnh hung nh vy, ni chung l ti u ha i vi

cc bin u tin trong khi cc bin s khc khng i, sau ti u ha i vi bin

th hai, v..v. t c im ti u trn ton cu. iu ny c gi l thut ton

nng khi rng buc v hi t c th c m t di nhng iu kin tng i ph

bin.

Kh nhiu ni tip SIC c ngha l ngi dng c gii m tun t. Mt b

thu SIC c th tm v gii m cc t m ca cc lung d liu trong mt cch m nu

t m ca mt lung d liu l c gii m thnh cng (c ch nh bi mt m

CRC). D liu c gii m sau m ha li, li c iu ch, vv. V c loi

b ra khi cc tn hiu ban u nhn c. V do , nhiu c gim cho cc lung

d liu cn li.

n gin ha ta xt mt kch bn n gin cho vng dung nng a ngi

dng knh MAC trong h SISO vi s ngi dng K=2, s anten pht cho mi ngi

dng l 1, v s anten thu ti trm c s l 1: ((K=2,1),1).

Dung nng i xng l tc chung cc i m c hai ngi dng c th ng

thi truyn tin ng tin cy:

:= max(,)

(2.9)

Dung nng tng cng l tng thng lng ti a c th t c:

: = max(,)

+ (2.10)

log 1+ ||

log 1+ ||

(2.11)

+ log 1+ ||

+ ||

Vi b thu s dng k thut SIC trong giai on u, n gii m d liu ca

ngi dng 2, coi tn hiu t ngi dng 1 nh nhiu Gauss. Tc ti a ngi dng

2 c th t c l:

= log 1+ ||

+ || (2.12)

Sau khi b thu gii m d liu ca ngi dng 2, n c th ti to li tn hiu

ngi dng2 v tr n i t tn hiu tng hp nhn c. Sau b thu c th gii m

d liu ca ngi dng 1. Lc ny ch c nn Gauss ting n cn li trong h thng,

tc ti a dng 1 c th truyn l bin ca n ngi dng:

= log 1+ ||

(2.13)

Khi dung nng tng l:

+ = log 1+ ||

+ ||

(2.14)

Hnh 2.1: Vng dung nng MAC vi k thut thu SIC h thng SISO ((2, 1), 1)

2.3. Vng dung nng knh qung b (BC)

Knh MU-MIMO ng xung ni chung thuc v lp ca cc knh Gauss

khng suy bin. Dung nng tng ca mt knh qung b Gauss, cho a ngi dng,

mi ngi dng c nhiu anten c m t li nh sau:

= min,[],

max()

logdet( +

)

det() (2.15)

y l cn trn ca Sato v vng dung nng ca cc knh qung b ni chung,

l dung nng ca mt h thng m nhng ngi dng trong cc ng xung c th

tun theo. Ni chung, cn Sato khng d c c, nhng bng cch gii thiu tng

quan tp m ti cc my thu khc nhau, chng ta c th tnh ra mt cn trn ln hn

nhiu.

Vn ng xung ti BS l pht qung b cc tn hiu ngi dng vi x

l thch hp v trng s khng gian, sao cho mi ngi dng nhn c mt t s tn

hiu trn nhiu v tp m (SINR), tc thng tin hoc BER ti a hay mong mun.

Anten ca trm c s c th tun theo trong giai on m ha. S hp tc gia nhng

ngi dng c th l iu khin tnh hp tc k tha th t ca cc tc hoc SINR

mi ngi dng.

n gin ha ta xt mt kch bn vi K=2 ngi dng, s anten pht trn

mi ngi dng l N1 v s anten ti BS bng 1, (1,(K=2,N)).

Vng dung nng ca hai ngi dng ng xung knh qung b c cho bi

cp tc , sao cho:

log 1+ ||

+ ||

log 1+ ||

(2.16)

y , = 1,2 l bt bin theo thi gian SIMO cho mi ngi dng. ,

l cc cng sut khc khng c phn b cho hai ngi dng p ng hn ch cng

sut + . Nu hai knh truyn l i xng || = || tc l SNR ca c hai

ngi s dng s l nh nhau. iu ny c ngha rng nu ngi dng 1 thnh cng c

th gii m d liu ca n, th ngi dng 2 cng s c th gii m thnh cng d liu

ca ngi dng 1 (v ngc li). Do tc thng tin tng b chn bi dung nng

n ngi dng:

+ log 1+ ||

(2.17)

Ni chung, vng dung nng ca cc knh qung b khng suy bin l khng r.

Tuy nhin, ta thy rng m ha "trang bn" Costa l ti u trong vic t c dung

nng tng, bng cch chng minh rng, tc c th t c p ng cn trn Sato.

Cc gi thuyt c bn ca cc DPC l nu my pht l hon ho, hiu bit knh khng

lin quan ca tp m nhiu Gauss cng sinh trong knh, khi dung nng ca knh

cng ging nh th nu khng c nhiu cng sinh. DPC cho php nhiu khng lin

quan ti "pre-subtracted" ti my pht, nhng vi iu kin cng sut pht khng tng.

Cho bit (.) biu th mt hon v ca cc ch s ngi dng v ,k =

1,. . . ,K, l tp cc ma trn tng quan bn xc nh dng vi (

) ,

trong l tng cng sut pht cc i. Theo DPC, nu tn hiu ngi dng th

(1) c m ha u tin, tip theo l ngi dng th (2) do tc sau c

th t c :

()= logdet +

() ()()

()

det + () ()()

()

, = 1 (2.18)

Vng dung nng l bao li ca s kt hp tt c cc tc trn tt c cc

hon v v tt c cc ma trn tng quan bn xc nh dng p ng cc cng sut

tng bt buc:

(,)= max ()()

()

(2.19)

Trong c a ra trong phng trnh trc. DPC c ngha l cc tn

hiu ngi s dng khng tng quan.

Hnh 2.2: Hnh bn tri l hai vng dung nng s dng cho mt BC suy bin vi M=1.

Hnh ph bn phi l hai vng dung nng s dng cho mt BC khng suy bin vi

M>1. Khu vc ny l phn li ca s kt hp t l dung nng ca hai ngi dng.

2.3.1. Dung nng tng BC c th t c v i ngu UL/DL

C th d dng thy rng hm mc tiu cho vng dung nng tng cng DPC

khng phi l mt hm li ca cc ma trn tng quan. Nh vy, vic tm kim con s

ti a khng phi l mt vn d dng v i hi mt s tm kim ln trn ton b

khng gian ca cc ma trn tng quan p ng cc hn ch cng sut. Tuy nhin,

bng cch thit lp cc tnh i ngu gia ng ln v ng xung, ta thy rng n

c th c c dung nng tng ti t c ca cc knh BC t knh ng ln i

ngu.

Dung nng knh l khc nhau cho cc ng ln v ng xung do s khc

bit c bn gia cc knh ny. Tuy nhin, thc t l cc knh ng xung v cc

knh ng ln trng ging nh hnh nh phn chiu ca nhau hm rng c mt s

i ngu gia cc knh cho php cc vng dung nng ca mt trong hai knh c ly

t vng dung nng ca knh khc.

S tng ng gia vic thc hin cc chin lc thu v pht khi vai tr ca

cc my pht v my thu nghch o ngc cho vector knh Gauss c tin hnh

trong nhiu tnh hung khc nhau. Trong giao tip im-im, dung nng l khng

thay i khi vai tr ca my pht v my thu i ch cho nhau. Trong trng hp

ng xung x l tuyn tnh bi b thu n ngi dng (SU) ti cc u cui ngi

dng (UT), s la chn cc ma trn truyn v nhn c lin quan cht ch n vn

ng ln o. Cui cng, vng dung nng ca cc knh Gauss suy bin tng t nh

vng dung nng ca MAC tng ng vi cc gii hn cng sut pht ca BC chuyn

i ti tng cng sut trong MAC.

S khc bit gia knh ng ln v ng xung m trn ng xung c s

hng tp m km theo vi mi thit b u cui ngi dng, trong khi trn ng ln

khng tp m. Mt khc bit quan trng l trn ng xung c mt gii hn cng

sut n km theo vi my pht, trong khi trn ng ln c mt gii hn cng sut

khc nhau km theo vi mi ngi dng. Cui cng, trn ng xung c tn hiu v

nhiu km theo vi mi ngi dng di chuyn thng qua cng mt knh, trong khi

trn ng ln cc tn hiu di chuyn thng qua cc knh khc nhau.

Chng ta ni rng, knh ng xung v ng ln i ngu vi nhau nu p

ng xung ca knh cho mi ngi dng u ging nhau ng xung v ng ln,

mi b thu trong ng xung c cng thng k tp m v nhng thng k ny cng

ging nh nhng tp m ca b thu ng ln, v gii hn cng sut PT trn ng

xung bng tng ca gii hn cng sut thnh phn ,k = 1,,K, trn ng ln.

Tp cc ma trn tng quan BC ,k = 1,,K , c cn c vo nguyn tc i

ngu t knh MAC i ngu s dng cng mt gii hn cng sut tng. Chng ti cho

rng trong cc ng ln ngi dng u tin th c gii m u tin, sau ln

lt th hai, vv Trong ng xung, chng ti gi nh rng ngi dng c m

trc theo th t ngc li, ngha l ngi dng th c m trc trc, sau ln

lt th ( 1), vv. Khi , tc t c bi ngi dng th trong cc

ng ln c cho bi :

= log det +

+

(2.20)

V i vi ng xung :

= log det

+

+

(2.21)

Di y l ma trn ph tr :

=

+

= +

(2.22)

Phng trnh 2.21 by gi c th vit li :

= log det

+

= log det +

/

/

= log det +

/

/ (2.23)

V phng trnh 2.20 s dng tnh cht det()= det() th :

= log det +

= log det + /

/

= log det + /

/

(2.24)

nh ngha ca ma trn cn bc hai tng t mc (1.2.1).

Xem

l hiu ng knh ca h thng, chng ta lu rng khi

chng ta ly Hermitian ca knh ny chng ta c hiu ng knh ca knh ng ln

. iu ny cho thy trong trng hp ny chng ta c th s dng cng

mt logic nh trong trng hp h thng im-im m dung nng knh trn ng

ln v ng xung l ging nh vi cc iu kin trn y, tc l, chng ta c th

vit rng =

. Do , by gi chng ta c th s dng cng php bin i cc

ma trn tng quan nh i vi cc h thng im-im bin i ma trn tng

quan knh MAC thnh cc ma trn tng quan knh BC. Chng ta hy nh ngha

SVD ca knh hiu dng nh

=

. Khi :

=

/

/

(2.25)

Nh vy, dung nng tng t c ca BC bng vi dung nng tng ca knh

MAC i ngu, tc l

= max

log det +

(2.26)

y, ti u ha c thc hin i vi cc ma trn tng quan ng ln

,k = 1,,K, ty thuc vo cng gii hn cng sut tng . iu ny cho

php chng ta thay th hm tc khng li ca kt qu tng quan ngi dng t

vng BC vi MAC i ngu m c tc l cc hm li ca cc ma trn hip phng

sai. Bng cch s dng bin i c a ra trong (2.25), chng ti nh x ma trn

tng quan truyn ng ln ,k = 1,,K ti ma trn tng quan truyn ng

xung ,k = 1,,K m t c tc nh nhau di cng mt gii hn cng

sut tng.

Thut ton nc lp c xut trong phn trc tnh ton ma trn

tng quan ca mt knh MAC i ngu. Thut ton ny c da trn cc thut ton

nc lp cho vn MAC thng thng, m nhn c dung nng tng ca MAC

vi nhng gii hn tc ring trn mi ngi dng. S khc bit t (2.26) ch trong

cu trc ca cc gii hn cng sut. Trong tnh hung nh vy, ti u ha c thc

hin bng cch s dng thut ton nng khi rng buc, v d, bng cch ti u i vi

cc bin u tin trong khi cc bin s khc khng i, sau ti u ha i vi bin

th hai, vv t c mt im ti u ton cc. Ni cch khc, ti mi bc ca

mt thut ton ti u ha ngi dng ma trn tng quan ca mnh trong khi x l cc

tn hiu t tt c ngi dng khc nh bao gm tp m ca c nhng ngi dng vi

cc ma trn tng quan c cp nht trc . Trong trng hp ca MAC i ngu

c mt gii hn cng sut tng, tc l, mc nc ca tt c ngi dng phi bng

nhau. Khng ging nh trong MAC thng thng, vi gii hn tc tng chng ta

phi cp nht tt c cc ma trn tng quan ng thi duy tr mc nc lin tc.

Thut ton ny rt phc tp v i hi nhiu tnh ton ca SVD v cc thut

ton nc. Bng cch s dng bt ng thc Hadamard chng ta tm thy mt gii

hn cn trn m khng phi lc no cng cht ch nh trc nhng i hi n lc

tnh ton t hn.

Phng trnh (2.26) c th c vit li nh sau :

= max

,

log det( + ) (2.27)

Cc biu thc trong phng trnh (2.27) c th c vit trong mt dng ma

trn khi nh sau:

=

(2.28)

Bng cch s dng bt ng thc Hadamard det() , , trong , l

nhng nhn t ng cho ca A, chng ta c th vit :

log det( + )

logdet +

=log det +

(2.29)

ng thc c = , y ct l c s ca khng gian ct ca

= v l ma trn ng cho ti cng sut.

Vic so snh cc vic so snh gii hn dung nng tng DPC ca BC v gii hn

dung nng tng ca BC rt n gin (VS) c gii thiu trc y c th hin

trong hnh 2.3 v 2.4. Gii hn dung nng tng ca VS BC u tin thu c bng

cch s dng phng trnh (2.29) tng ng vi dung nng ca knh MU-MIMO ni

m tt c ngi dng l trc giao trong khng gian. Tuy nhin, nh hng ca MUI

c b qua l qu ln v kt qu gii hn ny l qu nh. Cc ty chn khc l

thay th cc ma trn m trc thu c bng cch ti a ha (2.29) trong biu thc

MAC i ngu trong (2.27). V n c th c nhn thy t hnh 2.3, trong trng hp

ca MUI thp, tc l, khi tng s anten ti thit b u cui ngi dng l t hn hoc

bng s lng anten ca trm c s, th hai l xp x gii hn VS, khi nhiu gia

ngi dng cng c a vo tnh ton khi tnh ton dung nng h thng, cng ging

nh gii hn DPC. Trong trng hp MUI cao, tc l, khi s lng anten ca thit b

u cui ngi dng ln hn nhiu anten ti trm gc, xp x gii hn dung nng tng

VS BC l rt gn vi gii hn DPC v SNR cao, n ngang bng vi gii hn DPC.

Cu hnh anten ca h thng trong hnh 2.3 v 2.4 l: ti cc trm c s chng ta c 6

anten, v c ba ngi dng trong h thng. Trong hnh u tin tt c ba ngi dng

c trang b 2 anten v trong con hnh th hai tt c ngi dng c trang b 4

anten.

Hnh 2.3: Gii hn cn trn ca BC, dung nng tiu hao 10%. Trng hp MR < MT

Hnh 2.4: Gii hn cn trn ca BC, dung nng tiu hao 10%. Trng hp MR > MT

2.4. T MIMO n ngi dng n MIMO a ngi dng

Nh ta bit SU-MIMO c nhiu u im nh tng bc t do nhng ch l

lp vt l v trong vng 15 nm qua chng kin s thay i rt nhanh chng ca

truyn thng MIMO t khi nim l thuyt ti thc tin nhm tng cng hiu nng

ca mng khng dy. Truyn thng im-im trong h MIMO ha hn li ch cho c

dung lng knh v tin cky khi s dng c m khng gian thi gian (hng ti

li phn tp). Vi cch nhn n ngi dng truyn thng nh vy, s bc khng gian

t do ln c c do s dng nhiu anten c khai thc m rng chiu kh dng

cho vic x l v tch tn hiu. Do n mi hot ng nh mt b tng cng lp

vt l (PHY). Theo cch tip cn ny, cc giao thc lp lin kt cho a truy cp

(ng ln v ng xung) gin tip thu c nhng li ch v mt hiu sut ca

anten MIMO (v tc v cht lng knh) tt hn.

2.4.1. Nhc li khi nim ng ln, ng xung.

S pht trin gn y ca cng ngh lp cho (Cross-layer), nhm vo thit k

kt ni gia s iu ch cc lp vt l v cc giao thc a truy cp cc lp lin kt.

iu ny c bit ng trong mng MIMO ni chiu khng gian ng mt vai tr tch

cc vo a truy cp v lp lch ngi dng thay v ci nhn n thun l mt cng

ngh lp vt l. Nh s tin b trong lnh vc l thuyt thng tin cho thy r hn tc

ng ca anten trong h MIMO i vi truyn thng a ngi dng. MU-MIMO s

dng s chia s khng gian ca knh cho ngi dng. iu ny khc vi a truy cp

phn chia theo thi gian (TDMA) v a truy cp phn chia theo m (CDMA). Trong

TDMA, can nhiu a ngi dng hp thnh c x l bi nhiu anten cng thm vi

phn tp trn mi lin kt cho trc, cho ta bc t do cn thit phn tch v khng

gian gia cc ngi dng.

Trong thc t cc h thng MU-MIMO khi c s dung ha tt gia phc tp

v hiu nng gip ta thc hin cc tng trn.

Trn ng ln, hoc knh a truy cp (MAC), s pht trin ca cng ngh

MU-MIMO nh l mt tng hp khi nim n SU-MIMO vi cc trng hp a

ngi dng. MAC c m t ngn gn nh sau :

- Ch dng cho ng ln.

- Nhiu b pht ti mt b thu ng thi.

Trn ng xung c knh qung b MIMO-BC, c c im :

- Ch dng cho ng xung.

- Mt b pht ti nhiu b thu ng thi.

2.4.2. Cc c im ni bt ca MU-MIMO so vi SU-MIMO.

K thut MU-MIMO c nghin cu mnh m v mt s u im ni bt ca

n so vi SU-MIMO :

- Cho li trc tip v dung nng a truy cp t l thun vi s anten ti

trm c s (BS) nh vo k thut hp knh a ngi dng.

- MU-MIMO th hin tnh khng nhiu tt hn, vi cc loi nhiu thng gy

kh khn cho cc h thng SU-MIMO nh s gim bc ca knh truyn hay

s tng quan ca anten. Mc d tng quan tng vn nh hng ti s

phn tp i vi mi ngi dng song vi MU-MIMO c k thut lp

lch a ngi dng thay th. Ngoi ra s truyn thng l nguyn nhn gy

nn s suy gim cht lng nghim trng vi s hp knh hp knh

khng gian n ngi dng s khng cn l vn g qu ln trong thit lp

a ngi dng.

- Cho php t c li ghp knh theo khng gian cho trm c s, m

khng cn quan tm qu n cc thit b u cui ca anten. Do , cho

php pht trin cc thit b nh v r trong khi cc thit b thng minh t

tin ang dng vn c ti s dng.

Tuy nhin c c cc u im trn th cc knh truyn phi bit c

trng thi knh. V vy, thng tin v trng thi knh (CSIT-Channel State Information

Transmiter) l vn ct li ngi dng c th thc hin c ghp knh theo

khng gian, c bit l i vi k thut tin m ha vi ng xung.

Trong nhng nm gn y cc m hnh, chin lc ln lt c xut nhm

tng tc , hiu qu s dng knh v dung nng knh MU-MIMO nh l:

- Cc k thut tin m ha c ch nh trc vi knh phi tuyn v tuyn tnh

- Phn hi trng thi knh t pha thu v cc k thut ti u cho my thu a

ngi c a ra nh cc my thu kt hp MMSE-SIC.

- K thut lp lch cho a ngi dng v cc k thut la chn ngi dng.

2.4.3. Nhng kt qu t c v vn tn ti h MU-MIMO so vi SU-MIMO

a) V tnh dung nng theo l thuyt

Hin nay cc tng MU-MIMO c xem nh l tha k mt lot cc k

thut tin b bt u t nhng nm 1970 v 1980 trong lnh vc truyn thng da trn

l thuyt anten mng. Trn thc t vic s dng anten mng trong hn 3 thp nin qua

c th cho php truyn thng ng thi nhiu n ngi dng c lp cch xa

nhau trong khng gian. Khi nim ny trc kia c a ra nh l a truy cp

phn chia theo khng gian (SDMA) v lin quan cht ch ti hp knh khng gian

MIMO hin nay, c th hiu nh l hp knh cc lung d liu ca cc ngi dng

o.

Xt trng hp c th l truyn thng gia mt BS hoc mt im truy cp

anten v K cc thit b u cui hot ng, ngi dng hot ng th k c trang b

vi anten (hnh 1.1). Trong s tt c cc thit b u cui, tp hp cc ngi dng

hot ng hiu l tp cc ngi dng ti xung v ti ln ng thi cc gi tin trong

mt ca s lp lch cho trc. di ca s l ty nhng khng nn vt tr ti

a (c th nh vi chc ms n vi trm ms). iu c ngha l tt c cc ngi dng

ang hot ng trn cng mt ca s s l mt tp con nh ca tt c cc ngi dng

c kt ni, t to thnh tp con ca cc thu bao.

Trong ng ln tn hiu nhn c ti BS c th c vit li nh sau :

=

+ (2.30)

Trong xk l vector tn hiu ngi dng kch thc Mk x 1, c th bao gm

iu khin cng sut, t hp tuyn tnh, cc k hiu chm sao. biu din

ma trn knh fading phng v vecto nhiu Gauss cng tnh, phng sai n v, phn

b c lp, ng nht ti BS, my thu gi thit l c bit trc hon ho, tc thi

trng thi knh truyn (mt bi ton ging nh n ngi dng, ch khc dung nng h

K ngi dng).

Trng hp ng xung, tn hiu nhn c ti ni nhn th k c th c

vit li nh sau :

= + , = 1,2,, (2.31)

Trong , biu din knh ng xung v

l nhiu

Gauss cng tnh ti b thu th k. Cng nh ng ln, gi s rng mi b thu c s

hiu bit tc thi ca bn thn knh ca mnh. Tn hiu pht l mt hm ca d

liu thng tin a ngi dng chng hn, c dng :

=

(2.32)

Trong xk l tn hiu mang bn tin ngi dng th k, c th m ha phi tuyn,

vi phng sai = (), vi (.) l ton t k vng, cng sut phn phi cho

ngi dng th k l = (), trong Tr l ton t vt, vi mt tng cng sut

rng buc ti BS, s phn phi cng sut cn duy tr l .

Tri vi h thng SU-MIMO vi dung lng l mt mt s n, tc l tc l

mt hng s xc inh, dung lng ca h MU-MIMO vi K ngi dng c c

trng bi tc K chiu, trong mi im l mt vecto tc c th t c bi c

K ngi dng ng thi. S tin b ng k ny c thc hin cho cc knh

MIMO Gauss. Mc d khng b suy gim knh Gauss MIMO BC cung cp cu trc

quan trng m c th c tn dng m t c im vng dung nng ca n.

Xt h CSIT bit y , khi dng m trang bn (DPC) phng sai ca nhiu l

n v, vng dung nng vi ma trn cho c th c vit li nh sau :

= (,,) , log

det[ + ]

det[ + ]

,, ..

(2.33)

Trong , biu thc trn c ti u qua mi ln sp xp ngi dng kh d.

Mc d l kh thc hin trong thc t, nhng tnh ton v vng dung nng trn

bng vic tn dng cc kt qu c gi l tnh i ngu gia BC v vng dung nng

a truy cp MAC, t gip ta tnh vng BC thng qua php hp vng MAC i ngu

vi tt c cc vector ng ln, p ng iu kin rng buc tng cng sut l .

Tc dng ca a anten ti BS hoc ti my u cui ngi dng ln s m rng

dung nng knh c th thy r nht thng qua vic kim tra tc thay i nh th

no theo s ngi dng ang hot ng.

n gin, xt s khi gm knh fading v mt dng ng nht trong

tt c ngi dng c cng t s tn hiu/tp m (S/N), lut nh c ca dung nng tng

knh Gauss MIMO BC, k hiu l , cho trng hp = , c nh , v

ln c cho nh sau :

lim

()

log log()= 1 (2.34)

Kt qu trn cho thy rng vi CSIT y , h thng cho ta li hp knh l

, thu c bng cch BS gi d liu cho ngi dng c la chn thn trng t

tng ngi dng . V mi ngi dng c cc h s fading c lp, tng s bc t

do cho phn tp a ngi dng l , do i vi h s ny c li b sung l

log log().

Ngc vi cng thc trn, dung nng thu c trong trng hp BS thiu thng

tin knh ngi dng, s gim bt cn (khi ch SNR cao):

() min(,)log (2.35)

b) V mt thit k

L thuyt thng tin lm ni bt mt s kha cnh c bn ca cc h thng MU-

MIMO khc rt nhiu so vi thit lp SU-MIMO.

Th nht, cc kt qu trn l ng cho s phc v a ngi dng ng thi

trong SDMA, vi mt s la chn k thut m trc thch hp ti ni pht v cc k

tht gii m kt hp kh nhiu ti b thu. Mc d, li hp knh b hn ch bi s

anten pht, nhng s ngi c phc v ng thi l ty . Bao nhiu ngi v

ngi dng no c phc v hiu qu vi cng sut khc 0 ti bt k thi gian no

cho trc l vn c gii quyt bi thut ton phn phi ti nguyn.

- S ngi dng l ty

- C th dng anten n b thu (phn tp khng gian v phn tp ngi

dng)

- Hn ch tc ng xu ca knh (LOS, st hng)

- Do tm quan trng ca CSIT nn buc phi c knh phn hi b thu.

2.5. Kt lun chng

Chng 2, chng ta tm hiu v dung nng knh MIMO n ngi dng v

knh MIMO a ngi dng qua c ci nhn khch quan gia knh MU-MIMO so

vi dung nng knh n ngi dng. Chng ta phn tch h MU-MIMO thy

c tnh k tha v pht trin t SU-MIMO nh th no, nhng u im so vi SU-

MIMO v cc kt qu t c ca h thng a ngi dng.

Qua chng ta thy c mt s vn then cht sau :

- Cu trc v hot ng ca h thng MIMO a ngi dng nh th no.

- Dung nng ca h thng qua h thng cc knh truyn MU-MIMO.

- Chng ta a ra c m hnh tn hiu vo ra ca h thng.

- MIMO a ngi dng k tha v pht trin t MIMO n ngi dng nh

th no.

- u im ca MIMO a ngi dng so vi MIMO n ngi dng.

- Mt s kt qu t c v tnh l thuyt v thc nghim.

Chng sau chng ta s i tm hiu, nghin cu v cc k thut x l tn hiu

b thu, pht a ngi dng tng dung nng h thng. Phn tch tm hiu mt b thu

p dng mt k thut tch sng a ngi dng l k thut kh nhiu ni tip SIC p

dng cho b thu ti trm c s (BS) trn ng ln, qua s thy c li ch ca k

thut ny cho h thng MU-MIMO.

CHNG III: K THUT SIC VI MU-MIMO UPLINK

H thng a truy cp phn chia theo thi gian (TDMA) khng th t c mt

s gia tng tuyn tnh ca dung nng tng ca h thng MU-MIMO. Mt gii php

cho vn ny l s dng a truy cp phn chia theo khng gian phc v ng thi

nhiu ngi dng. Vi ng xung c nhiu k thut c p dng t c

dung nng tng nh m trang bn Costa (DPC) hoc m trc Tomlinson- Harashima.

DPC t c tc tng ti a ca h thng v cung cp bc phn tp ti a. Dung

nng tng i vi ng ln trong h thng MU-MIMO c th t c thng qua b

thu MMSE, VBLAST, ML vi vic s dng kt hp kh nhiu ni tip (SIC). Hnh

3.1 l kin trc b thu ti u s dng k thut SIC.

Hnh 3.1: Kin trc b thu MIMO ti u

Dung nng tng ca ng xung h thng MU-MIMO s dng m DPC v

ng ln ca h thng MU-MIMO s dng k thut SIC l ti (,) ln hn

nhiu gi tr ln nht ca dung nng tng ca h thng TDMA.

trnh vic x l tn hiu ti cc b thu u cui do s lm tng gi thnh sn

phm v tng in nng tiu th ti thit b ngi dng cho vic x l tn hiu. Do vy

ti tp trung nghin cu x l tn hiu ti b thu ca trm c s BS. iu c

ngha l mt ngi dng s khng bit c cc ngi dng khc chia s cng thi

gian v ti nguyn tn s v trm c s s c ngha v phi gim nhiu a ngi dng.

Chng ny chng ta s cp n vn thit k cc ma trn m ha v gii m

trong h thng MU-MIMO. S tp trung vo gii m SMMSE vi b thu SMMSE-

SIC.

Trn ng xung cc trm c s s s dng bt k thng tin trng thi knh c

sn gim thiu hoc loi b hon ton l tng nhiu a ngi dng thng qua m

trc tuyn tnh hoc phi tuyn tnh (DPC hoc THP), dn n tng tc thng tin

ng k. Thit b u cui ngi dng c tnh knh hiu dng v d liu truyn trong

khung ng ln tip theo. Cc knh hiu dng tng ng vi mng li knh kt

hp sau khi m trc ti cc trm c s. Tuy nhin, trn ng ln trm c s c kh

nng s dng kh nhiu ni tip, do knh hiu dng trn cc ng ln bao gm

cc x l khng gian khng phi l ging nh trn ng xung. V vy, n l khn

ngoan khi cho rng thit b u cui ngi dng khng c gi tr CSI trn ng ln

m xut vic s dng cc k thut MIMO open-loop trn ng ln. V vy, trn

ng ln chng ta c th xc nh hai trng hp c th. Trong trng hp u tin,

cc thit b u cui ngi dng m ha d liu s dng OSTBCs. Trong trng hp

th hai, cc ma trn m trc ca ngi dng trn cc ng ln c to ra cc

trm c s v sau c truyn thng n thit b u cui ngi dng. li phn

tp ca MIMO l mong mun nhiu hn li ghp knh khng gian nu chng ta

a vo bn m t gii hn cng sut cho cc thit b u cui ngi dng v do n

l cc trm c s truyn li cho cc thit b u cui ngi dng ch vector ch

o ca knh hiu dng ng ln.

3.1. Ghp knh khng gian

Vic s dng nhiu anten c pha thu v pha pht c coi nh l mt cch

ci thin t s tn hiu trn tp m v phn tp chng li fading so vi vic ch s

dng nhiu anten pha pht hoc pha thu. c th c gi l ghp knh khng

gian, cho php tn dng hiu qu hn t s tn hiu trn tp m v tc d liu tng

ln ng k qua giao din v tuyn.

3.1.1. Nguyn l c bn

Nh ta bit l k thut a anten pha thu v pha pht gip ci thin t s

tn hiu trn tp m pha thu tng ng vi s lng anten bng cch p dng k thut

x l tn hiu my pht (nh to bp song, m trc ) v my thu (nh cc k

thut tch sng a ngi dng tuyn tnh v phi tuyn hoc kt hp c hai). Trong

trng hp tng qut vi an ten pht v anten thu, t s tn hiu trn tp m c

th tng ln tng ng vi , v cho php tng tc d liu vi gi thit

bng thng khng gii hn. Tuy nhin, nu trong trng hp bng thng b gii hn

trong di hot ng th tc d liu s bo ha khi bng thng khng th tng c

na.

hiu v bo ha tc d liu, xem xt biu thc c bn v dung lng

knh chun ha sau y:

= log 1+

(3.1)

Bng phng php to bp, t s S/N c th tng tng ng vi .

Nhn chung, xx )1(log2 khi nh. Tc l vi S/N thp, dung lng knh s tng

theo t s S/N. Vi ln, )(log)1(log 22 xx , tc l vi S/N ln th dung lng

knh s tng theo hm logarithm ca S/N.

Tuy nhin, trong trng hp nhiu anten pht v anten thu mt iu kin c

th, ta c th to ra = min(,) knh song song (cng sut tn hiu c chia

ra cho mi knh) vi t s tn hiu trn tp m gim xung ML ln. Dung lng mi

knh c tnh nh sau:

= log 1+

(3.2)

Khi , dung lng tng i vi mi cu hnh a anten c xc nh nh sau:

= log 1+

= min{,} log 1+

min{,}

(3.3)

Do , trong nhng iu kin c th no , dung lng knh c th tng tuyn

tnh vi s lng anten, trnh khi b bo ha tc d liu. c gi l ghp

knh khng gian. Thut ng x l anten MIMO thng hay c s dng mc d

thut ng ny dng chung cho tt c trng hp a anten pht v thu, bao gm c phn

tp pht v thu.

hiu c nguyn l c bn m cc knh song song c to ra, ta xem xt

cu hnh 2 2 anten bao gm 2 anten pht v 2 anten thu v gi thit l tn hiu c

pht ch b nh hng bi fading phng v nhiu trng, tc l khng c tn thi knh

v tuyn.

1,1h

1,2h

2,1h

2,2h

1

2

1x 1y

2y2x

Hnh 3.2: H thng MIMO cu hnh anten 2x2

Da trn hnh 3.2, tn hiu thu c th c biu din nh sau:

= =

, ,, ,

+

= . + (3.4)

Trong l ma trn knh 2 2. Gi thit khng c tp m v ma trn kh

o, vector v tn hiu v c th c phc hi hon ton pha thu m khng

c nhiu gia cc tn hiu bng cch nhn vector thu vi ma trn = ta c:

= . =

+ . (3.5)

Biu thc ny c minh ha trong hnh 3.3:

Hnh 3.3: Thu tuyn tnh/Gii ghp knh cc tnh hiu c ghp khng gian

Mc d vector c th c phc hi hon ton trong trng hp khng c

tp m, min l ma trn kh o, c tnh ca cng quyt nh phm vi no m

vic gii iu ch hai tn hiu s lm tng mc tp m.

hiu v ma trn th ta cng phi hiu rng tn hiu pht i t hai anten

pht s gy nhiu cho nhau. Hai anten thu c th c s dng thc hin s IRC,

bn cht l trit nhiu ca tn hiu t anten th nht ln anten th hai v ngc li.

Cc hng ca ma trn thc hin chc nng ny.

Trong trng hp tng qut, cu hnh a anten s bao gm anten pht v

MR anten thu. S lng tn hiu song song c th c ghp knh khng gian s ln

hn = min(,). C th hiu c bng trc gic l:

Hin nhin s khng th c nhiu hn tn hiu c c th c pht i t

anten pht, tc l s lng tn hiu c ghp knh ln nht l .

Vi anten thu, s lng tn hiu nhiu c th b trit tiu ln nht l

1, tc l s lng tn hiu c c ghp ln nht l .

Hnh 3.4: Ghp knh khng gian da trn m trc

Tuy nhin, s lng cc tn hiu c ghp khng gian hay cn gi l bc ghp

knh khng gian, s nh hn trong nhng trng hp sau y:

- Trong iu kin knh xu (t s tn hiu/ tp m thp) th ghp knh khng

gian khng c li v dung lng knh l mt hm tuyn tnh vi t s tn

hiu/ tp m. Trong trng hp ny, s dng a anten pht v thu cho to

bp sng ci thin t s tn hiu/ tp m hn l ghp knh.

- Trong nhiu trng hp, bc ghp khng gian c xc nh da trn cc

thuc tnh ca ma trn knh kch thc . Nhng anten tha s c

s dng to bp sng. S kt hp gia to bp sng v ghp knh khng

gian c th t c ghp knh da trn m trc.

3.1.2. Ghp knh da trn m trc

M trc tuyn tnh trong ghp knh khng gian tc l x l tuyn tnh bng

ma trn m trc kch thc c p dng pha pht nh c minh ha

trong hnh 3.3 trong trng hp tng qut bng hoc nh hn , tc l tn

hiu c ghp knh v c pht i bi anten.

Ch l ghp knh khng gian da trn m trc c th c coi l tng qut

cho to bp da trn m trc vi vector m trc c kch thc MT x 1 thay cho

.

M trc trong hnh 3.5 c th v hai mc ch sau:

Trong trng hp s tn hiu ghp khng gian bng s anten pht = , m

trc c s dng trc giao cc lung song song, cho php tng cng cch ly

tn hiu pha thu.

Hnh 3.5: Trc giao ha tn hiu ghp khng gian thng qua m trc. i,i l gi tr

eigen th i ca ma trn HHH

Trong trng hp s tn hiu ghp nh hn s anten pht < , m trc

c s dng sp xp tn hiu ghp knh ln anten pht bao gm c ghp

knh khng gian v to bp sng.

xc nhn rng m trc c th tng cng cch ly cc tn hiu ghp knh, ta

biu din ma trn knh H di dng SVD:

= (3.6)

Trong , tng ct ca v to nn mt tp trc giao v l mt ma trn

vi cc gi tr c trng ca l phn t trn ng cho. Bng cch

p dng ma trn l ma trn m trc pha pht v ma trn pha thu. Nu ma

trn knh tng ng = l ma trn ng cho th s khng c nhiu gia cc tn

hiu ghp knh pha thu. ng thi, nu c v c cc ct trc giao, cng sut

pht cng nh mc nhiu b gii iu ch (gi thit l nhiu trng) c thay i.

Ni mt cch r rng hn, trong trng hp m trc, mi tn hiu thu s c

mc cht lng no , ph thuc vo gi tr c trng ca ma trn knh. iu ny ch

ra li ch tim tng ca vic p dng s tng thch kt ni ng trong min khng

gian, tc l la chn tng ng t l m ha hoc s iu ch cho mi tn hiu

c truyn i.

Trong thc t, ma trn m trc khng bao gi tng ng vi ma trn knh mt

cch hon ho, v lun c nhiu gia cc tn hiu ghp khng gian. Nhiu ny c th

c x l bng cch thm vo b thu chc nng x l tuyn tnh hoc phi tuyn.

Hnh 3.6: Truyn dn mt t m (a) v a t m (b)

xc nh ma trn m trc , cn phi bit v ma trn knh . Tng t

nh to bp sng da trn b m trc, cch tip cn chung l c tnh knh pha

thu v quyt nh ma trn m trc ph hp t mt tp cc ma trn m trc kh dng

(codebook). Pha thu sau s phn hi li thng tin v ma trn m trc la chn

pha pht.

3.1.3. X l b thu phi tuyn

tng hiu sut gii iu ch th c th p dng x l b thu phi tuyn. Mt

phng php phi tuyn khc cho gii iu ch tn hiu ghp knh khng gian l s

dng SIC (kh nhiu lin tip). SIC yu cu cc tn hiu a vo phi c m ha

ring bit trc khi ghp knh khng gian. Do vy thng c gi l truyn dn a t

m. Ngc li vi truyn dn a t m l truyn dn mt t m, trong cc tn hiu

ghp knh c m ha cng nhau. N c th c hiu mt cch tng quan l d liu

xut pht t mt ngun nhng sau s c gii ghp knh thnh cc tn hiu khc

nhau c th ghp khng gian trc khi m ha knh.

Nh trong hnh 3.7 ch ra, vi SIC, trc tin my thu s gii iu ch v

gii m tng tn hiu ghp khng gian th nht. D liu sau khi c gii m chnh

xc s c m ha li v loi tr dn trong tn hiu thu. Do , tn hiu ghp th hai

c th c gii iu ch v gii m m khng b nhiu t tn hiu th nht (t nht l

trong trng hp l tng). Sau d liu c gii m chnh xc ca tn hiu th hai

s c m ha li v tr dn trong tn hiu thu trc khi gii m tn hiu th ba. Cc

bc c th c tip tc thc hin cho n khi tt c cc tn hiu c gii iu ch

v gii m.

Hnh 3.7: Gii ghp knh/gii m tn hiu ghp khng gian da trn SIC

R rng l vi SIC, tn hiu u tin c gii m s mc nhiu cao hn so

vi cc tn hiu c gii m sau ny. Nh vy, thc hin mt cch chnh xc hn

th tn hiu c gii m trc phi mnh hn nhng tn hiu sau. Vi gi thit truyn

dn a t m nh hnh 3.6b, iu ny c th thc hin c bng cch p dng cc s

iu ch v t l m ha khc nhau i vi cc tn hiu khc nhau. S iu ch

bc thp, t l m ha thp tc l tc d liu thp s c p dng cho tn hiu

c gii m trc. K thut ny thng c gi l iu khin t l trn anten

PARC.

3.2. M trc SMMSE

Mt thut ton mi c xut nhm gii quyt vi nhng nhc im ca

m trc MMSE bng cch lin tc tnh ton cc ct ca ma trn m trc tng

ng vi cc anten thu khc nhau.

Cc b lc m trc MMSE lin tip (SMMSE) nhn c t vic ti u m

trc MMSE truyn tuyn tnh bng cch b qua thnh phn nhiu gia cc tn hiu

mng anten ca mt ngi dng MSE ca ngi dng ny. V mi ngi dng c

th phi hp x l trn tt c cc anten ca n, chng ta c th kt hp cc tn hiu ti

cc anten khc nhau ca mt ngi dng tch ra phn tp cao hn v li mng

anten. Nhiu ng knh ti tn hiu t c anten th ca ngi dng th i l

c kh nhiu mt cch c lp t cc anten khc cng thit b u cui. iu ny

c thc hin lin tc cho mi anten ti cng mt thit b u cui ngi dng lin

tc. Do , ct th ca ma trn m trc ngi dng th , tng ng vi anten

thu th ca ngi dng th l tng ng vi ct th nht ca ma trn , m l

thu c t vic ti u ha sau y:

, = argmin,

(),

()+()

()

(3.7)

Nh vy m . Ma trn

() v cc vecto

() v

() tng

ng vi cc anten thu th ca ngi dng th vi = 1,,; = 1,,

c nh ngha:

()=

,

...

...

; ()=

,...

...

; ()=

,...

...

(3.8)

y , l hng th ca knh ma trn ca ngi dng th , , l phn

t th ca vector ngi dng th v , tp m ti u vo ca anten

thu th ngi dng th . Cc phn t ca vector c trung bnh 0, n v phng

sai l cc bin ngu nhin ng u phc, phn phi u v c lp. Cc phn t ca

vector l cc bin ngu nhin Gauss phc trung bnh 0 vi phng sai , ch

rng vector = , = 1,, l d liu c m trc ca ngi dng th . Cc

thuc tnh thng k ca cc phn t ca vector , ni chung ph thuc vo ma trn

. Tuy nhin, khi chng ta to ra ma trn chng ti gi nh rng cc ma trn

l n nht. Gi nh ny l ng nu mi ngi dng ang nhn c dng d liu

c lp vi cng sut tng t trn tt c cc anten thu. Trong trng hp s liu

thng k cc phn t ca cc vector cng ging nh s liu thng k ca cc phn

t ca cc vector . Bng cch gi nh rng ma trn n nht, chng ta ch nh

cng mt u tin truyn d liu cho tt c cc ch ring ca knh hiu dng

ca ngi dng th .

Mi ct ca ma trn m trc , tng ng vi mt anten nhn c, c

tnh ton lin tc. Cc ct tng ng ca ma trn m trc bng vi ct u tin

ca ma trn sau y:

, = ()

()+

()

(3.9)

Cc tham s : = /.

Sau khi tnh ton cc vector m trc cho tt c cc anten thu, ma trn knh kt

hp c hiu dng ca tt c ngi dng bng sau khi m trc. i vi

t l SNR cao v khi , ma trn ny cng l ng cho khi. By gi chng

ta c th p dng bt k nh ngha trc no khc ca k thut SU-MIMO ca ma

trn knh hiu dng ca ngi dng th . Sau khi m trc bng cch s dng

ma trn , trc tin chng ta thc hin phn tch gi tr n (SVD) v sau , nu

chng ta mun ti a ha dung nng ca h thng, chng ta s dng thut ton

nc trn ch ring ca tt c ngi dng hoc nu chng ta mun tch ra phn tp

cc i v li mng anten, chng ta ch truyn trn ch ring ch o ca cc

knh hiu dng ca ngi dng. Truyn ch ring ch o cung cp SNR ti a

b thu v hiu nng BER ti thiu. S phc tp ca thut ton ny l ch cao hn mt

cht so vi thut ton BD. Bng cch s dng thut ton ny, chng ta ci thin c

hiu qu li phn tp v mng ng ca h thng bng cch gii thiu MUI v bng

cch kh nhiu lin dng. Sau khi phn tch tng t nh i vi MMSE, chng ta hy

vng rng ti SNR cao, trong trng hp ca mt knh , SMMSE to ra mt trt t

phn tp ca +. Di y l m t thut ton SMMSE:

3.3. Gii m vi b thu SMMSE-SIC

Nh c gii thiu, t c mt s tng tuyn tnh ca dung nng h

thng MU-MIMO vi s lng anten chng ta cn hp knh khng gian ngi dng

v a lung d liu cho mi ngi dng. Mt lu lng cao trn ng ln a ngi

dng c th t c thng qua mt my thu MMSE vi kh nhiu ni tip (SIC). Tuy

nhin, nh trc, gii thiu mt mt mt nu chng ta c gng gim thiu s nhiu

gia cc dng d liu truyn t hai anten gn nhau nm thit b u cui ngi dng.

Cc k thut, nh V-BLAST l truyn lung d liu c lp vi tt c hay ch mt

nhm cc anten, l km ti u v n khng cho php s phi hp x l y ti cc

anten trn thit b u cui ngi dng. ci thin hiu sut h thng, chng ta c

th s dng phng php tng t nh trong SMMSE. y, mt thut ton mi

c gii thiu cp vi vn ny tng t nh SMMSE bi vic lin tc tnh ton

cc hng ca ma trn nhn c cho mi anten truyn ring. Bng cch p dng SIC

ci thin thm tnh phn tp, tng t nh SMMSE-THP, nhng vi mt s khc

bit. Trn ng ln chng ta khng cn phi s dng mt modun iu khin no, y

mt li th nh ca SIC i vi THP.

Cc b lc gii m SMMSE-SIC c ngun gc t b lc ti u thu tuyn tnh

MMSE bi b qua s gp phn ca s nhiu gia cc tn hiu t mt mng anten

ngi s dng ti MSE ca ngi dng ny v nh hng ca cc ngi dng c

gii m trc . By gi chng ti gi nh rng ngi dng c sp xp theo mt

cch m ngi dng u tin c gii m u tin, sau l ngi dng th hai, th

ba, vv. Khi ma trn m trc ca ngi dng trn cc ng ln , = 1,. . . ,

c xc nh, b lc thu MMSE thu c bng cch s dng ti u ha sau y:

= argmin{(

+ ) } (3,10)

Cc ma trn , v vecto c xc nh trong trng hp ny l:

=

; =

0 00 0 0 0

; =

(3.11)

Trong , v ln lt l ma trn ma trn knh, ma trn m trc ng

ln, vector d liu ca ngi dng th .

Trong phng trnh (3.10), bao gm vic x l ti cc thit b u cui

ngi dng trong cc tiu ch ti u. Tuy nhin, trong mt kch bn nhiu ngi dng,

cc thit b u cui ngi dng c tnh knh hiu dng trn ng xung cng

bao gm vic x l v c thc hin ti cc trm c s. K t khi x l ti cc trm

c s khng nht thit phi ging nhau trn ng ln v ng xung, n l hp l

gi nh rng cc thit b u cui ngi dng khng c thng tin chnh xc trng

thi knh. Chng ta c th phn bit hai tnh hung. Trong trng hp u tin ngi

s dng truyn s dng mt trong nhng k thut m khng yu cu CSI my pht.

Trong trng hp th hai trm gc to ra cc ma trn m trc ti u v sau np

tip chng vo thit b u cui ngi dng. Hn ch cng sut c th s dng cho cc

thit b u cui ngi dng, li phn tp c nhiu thch hp hn so vi li ghp

knh khng gian.

V vy, chng ta cho rng ngi dng truyn d liu hoc s dng STC hoc s

dng cc vector ring ch o bn phi ca knh hiu dng ng ln ca ngi dng.

Trong c hai trng hp ma trn gii m Da c to ra trm c s, gi nh rng

= ,, v nhng phn sau chng ta s lun lun s dng gi nh ny.

Cng ging nh i ng xung, nhiu t ngi s dng ng knh ti tn

hiu truyn t anten th ca ngi dng th l c kh mt cch c lp t cc

anten c sp xp khc. V vy, hng th ca ma trn gii m ca ngi

dng th , tng ng vi anten truyn th ca ngi dng th i bng vi hng u

tin ca ma trn ,, m c thit k nh sau:

, = argmin, ,

()()+

()

, , (3.12)

Ma trn ()

v vector ()

c nh ngha trong trng hp ny l:

()=

,

...

; ()=

,...

(3.13)

y , l hng th ca ma trn knh ca ngi dng th , v , l

phn t th ca vector ph tr ca ngi dng th , , y =

, vector l tp m ti u vo ca mng anten thu ti trm c s. Phn

t ca vector c gi nh vi cng l do nh trong trng hp ca SMMSE vi

trung bnh 0, n v phng sai l cc bin ngu nhin ng u phc, phn phi u

v c lp. Phn t ca vector n l cc bin ngu nhin Gauss phc vi trung bnh 0 v

phng sai l .

Mi hng ca ma trn thu tng ng vi mt anten truyn c tnh ton

lin tip. Hng th ca ma trn thu bng hng th nht ca ma trn sau:

, = ()

()()

+

(3.14)

y l phng sai ca tp m Gauss trng cng sinh trung bnh 0 ti u

vo ca mt anten thu.

nh ngha hng ca ngi dng, chng ta s s dng ging nh phng

php th v sai cho SMMSE THP. Bnh phng trung bnh ng (MSE) tng ng

vi anten truyn th ca ngi dng th bng:

, =

()()

+

, (3.15)

Chng ta nh ngha tng MSE ca ngi dng th nh sau:

= ,

(3.16)

Chng ta tm kim ngi dng vi cc msei ti thiu, gii iu ch d liu ca

n v sau tr i tn hiu ti to t cc tn hiu nhn c. Sau , chng ta hnh

thnh ma trn knh kt hp mi ()

m khng c ma trn knh ca ngi dng ny

v s dng n trong phng trnh (3.14). Chng ta lp li cc bc cho n khi ma

trn knh kt hp () rng. l thut ton SMMSE-SIC v c vit li nh sau:

Chng ta s dng cc k hiu sau y: SMMSED() l hm gii m SMMSE

nh c m t trc y, l mt ma trn ph tr m lu tr ma trn gii m

c to ra bng cch s dng b lc thu SMMSE v S l mt tp hp cc ch s ca

ngi dng c x l. Trong mi bc chng ta tm thy nhng ngi dng vi tng

s ti thiu MSE cho mi anten v t n nh ci u tin. Sau , chng ta hnh

thnh ma trn knh kt hp mi m khng c ma trn knh ca ngi dng

ny. Chng ta lp li cc bc cho n khi ma trn knh kt hp rng.

3.4. Kt lun chng

Chng ny chng ta tm hiu c mt s k thut thu/pht trong h thng

MU-MIMO. K thut x l a truy cp phn chia khng gian s dng trong h thng

MIMO gii quyt vn phc v ng thi nhiu ngi dng. Vi ng xung c

nhiu k thut c p dng t c dung nng tng gii php vi m trc

SMMSE, vi mt thut ton mi c xut nhm gii quyt vi nhng nhc

im ca m trc MMSE bng cch lin tc tnh ton cc ct ca ma trn m trc

tng ng vi cc anten thu khc nhau. Vi ng ln t c dung nng tng

trong h thng MU-MIMO, ti b thu ti trm c s chng ta a ra mt gii php

thng qua b thu SMMSE vi vic s dng kt hp kh nhiu ni tip (SIC). SIC l

mt k thut t c mt s tng tuyn tnh ca dung nng h thng MU-MIMO

vi s lng anten chng ta cn hp knh khng gian ngi dng v a lung d liu

cho mi ngi dng. chng ta c ci nhn r hn v cht lng, hiu sut ca b

thu ti u ny, chng ti s m phng cc gii php cho b thu tn hiu trong h

thng MIMO a ngi dng v nh gi kt qu t c theo m hnh l thuyt

phn tch.

CHNG IV: M PHNG NH GI H THNG

4.1. nh gi hiu sut b thu qua dung nng tng t c ca b thu

Hnh 4.1 chng ta m phng dung nng knh a ngi dng ca cc b thu

tuyn tnh (MF, ZF, MMSE) v phi tuyn (ZF-SIC, MMSE-SIC) trong h thng MU-

MIMO vi mt kch bn n gin c s ngi dng K=4, mi ngi dng c Mue=1

anten, v s anten trm c s l MB= 4; knh truyn Rayleigh fast fading khng khng

m ha.

Hnh 4.1: Dung nng cc b thu tuyn tnh v phi tuyn (4x4)

y ta thy rng vi mi trng cng thu tt (SNR ln) th dung nng tng

t c ca h thng cng tng, b thu c p dng k thut SIC t c dung nng

ti u nht. B thu MMSE c dung nng tng t c ln hn ZF. Cc b thu ZF,

MMSE, ZF-SIC, MMSE-SIC c dung nng tng tng tuyn tnh theo hm logarit, cn

vi b thu thng thng th ch tng n mt tc khong 6 bits/sec/Hz tng ng

vi SNR khong 10dB th bo ha. S d vi b thu thng thng khi t n mt tc

nht nh th bo ha mc d t l SNR tng l do b thu vi phng php tch

sng thng thng ch x l n mt

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