Ứng dụng kỹ thuật điều chế lọc đa tần kết hợp với kỹ thuật cân bằng trong các hệ thống thông tin băng rộng

Serial to parallel Multicarrier Modulator IDFT Add cyclic prefix, parallel to serial convert D/A converter Parallel to serial Multicarrier Demodulator DFT Remove cyclic prefix, serial t

-

-xy

-r t 2 t

2 2

2 / h 2 y

2 / h 2 x

e2

1)

h

(

p

e2

1)

=

2 y 2

x hhh

htan

0r0

0re

r)(

p

2

2 / 2 r 2

=

2

1)(

p

•

y

x jh h A

2 h 2 y

2 h 2 x

e 2

1 h

p

e 2

1 h

=

( ) 2

y 2

x hhAh

+

−

0r0

0r

ArIe

rr

r A 2

2 2 2

2

22σ

0re

r

1r

p

2 2

2 ) log(

σ

=

+

=

)t(nd)t(

ng(t nT)S

)t(x

( )

( )tnnTTN

itgsT

N

icNT

tnd)nTt

(gs)(c

)t(n)nTt(gs)t(c

)t(n)t(x)t(c)t(y

n n uN

0 i

n n

n n

∞

−

∞ +

( )kTnsh

kTnGsc

kTnTnN

ikgsT

N

icNT

kTyy

T T

n n uN

0 i k

N

1c0cN

T

cT

1) u 1)x(v (uN T T

T

p0

00

0Q

000

0

p

00

Q0

00

00p

G

+ + +

s

ss

TN

1N2gTN

1N1g

TN

2vg

TN

22gT

N

21g

TN

1vg

TN

12gT

N

11g

=

φ ∂ −τα

t ( j

j

l.e [t ])

=ττ

−τ

0 l

j l

l.x(t t ).e w(t)d

)

t(c)

(x

≤σ

≥α

ασ

α

=

α +

−

00

0

AIe

)

(

A 2

2 2 2

τ

∑

[ ]T

N k 2

k 1 k

k

n k N

k k

k T k k

k

k T k k k T

T k k T k 2

k

2

k Ex Ey y 2Ex ye

ω

[ ] [ ]T

N k k 2

k k 1 k k k k k

k N k 1 k N k k N k

N k 1 k 2

k 1 k 2

1 k k

1 k

N k k 2

k k 1

k k 2

yyyyyy

yy

yyy

yy

yy

yyy

yy

Ey

=

≡

N 1

∂

ξω

( ) ( ) ( )n x n g n n ( )n h ( )n

( ) ( ) ( ) ( ) ( ) ( )n d n dˆ n d n [x n g n n ( )n h ( )n ]

( )t =∑x(k)h(t−kT)+v(t)y

h

)n(v)k(h)kn

0

0

)2l(h

)0(h0

0

)1l(h

)1(h)0(hH

h

h h M

M n y n , ,y n M 1

)n(v)n(xH)n

2 ( ) 1 (

) 2 ( )

0 ( )

1 (

) 1 ( )

1 ( )

0 (

r M

r M

r

M r r

r

M r r

r R

h h

H M

0 n ,g n , ,g ng

n

M , f 1 M 1

,

M

P0

00

00

0PR

I

B

B

A

A

I

1 M , f H 2

L ZF

H

ZF

)1L

(

h

)1L(

h

∑

∑

2 1 θλ

−1

1

)1L(

=

=

=

1mLd)n(

b

0d)

n(

0d)

n(P

1 M

,

b

1

1 M

,

f

) (

ˆ d

h

)n(u)n(

)'d(hˆ)

n k

π

dNe

F

N2

n k 1 n Bn n

k 1

0 min

2

dNe

F

Nln

2

Texpn

e

E

•

•

( ) 2p 2R 0

J ωN =− N + NN N =ω

∂

∂

ω

= λ

<α

< N

1 i i20

n,en,en

J

≤ ≤

( )n R ( )n 1 y ( ) ( )n y n

−

−

−λ

−

n

1nRnyny1nR1nR

1

n

R

1 NN T

N N 1

NN 1

NN 1

n

1 NN N

µ+λ

ny1nRn

k

1 T

1

−+

Serial to

parallel

Multicarrier Modulator (IDFT)

Add cyclic prefix, parallel to serial convert

D/A converter

Parallel to

serial

Multicarrier Demodulator (DFT)

Remove cyclic prefix, serial to parallel convert

A/D converter Detector

Channel

noise

=

π

kn ) N / 2

ν ν

ννν

N / nk 2 j n

jdte

*fT

)fTsin(

.T.e)ff

)f

fif(csin.T.ef

fif

)f

fifsin(

.T.e

)

(

fi f j f

fi f

j

i

∆

−π

=

∆

−π

∆

−π

− π

=

∆

ν

M points IDFT

M points DFT

∆

i

j

i j i

=

σ

i j

2 i

j 2 Aj 2

)fB.δ

=δ+

f

f)ji(csin)f

Bj i

2 2

1 2

=

σ

SNR/

)

f(g

a 2

2σ+σ

σδ

=

( SNR)

Q)SNR

2

1dxe

2

1)

y

(

Q

y 2 /

x2

?

;1M, ,1,0ne

)

n(hM

z(H

−∞

=

− +∞

1 M ( n

nM n

nM h(nM 1).z z h(nM M 1).zz

)

nM(h)

z(H

M / ni 2 j ) i ( k

k

M / ) kM n ( ni 2 j )

i ( 1

M 0 i

e)

k(AM

1)kMn(h)

n(x

e)

kMn(h)

k(AM

1)n(x

l(x

e)

k(AM

1)kl(h)

l(x

) m ( k

) m ( )

m (

M / im 2 j ) i ( k

) m ( )

m (

∑

∑

∑

∞ +

−∞

=

π

∞ +

kn N

2 j k n

1 N 0 n

kn N

2 j k k

e.XN

1x:IDFT

exX

:DFT

↑

↑

↑

↑γ

)n(hM

1)n('g

*))n(h()n(g

i ) n ( M

2 j )

i (

) i ( )

i (

+γ

−

γγ

γ

γ

=

−γ

=

⇒

γ

=γ

M, ,2,1n,.e

)nh(MM

1 (n)g

M, ,2,1n,].e

)M-h[-(nM

1 (n)g

)M-(n

g (n)g

M / ni j2 (i)

M / ) M - (n j2 (i)

(i) (i)

γ

=

M, ,2,1n,.e

)1-h(nM

1 (n)

=

π γ

M / ni 2 j M

1 n

) i ( )

i (

e)

1n(h)

nkM(yM

1)n(g)

nkM(y)

k(B

=

π

=

− γ

=

+ π

−+

−

−

=

−+

−

−

=

M 1 t

1 0 l

M / ti 2 j )

i (

M 1 t

1 0 l

M / ) t lM ( 2 j )

i (

e)

1tlM(h)

tM)lk((

yM

1)k(B

e)

1tlM(h)

tlMkM(yM

1)k(B

=

+ π +

−

−

− γ

=

+

0 p

M / ) 1 p ( i 2 j ))

1 p ( M ) l k ((

1 0 l

) i (

e)

plM(h.y

M

1)k(B

M / ) 1 p M ( 2 j M / ) 1 p ( 2 j

− +

−

−

− γ

M / 1 p M ( 2 j ))

1 p ( M ) k ((

1

0 l

)

e.)plM(h.y

M

1)k(B

↓

↓

↓

MpointsDFT

M points IDFT

)knM(g

n()knM(g

γ

γ

↑ ↓

1 L 0 p

) i ( )

i ( overall

) i (

)pn(h)

p(c

*)n(g)k(h

1 L 0 p

) i ( )

i ( overall

) i (

)pnkM(h)

p(c)n(g)k(h

−

0 n

1 L 0 p

M / ) p n nM ( 2 j M

/ ni 2 j overall

) i (

e)

pnkM(h)

p(ce

)

1n(hM

1)k(h

1 L 0 p

M / pi 2 j overall

) i (

e)

pnkM(h)

p(c)1n(hM

1)k(h

1 M

/ n 2 j 1

1 M 1 1

1 1

) i ( )

i (

r (k) g (n ).n(kM n ) h(n 1).e n(kM n )

∆

∆

(

e(i) = (i) − (i)

) i ( )

i ( 2

)

i

(

)k(y)k(dE)k(e

)]

1N(w), ,2(w),1(w),0(w[

wFFi = FFi FFi FFi FFi FF−

)]

N(w), ,2(w),1(w),0(w[

wFBi = FBi FBi FBi FBi FB

)]N(w), ,1(w),0(w),1N(w), ,1(w),

i ( )

i ( )

i ( FF )

i ( )

i ( )

k

(

B(i) (overalli) (i) (ri)

(

y(i) = iT (i)

T FB )

i ( )

i ( )

i ( FF )

i ( )

i ( )

i ( w

, w 2

i DFE MMSE min E d (k) y (k)

i FF i

=

)k(xw)k(A)k(y)k(A)k

(

i

) i ( )

i ( )

i ( )

* ) i ( H

) i (

~

H i )

i (

* ) i ( )

(

e(0i) = (i) −∆ − H0i

H i 0 H

) i (

* ) i (

, ) i ( xx ) i (

) i ( i 0 H ) i (

* ) i ( 0 )

i (

)k(x.w)

k(x)k(AE)k(x)

n(h

)k(A)1k(n)1nk(A)

n(h

)k(A)k(n)nk(A)

n(h

E

p

* ) i ( 1

Noverall

0 n

FF )

i ( r FF

) i ( eq

* ) i ( 1

Noverall 0 n

) i ( r )

i ( eq

* ) i ( 1

Noverall 0 n

) i ( r )

i ( eq

i ( )

i

(

) i (

)pjk(A)

tik(A

2 A i

eq

1 N

0 n

* ) i ( )

i ( r )

i ( i eq

* ) i ( )

i

(

) i (

eq

)

i(h

)k(A)

ik(n)ink(A)

n(hE

)k(A)

ik(B

FF i

eq 2 A

i eq 2 A

i eq 2 A

)

i

(

FB FF

) i (

) i (

) i (

0

0

)1N(h

)1(h

)(h

p

× +

−

∆σ

∆σ

=

⇒

)i(Rxx

{x (k).x (k)}

E)

i

(

R = (i) (i)H

)1k(A

)1Nk(B

)1k(B

)k(B

i

(

) i ( FF )

i

(

) i (

) i (

FB FF FB FF

BD

CAR

+

× +

eq eq 2

A

* 1

N 0 p eq

1 N 0 t eq

* j

N, ,2,1li)

lit(h)

t(h

)p1ik(A)

p(h.)t1ik(A)

t(hE

)1lk(B)

lik(BEA

eq

eq eq

=

−+σ

li(

[ ] { }

FB FF

eq 2 A

*

* 1

N 0 t eq

* j

N, ,2,1lN, ,2,1i)

ijD(h

)1jDk(A.)t1ik(A)

t(hE

)1jDk(B)

1ik(BEC

eq

=

=

−+σ

)1Dk(A

)1Nk(n

)1k(n

)k(n

E

r r

xxnoise

) N N ( ) N N ( xxnoise

FB FF FB FF

00

0ER

+

× +

−

γ

=

− + π

− π

−σ

=

−

−+

−σ

=

−+σ

M / ) j l ( 2 j 1

* 1 2

n

M 1 n

M / ) j l n ( 2 j 1

* M / n 2 j 1 2

n

M 1 n

1

* ) i ( 1 ) i ( 2 n

M 1 2

2

* 2

* ) i ( M

1 n

1 1

) i (

1 1

e)

1jln(h)

1n(h

e)

1jln(h.e

)

1n(h

)jln(g)

n(g

)jnkM(n)

n(g.)lnkM(n)

n(g)

jk(

[ ]) 1 ) xx i

=ψ

=

−M 0 n

M / in 2 j ) i ( )

i ( ) i ( 1 ) i ( 1

1M, ,1,0n)

n(h.e.)n(h.)n(h)

nn(cψ

1M, ,1,0i)

l(c.e1 L 0 l

M / li 2 j )

i

= π

1M, ,1,0i

=

=M 10 n

) i ( ) i ( )

=

− γ

=

− π π

) i ( overall

1 M 0 n

M / ) n kM ( 2 j M

/ ki 2 j )

i

(

overall

)1nkM(h)

n(hM

1)k(h

e)1nkM(h.e

)n(hM

1)k(h

γγ

M points

wFF,0(k)

 (0) (k- ∆ )

{ (i) (i) 2}

w , w 2

i

DFE

MMSE min E b (k) a (k)

i FF i

=

M points IDFT

↑

↑

x = (i) −

)z(F

1]1)z(F[1

1)

z(A

)z(X) i

−+

nz)

n()

z(F

)k()k(v.L2)k(A)L2mod(

)]

k()k(A[)k('

)z(F

)z(V.L2)z(A)z('X

]1)z(F).[

z('X)z(V.L2)z(A)z('X

) i (

) i (

=

z(

)

k

( = (i) +

)L2mod()]

k(v.L2)k(A[)L2mod(

{ } {2 2}

)k(y)k(AE)

−

-)k(x.w

i (

k(x.w

k 1

k = +µ

− +

−

µ

S)

NN(

20

+

<

µ

<

)m(e.)

k

(

∆k

w

−

)m(x.w)m(A

k(x)

k(K.)1k(P

k(Kw

w

)k(x.w)k(

k(x

)k()

k

(

K

)k(x)

1k

1

* 1

−

−λ

=

ξ+

n n

* n N

{ 2 }

1 n 1 n 1

1 n 1 n N

1

E − = θ∈ θ−θ − −− θ−θ − ≤σ −

σθ

n 2 1 n n n T n n 1 n 1

1 n 1 n n N

≤λ

=β

1

n n

n

n n

σ

2 n 2 1 n n 2

n =α σ +β ρ

λ

2 2

1

n + δ ≤ρ

T 1 n n

n =y −θ − xδ

2 n n 2 n 2 1 n n

2

n

n

* n n n

1

n

n

n n n

1 n T n

* n 1 n n 1 n n

n

G.1

)

1(

)

1

(

.x.P

G.1

P.x.x.P.P

1

1

P

λ+λ

−

δλ

−λ

−ρλ+σ

−

λ

−λ

n n max

n n n

n n n

n n

n max

n

max n 0

n n

* n 1 n T n n

0)1G(1if

0)1G(1if])1G(1

G1

[G11

1Gif

2

)1(

0if

),min(

x.P.xG

δ

σ

−γ

+λ

>

−µ

+

−µ

+

−

−

=µ

=λ

θθ

S)v,A()

v,A,(z

)(

N ρΘ

S )

T n 1 N 2

n 1 N 2 N

)v,A(x.a

:C

)v,A,(za:C)

−

∈θ

=

ρ

≤θ

−

∈θ

=

ρ

Θ

)(

N ρΘ)

N ρΘ

0l);

()

−

D

1 D _ D D

1 D

D 1 D D

N

c00

0

c

c0

0c

c

cc

00

c

C

)ws.C(

zn =θT TN n + n

H)w,s(w

.s

N ρ

Θ

H ) w ,

s

(

2 2 T 0 N 1 N 2

−

−θ

∈θ

=

ρ

Θ

ν+

=D i

n i n i

n c au

ρ

− ν

−

N N i

) 1 ( i K

)

1

(

e

a

2 N

H N )

1

(

e.C.I.K

)

1N2(C.C

− ν

=

θ

θ ∈ ΘN(ρ))

(

N ρ

Θ

2 2 2 ) 2 ( 0 2 2 a

2(cos

0 ) 2 ( N

)

2

(

e

=

ε

0 H N 1

0 2 2 a

2 N

H N )

2

(

e.C.I)2(cos

C.C

− ν

ρ+

=

θ

i

Q i

i

N

)1/0(P

ri=∆ U /Q

i,r)

p1.(

p.1k

1M.k

Lk

1k(

)!

1M(1

k

1M

Q

N

k M k

N p (1 p)

k

M)

k Q

/

1k

1M)1

k N

, Q / U

, Q / U

i

)p1.(

p.1k

1M)

k,1/0(P

)1/k(P)

k,1/0(P

r

Q i i

i Q Q

i i

k

Lk)k,1/0

0U,1Q

N (k) r pP

M 1 i

i j { 1 , 2 , , M } \ { i i , , i }

j i

i i

1 k M 1 i N

1 2 1 1

Q(k) p p p (1 p )P

M

1 L

k

Np

)k(P)Lk(r

Q

i i Q Q

/ R Q

Q / R

1 i

R rp

N

LNLN

k =δ +σ −ρ

~

ip

~

→∞

)t(Q)

1()1t

1()1t

i

i i

i

ζ

−+

r)t(p

~

i

) t ( i

i ≈

)t

(

p

×

γ

γ

γ

[1] J.G Proakis, "Digital Communication", McGraw-Hill, 1995 - (book)

ç