Выбор оптимального метода модуляции сигнала в современных цифровых системах радиосвязи. Моделирование в среде AWR DESIGN ENVIRONMENT

Citation preview

, .

. .

“ . AWR DESIGN ENVIRONMENT”

– 2008 .

С ...........................................................................................................................................2  1 .............................................................................................................................................3  1.1 .........................................................................................3  1.1.1 ..................................................................................................................6  1.1.2 .........................................................................................................................7  1.1.3 ............................................................................................................................9  Baseband.....................................................................................................................11  1.2 1.2.1

.....................................................................................................16  (OOK, ASK, M-ASK)...................................................17  (M-ASK) ......................................................19 

1.2.2

(BPSK, QPSK, M-PSK) .........................................................20  (BPSK – Binary Phase Shift Keying)....................................21  (QPSK – Quadrature Phase Shift Keying) .....................22  (M-PSK) ...............................................................24 

1.2.3 1.2.4

-

(QAM) ..............................................................24  (FSK, MSK, M-FSK, GFSK, GMSK). ...............................25  (M-FSK) ............................................................26  (MSK) ......................................................26  (GFSK, GMSK) ..........................27  .........................................................................28  ........................................................................32  .........................................................................40  ..............................................................................................................40 

1.2.5 1.2.6 1.2.7

(TCM) ................................................................41  . N2 2.1 2.2 3 1. 2. 3. 4.

4

..........................42 

Visual System Simulator (VSS) ..................................................................43  . .................................................................................................44  BPSK ...........................................................................................................45  ..........................................................................................................................46  ..........................................................46  . .....48  ...................................................................49  . ................................................................................................................................49 

5. . ..................................................................50  6. . ........................................................................................................................................51  ........................................................................................................................................52 

2

1В . (

, ,

),

, . :

(GSM, CDMA, (GPRS .),

3-

(CDMA-2000, UMTS(WCDMA), (IEEE 802.11 Wi-Fi), (IEEE 802.16 WiMax), (Eureka). (DECT),

,

(TETRA

.). (DVB)

, . .

(

)

. (

,

).

, (

,

-

.).

,

. ,

(

,

). ( (

).

. (Digital Signal Processor – DSP) ,

. , ,

,

,

. .

1.1 С .1.

1.

, . .2. 3

2.

. ( (

.3, ).

,

)

.

, .

. –

(

)

.

,

,

-

,

.

,

, (

-

).

– .

(

)

, .

,

– ,

(

.3, ).

, ,

,

.

, ,

, (

).

4

3.

: –

(

; – .

;

–

): f d ≥ 2 f max , .

ω max = 2πf max , s k –

s (t ) =

∑s ∞

k = −∞

(

k

, f max –

sin(ω max t − kπ ) , ω max t − kπ ) .

(1): (1)

(1),

, .

,

, , . . .

, (

), ,

, . 5

. . , 2 = 4096

-5 ..+5 .

12

12

, ,

, 10/4096= 0.00244 +2.5 .

.

1024, 1024(10)=0100

0000

0000(2). 0100 0000 0000, .

,

.

1.1.1 (

.2).

–

.

, , ,

, . ,

. (

MP3(

), ,

),

, (

Wi-Fi). ,

,

.

,

. (

,

, ),

. . .

,

, .

, (

,

).

, , . .

, . -

(

).

. , . –

. ).

,

,

GSM

(

.1 .

-

( ,

. 8 96

.1 12 /c.

)

. .

.

6

1.

К

,

12 7..8 4..6 3..4 1 1

/

96000 56000..64000 32000..48000 24000..32000 32000..64000 16000..32000 2400..4800

1.1.2 К

. –

. , .

,

. : ,

,

. . ( -1.6

,

–

,

(

.

),

). . . –

(BER – Bit Error Rate). BER , .

,

,

, [

/ ].

,

(

100%

). /

:

S C = W log 2 (1 + ) , N ( / ), W –

C – ( ), S –

(2) ,N– : N = N 0W ,

.

,

N0 –

. / , . . .

,

Eb / N 0 – –

,

,

. (2)

: 7

(

)

Eb W C / W 2 = −1 N0 C C /W – – Eb / N 0 .

(3)

.4.

4.

Eb / N 0

:

,

Eb / N 0 , Eb / N 0 ,

.

: Eb / N 0 = −1.6 . ) .

. Eb / N 0 –1.6 Eb / N 0 < −1.6 . (2) (3)

C /W

(

100%

Eb / N 0

, ,

.

. ,

(

)–

, ,

, .

,

(2)

(3) , ,

/

,

/ .

(M

), M-

. .

,

, M-

.

M-

.

, .

, 8

p0 , .

(

/c),

:

p ⎡ ⎤ C = F ⎢log 2 M + (1 − p 0 ) log 2 (1 − p 0 ) + p 0 log 2 ( 0 )⎥ , M −1 ⎦ ⎣ (BER), M – ,F– , . F, ( C, .

p0 . . C f N (1 + α ) ⎩

:

α α,

(14)

0 ,

(

),

α=0

. α=1

fN .

1.

2 fN

,

α=0.35.

.

. .

, ( ).

-

(QAM) ,

(

)

. 0 .

( .

GSM)

, GMSK .

CDMA , . ;

(

)

. ,

IQ-

.

, .

,

(

) . , . , (

, ( IQI(t)

.10).

)

, Q(t), (DSP).

baseband.

,

, , 14

(

,

)

.

10.

. ,

,

:

( (

)

).

, , . . ( 3

), (

.

,

, QAM , ,

.

.) ,

,

, GMSK, . , . .

( loop),

,

,

-

) (Costas [2]. ( .10). 15

Δϕ . , ,

Δω )

( Δω .

(

Δω

),

.

(

I(t)

±π /4.

, )

Q(t)

. (

.

) , (

.

,

baseband-

.

).

,

(

)

( ,

) ,

,

.

( ,

–

)

,

. .

. ,

, , . . . ,

-

,

(

. (

,

)

,

,

, ,

).

,

, ,

.

1.2 Ц (

),

, (

,

,

-

,

s (t ) = A(t ) cos(ω (t )t + ϕ (t )) . , {0,1} ),

),

(

,

. baseband-

, ( )

, ,

.

16

1.2.1 А

я

(OOK, ASK, M-ASK) .

: s (t ) = A(c(t ) + B) ⋅ cos(ωt + ϕ 0 ) , c(t) –

ϕ0 –

, A, B

B ≥ 0, ω –

(15)

,

.

s (t ) = Ac(t ) ⋅ cos(ωt + ϕ 0 ) , A OOK (On-Off Keying, .

11.

c(t) {0,1}, B=0. 0 ( -

.11).

)

OOK: –

; –

;

–

B=1. B ≥ 0,

A ,

2A ASK (Amplitude Shift Keying – ASK B=0.

). OOK .

.

. , .

, (

).

[2], (baseband) , ,

, ,

, ASK

. baseband-

, .

.12.

.13 baseband-

.12

.13

.

, .

17

1–

,2–

.Ф ,3–

1–

13. ,2–

,3–

12.

ASK-

:

⎧⎪ sin (π f − f c Tb )⎫⎪ ⎨ ⎬ ⎪⎩ π f − f c Tb ⎪⎭ , Tb – – .

OOK

:

A 2Tb PSD( f ) = 4

fC –

: .

2

⎤ ⎡ 1 ⎢1 + δ ( f − f c )⎥ , ⎦ ⎣ Tb . ,

(15) , . .

(16)

baseband,

.

(5).

(15)

(5),

: I (t ) = A(c(t ) + B) , Q(t ) = 0 .

OOK ,

. I(t)

. , –

Q(t)

, I(t), (x,y)

Q(t). ,

x,

,

y.

–

. (5),

A(t ) = I 2 (t ) + Q 2 (t ) ,

[5], ,

(I,Q),

. 18

OOK

ASK

.14.

14. – –

OOK, ASK

(M-ASK) ASK (

baseband-

).

, . . {0,1},

. {00, 01, 10, 11}.

{0, A, 2A, 3A}. , .

( .

, 8 ,

M-ASK

Tb ASK )

(15), , {0,1,2...M-1}.

) M-ASK k– M = log 2 k , 256-ASK 256

. c(t) M-ASK Ts = Tb log 2 M . .15 8-ASK ( baseband( , . . .

(16)

).

19

15. ASK, –

–

: 8-ASK

8-ASK

.16.

16.

8-ASK

( ), . -

, . . . .

,

. . .

я

1.2.2

A

ϕ0 –

(BPSK, QPSK, M-PSK)

: s (t ) = A cos(ωt + ϕ (t ) + ϕ 0 ) ,

, ω –

ϕ (t ) .

(17)

.

sC (t ) = A cos(ωt + ϕ 0 ) , ϕ (t ) . c(t).

ϕ (t )

(17)

20

(BPSK – Binary Phase Shift Keying) {0,1}

{0, π}. 180º.

,

⎧ A cos(ωt + ϕ 0 ), c(t ) = 1 s (t ) = ⎨ ⎩ A cos(ωt + π + ϕ 0 ) = − A cos(ωt + ϕ 0 ), c(t ) = 0 1 , s (t ) = A ⋅ 2(c(t ) − ) cos(ωt + ϕ 0 ) . 2 BPSK {-1,1}. 1 I (t ) = A ⋅ 2(c (t ) − ), Q (t ) = 0 . 2

BPSK

, , baseband-

.17.

17. –

; –

;

BPSK: -

–

;

–

BPSK

⎡ sin (π f c − f Tb )⎤ PSD( f ) = A 2Tb ⎢ ⎥ ⎣⎢ π f c − f Tb ⎦⎥ BPSK

OOK : 2

(18) (

) BPSK (DBPSK). ,

(

)

. 180º.

,

( ).

,

, . 180º,

, , ,

.

21

К

(QPSK – Quadrature Phase Shift Keying)

(M=4), ,

{±π / 4,±3π / 4}

π /2.

4

( ,

)

{00, 01, 10, 11}

.18. .

18.

QPSK

, , . . ,

,

, ,

(

)

.

. . 2

,

QPSK-

2

BPSK-

.

Tb

Ts = Tb log 2 M .

M=4 , QPSK(18)

⎡ sin (π f c − f 2Tb )⎤ PSD( f ) = 2 A 2Tb ⎢ ⎥ ⎣⎢ π f c − f 2Tb ⎦⎥ , Δf = 1 / Tb , QPSK 2

, [2], , Ts = 2Tb .

:

2

BPSK.

, BPSK. QPSK

(I,Q),

, QPSK

,

baseband-

(19)

.

I(t)

ϕ0

2

Q(t) , . .

, . :

, I (t ) = cos(ϕ (t )) , Q(t ) = sin(ϕ (t )) 22

2. Ф

QPSK-

00 1 π/4

ϕk

I k = cos(ϕ k )

Qk = sin(ϕ k ) ,

01 3 3π/4

1/ 2

− 1/ 2

1/ 2

1/ 2

baseband-

11 -3 -3π/4

10 -1 -π/4

− 1/ 2

1/ 2

− 1/ 2

− 1/ 2

, I(t)

.2.

Q(t)

basebandI(t) Q(t). QPSK

(DQPSK) DQPSK, ,

DBPSK,

(OQPSK – Offset QPSK). DBPSK,

π /2.

. OQPSK

,

.

QPSK, QPSK (

.18),

,

90º, 180º.

,

180º. QPSK

. (

baseband-

) .

.

, , . . ,

π /2.

.

OQPSK 100% I(t)

. QPSK (

OQPSK QPSK.

OQPSK

Q(t)

30% :

, ) .

23

(M-PSK) M-PSK

k = log 2 M

,

, -

.

. .19

8-PSK

.

19.

1.2.3 А

8-PSK

я

-

(QAM)

, ,

. . . . [5].

. ,

2

.

, –

-

–

. , , . . .

,

. QAM M

(QAM – Quadrature Amplitude Modulation). . M=4 QPSK, QAM M ≥ 8 ( . . k = log 2 M , k ∈ N , 2: 2, 4, 8, 16 . .). .20 16-QAM .

24

20.

16-QAM

,

1024-QAM. .

,

, ,

QAM .

, QAM-

I(t) .

, baseband-

. I(t)

Q(t).

1.2.4 Ч

я –

(FSK, MSK, M-FSK, GFSK, GMSK). ω (t ) .

–

s (t ) = A cos(ω (t )t + ϕ 0 ) = A cos(ω c t + ω d c(t )t + ϕ 0 ) =

:

ωc – c(t) – ,

(

. Q(t),

)

{ω c − ω d , ω c + ω d } .

= A cos(ω c t + ϕ 0 ) cos(ω d c(t )t ) − A sin(ω c t + ϕ 0 ) sin(ω d c(t )t ) , , ωd – ( . , ϕ0 – 2 , (FSK – Frequency Shift Keying). , . . {-1,1}, -1 0, 1 – . ,

(20) )

,

(20)

{0,1} FSK

.21.

25

21.

FSK: – –

; –

;

-

(20) : I (t ) = A cos(ω d c(t )t ) , Q(t ) = A sin(ω d c(t )t ) . [-1..1],

FSK-

: sin

I(t)

Q(t)

cos

FSK –

A.

(M-FSK) (

M-FSK k = log 2 M

) ,

-

2ω d .

(20),

,

.

M-FSK

M-FSK FSK.

,

,

(20), , .

4-FSK

, {00, 01,

10, 11} c(t) {-3, -1, 1, 3}.

m = 2 f d Ts ,

(MSK)

f d = ω d / 2π – .

, Ts – ,

,

, ),

(

0 .1 ≤ m ≤ 1 .

[2],

. m ≥ 0.5

FSK m,

. 0.5

.22

FSK

. m = 0.5 . FSK (MSK – Minimum Shift Keying).

26

22.

: 1 – m=0.25; 2 – m=0.5; 3 – m=1

MSK

cos(2πfTb ) PSDMSK ( f ) = 1 − (4 fTb ) 2

2

(21) MSK

QPSK

.23.

23. 1–

: MSK; 2 –

QPSK.

, QPSK

MSK

(

, . .

. MSK , ,

QPSK).

f

(

50%)

f −2 MSK

−4

, QPSK.

(GFSK, GMSK) basebandShift Keying)

FSK MSK . GMSK (Gaussian Minimum Shift Keying,

GFSK (Gaussian Frequency GSM). ,

, .

,

baseband.

, (

,

,

(

)

, ).

, 27

. . .

:

⎛ f ⎞ ln 2 G ( f ) = exp[−⎜ ⎟ ], ⎝B⎠ 2 3 . 2

B–

(22)

: -

( baseband-

-

). (B,C); (

), ;

-

. , . IQ-

,

. baseband,

,

(

).

, ,

.

,

. . (

)

,

, FSK-

,

FSK

.

.

-

FSK,

. . (

,

) . , . . , .

( .1.2.7),

.

1.2.5 С

я , . , ( ,

). , 28

.

,

. ,

, . ,

.

-

,

, .

–

,

,

,

(

k = log 2 M

)

QAM) MSK c BTb = 0.3 α = 0.35 (

MSK.

,

. M-ASK, M-PSK

(

.

, (

) 1

, MSK

2.6 ,

GMSK)

QPSK

99%

GMSK. 1.3

M-

QPSK ,

2.6 QPSK

BPSK. . .

[2], [10] Eb / N 0

, :

⎛E ⎞ BER = f ⎜⎜ b ⎟⎟ , ⎝ N0 ⎠ Eb – ,

BER –

(23)

, N0 –

Eb = PTb ,

. P,

,

Tb –

.

, .3

Eb / N 0

.

3.

(BER)

OOK M-ASK BPSK DBPSK DBPSK

Q( Eb / N 0 )

2( M − 1) ⎛⎜ log 2 M E b ⎞⎟ Q M log 2 M ⎜⎝ ( M − 1) 2 N 0 ⎟⎠ Q( 2 Eb / N 0 ) 1 exp(− E b / N 0 ) 2 ⎛ 2 Eb ⎞⎛ ⎛ 2 Eb ⎟⎜1 − Q⎜ 2Q⎜ ⎜ N ⎟⎜ ⎜ N 0 ⎠⎝ 0 ⎝ ⎝

QPSK

Q( 2 Eb / N 0 )

DQPSK Eb / N 0 >> 1

2 Q( 2 Eb / N 0 )

⎞⎞ ⎟⎟ ⎟⎟ ⎠⎠

29

⎛ 2 Eb log 2 M 2 ⎛π Q⎜ sin 2 ⎜ ⎜ N0 log 2 M ⎝ ⎝M

M-PSK

FSK

⎛ ⎡ sin( 2π ⋅ m) ⎤ E b Q⎜ ⎢1 − ⎜ ⎣ 2π ⋅ m ⎥⎦ N 0 ⎝

MSK

Q( Eb / N 0 )

⎞ ⎞⎟ ⎟⎟ ⎠⎠

⎞ ⎟ ⎟ ⎠

E ⎫⎪ 2( M − 1) ⎧⎪ Q ⎨ log 2 M b ⎬ N 0 ⎪⎭ M log 2 M ⎪⎩ : k = log 2 M , k –

M-MSK

2 P − P0 BER = 0 , log 2 M 2

2( M − 1) ⎛⎜ 3 log 2 M E b ⎞⎟ Q ⎜ M − 1 N 0 ⎟⎠ M ⎝ k: 2 ⎡ ⎛ 3 log 2 M Eb ⎞ ⎞ ⎤ 1 ⎢ ⎛⎜ ⎟⎟ ⎥ BER ≤ 1 − 1 − 2Q⎜ ⎜ ⎟⎟ − log 2 M ⎢ ⎜⎝ M N 1 0 ⎠⎠ ⎥ ⎝ ⎣ ⎦

P0 =

QAM

Q( x) =

.3

1

2π

−t ∫e

∞

2

/2

–

dt

, M –

x

,m–

, BER –

. .3

, (

.,

,

, M-PSK, Q(x)

M-ASK

).

,

, .

QPSK

BER 2

BPSK

, ,

BPSK.

QPSK BPSK, ,

,

, ,

:

( . 3), , QPSK QPSK,

BPSK. QPSK

Q(t).

BPSK

I(t). , . DBPSK

DQPSK ( ,

BPSK ( 0.5 Eb / N 0

),

QPSK (0.3 – 0.9

).

BER (

.24).

). DBPSK c DBPSK

.24. .

30

24.

: DBPSK, DQPSK

DBPSK

,

. OOK, BPSK 3

(

MSK. BPSK ( , .25).

.3, OOK , QPSK)

25.

OOK, MSK

MSK

BPSK

, 4

QPSK . GMSK. . GMSK, .

( GMSK QPSK (

,

QPSK, , , ,

QPSK ). , GMSK, CDMA – OQPSK. , FQPSK)

M=16

QPSK. , GMSK ( M>4. ,

,

, GSM

. .1.2.7). . 26 -

M=64. 31

26.

M-ASK, M-PSK

M-QAM:

– M=16, – M=64

.26, M-PSK

(

M-QAM 4

,

,

10

M=16) . M-PSK, , M=16 , M-QAM.

M=64

, M-QAM M-QAM M=64 10

M. . M-PSK

,

M-PSK ,

M-QAM – .

, . , ,

,

,

M . log 2 M

.3,

M-MSK, .

,

, M ≤4

. , M > 4 – QAM. QPSK

, QPSK, QAM

QAM QPSK

,

, (TCM),

M=4. .

QAM (FQPSK, FQAM),

( .1.2.7).

1.2.6 В

я ,

. ,

.

, ,

BER ≤ 10 −3 . .

BER (

10-9..10-12).

BER (

BER,

, TCP/IP),

, 10-20.

32

,

,

,

. .

,

, ,

. (UWB).

.

UWB (

1 )

, . UWB

–

. Eb / N 0 ,

, .

.

Eb = P ⋅ Tb =

, Tb –

P = P0 ⋅ GTX ⋅ G RX

,R– ⋅K ,

( P0 – , G RX

K –

), 1 Loss = – K

P , R

P –

,

/ ). , GTX –

– .

,

–

Eb ( : Eb = P0 + GTX + G RX − Loss − 10 log R ,

, .

(

). N 0 = −174 + NF ,

, , ,

–

. ,

/ – . 17º , NF –

:

Eb / N 0 (

, -174

Eb = P0 + GTX + G RX − NF − Loss + 174 − 10 log R N0 .

(24)

= P0 + GTX + G RX − NF − Loss + 174

):

(25)

,

. Eb = N0

,

− 10 log R

(26)

Eb / N 0 ,

. –

. (Loss). , -

( ).

-

, .

,

33

.

,

, ,

, ( ). (

-

,

) (Loss). .

, ,

Д

. W, BERmax )

( (

)

С ШД ( ).

-

. . Eb / N 0 , BER Eb / N 0 ,

, Eb / N 0

, BERmax. BER

.3.

, . .

, Eb / N 0

, .

,

,

; . BER

Eb / N 0 .

.3 ,

Eb / N 0 BER ,

,

Eb / N 0

. , QPSK, 16-QAM 64-QAM AWR Design Environment.

BER .27

34

Eb / N 0

27. QPSK, 16-QAM

64-QAM,

, Eb / N 0 , ,

BER. ,

. “

”

“ ”

:

W = (1 + α )

W – M – (1

, α – ). .

α

,

R 1 , log 2 M Rc ( ), R –

(27) (

/ ),

, Rc – ,

: 1+α 10 log W = 10 log + 10 log R = 10 log R + K ( M ) , log 2 M ⋅ Rc 1+α . K ( M ) = 10 log log 2 M ⋅ Rc 10 log R (28) (26). (26)

:

(i- )

Eb / N 0 = Eb / N 0 ,

− 10 log W + K ( M )

(Eb / N 0 )imin . min i

⎛E = ⎜⎜ b ⎝ N0

(28)

(29) BERmax,

⎞ ⎟⎟ ⎠i

min

(29),

+ 10 log W − 10 log

1+α , log 2 M ⋅ Rc

: (30)

35

min i

– BER (27):

R

(31)

, .

Rmax = W ⋅ log 2 M ⋅ Rc

,

( ) (

1 1+α

(31)

), . (30)

(31)

.

(Eb / N 0 )imin .

min i

(30)

. (

log 2 M ⋅ Rc

), (

min i

BER),

(

). (31)

(

)

, .

(30)

(31)

.

, QAM (

,

. .

). QAM BER=10-4, “ BER=10-4

(E b / N )

10

min 0 i

(M=4), 16-QAM 64-QAM. 79.8 ; 86.7 ; 92.8 . 29.6 / ; 44.4 / .

, ” 8.1; 12.0; 16.3

. . , 0.35.

.27 QPSK min i

(30), (31): 14.8

: / ;

.28.

36

28.

,

≥

min 1

.

-

, , (