.. .. ..

2010

1

..

.. , .. , ..

-

. .. , 080801

( ), 090103 ,

210400.62

2010

2

621.39 32.94 73 19

- ..

:

, .. ;

, ..

19

..

: . / .. , .. , .. ; - . , . . - . . . . : . . . , 2010. 186 .

, , - 090103 - , - 080801 -.

621.39 32.94 73

.., .., .., 2010 .. , 2010

3

MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION

STATE EDUCATIONAL INSTITUTION OF HIGHER PROFESSIONAL EDUCATION

TAMBOV STATE UNIVERSITY named after G.R. DERZHAVIN

I.I. Pasechnikov, I.G. Karpov, I.. Stepanenko

INFOCOMMUNICATION TECHNOLOGY IN COMMUNICATION SYSTEMS

Permitted by the Editorial-Publishing Board of TSU named after G.R. Derzhavin as a study guide for students,

training for the specialties 080801 Applied Informatics (in Humanitarian Field),

090103 Organization and Technology of Information Protection, 210400.62 Telecommunication

Tambov 2010

4

Recommended for Publishing by the Editorial-Publishing Board of TSU named after G.R. Derzhavin

R e v i e w e r s :

Doctor of Technical Sciences, Professor .. Arzamastsev;

Candidate of Pedagogy, Associate Professor of General Physics Department .I. Sterelyukhin

Pasechnikov I.I. Infocommunication Technology in Communication Sys-

tems : Study Guide / I.I. Pasechnikov, I.G. Karpov, I.. Stepanenko ; Ministry of Education and Science, SEIHPE TSU named after G. R. Derzhavin. Tambov : The Publishing House of TSU named after G. R. Derzhavin, 2010. 186 pp.

The study guide includes the essential part of the subject Theories

of Electrical Connection in the area Telecommunication, as well as au-thors believe that the study guide will be useful at the detailed learning of the issues of transformation and transmission of information in subjects Protection of Data Transmission in the specialty 090103 Organization and Technology of Information Protection and Computing Systems, Networks and Telecommunication in specialty 080801 Applied Infor-matics in Humanitarian Fields.

Pasechnikov I.I., Karpov I.G., Stepanenko I.., 2010 SEIHPE Tambov State University named after G.R. Derzhavin, 2010

5

................................................................. 9 .................................................................. 10 .................................................................................... 12 1.

1.1. , , ..................... 141.2. -

.................................................. 171.3. . ................ 201.4. , -

......................................................... 231.5. ... 301.6. ............................ 341.7. ............................ 37

2. 2.1. ............. 462.2. .................. 472.3. . 49

2.3.1. - ............................................................ 492.3.2. ............ 52

2.4. . - .............................................. 542.4.1. - ........................................... 542.4.2. - - .............................................................. 552.4.3. .......................................................... 582.4.4. 61

2.5. ............... 622.6. -

........ 662.7. -

............................................................ 692.8. .................. 72

6

2.9. ....................................................... 74

3. 3.1.

.................................................................. 783.2. -

...................................... 813.3. 833.4. ................................... 903.5. ......................................... 963.6. .................................. 993.7. ( ) ....... 1043.8. -

...................... 113 4.

4.1. .................................................................. 117

4.2. .. 1234.3. ............................... 1264.4. ..................................... 1404.5. ........................................ 1504.6. .............. 1574.7. -

.............................................................. 1624.7.1. - - ....................................................... 1624.7.2. - - .................................... 1634.7.3. 1664.7.4. - .......................................... 172

............................................................................... 178 1. 179 2. ............. 180

7

INDEX

List of Symbols .......................................................................... 9List of Abbreviations .................................................................. 10Introduction ................................................................................ 12Chapter 1. Overview of communication systems

1.1. Information, communication, signal ................... 141.2. Generalized structure diagram of signal trans-

mission systems ................................................... 171.3. Communication channel. Interference in the

communication channel ....................................... 201.4. Mathematical models of messages, signals and

interference .......................................................... 231.5. Key indicators of communication systems quali-

ty ........................................................................... 301.6. Classification of communication systems ............. 341.7. The main types of communication systems ........ 37

Chapter 2. Information characteristics of communication systems

2.1. The basic problems of information theory ........... 462.2. Quantitative measure of information ................... 472.3. Entropy of the source of discrete messages ......... 49

2.3.1. Entropy as the average amount of infor-mation .................................................................. 492.3.2. Entropy of a binary message ...................... 52

2.4. Information in continuous messages. Epsilon-entropy ................................................................. 542.4.1. Discretization and quantization of a conti-nuous message ..................................................... 542.4.2. Epsilon-entropy of a continuous message .. 552.4.3. Entropy of uniform and Gaussian messages 582.4.4. Performance of the source of messages 61

2.5. Information at the output communication channel 622.6. Data transmission speed and the bandwidth of a

digital communication channel ............................ 662.7. The capacity of a continuous communication

channel ................................................................. 69

8

2.8. Redundancy of messages and its role ................. 722.9. Coding theorems for channels with and without

interference .......................................................... 74Chapter 3. Sending and receiving continuous messages

3.1. Transformation of a continuous message into signal .................................................................... 78

3.2. Criteria of interference immunity of receiving continuous messages ............................................ 81

3.3. Optimal reception of continuous messages 833.4. Amplitude modulation ......................................... 903.5. Balanced modulation ........................................... 963.6. Single-band modulation ....................................... 993.7. Angular (phase and frequency) modulation ......... 1043.8. Comparative analysis and the application area of

various kinds of modulation ................................. 113Chapter 4. Sending and receiving discrete messages

4.1. Transformation of a discrete message into signal 1174.2. Optimal reception of discrete messages ............... 1234.3. Amplitude manipulation ...................................... 1264.4. Frequency manipulation ....................................... 1404.5. Phase manipulation .............................................. 1504.6. Relative phase manipulation ................................ 1574.7. Ways of increasing the speed of message trans-

mission ................................................................. 1624.7.1. The problem of increasing the speed of message transmission in case of a limited band of operating frequencies ....................................... 1624.7.2. Signals with low-band radiation and op-timal spectral characteristics ................................ 1634.7.3. Multiple station digital signals 1664.7.4. Interference immunity of multi-position signals reception .................................................. 172

Bibliography .............................................................................. 178Appendix 1. The main types of modulation and manipulation 179Appendix 2. Determination of benefits for the optimal recep-tion of analog modulation signals ............................................... 180

9

A B (t) ( )t

D Ds Es Fs F f0 ( )

sf , Q q q q h h(t) L(u) m m P Pn Ps P () N0 n(t) () R Rn() n(t) rij C Sn(f) n(t) s(t) T T V (t) (t) 0

10

-

- - - - - - - -

11

- - -

12

- , , , , - . , , - . - .

- -, , , , , . - , - , ..., .. , ..., - .. , ..., .. , - - -.

- - , , - , - , , .

13

, , - .

, , , - , , - , , - . - .

: ; - , - ; - . - , , - . - , - -.

- . , - , - , , , - . - .

. , - , , , . . .

14

1.

1.1. , ,

- , - - , , . -, , () , . . , , - .

. - . , , -, . . , - . . , 80...90% 10...20% . (, , ) 1...2% . - (), -. , , , - .

. - (. 1).

15

, - . - -.

, , -, . .

, , , . .

. 1.1. -

- (, , . .) (-, , . .). , - - . , () , .

1 - . - , .

. . -, . -

1 ,

.

16

-. , - , (. 1.2).

, , - - . - (, , ) - (, 0 1), - - . , - , (. 1.2). - , - - .

(t)

t t

(t) 1 0 1 1 0 1

) )

. 1.2. : ;

, , .

s, Ds Fs. - Ts , - . Fs , . Ds - - , -

17

. . :

.ssss DFTV = (1.1) Vs

. -, .

: ( ) - , ( -) D F. - :

. DFTV = (1.1)

s VV (1.1)

. , - , (1.1) - . , . . - , , , .

1.2.

1.3

. - , - .

18

, . .

, . .

x (t)

n(t)

(t) s(t,x)

x(t) -

(t) -

( )t-

. 1.3.

(t) x(t). , - . - . - -. x(t) s(t,x) - .

- ( ) . - .

, . , - , , -

19

-. , . , ( ), .

, , . s(t,x), - n(t). :

).(),()( tnxtst += (1.2)

(t), - )( t , - (t). (t) - )( tx , x(t). x(t) (t) . - - .

, 1.3, . - )( tx )( t - . - , - .

20

1.3. .

, . , - (-), (, AA BB . 1.4). , .

A B B A n(t)

(t) -

(t) -

. 1.4. ,

, (), - . - (), . - - , , , .

( ) - . - - .

21

, - - . 1.5.

-. x1, x2,..., xn x, - . - (t) = s(t,x) + n(t) - x, - , - naaa ,...,, 21 . , . , - .

a n(t) x n(t) n

a 2(t) x 2(t) 2

an(t) xn(t) n

a2(t) x2(t) 2

a1(t) x1(t) 1

x (t)

n(t)

(t) s(t,x) x(t) -

a 1(t) x 1(t) 1

. 1.5. -

. , . - , -

22

. - , , , . , , . - . -, - . , , - . . - , - .

- () , - . . - , , - , .

, , - : .

(t) s(t) n(t) , . . (1.2), - . - k(t), . .

)()()( tstkt = , (1.3) .

- ( -) , ( ) , - . - , - . - . .

23

.

-, - , - .

1.4. ,

, -. , . , - .

- { }i -, - . , i ( - it ) .,,, 21 m K

(- ). i

m ,,, 21 K .,,2,1,)( mrPP rr K== -.

24

- . - [10].

, it .

)(t . - n-

1, , ; 1, , 1 1,, (1.4) n-

1, , ; 1, ,

11, , ; 1, , (1.5)

n . , (1.4) (1.5),

, . , -, -. , - , - , - -.

, , , - . , - . - : - .

, . - , -, . - :

25

( ) ( )( )[ ]( )

= tD

tmxtD

txpx

x

x 2exp

21,

2

.

: 1) :

dxtxpxtmx ),()(

= ; (1.6)

2) :

)(),(),()]([)( 222 tmdxtxpxdxtxptmxtD xxx ==

; (1.7)

3) :

2121212221121 ),;,()]()][([),( dxdxttxxptmxtmxttR xxx =

; (1.8)

4) :

212121212121 ),;,(),( dxdxttxxppxxttK x

= . (1.9)

:

dxxpxmx )(

= ; (1.10)

222 )()()( xxx mdxxpxdxxpmxD ==

; (1.11)

2121221 );,())(()( dxdxxxpmxmxR xxx =

; (1.12)

21212121 );,()( dxdxxxppxxK x

= . (1.13)

(1.10)(1.16) , xm ; xD - , t (. . -

26

) ; )(xR )(xK , , t1 t2 - , 12 tt = .

-, - :

.)()( =

deRS jxx (1.14)

(1.14) , , )(xS - )(xR :

.)(21)( =

deSR jxx (1.15)

, - , - . , (., , (1.10)(1.13)), , )(tx . , - :

=T

TTx

dttxT

m )(21lim ; ( 1.16)

=T

TxTx

dtmtxT

D 2])([21lim ; (1.17)

( ) dtmtxmtxT

R xT

TxTx

])([])([21lim =

; (1.18)

( ) dttxtxT

KT

TTx

)()(21lim =

. (1.19)

, , - ,

27

0 . - :

+= )(,0)()],(cos[)()( 0 ttAtttAt , (1.20) A(t) (t) -

t0cos .

: 1. , . . -

: ( ) ( ) ( )( )0cos ++= tttAts , (1.21) 0 .

2. : ( ) ( ) ( )( )++= tttAts cos, . (1.22)

-:

.,21)(

28

2)( 0NSn = + (. 1.6).

. 1.6.

( )nR

0

( )nS

0

20N

( )nS

0

20N

0 0

)

)

( )nR

0

( )nR

0

( )nS

0

20N

)

29

(1.18)

( ) ( ) ( )2

exp41

00NdjNRn ==

, (1.26)

. . , 0 = . , . - . - , = )0(nn RD , , - .

n-

=

T

n dttxNktxp

0

2

0)(1exp)]([ , (1.27)

k . 2.

, 0=nm - 2)( 0NSn = - 0 0+ (. 1.6). (1.15) :

( ) ( ) ( )sin2

exp41

00

0

0

0

==

NdjNRn . (1.28)

, - == 2)0( 00NRD nn . -

( ) .2

exp2

1 2

= nn D

nD

np (1.29)

3. - . -

30

0=nm - , :

22

2)( +=

nn

DS . (1.30)

nD , nD . 1.6. - , . 0 )(nS -. )(nS - .

( ) ( ) ( )expexp221

22 ==

+ n

nn Dj

DR . (1.31)

1.6, = nDN 40 .

1.5.

. : - , , - . .

- . .

- . - - n - n:

31

n

nk = . (1.32)

. - ( n) k . -, k , . . . - k .

:

[ ] 222 )()()( ttt == , (1.33) (t) )( t . . -

- . ( ), , . . - - .

- . , - Ps P ( )

s P

Pq

= , (1.34)

2. q, .

32

= f(q) 2 = f(q), - q. .

- . , . . , - . - (, ), -, ( ) - .

- , - .

R - , - 1 . - (). . : , .

, , - V ( , ). - , - , , . .

TV 1= , (1.35) T .

. -

33

, 1 . .

. , - . , , . . . , , , , . ., - . , , - .

, . -, - . - . , .

[6] :

1) CR= ; (1.36)

2) sfR = ; (1.37)

3) ( )0NPR s= . (1.38)

34

sf ; Ps ; 0N . , -

- -, - . , , , , , , .

1.6.

- , -, , . . - .

(, , - . .) (, -, .).

: ; ; - ; ; ; ; ; .

: , - ; , - , , ; , - ; -, .

35

, , -, - . , - - , .

: ( ); ( ); ( ).

- . - (), () ().

(, ) ( , ), -. - : , . - - (), - () - (). - - : (), - (), () .

( ) . : - (), -- () (). - - (, .).

36

- 1. ()

1.1. - , , - .

1.1

30...300 1...10 () ()

300...3000 100...1000 () ()

3...30 10...100 () ()

30...300 1...10 ()

300...3000 10...100 ()

3...30 1...10 ()

30...300 1...10 ()

300...3000 0,1...1 ()

. - - ( ). - , . .

.

37

, , - . , - .

. - , . - . ,

. - . - . , .

, , , -, , . - . 1.7.

1.7. .

, , . 3 10 (100 f 3 ). - :

, - - , - ;

38

, - ;

;

. -, , - .

- ( ) : ( )2112.4 hhD += . (1.39)

D , h1 h2 . (1.39) , - 1,52 10 .

. . . .

.

() 1.7. - - . . - .

39

f4

f3

f2

f1

. 1.7. -

, , , . - - , . . , - 15 - 40 . - . - , , . . -

.

1. 10...12 . 80% - , ( )

1 ()

. , , -, .

40

( ). , - -, .

1.8.

. 1.8. , -

, -, . , , -, . . . - - - ( ), - - . 150 600 . - 300 ... 6 .

41

. . - 60 1200 . , , . - , .

, 75...95 . 900 2000 . 30...60 . - , -. - -. .

- .

80...120 . , - . - 1010 . (10...75 /) . -, . - . - . , .

, - .

42

, . (30...50 ) - 2000 . - . .

(). , , .

-: (. 1.9). - (, , ) , 12- , 10 . .

36000 , . - - . - . - - .

- , - , . , , - . 4 11 6 14 .

43

. 1.9. . -

() ( 3 30 ). - . - . , . , , , - - , .

- -, , -. , , , . , ,

44

, -; . , -. , 1.10, , , . - - . - - , .

B

. 1.10. , ,

, () ; , , , . - , . - , -. , (, . .).

45

1

1. -. ?

2. , .

3. , .

4. ? 5. ,

. 6. -

, . 7.

, . 8.

(, , ), - : 1011001.

9. , .

10. . 11. -

. 12.

.

46

2.

2.1.

- . - , . , , -, . . . - . - , , - , , - .

, - . - , - , -, . , , -, , -. - , - .

: , -

; , -

, - ;

- - ;

47

.

- . , - 1949 . - - - .. 1956 .

2.2.

, , , - , .

- . , - .

- 1 -. 2, 2 > 1. , - , -:

1

22log P

PI = . (2.1) -

, 12 =P 12

12 log

1log PP

I == . (2.2)

48

- , .

- , 2 = 1

01loglog 21

22 === P

PI ,

. . - . 2

1, -. (2.1) - , - , , , , . , [ ] )(log)(log)()(log BPAPBPAP += .

. (2.1) - 2. , , : 0 1. -

, , - . - , - binary unit, .

1 , 1 = 0,5, 2 = 1. , (2.1),

PPI 12log

5,01loglog

1

22 ==== ,

49

, . 2 .

2.3.

2.3.1.

, , - 1, 2, ..., m P1, P2, , Pm.

, - -, - :

< f( ) > = =

mi

ii pxf1

)( .

- , :

i

m

iii pppH loglog

1=

== . (2.3)

(2.3) . - . en trope, -, , .

. . , , , 32 . , - , .

50

, , , . - , - . , , , , , : = 0,11; e= 0,089; a = 0,076. . , , . - : = 0,003; p = 0,002; = 0,002. - , , 50 . - . m -. 1, x2, ..., m .

, 1- , i, - , - (2.2) - :

ii pI log= , (2.4) i i.

: I m? (2.4) :

i

m

iiii pppII loglog

1=

=== . (2.5)

, (2.3) (2.5) . , -, :

i

m

iii ppIH log

1=

== . (2.6)

- , -:

51

mppi

1== . (2.7) (2.7) (2.6), :

=

=== mi

mmm

mmm

H1

max log1log11log1 , (2.8)

. . Hmax . . -

, , x1, : 1 = 1, : 2 = 3 = ..,= m = 0. (2.6), :

0loglog2

11min == =

i

m

ii ppppH , (2.9)

, 1, - .

p1 = 1 : log p1 = 0. . i = 0, i =2,3,..., m , - , . , - = 00log0 , , . -, : min = 0. , , -

mH log0 . (2.10) (2.6), -

, , - , (2.4). -, (2.6), - , - , -, .

52

2.3.2.

: 1 2, 0 1. ( -) . - , - , .

, n = 1, 21 = 2 : 0 1. , n = 2, , 22 = 4: 00, 01, 10, 11. - , n = 3, 23 = 8: 000, 001, 010, 011, 100, 101, 110, 111. n2 , m = 2 , , a n - .

. (m = 2), , - (2.5), :

( )22111

logloglog ppppppH im

ii +==

= . (2.11)

, - , 1 + 2 = 1, 2 = 1 1. : 1 = , 2 = 1 . (2.11) :

() = [plog + (1 p)log(1 p)]. (2.12) (2.12) -

, . - 2.1.

(2.8) 5.021 ==p , :

H /12logmax == . (2.13)

53

. 2.1. = 0 = 1, -

(2.9) (2.12) (1 ).

, . - 0, 1 - , , - nn = 2)21( . , :

nnI nn ==== 2log2log21logmax . (2.14)

(2.14) . , . (2.14) n , - , 1 / (2.13). 0,5, , - 2.1, , , - :

= HnI , (2.15) , (2.12).

54

2.4. . -

2.4.1.

, -

. , . , - , , -, . . .

(. 2.2) - , , t = 1/2Fc, Fc - x(t), x(t) [0,T] - :

x(t) = [x(t), x(t2), .... x(tn)], (2.16)

n = T/t = 2FcT. (2.17) , (2.17) -

- .

x(t) (2.16). x(t) - , - (. 2.2). - - , m , . (2.16) . = , -

m:

m =

. 2.2.

(2.18) x(ti), m m

2.4.2.

, (1, x2, ..., xm)

55

xmax, xm

xxx

= minmax .

)

(

m

-

(t) () (. 2.3 2.).

min

[xmax xmin x1 . 2.2 .

). 3

-

(2.18)

)

n] -1, x2, , xm. ,

x(ti) xi). ,

.

- -

56

/2 /2 - i , i,

( ) xxpxxxxpp iiii

+

57

)(,logloglog ixp=+= , = .

xdx, (2.20) , . logx, , , . (2.20) :

( ) ( ) ( )dxxpxdxxpxpH

= loglog . (2.21)

:

( )

=1dxxp ,

(2.21) :

( ) ( ) =

loglog dxxpxpH , (2.22)

x= . (2.22) , -

, -. - (2.22),

= 0lim . (2.22) -

- , . - , , -.

- , , log . log (

58

= 1) -

( ) ( )dxxpxpH log

= , (2.23)

-. () . , - () , - .

(2.23) , - . [0, ] , - - , -, , -

HTFHnI c == 2 , (2.24) n (2.17).

(2.24) (2.15) - n .

2.4.3. -

, . , (x). - . (. 2.4) : ( ) ( ) bxaabxp = ,1 . (2.25)

59

) )

. 2.4. (2.25) (2.23), -

===b

a

b

adx

ababdx

ababH 1log11log1

( )abababab

ab === log1log1log . (2.26)

(2.26) , - . -, , - , - , , (b ) .

( ) ( )

= 2

2

2exp

21

mxxp . (2.27)

(2.27), ,

( ) ( ) emxxp log22

1loglog 22

= . (2.28)

60

(2.28) (2.23), :

( ) ( ) ( ) ( ) =

+==

dxxpemxdxxpxH log22loglog 2

2

( ) ( ) ( ) =+=

dxxpmx

edxxp 222

log2log

=+=+= eee 2loglog2log

2log2log 22 . (2.29)

(2.29) , . - , - , -, . . 2. , - , .

cp - (2.27) 2 m2:

= 2 + m2. (2.30) , -

, - (. 2.4).

( )

= 22

2exp

21

xxp , (2.31)

(2.29) . , ,

(2.31), - , - , -, - . - , (2.31) . -

61

- , - .

H= , , (2.26), (2.29), :

( ) 22loglog = eab ; ( ) 22 = eab ; ( ) 22 2 = eab .

12, : ( )

122

12

22 = eab . (2.32) , (2.32)

D , D 2, -:

DD 45.1 . (2.33) (2.33) , -

1,45 , -. , - -, . . .

2.4.4.

, - , . . .

. - R

c

HR =

, (2.34)

62

c ; -, , .

(2.34) , . , c . -

/== HFRR , (2.35) F = 1/c .

, (2.35), - . (2.34), - , c = t , t = 1/2Fc . - :

/2 == HFRR c , (2.36) Fc - .

2.5. .

- m 1, x2, ..., xm, (x1), (2), ..., (xm). , , (2.3), :

( ) ( )ii xpxpH1loglog == , (2.37)

. . , .

(. 2.5). (x1, x2, ..., m) (y1, y2, ..., ym)

63

. , (1) = (x1), p(y2) = p(2), ..., (ym) = (m)

( ) ( ) HypypH ii === log1log (2.38)

.

. 2.5. (a) () (2.38) , -

, -, , - , , - .

(. 2.5). j xj , i . , , - , , , . , j, i, :

64

( )( )j iji ypxyp

I log= , (2.39) p(yj) j . (j) = p(xj), (yj) 1 (2.1). (j|1) , i 2.5

( ) .11

==

m

jij xyp

(yj|xi) 2 (2.1), ,

12 P , . . j - , .

(2.39) , . . i j , - , : ( )( ) ( ) ( ) === jijj iji ypxypyp

xypI logloglog

( ) ( ) == HHxypyp ijj loglog , (2.40) ( )jypH log= ; ( )ij xypH log= - , .

H

HH0 . (2.41) , j i ,

(. 2.5),

65

( ) ( ) ijxypijxyp ijij === ,0;,1 . , (2.9), 0=H . , j -

i, -: ( ) ( ) ( ) ( ) ==== HypxypHypxyp jijij loglog, .

, -, , :

=== HHHHIi . (2.42) ,

i, j, j i , - j, :

0=== HHHHIi . (2.43)

, < HH . , - (2.40):

= HHIi . (2.44) , ,

, HHIi == . - -

H . , (2.40), (2.41), (2.43), (2.44)

. - , - j i - (2.44), .

66

2.6.

,

. , , , x1 2 - 1 0. , , 221, x2x1x2, x2x1x1, - 001, 010, 011, 1, 2, 3 .

R (2.35). - Rk : ( ) HHFIFR ik == , (2.45) iI , (2.44); F - .

, - : [ ] [ ] HHFIFRC ik === maxmaxmax . (2.46)

. , F H , - . maxH ,

maxmax HH = , - ( )HmFC = log . (2.47)

(2.47

, , . 1(1) (1 e) 1(1)

. 2.6.

7), :

C =, logm , 1, 2 ( )1 =xp

plog i, < >

67

. , - , . (

( )HF = 1 ,m = log2 = 1. , ( ) (;5.01 = pyp H

pH log=( )ij xyp , j. ,

1( e ) x2.

, (2.8), 1 2 , :( ) ( ) 022 == ypx , (2.4( )ij xyp .

- -2.6. - (1) - e 2(0).

,

(2.48)

(2.48) , , :

5.0 . 40):

-

68

- -. < > -, i, j:

( ) ( )iji j

ji xypyxpH log,2

1

2

1=

= = , (2.49)

(i, j) i j. i j -

, , , ( ) ( ) ( )ijiji xypxpyxp =, . (2.50)

(2.50) (2.49), :

( ) ( ) ( ) = =

= 21

2

1log

i jijiji xypxyxpH , (2.51)

, j, a , i. , (1,) = (2) = 0,5, (11 ) = (22) = 1 e , p(y1x2) = p(y2x1) = Pe. (2.51), : ( ) ( )[ ]eeee PPPPH += 1log1log . (2.52)

(2.52) (2.48), - : ( ) ( )[ ]eeee PPPPFC ++= 1log1log1 . (2.53)

- F - e. - e, 2.7.

, ( ) ( )[ ]eeee PPPP ++ 1log1log1 , e< 1, (1 e) < 1 , , : log < 0, log (1 ) < 0. , e = 0,5, = 0. . e = 0,5 1, 2

2.7

F

. 2.7.

x1, 2. , . y2, 0

7.

, ,

C =t

69

,

y1,

mamax 2 ii IFt

I == , .

. , , .

. ,

ax,

; miI

- e > 0,5, - - 1

, - - - -:

(2.54)

; , -

max - -

70

, F , maxiI . s(t) n(t) N0: ( ) ( ) ( )tntst += , (2.55) , 2s , ( )fSs+ F. , .

- , 1 F 0 -. ( ) ( ) ( )tntst += , (2.56) 2s :

222ns += . (2.57)

(2.57) , s(t) n(t) . , n(t) :

FNnn 022 == . (2.58)

, maxiI (2.54) , - consts =2 . , - , - (2.31). 2n , n(t) .

(2.44) (2.51), (2.57) :

(

=i HI max= 22log e

(2.59)

=C (2.60) F,

N0

. 2.8). F = 0 F = 2s /N0F

. 2.8.

71

HH = 2

212log ne

(2.5

=

+= FF

n

s2

21log

2s . . , F

. F >> 1, (2

FNF s

0

2log .

= n HH

+=2

21log

21log

2 nn

54) (2.58

+

FNF s

0

21log .

2 (2.60) 2s = const 2.8 2.60)

=

+ 2

2

n

s

. (2.59)

8), : (2.60)

- - ) - . N0 = const

:

(2.61)

72

F = 0 (2.61) 0 . , , C = 0. - F = (2.60) - 0 . , , :

.443.12ln

1

0

2

0

2

NNC ss = (2.62)

2.8 , F ( ) F . F ( ) - F , (2.62), F. , F 2s , N0, . . (2.62).

2.8.

- - . -.

maxH H . maxH -, . m (2.8)

mH logmax = . (2.63) H , -

,

73

, .

mH log . (2.64)

K ,

mH

HHH

K log1

max

max

== . (2.65)

Hm /52log32log,30 5max ==== . . - max5,0 HH . - 5,0=K . - , H , - , -, . .

, - . .

. -, (m = 2, n = 1), 1 0. 1loglogmax === mH /. - , , e = 0,1. , .

(m = 2, n = 3), 111 - 000. 1 - : H = 1/3 /. -

74

, mH log== mPP e

( ) ( ) =+== =

33322332

11 pCppCppCP mnmm

mn

( ) 028,01,09,01,0313 3232 =+=+= eee PPP . ,

- = 0,1 0,1/0,028 3,5 .

2.9.

. -

(2.35): HFR c= /, (2.66)

F ; H .

75

, - , (2.46), - :

,logmax mFHFC == /, (2.67) m ; F - .

- , F F, , R .

- . - , . . -

HFmFHFHFRC cc >>> log,, max , (2.68) , - R . - (2.68) , .

, , (2.46), ( ) ( ) HmFHHFIFC === logmaxmax1 . (2.69)

. - -, - , , - , . .

C > R, ( ) HFHmF c > /log . (2.70) (2.70) , -

, -, .

-.

76

, -. . : -, , - . -. . -, , - . - . - .

2

1. , . 2. . 3.

? 4. ?

? 5.

? 6.

. 7. ,

. 8. -. 9. -

. 10. -

. 11. -

. 12. .

?

77

13. . -?

14. - .

15. ? 16.

. ? 17.

. ?

78

3.

3.1.

, -

(. . 1.1) - . , , , , - . .

. , - . . , , , . . . , , - , . . 340 /. -, , , - . - , 1620000 . - , 808000 .

, , . 3.1 . . . 3.2 , -

79

1 ( ). - . 80 8 . . , 500 . 400 600 , .

, - 300 3400 . , 300 , 3400 , - , : 8 - 3,4 . 3.2 , - . .

- . - , - , (0 ). - , , 2530 , 7095 . . - 120125 .

t

(t)

0

. 3.1.

. 3.1.

80

2

1

0 100 200 500 1000 3000 f,

S(f),

10

20

30

40

. 3.2. : 1 ; 2

-

, , - , - - (). , , (t) () s(t,), . (t) -, )( t . . , -- .

3.3.

() - .

. 3.2. : 1 ; 2

81

: (), (), (); : - (), - (), (); - : - (), - - () - ().

. ()

t

(t)

t

(t)

t

(t)

t

s(t,)

)

)

. 3.3. : ;

3.2.

-

( ) (t) - (t). - - , - . )( t .

. 3.3. : ;

82

- , . 1.4, - 2, - (1.36).

2, . . :

(t) = )( t (t), (3.1) :

)( t = (t) + (t). (3.2) (3.2) , (t) -

, , :

= . (3.3)

(t) = < 2(t)>, (3.4)

:

=

PP

. (3.5)

, , . , - . - , :

n

s P

P= , (3.6)

s s(t,) , n n(t) .

83

n

s

PP

PPq=

= . (3.7)

q > 1 -. q < 1. , , .

- :

sFFqQ

= , (3.8)

F ( ); Fs .

, - (3.8), (3.7), :

.sn

s

FPP

FPPQ = (3.9)

P/F - ; Pn/Fs - . , - .

, - , , -, .

3.3.

. , ,

84

, - . , - () - . , -, .

- . , - , - , .

-, (- N0), - . - .

(t) - s(t,) n(t):

(t) = s(t,) + n(t). (3.10) , (t)

() )( t , , , - (t). )( t () , .

- , ( - ) (t) (t). , (t) - (t) (3.10) - p(/), :

(/) = () (/) / p(). (3.11) (3.11)

(t)

85

t. , , - , - :

(t) =

dp )( . (3.12)

(/). - . - :

(/) = k ()exp[ z()], (3.13) k ; () ; z() ,

=T

dttstN

z00

),()(2)( . (3.14)

, -1 () - (3.13) z(), . . - (t) - () s(t,).

s(t,) - . . , , -, , . . - - (t) . ),( ts )(z :

= T dttstNz 00 ),()(2)( . (3.15)

1 p()

p() = const.

86

)(z (. 3.4). , ( )t , ),( ts . - ),( ts - ( )t , . - () .

. 3.4.

( F)

(t) = s(t,) + n(t) )( t

s(t, )

, ,

, - . . - () -

. 3.4.

87

, F

.2

1

FT = (3.16)

, -, ),( ts . - . , -. , - - (t). , . ,

s(t,) = s(t) (t), (3.17) s(t) ( ), (. 3.5).

. 3.5.

( F)

s(t)

(t) = s(t)(t) + n(t) (t)

. 3.5.

88

. - . - ( ) - . - ( ).

- (3.9) :

sns FF

PPPPQ

= . (3.18)

:

=T

s dttsTP

0

2 ),(1 , (3.19)

( ) =T

dttT

P0

21 , (3.20)

() - ( ) .

, - Sn(f) s(t,) N0,

s

f

fnn FNdffSP == 02

1

)( , (3.21)

f1 f 2 , Fs = f2 f1 s(t,).

P - - S(f). - -

89

s(t,), (t).

, - (t) s(t,), , (t) - :

,),())(,(),(0 ==t

tSdtttStS (3.22)

=t

dtt0

.)(

S(f) - :

:

dttsT

NfST 2

0

0

),(1)(

= ;

(3.23)

: 2

2

0

0 )2(]),([1

)( fdtts

T

NfS T =

.

(3.24)

- F c (3.23), (3.24), :

=F

dffSP0

)( . (3.25)

, (3.19)(3.25), , . . - .

- .

90

(), (), () ( ).

3.4. . -

, . - 0 , 0 0:

)cos()( 000 += tAts . (3.26) (3.26)

- ( ) (t).

(t) . (3.27) || = 1 , ,

1 (t) 1. (3.28) -

: s(t,) = A0[1 + m(t)] cos(0t+0), (3.29)

m ( ). , m = 0, - . m = 1, , , . m > 1, - , . . 3.6 -

- . (t) , F F . -, 3003400 , 3.2.

91

sAM(t)

t

SAM(f)

f f0

f0-F

FS=2F

f0+F

f0-F f0+F

s(t) SS(f)

f f0

(t)

t

max

-max

S(f)

f F F F

. 3.6. : a ; ;

t

Ao

. 3.6. : ; ;

92

(. 3.6).

= 200f , () () (. 3.6), .

- :

Fs = 2F = 2F. (3.30) F ( 0

F). . -

3.7, s(t). - - , () )(t . .

- )(t , . -

. 2 , Fs=2F, - :

2

2

12

n

s m

mPP

PPq +== , (3.31)

2

2

1

s m

mFFqQ +=

= . (3.32)

, - m = 1 :

q = 1, Q = 0,5. (3.33)

93

. 3.7.

(t)

s(t,) s(t)

.

(. . 3.3) , 3.8. , -- s(t) ( ) . -, . (t) (3.10) s(t) = ks(t), k . - , (t) . () F

)()()( ttt += , (3.34) (t). - (t) .

- ( ) - , - (. 3.9). ,

. 3.7.

94

. 3.8.

f , f0 - 0 , . - , - (). () (). (t) s(t). - -, - .

, , (. . ) , -. 3.10. - , - ( - f = 2F , - f0), () f = F.

f=F

s(t)

(t)

95

f=F

. 3.9.

(t)

s(t)

(t)

-

-

f f0 0

.3.10.

(t) (t)

f=2F f=F (t)

() () . , - ( < 5) .

. 3.9.

. 3.10.

96

3.5. () -

, ( - ) 0 c P0 = A02/2. - (), - ( ). - , - - . -

(t) (3.28) s(t) (3.26) :

s(t,) = (t) A0cos(0t + 0). (3.35) . 3.11

S (f) - S(f) . , - f0. , :

Fs = 2F. (3.36)

. 3.11.

f0 F

FS=2F

f0 F f0 + Ff0

SM(f)

f

S(f)

f F F F

f0+F

97

. 3.12, - . . - 3.13, .

, . 1, 2 - - s(t) 1. (t). VD1, VD2 , . , 3 . (t), - ( ), 3 - .

, ( -).

. 3.12.

(t) s(t,)

s(t)

98

. 3.13. -

. 2 , Fs = 2F,

q = 2; Q = qsF

F = 1. (3.37)

, . f0. , . , , . . - ( ) . - , , - - (. . 3.6). - .

(t) s(t,)

s(t)

VD2

VD1 T3

T2

T1 C1

C2

99

3.6. . -

- , - () - , - :

s(t,) = (t)A0cos(0t + 0) + H[(t)]A0sin(0t + 0) + + B0cos(0t + 0), (3.38)

0 - ( ); [] .

(3.38) , . -, (t) = cost. H[(t)] = H[cost] = sint. , - /2. . -

- (. 3.14). - 3J ( - ), - : SSB ( . sinqle side band) ( ). ,

Fs=F fo f fo f f fo f fo

3 3J (SSB) 3H 3B

. 3.14. : ; ; ; ( )

100

. ,

Fs = F. (3.39) . -

: - .

- (3.38) 3.15, 1 (t) /2, 2 /2. - , .

, () - /2. , 1 .

. 3.15.

B1 /2

B2 /2

A0cos(0t+0)

A0sin(0t+0)

(t) s(t,)

101

- . - 3.16. - , - - .

. 3.16. -

. - -, . .

q = Q = 1. (3.40) , -

2, (3.39). . -

, , - -. -. -. - - , .

(t)

s(t)

s(t,)

102

3.17 . - - . -

f = f f0, (3.41) . . f f0, 10 . - - . - 400 . f . - ( - , ) , . - f 100 .

, , - ,

f+f f. (3.42)

. 3.17.

-

(t)

f

f = F )( t

103

- -, . , (3.42)

f+f+f f. (3.43) -

-, -. 3.18 - -.

-, - , , , - . - - , , . .

. 3.18. -

-

-

(t)

f

f = F

-

)( t

104

, (, -).

3.7. ( )

. , (3.26) 0, 0 0. - (t) - s(t),

s(t) = A0 cos0(t), (3.44) 0(t) = 0t + 0 .

( ) (3.44). , (t) , . , - .

.

s(t) = A0cos[(0t + (t)] = A0cos (t), (3.45)

(t) = 0t + (t). :

(t) = 0 + (t); (3.46) s(t,) = A0cos[0t + (t) + 0], (3.47)

. || = 1, -

(3.47). -

105

(t) = 0 + (t), (3.48) 0, - - .

, (t) , (t):

+=t t

dtttdtt0 0

0 .)()( (3.49)

, (3.48) - :

++=t

dtttt0

00 )()( (3.50)

++=t

dtttAts0

000 ].)(cos[),( (3.51)

. . :

, ;

f0;

- ;

( - , - ).

- , , -, ,

106

Fs 2 F, (3.52) F ( ).

, (3.52) - ( >> 1).

(3.52) - :

Fs 2 F; (3.53) Fs 2 F = 2f, (3.54)

Ff = . (3.53), (3.54) ,

f. - F , , . - .

, , - , - - .

. 2, , - :

=

FFq s

2 , (3.55)

=

FFq s

23 . (3.56)

(3.8) :

2Q = , (3.57)

23 Q = . (3.58)

107

, - . , .

, - . - . . . 3.19 -

.

() (t) - , , . - , - . -- - f f f0, . . - . f .

f f0 = f+ f

s(t,) (t) f

. 3.19.

108

. , , - (. . 3.3).

- . , (- ) , - (. 3.20). - - - Fs, . , 2F - .

3.21. , - (), 2F ( ).

2F 2F 2F

f f f0

FS

f

. 3.20.

109

f=ff

(t)

f

f

-

()

-

-

s(t, )

f = 2F f=F

. 3.21

-

, . , -. , , .

, . , , , - F. , -. , , )( t . - , . . - .

- , (t) )( t . ,

. 3.21.

110

. - , , .

. , -, - . - , 3.22 3.21 , , - (3.54). , . .

. 3.22. -

. (3.56) (3.58) , .

, - (. 3.23). S(f) . -

f = 2f -

()

- -

- -

(t) f = F

)( t

111

, S(f) (3.24). , )( fS , , -. ( - ) .

(. 3.23) - , 0F. , , . , f F, . . :

Ff

= . (3.59) -

. , - , , , - .

, (3.58) - , . . .

. 3.23.

)( fS

0 F f f

112

. 3.24. -

, , - . , 3.24. - ( 1) , - (1 < 2). , - , - . -, . . . , -, - . , - .

( - ) , . . , :

Fs 2F. (3.60)

>>1

= 1

2 1

113

( ) , - :

Fs 2 F = 2f. (3.61)

, - . - - . - .

3.8.

-

( - ( = 1, 2, 4, 8), 3.25, ), . - , , - - . . - .

-:

1. . , , - (, f = 3...30 ), (, f = 30...300 ) (, - f = 300...3000 ) . . - m < 1, q < 1

114

Q < 0,5, . . . , , -. , , . , , - - - - .

2. . (3.37) (3.42) , - , - , - .

3. . . - .

0

10

20

30

40

50

20 40

,

,

= 84

1

. 3.25. ,

115

. - , () .

, - , . - - (), . - .

, , , , . , -. , . - , -, .

4. . , -. : , - , -. .

3

1. ? - .

2. - ?

116

3. , .

4. ?

5. . 6.

? 7. ,

?

8. -. -.

9. - .

10. , .

11. - .

12. -.

117

4.

4.1.

. . (. . 1.1) - , . - , - . - , , - , . , , - . - ( ) , 4.1 -. ( ) - .

- , -, . -

00

11

22... mamamaN +++= , (4.1)

m ; a0, a1, an -, 0 m 1.

, 29 - : m = 10 ( ) 29 = 2101 + 9100; m = 5 ( ) 29 = 152 + 051 + 450; m = 2 ( ) 29 = 124 + 123 +122 + 021 + 120.

4.1 , - . 32

118

( ) -, . . - . , . , , .

4.1

4.1.

-

(

-

(

-)

-

-

-

-)

-

-

-

0 0 00000 16 31 10000 1 1 00001 17 32 10001 2 2 00010 18 33 10010 3 3 00011 19 34 10011 4 4 00100 20 40 10100 5 10 00101 21 41 10101 6 11 00110 22 42 10110 7 12 00111 23 43 10111 8 13 01000 24 44 11000 9 14 01001 25 100 11001 10 20 01010 26 101 11010 11 21 01011 27 102 11011 12 22 01100 28 103 11100 13 23 01101 29 104 11101 14 24 01110 30 110 11110 15 30 01111 31 111 11111

, -

, 0 1. -, (0 1), , -. - .

119

( 4.1) 4.1.

01100 01110

10001

01010

00010

00000

. 4.1. ,

, ,

, - 0 1. 0 1 -.

- . () . - , : -2 ( - ), -7, -8 ( ) .

- . , (-), . .

1 ( ) . 4.2 , : a(t) -; (t) ; s(t,) - ; n(t) (); (t) -

1 , . . -

- .

. 4.1. ,

120

; )( t ; )( ta () . , -. , - , - .

. 4.2.

a (t)a(t)

n(t)

(t) s(t,) (t)=s(t,)+n(t) (t)

-

() - . - (), () - (). 4.3 , (t). 1 - (), 0 (). f1 - 1, f2 0. 180 1 0 0 1.

(t) - (- , -). , - .

. 4.2.

121

T

t

t

t

s(t,) t

1 0 1 1 0 0 1

.4.3.

(t)

. , 1 ( , 0 1). ,

,/1 TV = . (4.2) , = 50 ,

V = 20 . -

, - . - 4.4 ,

,2/2/1 VTFM == . (4.3)

. 4.3.

122

. 4.4.

t

(t)

T 2T 3T 4T 5T

= 1/F

-

(. . 4.2). - (t) 1. - - )( t , . . (0 1). - (, , . .), . - .

, , () -, . - - . () , (0 1) . , , ().

1 -

. - .

. 4.4.

123

- , , . , - (, 1) , (0).

. , , , ( ) . .

, , (t). - , - . , -. - ( ). - - , .

4.2.

, )(t , - )( t . )( t . )( t

)(t . , -, . . , -

124

, . . .

- - [1, 2, 4, 7].

. - (t). (. 4.3) - : 0 1. , (t), , n(t) - s(t,).

, (. . 4.2) s(t,) n(t), , N0 s(t,). - , . 1.3. (t) ( -)

)(),()( tntst += . (4.4)

t )()()()](1[),( 21 tsttstts += . (4.5)

(4.5) , (t) = 0 s1(t), (t) = 1 s2(t), :

)(),( 1 tsts = = 0, )(),( 2 tsts = = 1, Tt 0 , (4.6)

, .

, t1, t2,, , -

125

(t) (- ).

. (t) , - ( = 0 = 1). . - ( ).

(t) n(t) s1(t), s2(t),, sm(t), m -. , .

, . .

- . , , -, , - . [7]:

2)()()()( 12

1

001

02

EEdttstdttstTT >

126

s1(t) s2(t) ( ), - ; - , :

212 EEh = . (4.9)

h, , - 1 )1( = , , , - 0 )0( = .

(4.7), - .

4.3.

- - - : - ( 1). . -

-

,)cos()(),( 000 += tAtts (4.10) 0, 0 0 , , .

, - , :

s1(t) = 0 = 0 , )cos()( 0002 += tAts = 1, Tt 0 . (4.11)

s(t,) = 0 = 0, .

127

. - - 4.5.

t

(t)

1 0 1 0 1

t

s(t,)

T

f 0-5F

f 0-4F

f 0-3F

f 0-2F

f 0-F

f0

f 0+F

f 0+2F

f 0+3F

f 0+4F

f 0+5F

f

Fs = 6F

. 4.5. () - ()

. 4.5. () - ()

128

- -, F (4.3).

- - :

nVnFF Ms == 2 , (4.12) n , V = 1/T .

3- 5- - . , - , 6F 10F. . -

, - 0 - () 1. . 4.6 - , - f0, - ( ) . (t) - 1. .

. 4.6. C

s(t,) f0

(t)

. 4.6.

129

- ( ). , - , . -.

(4.11) (4.7) s(t) = s2(t) = 2, -:

hdttstT >

3) - 2/Eh . - [5]:

)]}2(1[{5,0 82

qeP q + . (4.22) (4.21) (4.22) -

, , - 103 106 1530% . , . - - . .

( , - ) . . , 4.14. , - - f, - . u(t) (, ) h. u > h 1, 0.

139

. 4.14. ,

(t) u(t)

h

(t)

-

-

(. 4.14) -

4.12, , - - .

- , . , ,

f = 1,37/, (4.23) , 1,22 (0,8 ) , - . , - (), , . , . - . - ,

f T/3 . (4.24) -

, - , , , . - . - -

. 4.14. ,

140

, - . . -

, - .

, , - , . . , . .

. - , . - , . . , -; - . , - - .

4.4.

- . 0 f1 , 1 - f2 (. 4.3).

141

. - :

),cos()()cos()](1[),( 220110 +++= tAttAtts (4.25) 1 2 . -

, : )cos()( 1101 += tAts = 0,

)cos()( 2202 += tAts = 1, Tt 0 . (4.26) 2/)( 210 +=

.2/)( 210 fff += (4.27) -

: f = |f2 f1|, (4.28)

, . . , :

f = |f2 f1|/2. (4.29) -

4.15. (4.3):

Ff= (4.30) . f

f0 f2 f1

f

. 4.15.

f

. 4.15.

142

. . , . . , , -- , - (. 4.16).

. 4.16. -

f f2 f0 f1 f 3F 3F

, -

Fs = f + 2n F

Fs = 2f + n V, (4.31)

, f = 2f F = V / 2 (V ), n , .

, - - . (4.30). , , - [3]:

).1(2 ++= s FF (4.32)

. 4.16. -

143

. - . - .

(. 4.17) f1 f2 - , (t). . - , . , . . . -, .

- - (. 4.18). (t) LC1 C2, - . , - . (

). - (4.7). s1(t) s2(t) 0 1 (1 = 2), (4.7) :

0)()()()(1

001

02

>

144

. 4.17. C

s(t,)

(t)

f1 1

2 f2

. 4.18. C

(t)

L C1C2 s(t,)

, . - s1(t) s2(t), - . - )(),()( tntst += , - , ( 0 T). - , - ()

. 4.17.

. 4.18.

145

, . 1 = 2, (4.9) - (h = 0) - .

(. 4.20). - 1 2 -, , , s1(t) s2(t) (. . 4.3).

. 4.19. ,

s1(t)

(t)

-

1

2

-

(t)

t = T

h = 0

s2(t)

. 4.20. ,

(t)

1

2

(t)

t = T

h = 0

. 4.19. ,

. 4.20. , -

146

-. - [8]

= 1 ,)1(0

r

NE (4.34)

= 1= 2 s1(t) s2(t); N0 (); r - ,

=T

dttstsE

r0

21 )()(1

. (4.35)

, . . s1(t) s2(t), -. . , r = 0, -.

r = 0 (4.34)

= 1 .0

NE (4.36)

(4.20)

= 1 .2

q (3.37) (4.36), (4.37) -

. (4.21) (4.37) , -

P - q, . , -, . . -

,

147

, . . , - 4.19, 4.20, . 4.3. .

4.21. - , - 4.12, .

u2(t)

u1(t) ( )t 1 1

2 2

(t)

.4.21 -

-

= .5,0 4

2qe (4.38) ,

1530% , . . .

, 4.22, 1 2 , - f1 f2. -. () - (). , - .

. 4.21. -

148

. - .

4.23.

. 4.22. ,

(t)

h = 0

(t)

1

2

-

-

. 4.23. : - ; -

u2(f)

u1(f)

f0

u(f)

f f2 f1

VD2

VD1

u1

u2 u

f1

f2

R2

R1

C4

C3L1 C1

L2 C2u

. 4.22. , -

. 4.23. : ;

149

1 2 L1C1 L2C2, VD1 VD2, R1,C3, R2,C4.

, , . . -

- . (4.36) (4.18) , - , , .

- ( ) () -, 4.194.21. , , - . - , ( ) . , -, , - .

. , s1(t) s2(t) - 0 1. V (- , ). - (4.2) -. , , - .

150

(4.31) , -, nV

151

-. . -

, , - , - . 4.24 - .

f0 , . - , 0 1. - .

s(t,)

(t)

-

. 4.24. . -

(4.7), -

0)()(0

10

>im . , -

.

4.7.2.

, . , (, , ) , , - . .

- , , - (

164

) ( ) - (), - -.

, - :

s1(t) = A cos[1 t + (0)] = 0, s2(t) = A cos[2 t + (0)] = 1, 0 t T, (4.54)

(0) = (t = 0) - , .

4.33 , , ( ) ( ) .2,2 122121 +== (3.55)

1 2

.4.33 -

(. 4.1.2)

( ) .212 = T (4.56) (4.56) (4.54) :

,, 21 TT +== (4.57) (4.53) :

( ) ( )[ ] ( )[ ].cos0cos ttATttAts +=+= (4.58)

. 4.33.

165

(t) = (0) t/T ; = 1, = 0.

(t) 4.34. 5,0= , s1(t) s2(t).

0

3T

(t) 3/2

/2 /2

t

(t)

5T 4T

1

2T T 0

1 1 0 0

.4.34. (t) - -

. - = 0,715. - - f 2, f 4.

. 4.34. (t)

166

. - (. . 4.34), 1/f 8. ().

- . , GSM - - . - , . - .. , .. [9].

4.7.3.

,

(-) - 2>m . - . - , - .

: - . - :

( ) ( ) ,010

== dttstsEErT

jiji

ij (4.59)

i j- T; ( )( )dttsET

ji)j(i =0

2

i(j)- .

167

= 0,5.

-: -. - 4=m . , (-4) - - (-4).

-4 , - -.

s1(t) = Ao cos(ot + /4) , s2(t) = Ao cos(ot + 3/4) , s3(t) = Ao cos(ot - 3/4) , s4(t) = Ao cos(ot - /4) .

-4 - 4.35.

-4 -

s1(t) = Ao cosot , s2(t) = Ao cos(ot + 2/3) , s3(t) = Ao cos(ot + 4/3) , s4(t) = 0 .

- - 4.36.

() - . - : ( ) ( ) ( ) ,0sin0cos ttisAtticAtis = icA isA .

168

.4.35. -4 -

S1(t) S2(t)

S3(t) S4(t)

+

S2(t)

.4.36. A-4 -

+S3(t) S1(t)

S4(t)

( ) ( ) ( ),cos 0 iii ttUts += ( ) 22 isici AAtU += ( ).arctg icisi AA= . m1 m2 , m=m1m2 . nm 21 = im 22 = , - 2mm1log , - 2mmR 1log , kR 2log= , k . m = 8 m = 16 4.37.

. 4.35. -4 -

. 4.36. -4 -

169

. n- 1+= nm . -, - , 4.38.

- ( ) mitsi ...,,2,1, = - , , 2>m - , :

( ) ( ) ( ) ( ) .,22 00

jiE

dttstEdttstT

jj

Ti

i >

m=8m=16

.4.37.

.4.38. (-3)

S3(t) S1(t)

S2(t)

+

. 4.38. (-3)

. 4.37.

170

4.39. -

- 4.40.

.4.39 m

( )ts2

1u

mu ( )tsm

0

0

0

( )t i2u

( )ts1

1

m

i( )t

.4.40. m

. 4.40. m -

. 4.39. m

171

2 +

.4.41. ,

.4.42. ,

() -

, i- , - ( )tsi .

-, . (. 4.41) - - () mk 2log= .

. 4.41. ,

. 4.42. ,

172

ai bi .

, - (. 4.42), - , () () -. . 8m , m- .

4.7.4.

, -

, - (-) . , - ( ) , . , - (4.35) , , - . .

i-

( ) ( ) .......,,,... 2111i mu u immi dududusuuupdusP i i +

= (4.60)

( )imm suuup ...,,, 11 m- - u1, u2, um , - ( )tsi .

i- : ( ) ( ).1 iie sPsP = (4.61)

173

i-

( ) ( ) ( ) ( ) ( )dttstndttsdttstu iTT T

ii +==00 0

2i

- { } sEu =i .20u i NED s= -

ij,2D 0u j = NEs . muuu ,...,, 21 (4.35) - , -, . , m- - ( ) ( ) ( ) ( )imiimm supsupsupsuuup ......,,, 21i11 = , (4.62)

( )

= 0

2

0ii

)(exp22

1EN

EuEN

sup i , (4.63)

( ) .,exp22

1

0

2

0j ijEN

uEN

sup ji

=

(4.64)

(4.62) (4.60) (4.63) (4.64) - , [10], - i- :

( ) ( )dxxN

ExsP mi1-

2

0

221exp

21

+

=

. (4.65)

- ( ) mitsi ...,,2,1, = - , , 2>m , :

( ) ( ) ( ) ( ) .,22 00

jiE

dttstEdttstT

jj

Ti

i > (4.66)

174

m - , . . ( ) ( ) ( ) msPsPsP m 1...21 ==== , - : ( )[ ] ( ) ( )[ ] ( )

( ) ( ) ( ).111...1

1

11

i

m

ii

mme

sPsPmm

sPsPsPsPP

=

==++=

=

(4.67)

, , - m- m2log - , . 4.43 - - m = 2, 4, 32 256. - , - -. mEs 2B logE = , .

EB /N0,

m=2

m=4

m=32

m=256

.4.43. 0NEB m

10-6

10-6

10-6

10-6

10-6

Pe

0 4 8 12

. 4.43. EB/N0 -

175

. -, m - ( ) jimr ji = ,11 . , ,

( ) ( )[ ] 2112, jisji rssd = , , ( ) ( )1-2, mmssd sji = , ( ) sji ssd 2, = . - - ( )1-mm , . ,

( ) ( ) .1-

221exp

21 1-

2

0dxx

mm

NExsP mi

+

=

(4.68)

, -. m, m >> 1 . .

2m , . - ( ). - :

( ) ( ) .......,,,... 2212112m muu

u

uimii dududusuuupdusP

i

i

i

i

+

=

, -, :

176

( ) ( )[ ] .221exp12

211

2

0

12 dx

NExxsP

m

ie +

=

(4.69)

-, , m >> 2 - .

- , m = 128 -. : ( )[ ] ( )0221- NmP < . (4.70)

-, , , - .

4

1. - . , , .

2. - (). (-) 1 2, - : 10100001111. .

3. (,, ), - : 1011001.

4. . -, : 10100001111. .

177

5. , .. .. . . - .

6. .

7. . , - : 1010010.

8. . ?

9. - , ?

10. , ?

11. ( ), , ?

12. . -, , - ? .

178

1. / . .. -. .: . .. , 1986.

2. ., .., .. . .: . .. -, 1985.

3. .., .., .. . .: , 2001.

4. .., .. -. .: , 1982.

5. .. . .: , 1991.

6. / . .. . .: - . .. , 2004.

7. .. -. .: , 1982.

8. .., .. : . : . . .: , 1990.

9. .., .. : . . / . .. , .. . .: , 1980.

10. / .. , .. -, .. [ .]; . .. , .. . .: -, 2005.

179

1

,

0 1 2 3 3 3 3J F1 F2 F3

F6 (2F1) F9

P3D - P3E - P3F P3G -

180

2

. -

s(t,)=A0[1+m(t)]cos(0t+0) .

(2.24) S((f):

)cos()(),(

000 += tmAt

ts ;

);(2cos21)(cos

)(),(

0022

000222

0

2

+=+=

tmAtmAt

ts

++=

TT dttmA

TmAdt

tts

000

220

0

220

2

.)(2cos21

21

)(),(

21

, - , :

=

T mAdtt

ts0

220

2

.21

)(),(

21

, , :

.2)(22

0

0

mANfS =

(2.26) :

===FF

mAFN

mANdffSP

022

0

022

0

0

0

.22)(

:

.2 0

220

==FNmAP

PP

181

, = 1.

.2

)(

0

20

=

FNmA

(2.7) .

++=+

=+++

=++==

T T T

T

T T

s

dttTmAdtt

TmAAdttmA

T

dtttmAT

dtttmAT

dttST

P

0 0 0

222

020

2022

0

000

220

0 000

2220

2

)(2

)(2

)](1[21

)](2cos1[)](1[21

)(cos)](1[1),(1

.

- (20) - .

=T dttT 0 0)(1 .

( (t), - 1 1, )

== T PdttT 02 ,1)(1

);1(21 22

0 mAPs += ,2)1(

21)1(

21

0

220

0

220

+=+==FNmA

FNmA

PP

sn

s

Fs=2F . , (2.8)

.12

2

2

mmq

+=

= .

182

s(t,) = (t)A0cos(0t + 0) :

);cos()(),(

000 += tAt

ts

=

T Adtt

tsT 0

20

2

;2)(

),(1

;2)( 20

0

ANfS =

;220

0

AFNP =

==FN

APP

0

20

2.

,2

20APs =

,22

1

0

20

==

FNA

PP

n

s

, , , Fs = 2F.

, -

.2==

q

. s(t,) = (t)A0cos(0t + 0) + H[(t)]A0sin(0t + 0)

:

=

T Adtt

tsT 0

20

22

;)(),(1

183

;)( 20

0

NfS =

==F

AFNdffNP

020

0 ;)(

.0

20

==FN

APP

+== T T Ts dttHTAdtt

TAdtts

TP

0 0 0

2202

202 .)]}([{

2)(

2),(1

==T T tTdttHT 0 022 ,1)(1)]}([{1

Ps = A02;

===

FNA

FNA

PP

sn

s

0

20

0

20 ,

Fs = F . ,

.1==

q

. - (2.48) ( , 0 = 0):

s(t,) = A0cos[0t+ (t)]. s(t,)

)];(sin[)(),(

00 ttAtts

+=

)].([2cos22)(

),(0

20

220

2

ttAA

tts

+=

184

.21

)(),(

21 22

00

2

T

Adtt

ts =

:

;2)(22

0

0

NfS =

===

F

F

AFNdf

ANdffSP

022

0

0

022

0

0 .22)(

, ,

.2 0

220

==FN

APP

- ,

== Ts AdttsTP 0202 ;

2),(1

.2 0

20

sn

s FN

APP ==

.2

==

FFq s

. - (2.52):

)](2cos[])(cos[),( 000

00 tFtAdtttAts t

+=+= , 0 = 0; ;

2 ==

Fff

= t dttt

0

)()( . (2.25)

:

185

)];(2sin[2)(),(

00 tFtFAtts

+=

)]};(2[2cos1{)2(21

)(),(

02

0

2

tFtFAt

ts +=

;)2(21

)(),(1 2

00

2

T

FAdtt

tsT

=

.

)(2)(

20

20

FfNfS =

-

==== F

F

AFNF

FANdff

FANdffSP

022

0

03

20

0

0

22

0

0 .32

3)(2

)(2)(

, -

.23

0

220

==FN

APP

,2

20APs =

.2 0

20

sn

s FN

APP ==

.3 2

==

FFq s

186

..

..

27.09.2010 . 6084/16. . . . . . 10,81. .-. . 10,18.

50 . 3142.

. . 392008, . , . , 190

1,

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/CreateJDFFile false /Description > /Namespace [ (Adobe) (Common) (1.0) ] /OtherNamespaces [ > /FormElements false /GenerateStructure false /IncludeBookmarks false /IncludeHyperlinks false /IncludeInteractive false /IncludeLayers false /IncludeProfiles false /MultimediaHandling /UseObjectSettings /Namespace [ (Adobe) (CreativeSuite) (2.0) ] /PDFXOutputIntentProfileSelector /DocumentCMYK /PreserveEditing true /UntaggedCMYKHandling /LeaveUntagged /UntaggedRGBHandling /UseDocumentProfile /UseDocumentBleed false >> ]>> setdistillerparams> setpagedevice