Пасечников И.И. Инфокоммуникационные технологии в...
TRANSCRIPT
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210400.62
2010
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621.39 32.94 73
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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
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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
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................................................................. 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
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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
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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
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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
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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,
/ColorImageDict > /JPEG2000ColorACSImageDict > /JPEG2000ColorImageDict > /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict > /GrayImageDict > /JPEG2000GrayACSImageDict > /JPEG2000GrayImageDict > /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict > /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False
/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
/ColorImageDict > /JPEG2000ColorACSImageDict > /JPEG2000ColorImageDict > /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict > /GrayImageDict > /JPEG2000GrayACSImageDict > /JPEG2000GrayImageDict > /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict > /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False
/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