potekhin e n sintez and analiz

()

05.13.17

-

:

,

-

- 2014

2

-

-

BB brunch and bound

LABS low autocorrelated binary sequences

MF merit factor

PSL peak sidelobe level

3

.............................................................................................................. 7

1.

...................................................................................... 23

1.1. .............................................................................. 23

1.2.

................................................................................. 26

1.3

................................................................................. 30

1.3.1.

..................................... 31

1.3.2.

................ 32

1.3.3.

............................ 33

1.3.4. ........................................................ 34

1.3.5. .......................................................... 34

1.3.6. ......... 35

1.3.7.

............................................................................. 41

1.4. ...................................... 43

1.4.1. 4mod0N ............................................................................. 43

1.4.2. 4mod1N ............................................................................ 44

1.4.3. 4mod2N ............................................................................. 44

1.4.4. 4mod3N ............................................................................. 45

1.5. .......................... 52

4

1.5.1. 4mod0N ........................................................................ 52

1.5.2. 4mod1N ......................................................................... 54

1.5.4. 4mod3N ......................................................................... 59

1.6. ................ 59

1.6.1. Ding

................................................................................................................... 60

1.6.2. Ding, Helleseth, Lam

................................................................................................ 60

1.6.3. Ding

................................................................................................................................. 60

1.7. .................... 61

1.7.1. Davis ..................................................... 61

1.7.2. Davis ...................................................... 61

1.7.3. ,

................................................................................................................................. 61

1.7.4. ,

......................................................................................... 62

1.7.5. ,

........................................................................................ 63

1.8.

......................................................................................................................... 63

1.8.1. Yu, Gong - 63

1.8.2. Tang, Gong GMW- . 64

1.8.3. Tang, Gong . 64

1.8.4. Tang, Gong

................................................................................................................................. 64

5

1.9. ......................................................................................... 64

2.

............................. 66

2.1. "brunch and bound" ........................ 66

2.1.1. .................................................................................. 66

2.1.2. 69

2.2. brunch and bound ............................................. 71

2.2.1. .................... 71

2.2.2. ............................... 77

2.2.3. ........................................................................................ 78

2.2.4. NVidia

CUDA ...................................................................................................................... 81

2.2.5. ..................................................................... 84

2.2.6. ................................ 85

2.3. ......................................................................................... 87

3.

.............................................................................. 88

3.1. ............................................................ 88

3.1.1. -

............................................................................................. 88

3.1.2.

........................... 92

3.1.3. .................................. 97

3.1.4.

........................................................................................... 101

6

3.1.5.

............................................................................................................ 104

3.2. ..... 108

3.3. ..................................................... 110

3.3.1. ................................... 111

3.3.2. ..................................... 113

3.4.

. ....................................................................................... 116

3.5. .................................................................................... 117

4.

.......................................................................... 119

4.1. ...... 119

4.2.

................................. 124

4.2.1. ................................................................................. 127

4.2.2. ............................................................................... 129

4.2.3. .................................................................. 131

4.2.4. ............................................................... 135

4.3. ....................................................................................... 137

................................................................................................... 138

........................................... 139

..................................................................................................... 150

...................................................................................................... 153

...................................................................................................... 177

...................................................................................................... 179

7

.

.

,

, , .

,

..

1950- . 1953

[1] ,

.

,

.

: - MPS (minimum peak

sidelobe), PSL (peak

sidelobe) ; - MF (merit factor),

. ,

, ,

1. 1953

[2] c

(PSL peak sidelobe) 1PSL

8

13,11,7,5,4,3,2N . ,

13N

. 1968 [3]

2PSL 21N , ,

. [3]

,

13N . 2009 [4]

30102 N , ,

(

276678160401034441521892604680N ).

1960-

,

[],

.

-

Paley 1933 [5], Singer 1938 [6], Golomb

1954, 1955 [7], [8].

, , -

t-. , ,

Hall 1956 [9], Stanton Sprott 1958 [10], Gordon, Mill, Welch

1962 [11].

, ,

Golomb 1959 [12].

9

,

.

Zeirler 1959 [13], Golomb 1967 [14], Berlekamp 1968 [15]. Golomb

[14]

.

Golomb 1969 [16].

,

,

.. [17], .. [18], .. [19],

.. [20], .. [21], .. [22] ..

[23].

,

1970- [24].

N (

)

.

, 1970-

.

. ,

LABS (low

autocorrelated binary sequences) .

10

1975 [25], ,

40N .

.

50 .

.

,

NO 85,1 , 1990 MPS 48N [26] 2005

64N [27].

.

2008

105N [28]

MF 271N [29].

300N

, .

, 300N ,

[30].

,

(-, , ).

,

.

11

MPS MF

,

.

,

.

1970-

, .

Gold, Huffmann, Golay, Luke, Beth,

Helleseth, Arasu, Viterbi, Baumert, Coxson, Russo, Cohen, Beth, Jungnickel, Kasami,

Brenner, Carlet, Chan, Cheng, Dillon, Ding, Dreier, Smith, Frank, No, Kumar, Dobbertin,

Pott, Klapper, Moreno, Tirckel, Gong, Gaal, Glynn, Xiang, Boztas, Mow, Maschietti,

Segre, .., .., .., ..,

.., .., .., .., ..,

.., .., .., .., ..,

.., .., .., .. .

,

,

:

- Sequences and Their Applications (SETA),

- International Workshop on Signal Design and Its Applications in Communications

(IWSDA).

12

, ,

, ,

IEEE.

:

, ,

.

,

.

:

1PSL 13,11,7,5,4,3,2N ;

2PSL 28,25,21..14,12,10,9,8,6N ;

3PSL 51,48,29,27,26,24..22N ;

4PSL 80..52,50,49N .

,

80..65,63..52,50,49N [31], [32], [33],

[34], [35], [36], [37], [38]

,

[32], [39], [33], [34], [35], [36], [37], [40].

.

[41].

.

,

13

.

:

1.

,

.

2.

-.

3.

80;2N .

4.

,

.

5.

: , MF ,

, .

.

,

.

,

. ,

:

1.

.

2.

14

.

3.

. ,

.

4.

-

.

5.

80;2N .

80..52,50,49N .

6.

80;2N .

7.

:

;

;

;

;

;

MF .

.

,

15

.

() .

,

,

.

LABS- .

.

,

:

1. 09-07-00072-,

, 2009-2011 ().

2. 783 -

2009-2013 ,

1.2.1

, 2010-2012

().

3. 8112/12783

- , 2010-2012 ().

4. 02.120.11.5418-

-5418.2010.9,

16

, 2010-2011

().

5.

, 1

,

,

1.01.11, 2011

().

6.

, 1

,

1.07.2012 ,

, 2012-

2013 ().

7. 12-07-00552,

, 2012-2013.

8. GPS-,

GSM/GPRS/Bluetooth ,

- .....,

10508/16915 08.06.2012 ., 2012-2013 ().

9. ,

,

-

....., 12157/20835 29.07.2013 ., 2013-2014 ().

090303

()

, 090900

() ,

17

,

090303

( ).

. 67-

,

RDC-2012 (, 2012); 68-

RES-2013, 14-, 15- 16-

DSPA-2012, DSPA-2013 DSPA-2014 (, 2012, 2013 2014);

European Microwave Week (,

, 2013); 6-

- (, 2014),

(2011-2014).

. 15 . 4

, Scopus, 4

,

, 5

(DSPA-2012, RDC-2012, DSPA-2013, RES-2013, DSPA-2014),

, 2 ,

2 .

9 .

4 , Scopus, 5

, 7 ,

, 6

, 4 .

:

, Scopus:

18

A1. E.N.Potekhin. Exhaustive Search for Optimal Minimum Peak Sidelobe

Binary Sequences up To Length 80 / A.N. Leukhin, E.N. Potekhin//Sequence and

Their Applications-SETA2014, Proc. of 8th Internatinal Conference Melburn,

Australia, November 20-24, 2014, Lecture Notes in Computer Science, Springer.

A2. Potekhin, E.N. Optimal peak sidelobe level sequences up to length 74 / A.N.

Leukhin, E.N. Potekhin // IEEE Proceedings of the 10th European Radar

Conference, EuRAD2013, Nuremberg, Germany, pp.495-498

A3. Potekhin, E.N. Optimal peak sidelobe level sequences up to length 74 / A.N.

Leukhin, E.N. Potekhin // IEEE Proceedings of the 10th European Microwave

Conference, EuMC2013, Nuremberg, Germany, pp.1807-1810

A4. Potekhin, E.N. A Bernasconi model for constructing ground-state spin

systems / A.N. Leukhin, A.S. Shuvalov, E.N. Potekhin // Bulletin of the Russian

Academy of Sciences: Physics, March 2014, Vol. 78, Issue 3, pp.207-209.

, :

A5. , ..

/ .., ..,

.., .., .., .., ..,

.., .., .., ..,

.. // . :

, 2010, 3, .40-49

A6. , .. / ..

, .. , .. , .. //

.

" ", -,

2012. 1, .37-46.

A7. , ..

/ .. , .. // .

" ", 4-2012 . , 2012 . . 44-48

19

A8. , ..

/ ..

, .. , .. // ,

, 2013. 4, .45-54.

A9. , ..

/ .. , .. , ..

// , , , 2014. 3(78),

.316-318.

,

:

A10. , ..

/

.., .., .. , .. // 13-

DSPA-2011, , 2011, 2, . 142-144.

A11. , ..

/ ..

, .. , .. , .. // 66-

,

RDC-2011, , 2011, c. 180-182

A12. , ..

/ .. , ..

, .. // 14-

DSPA-2012, ,

2012. 1, . 30-33.

A13. , ..

/ .. , .. //

20

67-

, RCD-2012, , 2012. . 155-157.

A14. , ..

N=70 / .. , ..

, .. // 15-

DSPA-2013, ,

2013. . 33-37.

A15. , ..

/ .. , .. , .. , .. //

68-

RES-2013,

, , 2013. . 370-374

A16. , ..

/

.. , .. // 16-

DSPA-2014, ,

2014. . 64-66.

:

A17. Potekhin, E.N. Binary Sequences with Minimum Peak Sidelobe Level up to

Length 68/ A.N.Leukhin, E.N. Potekhin// arxiv.org on-line avalible

A18. , ..

/ .. , ..

// , .:Nota Bene,

2013. 2, . 192-198.

:

A19. , ..

/ .., .., .. //

21

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

, .2, 2011.

A20. , ..

/ ..

, .. , .., .. //

: . .

. . . . ., -: : 2 , .2, 2011.

A21. , ..

/ .. , .. , .. //

, -15: 15-

, .: , 2011 . 478-481

A22. , ..

/ . ., . .,

. ., . . // ,

-15: 15- , .: ,

2011, . 564-567

:

A23.

2011610941 Like-noise signals / .. , .. , ..

, .. , ..

A24.

2014616441

MarGrid v.1.0.0 / .. , .. , ..

, .. , ..

A25.

2011616284 Image Recognition 1.0 / .. , .. , ..

, ..

A26.

2013618999 AutoGaz

22

, 1.0 / ..

:

;

;

,

80;2N ;

,

, ,

, ,

MF .

23

1.

1.1.

110 ...,,, NaaaA - ,

1,0na , 1,...,1,0 Nn .

A

110 ,...,, NuuuU

1,1exp nn aiu . (1.1)

21 nn ua , (1.2)

na - 110 ...,,, NaaaA :

10 , 01 .

U

1

0

N

nnn uur , 1,...,1,0 N . (1.3)

,

1,...,2,1,0,1,2,...,2,1 NNN .

,

rr ,

1,...,1,0 N .

,

,

A ,

2 Nr , (1.4)

24

1

0

N

nnn aa (1.5)

- nn aa ,

xor

, .

(1.3) (1.4)

.

(1.3) ,

(1.4)

.

()

U

1

0mod

N

nNnn uuc , 1,...,1,0 N . (1.6)

,

,

A ,

2 Nc , (1.7)

1

0mod

N

nNnn aa (1.8)

- Nnn aa mod ,

xor

, .

1 A K .

(1.6)

:

25

1

0mod

N

nNnn aa . (1.9)

KNc 4 . (1.10)

(1.6), (1.7), (1.10)

.

(1.6)

, (1.7)

, (1.10)

.

0r 0c ,

r c , 1,...,2,1 N

().

Ncr 00 . (1.11)

Nrrc , 1,...,2,1 N . (1.12)

Ncc . (1.13)

2

1,...,2,1

N - N

2

2,...,2,1

N - N .

N

2N .

26

1.2.

.

1. cN 4 , ..

4modcN . (1.14)

(1.10)

2. (1.10) , 1,...,2,1 N

N :

) 4mod0N : ...,8,4,0,4,8...., c ,

) 4mod1N : ...,5,1,3,7...., c ,

) 4mod2N : ...,6,2,2,6...., c ,

) 4mod3N : ...,7,3,1,5...., c .

(1.15)

3.

4mod0N : 0c ,

4mod1N : 1c ,

4mod2N : 2c 2c ,

4mod3N : 1c .

(1.16)

0,

0,

C

N , C - ,

[24],

[42] Nc 0 .

.

0C .

27

1C .

, .

(1.16)

.

[7], [8]

,,kvD .

,,kvD

kdddD ,..,, 21 G , Gg

1 jiddg , v - G .

G ZZ vG . G -

t - - G , tgg

Gg G . t -

- v , .. 1,gcd vt

tT .

DgtD Gg , tta - .

aa tT sD

D :

sdsdsdDDt ksa ,...,, 21 . (1.17)

, gDtD Gg , tt -

. tT

tD D :

kt dtdtdtDDt ,...,, 21 . (1.18)

tT

, , -

.

28

1D 2D ,

t - v 1,gcd vt , gDtD 21 ,

Gg . D - ,,kv , sD

tD ,

D .

D :

.,0

;,1

Dnif

Dnifan . (1.19)

D ,,kv

DGD \ (1.20)

kvkvv 2,, .

4.

0

4mod0N : 0,4c 4,0c ,

4mod1N : 1,3c ,

4mod2N : 2,2c ,

4mod3N : 3,1c .

(1.21)

, 2 .

(1.21)

tkvADS ,,, , [43].

G - . kdddADS ,..,, 21

G . ADS

tk ,,, , gdADS t ,

1 tv 1 Gg

. gdADS ADSgADSgdADS .

29

,

0t 1 vt . ,

,

. D

tkv ,,, , DG \

tkvkvv ,2,, .

ADS

:

.,0

;,1

ADSnif

ADSnifan . (1.22)

5. , ,

s - . G -

. kdddADS ,..,, 21 G . DS

s -

121 ,...,,,,, stttk , gdDS 1t ,

1 2t .. , 1 s

1

1

1s

iiv

Gg . gdDS

DSgDSgdDS .

DS ,

s - ,

:

.,0

;,1

DSnif

DSnifan . (1.23)

s -

.

6. .

30

,

, :

1) (1.17)

Nn

en aa mod , (1.24)

2) (1.18)

Ndn

en aa mod , 1,gcd Nd , (1.25)

3) (1.20)

n

en aa , 10 , 01 . (1.26)

1.3

.

.

A

ArAMN

0max . (1.27)

AMNA

min AM

A N .

(PSL - sidelobe) :

NPSL . (1.28)

,

:

31

1

1

2

2

2N

Ar

NAMF

. (1.29)

MF (merit factor).

AMFNA

max AMF

A N .

MF :

NMFopt . (1.30)

1.3.1.

PSL .

[44] ,

NNAPSLNk ln2 , (1.31)

NONk . [45]

NNAPSL ln2 . (1.32) [46] ,

:

NNAPSLN ln . (1.33)

[47] Moon Moser [44]

NNeAPSLNNe log2log2 (1.34)

32

0e A

N . (1.34)

N

2log NNAPSL . (1.35)

1.3.2.

.

,

[24], [42] [24], [43],

N

N .

(1.35) , [46]

, M - N

NNOAPSL loglog . (1.36)

[48]

N

NNAPSL 2log2 . (1.37)

, ,

pxN 14 pxN 34 .

.

NAPSL . (1.38)

[24]

1000N ,

33

.

:

NAPSLN 9,05,0 . (1.39)

1.3.3.

, ,

[49], ,

NdAPSL , 435,0d , N . (1.40)

,

,

(1.40).

.

LABS ( lowest autocorrelation binary

sequences).

LABS . :

.

, , ,

( 100N ).

( 5000N ).

34

1.3.4.

(BB - ),

.

A

:

)

n

en aa , 10 , 01 , 1,...,0 Nn . (1.41)

)

1 nN

en aa , 1,...,0 Nn . (1.42)

)

n

n aa 22 , 1,...,0 Nn . (1.43)

8 . ,

,

MF , [50].

NO 85,1 .

.

,

. [25], [26],

[27]

.

1.3.5.

.

35

,

MF :

1998 - Militzer [51] (EA)

, ;

2001 Prestwich [52] constrained local search (CLS)

NO 68.1 ; 2007 Prestwich [53] local search relaxation (LSR)

NO 51.1 ; 2003 Brglez [54] Kernighan-Lin solver

(KLS) NO 46.1 (ES),

NO 4.1 ; 2005 [55] direct stochastic search (DSC)

NO 5.1 ; 2006 - Dotu van Henteryck [56] tabu search (TS)

NO 49.1 ; 2007 - Gallarado [57] memetic (MA)

NO 32.1 .

[58], [59], [60],

[61], scatter search [62]

[63].

.

1.3.6.

1953 [2]

c 1PSL 13,11,7,5,4,3,2N , 1968

36

[3] 2PSL

21N , ,

.

1975 [25], ,

40N .

.

50 .

1986 ,

, 88,69,51N [64].

51N

3PSL . [64] ,

,

3PSL .

.

[64]

4PSL 5PSL .

4PSL 69N 5PSL 88N .

4PSL 5PSL . ,

.

1990 [26]

]48;41[N .

,

,

, .

48N .

[64], ,

3PSL 50,49N .

37

1997 [65],

,

]61;49[N ( 51N ) 4PSL , 51N

3PSL , .

UltraSparc. Elders-Boll

[65] 1997 ,

61. [65]

,

]61;49[N .

2001 [66]

, .

,

48N ,

.

[66]

49 69. , ,

]60;49[N . , [66]

]60;49[N .

4PSL . ,

[66] [65]

2004 [27]

,

.

,

38

4PSL ]70;61[N .

,

]70;61[N .

64N

,

4PSL . 4- 750

MHz Sun UltraSPARC-III workstations 64-

.

2004 [67]

PSL 70N .

PSL 70N

, .

, 2006 [68]

.

PSL MF ,

]100;71[N ,

]100;71[N

PSL . ]82;71[N

4PSL , ]100;83[N ,

7,6,5PSL . ,

]100;83[N [64], [69], [70], [29].

2008 [28]

PSL ]105;71[N ,

39

, [68]. ]82;71[N

4PSL .

,

[66], ,

4PSL , ,

51N 3PSL . 5PSL

]105;83[N .

PSL [64], [69], [70], [29],

[51].

Beowulf 18- 2.2 AMD single Core Athlon

.

,

.

48N 64N .

105N

(PSL ) ( 1.1):

40

1.1. PSL ( 61N , 64N )

( 10561 N , 64N )

. [35]

74;2N , [71]

76,75N [40]

80;2N . ,

63;49N

80;65N , 40%

,

.

41

105N

:

) ,

. , [24]

1000N ;

) . , [72] c

300;100N , 353N

1019N , 1024N 4096N .

105;2N ,

,

1000;106N .

1.3.7.

, MF, 60N .

.

.

1982 [73],

MF 40N , skew-

symmetric 59N . :

- 1977

[74];

42

- [3], [75],

MF

32N ;

- [25],

40N .

40N

, NO 2 . 1996 [50],

, MF

48N .

NO 85.1

NO 2 . , MF 48N , 313

Sun SPARCstation 20 4 CPU.

2003

MF .

Heiko Bauke 2002 [76] MF

60N .

58N 2

160 CPU ( PIII, 800

MHz).

61N ,

.

[73]

32,12AMF , N . (1.44)

1.2

MF

.

43

1.2. MF ( 60N )

( 30561 N )

MF

, -

MF .

1.4.

,

N

,

.

1.4.1. 4mod0N

4mod0N

0c .

24uv ,

0

2

4

6

8

10

12

14

16

0 50 100 150 200 250 300 350

MF

N

44

uuuuuD 222 ,2,4 . 4v .

, .

[4], [77]

30102 v

276678160401034441521892604680v .

1.4.2. 4mod1N

4mod1N

1c .

21,,122 22 uuuuuD . 1u 2u .

, u

. [78] [79] 1003 u .

1.4.3. 4mod2N

,

2c

0,1,2D .

2c [80],

, 125457 v ,

910v ,

33895686,2433602,174726,12546v .

45

1.4.4. 4mod3N

4mod3N

1c .

43,21, vvvD

41,21, vvvD ,

-. 1954

[7]

1,12,14 ttktD ,

1c . ,

:

) pt 14 - ,

) pqt 14 , p 2 pq - ,

) 1214 ntv .

[81]

10000 , , 17 .

( , , ) .

[82] 17 4. [83]

, [84]

6 .

,,kv 10000

7 : 859,1719,3439 , 1088,2177,4355 , 2147,4295,8591 ,

2208,4417,8835 , 2283,4567,9135 , 2303,4607,9215 , 2355,4711,9423 .

46

,

( , pn 12 pqn 12 )

:

1) (

) 14 tv ;

2) (

) 27414 2 xtv ;

3) (

) pqv .

1214 ntv . 1955

[8]

12,12,12 21 nnn kD . : 1955

125 v [8], 1962 [11] 126 v , 1971

[85] 127 v , 1983 [86] 128 v , 1991

[87] 129 v , 2001 [88]

1210 v . , 1955

12,12,12 21 nnn kD 60 .

n .

12,12,12 21 nnn kD : 1) ;

2) GMW;

3) ;

4) , .

47

,

255,511,1023D 10n ,

10n , .

1211 v .

, 2020 .

,

1c .

1.4.4.1.

( )

4mod3p - .

4

3,

2

1,

pppD

pZ [5]:

pCD ,20 . (1.45)

,

( ) pZ .

.

( )

p - 274 2 xp x .

4

3,

2

1,

pppD pZ [9]:

ppp CCCD ,63,6

1,6

0 . (1.46)

( )

48

- p q .

1,1gcd qpd 11 qpde . x ,

1,...,1,0;1,...,1,0:Z* diesxispq . (1.47) [89] ,

1,...,1,0: esxC isi , 1,...,1,0 di . (1.48)

0C 1C 2d , ..

21,1gcd qp . 2 pq . [90] 2ppZ

:

pqpppCD 1,....,3,2,0 . (1.49)

, , ,

[10], ,

.

1.4.4.2.

12,12,12 21 nnnD . .

(-)

:

1Tr:2 axGFxD n . (1.50) -.

Gordon, Mills, Welch

49

mGF 2 nGF 2 , m - n .

1Tr:2

22 mn GFGF

nGFxR . (1.51)

D

21 2,2,12 mmm mGF 2 , rDRU (1.52)

nGF 2 , r -

12,2 m

C DyyD rr : .

f nGF 2

nGF 2 . ,

nGFy 2 20:2 yxfGFx n ,

2 1. [91] ,

nkn GFxxxGFD 2:\2 (1.53) , kxx

nGF 2 kxx 2 1. k , :

2k - ;

6k - ;

bak 22 , 21 na nb mod14 -

1- ;

423 ak , 21 na - 2-

.

1.4.4.3.

50

1971 [85] 7m

6

, 3 , 3

.

3-term .

,

[Baumert] 7m ,

, 5-term WG-

. WG-

1998 [92]

, H-,

[93].

2004 [94] (

kB ), 3-term, 5-term WG-

.

dx nqGF 2 , d - , 1222 kkd , mk

1, mk .

H-.

dd xxx 1 , mk mod13 . (1.54)

x 2--1 mqGF 2 . -

qGF .

.,Im\

,,Im

mqGF

mqGFxxH

(1.55)

D

H-.

kB -.

51

1, mk ,

11 ddk xxx , qGFx , (1.56)

d - . xk 2--1

qGF .

qGFxxB kkk Im ,

kk BxqGFxCk 12 . (1.57)

nbb nc

,

:

,,1

;,0

Bb k

n

n

.,1

;,0

c k

n

n

(1.58)

nc

nbb

12mod12 mkn

n bc .

[93] :

1. 2'k mkk mod1' , b 3-term

.

2. 3'k mkk mod1' , b 5-term

.

3. H WG-

.

4. mkk mod1' kB -

,

.

52

1.5.

1.5.1. 4mod0N

4mod0N

0,4c .

1.5.1.1. (Sidelnikov, Lempel, Cohn,

Eastman)

114 npqxN .

1qZ

4

1,

4

5,

2

1,1

qqqq , 4mod1q :

1log ,21 qCADS , (1.59)

- npGF .

n

pn 1.

[95]

[96].

1.5.1.2. ,

1. Arasu, Ding, Helleseth, Kumar, Martinsen ( [97])

D -

4

3,

2

1,

lll

4

1,

2

1,

lll lZ

, 4mod3l . l4Z

1,2,12,4 llll 1,,12,4 llll

llDllDlADS 4mod14mod1 (1.60)

53

llDlllDl 4mod314mod21 ,

D D

D D .

interleaved

[98].

2. Arasu, Ding, Helleseth, Kumar, Martinsen

[99], [97]

.

1D -

4

3,

2

1,

lll

4

1,

2

1,

lll

lZ

, 4mod3l . 2D - 4Z

0,1,4 . lZ4Z

1,2,12,4 llll 1,,12,4 llll

1*2*12 DDDDD . (1.61)

ll 44 ZZZ: - .

D

0,4c

1.5.1.3 Zhang, Lei, Zhang, Tang, Gong

[100] [101]

. 3210 ,,, bbbbb -

4; pCD ,20 -

; pCD ,210' - , ;

34 xpN . NZZ4

'32'10 3210 DbDbDbDbADS . (1.62)

1.5.1.4. Ke, Lin

54

[102]

. 3210 ,,, bbbbb -

4; D - -

41,21, lll 43,21, lll ,G ; kDDk

- , 1,gcd Nk , 34 xN .

NZZ4

kk DbDbDbDbADS 3210 3210 . (1.63)

1.5.1.5. Tang, Ding

[103] . A B

- 41,21, lll 43,21, lll

,G .

1,,12,4 llll

1,2,12,4 llll NZZ4

*3210 BABAADS . (1.64) A B

1,,12,4 llll 1,2,12,4 llll , *B -

B .

1.5.2. 4mod1N

4mod1N

1,3c . , 4

.

.

1.5.2.1. 2- (

)

55

pqN , 4mod1q - .

2

1,

4

5,

2

1,

qqqq qZ :

qADS ,20 . (1.65)

q .

.

1.5.2.2. 4- (

Ding, Helleseth, Lam)

pqN , 4mod1q - .

2

1,

4

5,

2

1,

qqqq [104] qZ

:

qiq

i ADS,41

,4 , 2,...,0i

qq ADS ,40,4

3 , (1.66)

42 xq 4mod1x .

1,3c .

qC ,40 i 13q .

1.5.2.3. 8- (

Ding)

2lpqN n , 42 lq

8mod322 tl , ,...227,83,3,11,3 22622q .

2

1,

4

5,

2

1,

qqqq [105] qZ :

qqqq ADS ,85,8

2,8

1,8

0 , (1.67)

56

1.5.2.4. 12- (

Nowak, Olmez, Song)

[106]

, 12- .

12mod112 xp - , 4mod1x .

....,3253,2029,1093,733,229,12p .

4

1,

4

5,

2

1,

pppp ,pGFG

:

pppppp CCCCCCADS ,129,12

8,12

5,12

4,12

1,12

0 . (1.68)

1.5.2.5.

- p q .

1,1gcd qpd 11 qpde . x ,

1,...,1,0;1,...,1,0:Z* diesxispq . (1.69) [89] ,

1,...,1,0: esxC isi , 1,...,1,0 di . (1.70)

0C 1C 2d , ..

21,1gcd qp . 4 pq

4

11 qp - .

4

51,

4

31,

2

31,4

pppppppp [90] 4ppZ

:

pqpppCADS 1,....,3,2,0 . (1.71)

57

1.5.3. 4mod2N

4mod2N

2,2c .

1.5.3.1. (Sidelnikov, Lempel, Cohn,

Eastman [95], [96])

1124 npqxN .

1qZ

4

53,

4

3,

2

1,1

qqqq , 4mod3q :

1log ,20 qCADS , (1.72)

- npGF .

n

pn 1.

1.5.3.2. No-Chung-Song-Yang-Lee-Helleseth

4mod3q - .

4

33,

4

1,

2

1,1

qqqq . (1.73)

[107]

1log2

1 ,20

qCq

ADS . (1.74)

.

1.5.3.3. Ding, Helleseth, Martinsen

1.

58

8mod5q - . ,

22 4tsq s t 4mod1s . 3,2,1,0,, lji

, qn 2 , qGFGFA 2

4

63,

4

6,

2

2,

nnnn [108]:

qjqlqjqi CCCCADS ,4,4,4,4 10 , (1.75)

1) 1t 3,1,0,, lji 1,2,0 ;

2) 1s 3,0,1,, lji 2,1,0 .

- qD ,401 1 , q - , qxxx mod,2mod: - q2Z qZZ2 .

2.

8mod5q - . ,

22 4tsq s t 4mod1s . 3,2,1,0,, lji

, qn 2 , qGFGFA 2

4

23,

4

2,

2,

nnnn [108]:

0,010 ,4,4,4,4 qjqlqjqi CCCCADS , (1.76)

1) 1t 0,3,1,0,2,1,3,2,0,3,1,0,, lji ;

2) 1s 3,2,1,3,0,1,2,3,0,3,0,1,, lji .

- qD ,401 1 , q - , qxxx mod,2mod: - q2Z qZZ2 .

59

1.5.4. 4mod3N

,

Paley-Hadamard c

1c .

3,1c .

1.5.4.1. Cai, Ding

[109]

. 2D -

*22mGF 12,12,12 24222 mmm .

1:2 2/221

xTrGFxD mmm .

*2mGF 2,22,22,12 22221 mmmmmm

221121 ,: DdDdddD . (1.77)

NZ :

DADS log , (1.78)

- *2mGF , 12 mN .

1.6.

,

( )

60

1.6.1. Ding

2

1,

16

13,

4

1,

qqqq [90] qZ :

qADS ,40 , (1.79)

2425 yq 249 yq

.

1.6.2. Ding, Helleseth, Lam

2

1,

16

5,

4

3,

qqqq [104] qZ :

qADS ,400 , (1.80)

241 yq 2449 yq .

.

1.6.3. Ding

2

1,

64

41,

8

1,

qqqq [90] qZ :

qADS ,80 , (1.81)

222 21419 byq y b 64mod41q

222 21413 byq y b [90].

.

61

1.7.

1.7.1. Davis

23nZH

13,323,332,34 2222 nnnnnn , H - 4.

1.7.2. Davis

2qEAH

1,,1,1 22 qqqqqq , H - 1q , 2qEA

,2qGF .

1.7.3. ,

,A ,B - n m .

f A B . ,

[110],

bxfaxfPBbAa

f

Prmaxmax0

, (1.82)

EPr

E . B

Pf1

. f

,

mPf

1 . (1.83)

sx mpGF mpGF , p -

mf pP 1

s :

62

2s ;

1 kps , kmm ,gcd - ;

213 ks , 3p , k - , 1,gcd km . (1.84)

2610 xxx

mGF 3 mGF 3 m . [97]

.

f - , ,A

n ,B n

nPf 1 . bxfAxCb .

Bb

b ABCbC

(1.85)

1,0,,2 nnn AB .

, sxxf

mpGF mpGF p . bxfpGFxC mb

mpGFb . mm pGFpGF

mmpGFb

b pGFpGFCbADSm

(1.86)

1,0,,2 mmm ppp .

1.7.4. ,

[97]

.

D -

16

3,

4

3,

nnn

d - D . d2

63

D ,

dDADS \ (1.87)

2

1,

16

13,

4

1,

nnnn .

1.7.5. ,

[97]

.

D A

16

5,

4

1,

nnn . d

DAd \ . d2

D ,

dDADS (1.88)

2

1,

16

5,

4

3,

nnnn .

1.8.

xN 4

4,0,4c ,

1.8.1. Yu, Gong -

[98]

-. 124 mN , km 2 , 1k . 1,0,0,0a 4 ibb

64

- 12 m , km 2 , 1k . icc

124 kn

12,

,12,0k

j

k

ijiz

jic , (1.89)

j - , 30 j 3210 ,,, zzzzz -

0,0,1,1 .

cbau , (1.90)

iiii cbau , 10 Ni

4,0,4c .

1.8.2. Tang, Gong GMW-

[101]

1244 2 kxN GMW-.

1.8.3. Tang, Gong

[101]

244 ppxN .

1.8.4. Tang, Gong

[101]

pN 4 .

1.9.

.

65

. ,

,

48;2N 64N .

80;2N , 40%

,

.

,

,

N ,

.

66

2.

Brunch and bound.

:

brunch and bound ;

, ;

,

.

2.1. "brunch and bound"

2.1.1.

. .

[111] ,

.

64N

[27].

, .

2

N- 4-

),( EVT , N -

() , }...,,{ 21 mvvvV -

67

, ix

iNx 1 , },...,,{ 21 neeeE - , ),( kji vve

.

M , :

. - ,12

; - ,2

NN

NN

M . (2.1)

, ,

.

0v , ,

.

0x 1Nx N ,

- , 1v

4 , ..

}1;0{ : 00, 01, 10 11.

1v

:

0,,...,,,0 2321 NN xxxxa , (2.2)

ix - .

,

.

minimum peak sidelobe (MPS)

. 1

1r , :

kr 1 , (2.3)

k - .

68

,

, , ,

1x 2Nx .

:

00,...,,00 32 Nxxa . (2.4)

, MPS

, ..

kr 1 , (2.5)

, 1v ,

1v 1r

.

: 01.

: 1,,...,,,0 2321 NN xxxxa . 2.1

.

2.1

, MPS

,

.

69

2.1.2.

MPS,

,

,

.

, .

: , .

t , ,

t2 , ,

.

.

. }{ naa - N ,

}1,1{ na , 1,...,1,0 Nn . N ,

, }{ nbb ,

nn xb 1 , 1,...,1,0 Nn .

. }{ naa - N ,

}1,1{ na , 1,...,1,0 Nn . N ,

, }{ nbb ,

nNn xb 1 , 1,...,1,0 Nn .

. }{ naa - N ,

}1,1{ na , 1,...,1,0 Nn . N ,

, }{ nbb ,

ixb nn , 1,...,1,0 Nn , - .

180 , nn

n xb )1( .

,

.

70

00 x , 01 Nx .

: 0,,...,,00 21 Nxxa .

. :

1,,...,,11 21 Nxxa .

: 0,,...,,02 12 xxa N 1,,...,,13 12 xxa N .

4 : 1,,...,,04 21 Nxxa ,

0,,...,,15 21 Nxxa , 1,,...,,06 12 xxa N 0,,...,,17 12 xxa N .

7 :

0,,...,,00 21 Nxxa

1,,...,,11 21 Nxxa

0,,...,,02 12 xxa N

1,,...,,13 12 xxa N

1,,...,,04 21 Nxxa

0,,...,,15 21 Nxxa

1,,...,,06 12 xxa N

0,,...,,17 12 xxa N

(2.6)

,

00 x , 01 Nx

10 Nxx . , T

1v

00. , T

00, 01 11,

:

0,0,,...,,0,00 32 Nxxa

0,1,,...,,0,01 32 Nxxa

0,1,,...,,1,02 32 Nxxa

(2.7)

71

2.2 .

2.2 ,

2.2. brunch and bound

2.2.1.

),...,,( 110 NaaaA ,

1,...,1,0},1,1{ Nan :

1

0

N

nnn uur , 1,...,1,0 N (2.8)

C ,

,

, .. min

.

,

, ,

:

};{ 1 mNm aa , (2.9)

72

2,...,2,1N

m - .

(2.8),

, .. , ..

2

Nm

, ,

, };{ 1 mNm aa

2

Nm

:

1

0

N

nnn uur

.,12

,...,1,0

,,2

,...,1,0,

NN

NN

(2.10)

,

, ,

,

:

.22

,...,2,1

,,12

,...,2,1

NN

NN

NN

NN

(2.11)

12

N

N 22

N

(2.5), , ,

(2.3).

, ,

,

, .

73

, (2.10), 0 ,

,

:

Nr 0 . (2.12)

2.3

.

2.3

,

50,...,6,4N , 4,3,2,1PSL

, . 2.4

. ,

18%.

74

0,00%

2,00%

4,00%

6,00%

8,00%

10,00%

12,00%

14,00%

16,00%

18,00%

20,00%

4 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

PSL 1

PSL 2

PSL 3

PSL 4

2.4

1,...,2,1 N

[27] XOR,

2. :

2 Nr , (2.13)

- , :

1

0

N

nnn aa

,

(2.14)

, 1,0,1,1a .

40 r ,

.

. XOR ,

( 2.1).

75

2.1 XOR

1 1 0 1

1 1 0 1

=

0

1 1 0 1

1 1 0 1

=

1 0

1 1 0 1

1 1 0 1

=

0 1 1

2

. (2.13)

. MPS

.

: 1013 r , 0112 r ,

1211 r .

, ,

.

r .

XOR ,

0 1.

, ,

Intel Core SSE4.2,

. /++ Microsoft

__popcnt64 intrin. GNU GCC G++

_mm_popcnt_u64 smmintrin.

4 ,

.

.

, k ,

76

XOR,

,

. ,

, :

,2 ,0

,2 ,1,

PSLkn

PSLknM nk

(2.15)

k -

, XOR,

n - ,

:

1Nn . (2.16)

2 :

k n .

True False, ,

PSL. 2.5

- .

2.5 -

,

m .

, (1.12), ,

.

c (1.13)

(1.15),

, :

77

, ,0

),( )2( ,1,

Nnk

rrPSLknM

(2.17)

,

N

:PSL

)(| xAxX , (2.18)

)(xA

-

:

).4)(div32(),...,4)(div32( ,3)4(mod,34

),4)(div22(),...,4)(div22( ,2)4(mod,24

),4)(div12(),...,4)(div12( ,1)4(mod,14

),2(div),...,2(div ,0)4(mod,4

)(

PSLPSLxNx

PSLPSLxNx

PSLPSLxNx

PSLPSLxNx

xA

(2.19)

2.2.2.

,

, ,

.

[27] ,

,

)(rREVl , (2.20)

)(rREV - r , :

iNi abB 1: , ),...,,( 110 Naaa , ),...,,( 110 NbbbB . (2.21)

,

.

,

.

78

65536216 N

, 2 .

M :

},...,,{ 110 TeeeM , )(iREVei , 1,...,1,0 Ti , 1216 T , (2.22)

ie 16- i .

i ie

M . 16-

4 , 4 6

.

reverseRightCode = ((unsigned long long

int)ReverseTable16bit[rightCode & 0xffff] > 16) & 0xffff] > 32) & 0xffff] > 48) & 0xffff]);

2.6 -

, 16 .

2.6

2.2.3.

[50] , brunch and

bound N

,

m .

79

T m , m -

.

m

N :

)2mod(232 22)( Nmmmc . (2.23)

2 . ,

N

. :

;

N , .. ,

.

,

4PSL

13m .

262 m

)(mc .

13m

.

N .

, .. 02mod N ,

26N

4PSL . N

,

,

80

.

13m 2122026)13( evenc

.

, .. 12mod N ,

27N

4PSL .

,

.

.

13m 2926269)13( oddc ,

.

, .

,

.

:

2926269 ,

27N

234101522)13()13( 3. oddeqodd cA . (2.24)

)13(.eqoddA

, .

2122256)13( oddc

.

,

, i - . ,

81

i ,

.

2.2.4. NVidia

CUDA

,

NVidia CUDA.

,

,

.

NVidia CUDA ,

GPU -

CPU.

, , CPU, GPU

. , GPU

,

.

GPU CPU ,

,

.

:

1. GPU;

2. CPU GPU;

3.

GPU;

82

4. CPU;

5. GPU.

GPU :

cudaStatus = cudaMalloc( (void**)&d_globVar, sizeof(GLOBVAR));

if (cudaStatus != cudaSuccess)

{

std::cerr

83

, GPU

:

if (isOdd)

start_kernel_odd>(d_vecInitBeg, d_Recurs, d_results);

else

start_kernel_even>(d_vecInitBeg, d_Recurs, d_results);

, ,

GPU, 4 5: GPU

CPU GPU:

cudaMemcpy(h_results, d_results, sizeof(RESULT) *

sGlobal.cntInitBeg, cudaMemcpyDeviceToHost);

FreeBeginVec();

8

NVidia Tesla C2050

:

GPU 1;

575 ;

448;

1150 ;

144 /;

GDDR5;

384 ;

3072 ;

3000 ;

1288 ;

515,2 ;

238 .

Intel Xeon X5670 2,93 GHz.

84

,

, , CPU.

2.2.5.

,

2N

2)1( N - .

T ,

. 2 NN

,

N , 12N -

2)1( N - . ,

,

,

, , .

.

,

, ,

,

, , ,

.

85

2.7 2, N , 2N

2.2.6.

, T ,

. ,

, ,

, -

. ,

( 2.8).

,

, ,

, , .

+ 2 ,

,

, , MPS

, , .

,

.

,

.

,

86

, ,

.

(2122026) (2122256)

13 T 4PSL ,

13 .

,

4PSL ,

50N , - 49N .

,

,

, 207323

206194 - ,

9,77% 9,72%

13 ,

4PSL .

N

, .

, , 78N ,

1%.

2.8

87

2.3.

brunch and

bound , .

, :

;

;

;

;

;

;

, , ,

.

88

3.

:

1. -

,

.

2.

.

3. MPS

.

4. MPS

MPS .

5.

.

6.

.

3.1.

3.1.1. -

MPS

,

.

89

, ,

.

, .

-

.

110 ...,,, NaaaA 110 ...,,, NbbbB N

-

1

0

,N

nnn

BA bar , 1,...,2,1 N . (3.1)

A

)max( ,,maxBABA rr , 1,...,2,1 N . (3.2)

,

, . ,

, BAr ,max A B ,

, N , ,

,

. 3.1

,

:

N - ;

ALLN - ,

, N ;

BAr ,max - A

B ;

k - A.

90

,

,

.

3.1 MPS

A

N ALLN BAr ,max k

BAr ,max k BAr ,max k

2 4 1 4 2 2

3 4 2 4 3 2

4 8 2 8 3 16 4 4

5 4 3 4 5 2

6 28 3 148 4 152 5 64

7 4 3 4 7 2

8 64 3 160 4 816 5 600

9 80 3 128 4 752 5 1288

10 40 4 192 5 320 6 136

11 4 6 4 11 2

12 128 4 336 5 2568 6 2576

13 4 5 4 13 2

14 72 5 192 6 688 7 680

15 104 5 224 6 1232 7 1816

16 80 5 32 6 512 7 792

17 32 5 24 6 40 7 24

18 16 7 24 8 16 9 40

19 8 6 8 7 8 15 8

20 24 6 16 7 32 8 48

21 24 7 72 8 88 9 40

22 3024 5 96 6 30768 7 401360

23 4084 5 16 6 21624 7 476704

24 6864 5 16 6 23816 7 839648

25 8 7 8 9 8 11 8

26 1936 6 192 7 21072 8 180080

27 3096 6 96 7 25240 8 317664

28 16 8 24 9 16 10 8

29 2244 7 3096 8 77248 9 336348

30 688 7 256 8 4936 9 24504

31 2008 7 280 8 20856 9 155240

32 3376 7 392 8 35280 9 354456

33 1112 7 32 8 2120 9 28080

34 408 8 192 9 2224 10 9400

35 888 8 360 9 7616 10 36304

36 1288 8 368 9 11360 10 65664

37 440 8 16 9 920 10 5872

91

N ALLN BAr ,max k

BAr ,max k BAr ,max k

38 136 9 104 10 392 11 1160

39 240 8 16 9 48 10 912

40 456 9 136 10 2528 11 9416

41 120 10 192 11 552 12 1024

42 32 9 8 10 16 11 16

43 96 10 48 11 256 12 528

44 120 10 32 11 352 12 928

45 32 11 24 12 40 13 48

46 8 13 8 14 8 17 8

47 8 17 8 20 16 47 4

48 32 11 8 12 32 13 96

49 392704 8 32 9 135456 10 28124088

50 201352 9 14448 10 4091328 11 113531072

51 8 12 16 49 8 51 4

52 264464 9 3248 10 1947424 11 85856504

53 189384 9 720 10 463968 11 27238336

54 86464 9 32 10 45992 11 3626344

55 95896 9 32 10 27056 11 2706920

56 122312 9 16 10 20032 11 2642960

57 75808 10 3088 11 564008 12 13225248

58 32208 10 256 11 60224 12 1696080

59 36992 10 176 11 43672 12 1522120

60 44336 10 112 11 35216 12 1474568

61 25968 10 16 11 5872 12 320992

62 9696 11 464 12 30904 13 391920

63 11376 11 368 12 26008 13 396744

64 14872 11 320 12 27432 13 495288

65 8024 11 64 12 5264 13 102744

66 2592 12 256 13 7016 14 57944

67 3048 11 8 12 264 13 7640

68 3912 12 232 13 8384 14 79440

69 1984 12 48 13 1448 14 16104

70 576 13 32 14 1112 15 4840

71 920 12 16 13 128 14 2176

72 856 13 112 14 1328 15 7504

73 368 13 40 14 192 15 1200

74 144 14 8 15 176 16 488

75 128 14 24 15 88 16 288

76 136 14 16 15 80 16 376

77 80 15 72 16 80 17 184

78 8 21 16 22 8 78 4

79 32 15 8 16 8 17 32

80 56 17 32 18 64 19 296

92

,

.

3.1.2.

,

,

, [1].

:

1

0

*, exp

N

nnn n

Fiuu , 1,...,1,0,1,...,1 NN ,

FF ,...,1,0,1,..., ,

(3.3)

- , ,

- .

,

8 .

, :

- -

-;

- -

-;

- - , ..

, .

,

, -

.

93

-

, MPS ,

-: 63,31,15N ( 3.1).

3.3

- PSL-

. ,

PSL

- 591,0)( dB ,

, 15N , .

3.2

, (3.3) :

N - ;

minPSL -

;

maxPSL -

;

meanPSL -

.

, :

N

PSLdbPSL log20)( , (3.4)

PSL ,

.

94

. - 15N . PSL- 15N

. - 31N . PSL- 31N

. - 63N . PSL- 63N

3.1. - PSL-

63,31,15N

95

3.2

N minPSL minPSL (dB) maxPSL maxPSL (dB) meanPSL meanPSL (dB)

2 1 -6,021 1 -6,021 1 -6,021

3 2 -3,522 2 -3,522 2 -3,522

4 2,236 -5,051 2,236 -5,051 2,236 -5,051

5 3,078 -4,215 3,078 -4,215 3,078 -4,215

6 3,235 -5,366 4 -3,522 3,576 -4,494

7 3,494 -6,036 3,494 -6,036 3,494 -6,036

8 3,692 -6,716 5 -4,082 4,428 -5,137

9 3,69 -7,744 5,424 -4,399 4,36 -6,295

10 4,645 -6,66 5,742 -4,819 5,196 -5,686

11 6,475 -4,603 6,475 -4,603 6,475 -4,603

12 5,403 -6,93 7,324 -4,289 6,337 -5,547

13 7,612 -4,649 7,612 -4,649 7,612 -4,649

14 6,764 -6,318 8,289 -4,553 7,249 -5,717

15 5,916 -8,081 8,692 -4,74 7,276 -6,284

16 7 -7,18 9 -4,998 7,984 -6,038

17 6,779 -7,985 8,441 -6,081 7,624 -6,965

18 9 -6,021 9 -6,021 9 -6,021

19 10,165 -5,433 10,165 -5,433 10,165 -5,433

20 8,811 -7,12 11,151 -5,074 9,654 -6,327

21 8,544 -7,811 9,119 -7,245 8,79 -7,564

22 7,599 -9,234 12,288 -5,059 9,45 -7,34

23 7,773 -9,423 14,104 -4,248 10,262 -7,01

24 7,611 -9,975 13,568 -4,954 10,197 -7,435

25 9,746 -8,183 9,746 -8,183 9,746 -8,183

26 8,831 -9,379 15,086 -4,728 10,987 -7,482

27 9,005 -9,537 15,677 -4,722 11,402 -7,488

28 10,778 -8,292 16,078 -4,818 13,428 -6,383

29 9,612 -9,591 16,905 -4,688 12,109 -7,586

30 9,855 -9,669 16,826 -5,023 11,962 -7,986

31 10,416 -9,473 17,041 -5,197 12,514 -7,879

32 10 -10,103 17,001 -5,493 12,399 -8,236

33 10,568 -9,891 17 -5,761 12,832 -8,204

34 10,89 -9,889 18,808 -5,143 13,308 -8,147

35 11,159 -9,929 18 -5,776 13,896 -8,023

36 10,87 -10,401 17,745 -6,145 13,581 -8,468

37 12,183 -9,649 20 -5,343 14,376 -8,211

38 12,145 -9,908 21,265 -5,042 14,966 -8,094

39 11,502 -10,606 18,052 -6,691 14,674 -8,49

40 12,52 -10,089 21,726 -5,302 15,407 -8,287

41 13,082 -9,922 17,236 -7,527 14,851 -8,82

42 18 -7,36 23,415 -5,075 20,202 -6,357

43 14,017 -9,736 20,511 -6,43 16,902 -8,111

96

N minPSL minPSL (dB) maxPSL maxPSL (dB) meanPSL meanPSL (dB)

44 14 -9,946 22,806 -5,708 16,498 -8,52

45 15,464 -9,278 16,79 -8,563 16,104 -8,925

46 17,279 -8,505 17,279 -8,505 17,279 -8,505

47 20 -7,421 20 -7,421 20 -7,421

48 16,097 -9,49 19,694 -7,738 17,364 -8,832

49 12,805 -11,656 26,482 -5,345 16,946 -9,222

50 13,533 -11,352 27,64 -5,149 17,478 -9,13

51 19,17 -8,499 19,17 -8,499 19,17 -8,499

52 13,624 -11,634 28,773 -5,14 17,986 -9,221

53 13,872 -11,643 28,695 -5,33 17,951 -9,404

54 14,407 -11,476 28 -5,705 18,461 -9,323

55 14,244 -11,735 27,802 -5,926 18,457 -9,484

56 14,706 -11,614 30 -5,421 18,944 -9,414

57 14,915 -11,645 29,523 -5,714 18,91 -9,584

58 15,009 -11,741 31 -5,441 19,441 -9,494

59 15,11 -11,832 30 -5,875 19,433 -9,646

60 14,944 -12,074 31 -5,736 19,849 -9,608

61 15,369 -11,974 30,159 -6,118 19,863 -9,746

62 15,842 -11,851 30 -6,305 20,328 -9,686

63 16,449 -11,664 27,866 -7,085 20,294 -9,839

64 16,738 -11,65 31 -6,296 20,787 -9,768

65 16,69 -11,809 29 -7,01 20,723 -9,929

66 17,104 -11,729 30 -6,848 21,452 -9,762

67 17,487 -11,667 28 -7,578 21,32 -9,946

68 17,466 -11,806 34,401 -5,919 21,722 -9,912

69 18,158 -11,595 29,891 -7,266 21,804 -10,006

70 17,619 -11,983 29 -7,654 22,388 -9,902

71 18,015 -11,912 28,439 -7,947 21,977 -10,186

72 18,662 -11,728 28,808 -7,956 22,087 -10,264

73 19,671 -11,39 31,823 -7,212 23,173 -9,967

74 19,96 -11,382 29,171 -8,086 23,338 -10,023

75 20,093 -11,44 27,082 -8,848 22,42 -10,489

76 20,796 -11,257 25,744 -9,403 23,534 -10,183

77 20,636 -11,437 27,036 -9,091 23,994 -10,128

78 21 -11,398 21 -11,398 21 -11,398

79 23 -10,718 26,595 -9,456 24,931 -10,018

80 22,334 -11,083 27,181 -9,376 24,264 -10,363

97

3.3 - PSL-

63,31,15N

N - PSL-

)(dB PSL PSL (dB) PSL PSL (dB)

15 6,151 -7,743 5,916 -8,081 -0,338

31 10 -9,827 10,416 -9,473 0,676

63 15,367 -12,255 16,449 -11,664 0,591

, PSL- -

c

.

3.1.3.

,

,

. .

,

-

, , :

NPSL . (3.5)

,

-

, .

PSL ,

.

, .

,

.

98

: .

:

1. ),( EVG , V - ,

E - ,

.

2. , PSL.

3. ,

.

-,

1973 [112]. , 2006 ,

[113] ,

33n

,

n - .

c PSL

, ( 3.4).

3.4

N PSL : N PSL : 2 1 2:4

43

10 2:48

3 2 2:4 11 2:304

4 2 2:8 12 3:800 ,2:144

3 4:16

44

10 2:32

5 3 2:4 11 2:336 ,3:32

6

3 4:96 ,3:32 ,2:20 12 3:1248 ,2:120 ,4:288

4 6:3072

45

11 2:24

5 14:16384 12 2:64

7 3 2:4 13 3:32 ,2:72

8

3 3:32 ,2:112

46

13 2:8

4 4:2048 ,3:352 ,5:1024 ,6:256 14 2:16

5 10:6144 ,9:77824 ,8:194304

,7:107520 ,6:2816 17

4:16

9 3 2:128

47 17 2:8

4 4:224 ,3:800 ,2:136 20 4:16

99

N PSL : N PSL :

5 6:64640 ,7:69120 ,5:9088 ,4:224

,8:38400 ,9:12288 48

11 2:8

10

4 2:64 ,3:96 12 2:40

5 5:1408 ,6:896 ,4:160 13 2:88 ,3:32

6 8:36864 ,7:12288 ,6:1024

49

10 2:>203008 ,3:>3456

11 6 2:4 8 2:32

12

4 2:336 9 2:>41654

5 4:10944 ,3:2336 ,5:384 ,2:8

50

10 2:>215864 ,3:>512

6

8:1252352 ,9:282624 ,7:1426944

,6:335104 ,5:18304 ,10:28672

,4:32

11 3:>11766928 ,2:>402794 ,

4:>73568

13 5 2:4 9 2:14448

14

5 2:192 51

12 2:16

6 2:280 ,3:864 ,4:96 49 4:16

7 5:13440 ,4:560 ,6:4992

52

10 2:>42498

15

5 2:224 11 3:>816120 ,2:>779340 ,4:>576

6 4:1760 ,3:928 ,2:144 9 2:3248

7

7:110592 ,5:13312 ,6:72448

,8:84480 ,9:67584 ,10:32768

,4:384 ,11:16384 ,12:8192 53

10

2:>38082

16

5 2:32 11 2:>1318632 ,3:>232192

6 2:184 ,3:384 9 2:720

7 4:3424 ,5:1024 ,3:640 ,6:128

54

10 2:46024

17

5 2:24 11 2:>2857896 ,3:>61568

6 2:64 9 2:32

7 2:88

55

10 2:27088

18

7 2:24 11 2:>1521142 ,3:>14528

8 2:40 9 2:32

9 4:64

56

10 2:20048

19

15 4:16 11 2:>662968 ,3:>2880

6 2:8 9 2:16

7 2:16

57

10 2:3088

20

6 2:16 11 2:>545592 ,3:>480

7 2:48

12 2:>6912768 ,3:>6107222

,4:>6624

8 2:96

58

10 2:256

21

7 2:32 ,3:32 11 2:60480

8 3:96 ,4:128 12 2:1532952 ,3:160416

9 4:784

59

10 2:176

22

5 2:96 11 2:43848

6 2:29712 ,3:768 12 2:1462000 ,3:72032

7 4:1242784 ,3:1545056 ,5:24192

,2:72 60

10 2:112

23

5 2:16 11 2:35328

6 2:21496 ,3:96 12 2:1454816 ,3:37408 ,4:32

7 3:1565440 ,4:316480 ,2:2520

,5:1920 61 10

2:16

100

N PSL : N PSL :

24

5 2:16 11 2:5888

6 2:23832 12 2:324192 ,3:1824

7 3:1915456 ,4:90496 ,2:34592

,5:128 62

11 2:464

25

11 4:16 12 2:31368

7 2:8 13 2:307400 ,3:90944 ,4:64

9 2:16

63

11 2:368

26

6 2:192 12 2:26376

7 2:19688 ,3:1120 13 2:348384 ,3:55168 ,4:128

8 3:560192 ,4:565568 ,5:16768

,2:104 64

11 2:320

27

6 2:96 12 2:27752

7 2:24616 ,3:480 13 2:458608 ,3:46112

8 4:292704 ,3:1085920 ,5:2176

,2:920 65

11 2:64

28

10 2:48 12 2:5328

8 2:24 13 2:104824 ,3:2208

9 2:40

66

12 2:256

29

7 2:3096 13 2:7272

8 3:47648 ,2:33616 ,4:64 14 3:16864 ,2:44272 ,4:160

9 4:9504480 ,5:3613568 ,6:90752

,3:160496 ,7:512 67

11 2:8

30

7 2:256 12 2:272

8 2:4856 ,3:224 13 2:7912

9 4:24640 ,3:56672 ,5:640 ,2:352

68

12 2:232

31

7 2:280 13 2:8568 ,3:32

8 2:19416 ,3:1184 14 3:12032 ,2:71776 ,4:64

9 4:209920 ,3:489568 ,5:3456

,2:400 69

12 2:48

32

7 2:392 13 2:1496

8 2:34120 ,3:1056 14 2:16808 ,3:544

9 4:326016 ,3:1259872 ,5:2048

,2:712 ,6:128 70

13 2:32

33

7 2:32 14 2:1144

8 2:2104 ,3:32 15 2:4264 ,3:1312

9 2:9592 ,3:21792 ,4:1088

71

12 2:16

34

10 3:19840 ,4:5408 ,2:360 13 2:144

8 2:192 14 2:2224 ,3:64

9 2:2152 ,3:192

72

13 2:112

35

10 3:92768 ,4:36896 ,2:312 ,5:128 14 2:1392 ,3:32

8 2:360 15 2:6656 ,3:1728

9 2:7048 ,3:640

73

13 2:40

36

10 4:47648 ,3:175424 ,2:552 ,5:512 14 2:232

8 2:368 15 3:64 ,2:1336

9 2:10568 ,3:832 74

14 2:8

37 10 3:4352 ,2:2344 ,4:192 15 2:184

101

N PSL : N PSL : 8 2:16 16 2:496 ,4:32 ,3:128

9 2:936

75

14 2:24

38

10 2:496 15 2:112

11 3:1728 ,4:192 ,2:264 16 2:352 ,3:32

9 2:104

76

14 2:16

39

10 2:928 ,3:32 15 2:96

8 2:16 16 2:472

9 2:64

77

15 2:72

40

10 2:2472 ,3:128 16 2:152

11 3:17696 ,4:2912 ,2:800 17 2:200 ,3:96

9 2:136 78

21 2:16

41

10 2:120 ,3:64 22 4:16

11 2:384 ,3:352

79

15 2:8

12 3:1376 ,4:1504 ,5:256 ,2:64 16 2:16

42

10 2:24 17 2:48

11 2:40

80

17 2:32

9 2:8 18 2:96

19 2:72 ,3:352

,

, ,

PSL ,

. , ,

.

3.1.4.

1 ,

. , ,

4.

( 3.5).

102

3.5 MPS

N

2 {-2} - 2, {2} - 2

3 {-1} - 4

4 {0} - 8

5 {1} - 4

6 {-2 2} - 20, {2} - 8

7 {-1} - 4

8 {-4 0} - 40, {-4 0 4} - 16, {0 4} - 8

9 {-3 1} - 80

10 {-2 2} - 40

11 {-1} - 4

12 {-4 0} - 56, {-4 0 4} - 16, {0 4} - 56

13 {1} - 4

14 {-2 2} - 72

15 {-1 3} - 104

16 {-4 0} - 32, {-4 0 4} - 48

17 {-3 1} - 32

18 {-2 2} - 16

19 {-1 3} - 8

20 {-4 0 4} - 16, {0 4} - 8

21 {-3 1} - 24

22 {-6 -2 2} - 996, {-6 -2 2 6} - 480, {-2 2} - 552, {-2 2 6} - 996

23 {-5 -1 3} - 3492, {-1} - 12, {-1 3} - 580

24 {-4 0} - 184, {-4 0 4} - 6524, {0 4} - 156

25 {-3 1} - 8

26 {-6 -2 2} - 456, {-6 -2 2 6} - 728, {-2 2} - 296, {-2 2 6} - 456

27 {-5 -1 3} - 2728, {-1 3} - 368

28 {-4 0 4} - 16

29 {-3 1} - 236, {-3 1 5} - 2004, {1 5} - 4

30 {-6 -2 2} - 180, {-6 -2 2 6} - 312, {-2 2} - 16, {-2 2 6} - 180

31 {-5 -1 3} - 1920, {-1 3} - 88

32 {-4 0} - 24, {-4 0 4} - 3340, {0 4} - 12

33 {-3 1} - 128, {-3 1 5} - 984

34 {-6 -2 2} - 112, {-6 -2 2 6} - 152, {-2 2} - 32, {-2 2 6} - 112

35 {-5 -1 3} - 860, {-1 3} - 28

36 {-4 0} - 24, {-4 0 4} - 1264

37 {-3 1} - 32, {-3 1 5} - 408

38 {-6 -2 2} - 24, {-6 -2 2 6} - 80, {-2 2} - 8, {-2 2 6} - 24

39 {-5 -1 3} - 240

40 {-4 0 4} - 452, {0 4} - 4

41 {-3 1} - 4, {-3 1 5} - 116

42 {-6 -2 2} - 12, {-6 -2 2 6} - 8, {-2 2 6} - 12

43 {-5 -1 3} - 96

44 {-4 0 4} - 120

45 {-3 1 5} - 32

103

N

46 {-6 -2 2 6} - 8

47 {-5 -1 3} - 8

48 {-4 0 4} - 32

49 {-7 -3 1} - 828, {-7 -3 1 5} - 354408, {-7 1 5} - 32, {-3 1} - 132, {-3 1 5} - 37304

50 {-6 -2 2} - 5032, {-6 -2 2 6} - 193320, {-2 2} - 32, {-2 2 6} - 2968

51 {-5 -1 3} - 8

52

{-8 -4 0 4} - 86672, {-8 -4 0 4 8} - 103404, {-8 -4 0 8} - 64, {-8 0 4} - 48, {-8 0 4 8} - 68, {-4

0} - 8, {-4 0 4} - 28648, {-4 0 4 8} - 45492, {-4 0 8} - 48, {0 4 8} - 12

53 {-7 -3 1} - 272, {-7 -3 1 5} - 176032, {-7 1 5} - 12, {-3 1} - 4, {-3 1 5} - 13064

54 {-6 -2 2} - 1344, {-6 -2 2 6} - 84084, {-2 2} - 8, {-2 2 6} - 1028

55 {-5 -1 3} - 9516, {-5 -1 3 7} - 86152, {-5 -1 7} - 4, {-1 3 7} - 224

56

{-8 -4 0 4} - 37132, {-8 -4 0 4 8} - 55080, {-8 0 4} - 12, {-8 0 4 8} - 16, {-4 0 4} - 10064, {-4

0 4 8} - 19992, {-4 0 8} - 16

57 {-7 -3 1} - 68, {-7 -3 1 5} - 71596, {-7 1 5} - 4, {-3 1} - 4, {-3 1 5} - 4136

58 {-6 -2 2} - 456, {-6 -2 2 6} - 31484, {-2 2 6} - 268

59 {-5 -1 3} - 2796, {-5 -1 3 7} - 34156, {-1 3} - 4, {-1 3 7} - 36

60 {-8 -4 0 4} - 13080, {-8 -4 0 4 8} - 21132, {-8 0 4 8} - 12, {-4 0 4} - 2952, {-4 0 4 8} - 7160

61 {-7 -3 1} - 12, {-7 -3 1 5} - 24736, {-3 1} - 4, {-3 1 5} - 1216

62 {-6 -2 2} - 84, {-6 -2 2 6} - 9556, {-2 2 6} - 56

63 {-5 -1 3} - 784, {-5 -1 3 7} - 10588, {-1 3 7} - 4

64 {-8 -4 0 4} - 3916, {-8 -4 0 4 8} - 7872, {-8 0 4} - 4, {-4 0 4} - 744, {-4 0 4 8} - 2336

65 {-7 -3 1} - 4, {-7 -3 1 5} - 7752, {-3 1 5} - 268

66 {-6 -2 2} - 8, {-6 -2 2 6} - 2568, {-2 2 6} - 16

67 {-5 -1 3} - 148, {-5 -1 3 7} - 2900

68 {-8 -4 0 4} - 1056, {-8 -4 0 4 8} - 2232, {-4 0 4} - 128, {-4 0 4 8} - 496

69 {-7 -3 1 5} - 1928, {-3 1 5} - 56

70 {-6 -2 2} - 4, {-6 -2 2 6} - 572

71 {-5 -1 3} - 36, {-5 -1 3 7} - 884

72 {-8 -4 0 4} - 208, {-8 -4 0 4 8} - 528, {-4 0 4} - 32, {-4 0 4 8} - 88

73 {-7 -3 1 5} - 352, {-3 1 5} - 16

74 {-6 -2 2 6} - 144

75 {-5 -1 3 7} - 128

76 {-8 -4 0 4} - 56, {-8 -4 0 4 8} - 80

77 {-7 -3 1 5} - 80

78 {-6 -2 2 6} - 8

79 {-5 -1 3 7} - 32

80 {-8 -4 0 4} - 16, {-8 -4 0 4 8} - 40

3.5 .

MPS

N . ,

. , ,

104

,

. ,

21;NN .

3.1.5.

, MPS ,

, ..

,

.

, 1,

,

.

3.6

105;2N

:

1. , , (DHM);

2. , , (DHL);

3. (JACOBI_BIF);

4. (LEGANDRE);

5.

(LEGANDRE_3L);

6. (SVERDLIK_4X);

7. (TWO_PRIME_1);

8. (TWO_PRIME_GOOD);

9. , (YU_GONG);

105

10. , [24]

(SVERDLIK_BOOK).

,

:

1. BARKER 1952 [2];

2. TURIN - 1968 [3];

3. LINDER 1975 [25];

4. KERDOCK , 1986 [64];

5. COHEN , 1990 [26];

6. ELDERS_BOLL -, 1997

[65];

7. COXSON_RUSSO 2004 [27];

8. FERRARA 2006 [68];

9. NUNN_COXSON - 2008 [28];

10. DU_WU_MOW , 2013 [72].

web- [114],

,

.

,

, ,

.

3.6 PSL

105;2N

N

PSL dB PSL dB

2 1 -6,021 LCE 1 -6,021 BARKER

3 1 -9,542 LEGANDRE SVERDLIK_BOOK 1 -9,542 BARKER

4 2 -6,021 LCE SVERDLIK_4X 1 -12,041 BARKER

5 1 -13,979 SVERDLIK_BOOK 1 -13,979 BARKER

6 2 -9,542 LCE SVERDLIK_BOOK 2 -9,542 TURIN


8 2 -12,041 SVERDLIK_BOOK 2 -12,041 TURIN

106

N

PSL dB PSL dB

9 - - 2 -13,064 TURIN



12 2 -15,563

LCE SVERDLIK_4X

SVERDLIK_BOOK 2 -15,563 TURIN

13 1 -22,279 SVERDLIK_BOOK 1 -22,279 BARKER

14 - - 2 -16,902 TURIN








22 3 -17,306 SVERDLIK_BOOK 3 -17,306 LINDER

23 3 -17,692 LEGANDRE SVERDLIK_BOOK 3 -17,692 LINDER


25 - - 2 -21,938 LINDER


27 - - 3 -19,085 LINDER





32 - - 3 -20,561 LINDER

33 - - 3 -20,828 LINDER

34 - - 3 -21,087 LINDER

35 4 -18,840

TWO_PRIME_1

SVERDLIK_BOOK 3 -21,339 LINDER


37 4 -19,323

LEGANDRE_3L

SVERDLIK_BOOK 3 -21,822 LINDER

38 - - 3 -22,053 LINDER

39 - - 3 -22,279 LINDER


41 4 -20,214 SVERDLIK_BOOK 3 -22,713 COHEN

42 5 -18,486 LCE SVERDLIK_BOOK 3 -22,923 COHEN

43 4 -20,628 LEGANDRE SVERDLIK_BOOK 3 -23,127 COHEN


45 - - 3 -23,522 COHEN


47 4 -21,401 LEGANDRE SVERDLIK_BOOK 3 -23,900 COHEN


49 - - 4 -21,763 ELDERS_BOLL

50 - - 4 -21,938 ELDERS_BOLL

107

N

PSL dB PSL dB

51 - - 3 -24,609 KERDOCK

52 4 -22,279 SVERDLIK_BOOK 4 -22,279 ELDERS_BOLL

53 5 -20,506

LEGANDRE_3L

SVERDLIK_BOOK 4 -22,444 ELDERS_BOLL

54 - - 4 -22,607 ELDERS_BOLL

55 - - 4 -22,766 ELDERS_BOLL

56 - - 4 -22,923 ELDERS_BOLL

57 - - 4 -23,076 ELDERS_BOLL


59 5 -21,438 LEGANDRE SVERDLIK_BOOK 4 -23,376 ELDERS_BOLL



62 - - 4 -23,807 COXSON_RUSSO

63 6 -20,424 SVERDLIK_BOOK 4 -23,946 COXSON_RUSSO

64 - - 4 -24,082 COXSON_RUSSO

65 - - 4 -24,217 COXSON_RUSSO


67 5 -22,542 LEGANDRE SVERDLIK_BOOK 4 -24,480 COXSON_RUSSO

68 - - 4 -24,609 COXSON_RUSSO

69 - - 4 -24,736 KERDOCK


71 5 -23,046 LEGANDRE SVERDLIK_BOOK 4 -24,984 FERRARA

72 6 -21,584 SVERDLIK_BOOK 4 -25,105 FERRARA

73 6 -21,703

LEGANDRE_3L

SVERDLIK_BOOK 4 -25,225 FERRARA

74 6 -21,822 DHM 4 -25,343 FERRARA

75 - - 4 -25,460 FERRARA


77 6 -22,167 JACOBI_BIF SVERDLIK_BOOK 4 -25,689 FERRARA

78 6 -22,279 LCE SVERDLIK_BOOK 4 -25,801 FERRARA

79 6 -22,390 LEGANDRE SVERDLIK_BOOK 4 -25,911 FERRARA


81 - - 4 -26,129 FERRARA

82 7 -21,374 LCE SVERDLIK_BOOK 4 -26,235 FERRARA

83 6 -22,819 LEGANDRE SVERDLIK_BOOK 5 -24,402 NUNN_COXSON

84 - - 5 -24,506 NUNN_COXSON

85 - - 5 -24,609 NUNN_COXSON

86 - - 5 -24,711 NUNN_COXSON

87 - - 5 -24,811 NUNN_COXSON

88 7 -21,988 SVERDLIK_BOOK 5 -24,910 KERDOCK

89 6 -23,425 SVERDLIK_BOOK 5 -25,008 NUNN_COXSON

90 - - 5 -25,105 NUNN_COXSON

91 - - 5 -25,201 NUNN_COXSON


93 - - 5 -25,390 NUNN_COXSON

108

N

PSL dB PSL dB

94 - - 5 -25,483 NUNN_COXSON

95 - - 5 -25,575 NUNN_COXSON


97 7 -22,833

LEGANDRE_3L

SVERDLIK_BOOK 5 -25,756 NUNN_COXSON

98 - - 5 -25,845 NUNN_COXSON

99 - - 5 -25,933 NUNN_COXSON


101 6 -24,523

LEGANDRE_3L

SVERDLIK_BOOK 5 -26,107 NUNN_COXSON


103 8 -22,195 LEGANDRE SVERDLIK_BOOK 5 -26,277 NUNN_COXSON

104 - - 5 -26,361 NUNN_COXSON

105 - - 5 -26,444 NUNN_COXSON

3.6 MPS

,

, ,

N .

3.2.

1, 2

:

.

PSL

,

, ..

))min(max()(1

0

N

nnn aaAPSL , 1,...,2,1 N . (3.6)

. ,

,

merit-factor:

109

1

1

21

0

2

2

)(N N

nnn aa

NAMF

. (3.7)

)(AMF ,

.

3.8 ,

, :

1 - N - ;

2 - )(min AMF -

N ;

3 - )(max AMF -

N ;

3.7

N )(min AMF )(max AMF N )(min AMF )(max AMF

2 2 2 41 5,125 7,504

3 4,500 4,500 42 5,919 8,733

4 4 4 43 4,997 6,748

5 6,250 6,250 44 4,990 6,286

6 2,571 2,571 45 5,329 6,575

7 8,167 8,167 46 6,491 6,491

8 2 4 47 7,126 7,126

9 2,025 3,375 48 4,800 6,128

10 3,846 3,846 49 2,858 8,827

11 12,100 12,100 50 3,117 8,170

12 2,769 7,200 51 7,517 7,517

13 14,083 14,083 52 2,759 8,145

14 5,158 5,158 53 3,094 7,890

15 3,214 4,891 54 3,321 7,327

16 3,556 4,571 55 3,267 7,451

17 4,516 4,516 56 3,039 8,167

18 6,480 6,480 57 3,198 7,963

19 4,878 4,878 58 3,586 8,538

20 4,348 5,263 59 3,559 8,328

21 5,803 6,485 60 3,346 8,108

22 2,547 6,205 61 3,620 7,563

23 2,383 5,628 62 4,116 8,179

24 2,323 8 63 3,853 9,587

110

N )(min AMF )(max AMF N )(min AMF )(max AMF

25 7,102 7,102 64 3,657 9,846

26 3,101 7,511 65 4,001 8,252

27 2,826 9,851 66 4,605 7,751

28 6,759 7,840 67 4,341 7,766

29 3,138 6,782 68 4,143 8,438

30 3,435 7,627 69 4,119 7,988

31 3,269 7,172 70 4,649 7,313

32 3,048 7,111 71 4,574 8,105

33 3,781 8,508 72 4,730 7,200

34 4,219 8,892 73 4,934 8,327

35 3,804 7,562 74 5,645 7,039

36 3,560 6,894 75 5,277 7,878

37 4,026 6,985 76 4,997 7,113

38 5,348 8,299 77 5,510 6,959

39 4,447 6,391 78 7,548 7,548

40 4,255 7,407 79 5,623 7,308

80 5,369 6,349

3.3.

. ,

.

. [115],

.

, ,

,

, . ,

,

. ,

N ,

.

, ,

111

,

. .

3.3.1.

( )(AL ),

,

.

-. ,

.

, 2 . 3.8

, ,

:

1 - )(min AL - ;

2 - N

AL )(min - ;

3 - )(max AL - ;

4 - N

AL )(max - ;

3.8

N )(min AL

N

AL )(min

)(max AL

N

AL )(max

N )(min AL

N

AL )(min

)(max AL

N

AL )(max

2 1 0,500 2 1 41 40 0,976 41 1

3 2 0,667 3 1 42 40 0,952 42 1

4 4 1 4 1 43 42 0,977 43 1

5 4 0,800 5 1 44 40 0,909 44 1

6 4 0,667 6 1 45 40 0,889 45 1

7 3 0,429 4 0,571 46 44 0,957 46 1

8 6 0,750 8 1 47 46 0,979 47 1

112

N )(min AL

N

AL )(min

)(max AL

N

AL )(max

N )(min AL

N

AL )(min

)(max AL

N

AL )(max

9 6 0,667 9 1 48 44 0,917 46 0,958

10 8 0,800 10 1 49 27 0,551 49 1

11 10 0,909 11 1 50 40 0,800 50 1

12 6 0,500 11 0,917 51 48 0,941 51 1

13 12 0,923 13 1 52 28 0,538 52 1

14 9 0,643 14 1 53 52 0,981 53 1

15 10 0,667 15 1 54 40 0,741 54 1

16 10 0,625 16 1 55 40 0,727 55 1

17 16 0,941 17 1 56 30 0,536 56 1

18 16 0,889 18 1 57 54 0,947 57 1

19 18 0,947 19 1 58 56 0,966 58 1

20 8 0,400 19 0,950 59 58 0,983 59 1

21 17 0,810 21 1 60 32 0,533 60 1

22 20 0,909 22 1 61 60 0,984 61 1

23 11 0,478 23 1 62 45 0,726 62 1

24 14 0,583 24 1 63 36 0,571 63 1

25 24 0,960 25 1 64 52 0,813 64 1

26 24 0,923 26 1 65 52 0,800 65 1

27 20 0,741 27 1 66 60 0,909 66 1

28 21 0,750 27 0,964 67 66 0,985 67 1

29 28 0,966 29 1 68 60 0,882 68 1

30 22 0,733 30 1 69 57 0,826 69 1

31 20 0,645 31 1 70 59 0,843 70 1

32 22 0,688 32 1 71 70 0,986 71 1

33 30 0,909 33 1 72 61 0,847 72 1

34 24 0,706 34 1 73 72 0,986 73 1

35 27 0,771 35 1 74 72 0,973 74 1

36 26 0,722 36 1 75 8 0,907 75 1

37 36 0,973 37 1 76 72 0,947 76 1

38 36 0,947 38 1 77 73 0,948 77 1

39 36 0,923 39 1 78 76 0,974 78 1

40 35 0,875 40 1 79 78 0,987 79 1

80 74 0,925 80 1

,

, 1)( AL , ,

.

113

3.3.2.

,

,

[14].

. ,

,

, .

),...,,( 110 NaaaA - N ,

}1;0{ia , 1,...,1,0 Ni .

1n 0n :

1101 ... Naaan ,

10 nNn . (3.8)

sn1 sn0 s -,

.

:

1. : 110

11 nn ;

2. ssss nnnn 22 0011 , Ts 2log,...,2,1 ;

3.

.

( 3.9).

114

3.9

N

2 1 1 4 2

3 1 1 4 4

4 1 0 8 0

5 1 0 4 0

6 4 2 28 6

7 1 1 4 4

8 8 1 64 8

9 10 8 80 36

10 5 1 40 4

11 1 1 4 4

12 16 2 128 16

13 1 0 4 0

14 9 0 72 0

15 13 0 104 0

16 10 0 80 0

17 4 0 32 0

18 2 2 16 8

19 1 0 8 0

20 3 0 24 0

21 3 1 24 4

22 378 76 3024 304

23 515 169 4084 772

24 858 66 6864 276

25 1 0 8 0

26 242 34 1936 136

27 388 124 3096 572

28 2 0 16 0

29 284 56 2244 232

30 86 4 688 16

31 251 106 2008 484

32 422 38 3376 156

33 139 18 1112 76

34 51 5 408 20

35 111 28 888 120

36 161 20 1288 80

37 55 3 440 12

38 17 1 136 4

39 30 8 240 32

40 57 0 456 0

41 15 1 120 4

115

N

42 4 0 32 0

43 12 7 96 36

44 15 3 120 12

45 4 0 32 0

46 1 0 8 0

47 1 0 8 0

48 4 1 32 4

49 49088 11179 392704 46892

50 25169 2179 201352 8716

51 1 0 8 0

52 33058 2306 264464 9896

53 23673 5065 189384 21044

54 10808 936 86464 3744

55 11987 1417 95896 5772

56 15289 1513 122312 6452

57 9476 1879 75808 7760

58 4026 303 32208 1212

59 4624 426 36992 1732

60 5542 333 44336 1452

61 3246 543 25968 2232

62 1212 97 9696 388

63 1422 133 11376 536

64 1859 142 14872 600

65 1003 158 8024 652

66 324 17 2592 68

67 381 32 3048 132

68 489 17 3912 72

69 248 33 1984 132

70 72 4 576 16

71 115 10 920 40

72 107 9 856 36

73 46 5 368 20

74 18 0 144 0

75 16 1 128 4

76 17 0 136 0

77 10 0 80 0

78 1 0 8 0

79 4 0 32 0

80 7 0 56 0

,

80;2N .

116

3.4.

.

,

N . ,

,

PSL 2 5.

( 3.2). 3.10

MPS PSL.

3.2.

3.10

PSL PSL = 2 PSL = 3 PSL = 4 PSL = 5

O(20.71.42N

) O(18.31.57N

) O(9.91.7N

) O(6.91.79N

)

117

, ,

,

.

3.5.

.

.

,

, .

,

. -

, , -

, ,

-.

, ,

.

- .

,

, ,

118

,

.

,

,

.

,

,

.

119

4.

:

1.

.

2.

.

4.1.

N

.

, ,

, . ,

, ..

.

. ,

, :

;

;

;

, ,

120

, .

, ,

. , ,

,

.

, ,

,

.

, ,

.

. ,

76N

1 2000000 .

.

, ,

.

.

- .

, ,

,

.

,

grid, :

,

, .

,

.

121

,

, .

,

:

;

,

.

,

, , N

:

int find_even(unsigned long long int leftCode, unsigned long long

int rightCode, unsigned int partN)

{

addPartialCodesLength(leftCode, rightCode, partN);

if (checkReverseCode(leftCode, rightCode, partN))

{

if (WeightTable[getWeight(leftCode, rightCode,

partN)][partN])

{

if (partN != m_N_2)

find_even(leftCode, rightCode, partN);

else

{

bBranchValid = true;

if (checkRemainingSidelobeEven(leftCode,

rightCode, partN))

saveCode(leftCode, rightCode, partN);

}

}

}

incCode(leftCode, rightCode, partN);

if (checkReverseCode(leftCode, rightCode, partN))

{

if (WeightTable[getWeight(leftCode, rightCode,

partN)][partN])

{

if (partN != m_N_2)

find_even(leftCode, rightCode, partN);

else

{

122

bBranchValid = true;

if (checkRemainingSidelobeEven(leftCode,

rightCode, partN))

saveCode(leftCode, rightCode, partN);

}

}

}

incCode(leftCode, rightCode, partN);

if (checkReverseCode(leftCode, rightCode

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