Some Problems on Data Communication Systems

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SOME PROBLEMS ON DATA COMMUNICATION SYSTEMS Mao Xu-jin I nllillll!'

()t

.1111()/lIlIliul/ , Ami/I'll/ill Sil/im, B riji l/g. PRC

Abstract . This paper deals Kith transmi ssion line ch aracteri stics , keying technique , multichaILnel transmi~silJn and so fOI'th, A modified cost a s l oop is gi\,p.n "h ic h b">'al"p s I·"ry""ll. Tt I'"fel's to tf)" simple struct ure, 101, cos t and hi gh re liab ility. Addi tionally, an applicati! 'n of \!fals h funcli(ln is shown.

Furthermore, in this paper, \\'e

will attempt to s>,u" >' OK modern control t heory can be use d in

communi~ati on

syste~s .

Key"ords . Cu~munication control app l ications; Codi ng; State - space m" t >' ods ; l dpntifi cation; P"ase - Ioc '< ed loops. 1 'ITRO[)l'CT10)1

It "ill be changed with t he frequen~y, t~pn . the different par ts of the signa l spectr um Kill pro pagate at di fferent speeds . It i~ the phenomenon

I n data communicatio n syste;ns \\'e are concerned in

a great number of sub.jects to do

resea r ~ >',

such as

trans~ission

methods, codes , networl{ structures, link ~o ndi ti unin g, equalizati vns . error detect te chni q ups , communicati(n protocols, ~tc. This paper

I{no~n

NOW , our goal is to obtain the model stl'ucture and its parameters of trans mission lines, fortunately

does not dpa] with prublems mentioned alr"ady above, only that it investigates line characteristics , ':eying technique , detect lIcthod of th" carrier and ~u] ti - ch an ne] techniqup. It is suggested that there is a broad field of using mudprn control theory in data

~o mmunica tio n

There are many

diffcr'e!l~

o~l\'

tr ansmissiun line.

We no" let u lt) is a pseudo-random-binary- sequencp IPRBS I input to the transmi ssion line, vll) is tf)e re su l ting output , ~ is th" estimation o~ t~e

co~municati o n

take account of the

inpulse response of t he t r ansmission

'

T~us ,

1 am . . = m+l ~U (J)U (J-K) J =(

HI. i" I; IHl jWII ex;> .i il l" ) (11 is the ~agni l ude - fre qucncy character is~ i c, B (\\·' is the ph ;} se anQle - frf' quency c~arac ­ te ristic.

I

I H ( , 1\\"

lin~ .

,,'e have the autoco rrelation function fOI' innut :

Let H (.jh·) is the trar.sfer· functipn of the transmis sion I i~e , lhu~ ~e 11R\'e ....·t,ere

identifi-

cation has been de\'eloped and a lo t of identification ~ et f) o d s are already ~. i\'('n . 'nd tf)" ~ross-· correl a tio n identifi~ation used to attain the in pulse response of an obj ect is available .

systems .

ty pes o f

Here, Ke Sf)R: I

svste ~

since t wenty years and more , the

IIOIJELLI :-JG OF COI!)IL'NICATlO'J C: IA'I'iELS

channe ls.

as si gnal d ispersion.

and

t ~e

cross-corTelation function for

j nrJu~

;:l'

i

o utput:

~yu (K.)

Equat i on I I) 11 a,l" be a I so den ote d by

i+m.

1

.

= m + 1 LU J-I<)Y(l) C

I
J =1 \\'~ere ('o~parj

ng equat iOrl8

~

I)

and

(~ l,

\lne

.,~S

i is an-jlriitrary pnsiti,- e integer and

L'si ng PRBS an o\·e , h·e

in~ut

calcul at ina, fO!'llul
ohta in

0.:

thus

eX. 1,,1 ~

o/t
;-111 1H' ,j" : ', I

1 '., ' ; -

BI "

N CP~Jo

I

ll:.te r es":i!lg quan:i:y fur' :~le tr'arS 1l 1ssion line is t~e ti "Tie delay uP ~r"lup de l ay Jefin e j by :\r-,

- de(w) dw

)

cjJ

'''~

9"" ( p)

C')"

cjl"<-I ( P-I)

4'~" (0)

4'",,(0) ( ~

11

s >, ould be b ig enough.

the resul t :

\

1 2

0.

I

-7V I

-N I

- 'N 65

I

-fi I

-'N _.1. N

, h i

~[ a() Xll ~ji ll

66

""here a is the amplitude of PRB S , P is an integer, ~T is the period of PRBS, and T is the sample period. Additi onally , we may have

Z 1 1 2

Let verify Fig. 1 , i t wi 11 re'1l i nd us that it is a phase angle regu l at ing syste-n . i .e, PJ.L , The open transfer funct i on of this by

( 1)

1

6 5+ b. + Q;t S2 +

Z-

Selecting

is given

1

F(s) 53

1 1

s:y'stwll

a,s

(13 )

Xl ; 9 , X 2 =DX 1 ... a Z 9, and X3 ;DX +a e - b . e , 2 1

and we have

h=

(S )

Q2 1 0

XI

-ll., 0

X2.

4>y'r( K) It is obvious that the approach mentioned above for the trans mission line identification is effective and may be calculated off line by a micr ocomputer .

KE YING

TECH~IQUES

A~D

Xl

0 0 0

Xl

+ b, E

(14 )

b.

Xi

Furthermore, ,.e obtain X;AX+BE

(10)

and

When lines in the data transmission are longer than several kilometers, the keying technique is commonly u~ed, and the differential phase shift keying ( DPSK) is a better one . I n order to attain the 2- DPSK message, we may obey following principles:

(SI

-

BC T) X

A +

(16 )

B'

where XI

x,

X

~I

The peM signal is transformed i nto difference code suc'o as that

a.

A

(g)

where d· is the ith b it of difference, b· is the it h bit 10f binary code, and is an integer. The secquence d

0

9;c Tx

CODE RETRIE VAL

d. 1. =(d 1-1 . + 1,1' ) mod 2

XI

_11,

0

0

0

0

0

is modul ated in such a way:

bl

B

b.

e -r

c

10

0

I

E

0 0

where , is the output of the modulator, k is a constant and T, is th~ code period . A simple circuit to generate 2- DPSK has been de signe d and i t has a lower code error prabab ility which can be expressed by

P=

~ (1Z

where

erf

J.2.:/. N.E. )

(11 )

e

0 0

Ho~ever ,

the non linear characteristic in a system

is usually inevitable, it may be sketc hed in

x

Here

er f =-Z- j e.xp

mo

and

( _ X2)

dx ,

Fig.~.

( 171

(12 )

is the power fre quency spectrum densi ty and E. is the ""ave energy.

'i.

It is important that t'oe receiver terminal should correctly retrie\'e the PO!. Fortunately. we ha\'e a \'ery effectiv .. s k.. tc h sho,m in Fig. I which is des i gned by t'oe lab led by t'oe auther of this paper . It is a modi fi .. d type of the Costas loop . In Fig. I , L is an amplifier and al1plitude l i miter ,

and S(e) is t~e non linear fact or which is the function of e. According to the Popov c r ite rion, if 'It 0 I

;

0

and N (e )

0< t~ere

exists a

e.


li~i te d

e -:;t

0

(] 8)

constant q suc h t hat the re

are

E 1- E..., are four exclusive - or gates used as modems, F is the filter and compensator, T , G l and G2 con -

sititute the voltage ~ontrolled oscill a to r, ~ I ' Q~ and 03 are three D-type triggers and DI , D. are the registers to perform the function shown in- equa tion (9) Correspo nd i ng \\"ave s are

s~own

in Fig . .~ Khi c'1 can

be used to de l1 0nstrate the working principle of Fi g. 1. We now have t he so c alled pseudo difference code signal v (t) , the PC~ output f (t) which is wan ted to retrieve .

K f o r all the w > O, then t" " syste Ol is globally asymptotically stable. We may notice t"at !'ig . as fo110\'5:

has a 10

.)f advantages

It is very si~ple in str ucture and quitf' different from t"e tradition . ~ verific ation in ~ractice has been ta~en as that orobability of code e rr or is less than lxlO-' . Its cost is low and it is easy to integrateinachip.

SOllle Pr oh le llls oil Data CO llllllllllica tio ll S,·s te lll ,

APPLICATION Of TRAC'lS)1I SSI ON

flNCTION

~ALSH

MlLTI - CHANNEL

I~

Today, two basi c tec'lni que s are commonly used for multiplexing: frequency division multiplexing (fD,t) and ti me d ivision mult i plexing (TD)I). Act ually, there is code divisiun except fDM and TD~. ~alsh function can be used in this field. Mu lti - channel transmitting signals at t'le input node will be denote d by 1'l

L,

S. (t) Cj ( t ) ( ~Ol J J: L ,·;here n is an integer as ~ he o rder of c~annels, S (tl is the jth me ss age and C (tl is the jth carrier. S( t 1 =

50 ', (t)

,

K:l •

",,",el'e reprents the cut - off frequency of the filter and k is an integer. In order that signals in different channels do not disturb each othe r a group of ccndi t ions should be ruled as 'f

j •C.I (t) Cl( ( t)

d t :::.

0

Thus, we need that all the C; , CK (i=k ) are ortho gonal and Walsh function is a known one in this field. IValsh function may be deri ve d from several approa-, ches. t!sing Rademacher function. we have one of def i nitions for ~alsh function as follows: gefinition: Walsh functicn can be expressed by p-, ~

WQlcn,t)::=

tP_'_lCgk

(_1)",:0

(~3

The base of designing fig. 4 is equation (""I. Its distinguished merit is without race hazard because of no t"o or more than t",·o logical states changi n g at the sal1e time. finally, let us pay attention to t~at IValsh function is generated not only by hard"'are , but also by soft;'are. The detail is no l onger described.

Th is paper has presented some questions in data tr ansm issions as follows:

T

=5 , (t) L JC.(t)Ci(t)~t ( 211

+-

So called "kno"'n" items in Table 1 mean that they are easily obtained from a binary co ur.ter , and a IValsh function generator can be de s igned as sho",n in fig. 4 Here E" Eo are two exclusi\'e- or gates, OSI is a crystal ~sc i[lator, and Gc is a Gray code counter ,,~ich is easy to be realized.

CONCLL'SIO"S

Ne can obtain the ith retrie ve d signal as f ol lows n

tij

The modelling and ider:tification of the transmis sion line has been proposed. A modified Costas loop has been designed , arJ an analysis is given. This loop has a siOlple strllC ture, l a " cost and hig~ reliabili ty . A IVa) sh function generator whi,,~ is free fr om race hazard is designed. Applications of modern control t heory in data communications are suggested .

REfERENCES Bell,D.J., Cook, P . A. , ~Iunro (Ed.) (l9i'21. Design of ~odern Co ntr ol Systems. Peter Peregrinus Ltd. , Stevenage and New York. PP . 210 - 2~ 0 Beauchamp, K.G. (19751. IValsh functions ancl Their Application . Academic Press. Coates , R.f.IV. (1975). ~Iodern CommunicationSystems . The Macmillan Press Ltd . , London and Basingstoke.

)

where n=O,1,2 .... ,N 1 :.,r=~P, P is an integer, t is

Gilbert He l d (19791. Data Communication Components. Hayden Book Company, Inc. PP . 91 - 100

Equation (23) may be also transferred as follows:

Hsia T.C. (19771 . Syste m Identification - LeastSquares Meth ods. D. C. Heath and Company, Lexing, Massachusetts Toronto.

the generalized tim~ and gk is the kth bit of Gray code.

IVilliam Si nnema (19 8 "1 . Digit al, Analog, and I)ata Commun ic a t ion. Re ston Publis~ing Companv, Inc., A Prentice -Hal l Company, Rest on . Virginia.

~ -,

IVal (n, t) =

L,,)t P-,-K ( nx Gl nit.. ) K=o

i 24)

PP.

where [O J represen ts the SUl1 for mod 2 and ® is exclusive - OR. Owing to t~e s~mlle try of walsh function , equation ( !4) may be deduce d in

\~al(n , tl

p- ,

=

2. ,2Jnp_ I_KC f.tiJf,,-I)

(251

K:::.o

Additionally, one l1ay orove that i;a](n, tl Wal (m, tl =IVaI1n @ m, t l and N' if n=m,

',al \n ,t l Wal\n, t l ={

(

~6

0, if n=m.

Equations (2 4 1 (251 and I !61 may be used to perform the Walsh function generator. For example, supposing p=3, n=O,l t=0 , 1,2, ... 7, we have Table 1:

TABLE 1

, ~ ,

... ,7,

Components of Walsh function w al~o,t\

Wal I, t)

Wal ( ;, t)

kno "." k nOK!1

w~~ ~ ~... t 1 IVal ( 3 , t 1

IVal (3, t) Wa1\4,t l =\;al ( 3, t 1 \,al (7 , t 1 l~al(5,tl = l~al i c , tl i~al ( 7 , t) Wa1l6,t l =Wal(l,tl IVal(7,t l IVa l (i,t) Imo"n

'2 59- ~ 77

7e n g fen gc hi (191111 . An analysi s and de\'e! opme nt of a digitized Cost as phase loc ked loop. Acta Automatica Si ni ,~ a , -, 312 - 318

1

~Iao

68

XlI -jill

w .. lu ,O

+

17

Fig. 4.

I Modifie d Costas loop

Pig . 1.

f.(t~ -I'(t)

~o

1

~

"'"

tj(t)

Vl'( tlLJ~~

I '--__ _---"1

I

+,.ltl

f,,(O 1

Pig . 2 .

Fig.

3.

1

Waves fo r P ig . 1

Block diagram of PLL

~


Wa lsh function generat o r