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Page 1: Broadband hybrid analog/digital CATV trunk network

1EE.L'lKANSACl'IONS O N BROADCASTING. VOI.. 41. NO. 8, SEPTEMBER 1999 83')

Broadband Hybrid Analog/Digital CATV Trunk Network Jyh-Ping Lee, Shyh-Lin Tsao.t, a n d Hcn-Wai 'J'sao

Department of Electrical Engineering, Lab, 653 National Taiwan University Taipei, TAIWAN, R.O.C.

E-mail address: [email protected]".tw .+ Department of Electrical ~nginecr ing,

Yuan Ze University Chung-Li, TAIWAN, R.O.C.

Abstract ~ In t h i s paper, d i g i t a l s igna l s are exter- na l ly i n t e n s i t y modulated i n a w i d e b a n d SONET for- mat t o g e t h e r wit ,h a n a l o g TV s igna l s b y u s i n g SCM techniqucs. We also e m p l o y OAs(op t i ca1 amplif ier) to ampl i fy the s igna l s i n t h i s trunk n e t w o r k to increase t r ansmiss ion d i s t ance . A c c o r d i n g to onr result, the C- NR of the analog c h a n n e l s is larger than 49.5 dB and the BER of the SONET d i g i t a l channel i s less than IO-' at the rece ive r s of all headends. In this s y s t e m , the 3rd order n o n l i n e a r d i s t o r t i o n s h a v e been taken i n t o account. We present a method to a n a l y z e the 3rd order n o n l i n e a r dis tor t , ions.

Indezing Terms:CATV, SCM, SONET, O p t i c a l Amplif ier , Tsunk N e t w o r k

I . INTRODUCTION

CATV transmission systems have been widely stndied[l,Z]. Ry employing subcarrier multiplexing tcchnique(SCM), multi- chmnel T V signals can be transmitted in a singlc mode fiber. In additon to transmitting analog T V signals, i nmy topic- s about digital video transmission by using SCM technique have also becn shdied[3-5]. In diracl modulation systems, lvscr clipping noise and hsrr chirping cffect limit the nom- ber of chunnels and thc ttvusrnission performi~nce[6-8]. The literaturas about SCM syslems employing external modula- tion, ph tm or internsity modulation, have bccn presented for varioos applicatians[9-1 I]. The second-order distortion can be nulled ou1[12] and there is no chirping and clipping cffect[8] by insing external modulation.

SONET is B well ora,gniacd TT)M optical commnnicatian s- t , i d a r d for massive digital transmission scrvices[8]. It is suit- ddc lor high capacity digilal transmission services. In this pa- per, we considcr lransmitting the AM T V signals and SONET signals togethcr t o salisfy this reqoircrncnt. This transmissiou systcm can be connectcd convenienlly with other optical long distance networks employing SONET.

In order to provide additional services in thc CATV net- works, we can lransmit the digitid da t a by SCM lcchnique in the higher frequcncy b a d In lhis trunk uetwork, the ana- log T V channels are 1uc:ated in the frcqnency band from 50 to 660 MFIz and a ainglc digital channcl from 560 MHz to 1 CIIz. Tho center frequcncy of digital channel is assigned as 841 MIIz for currying an OC-3 SONFI' digital signal. We crnploy external intensity modulation and dircct delcction in I.liis system to climinate the chirping effect. '3 compensatc the power loss in this trunk nctwork, we

employ optical amplifiers t o amplify the SCM optical signal power aftcr a certain period of length. Unfortunately, opti- cal amplificr generatcs ASI.:(amplified spontaneous emission)

noise which will degrade the performance. These i m p x l fac- tors on the system should be considered carefully for obtaining better performance. We will analyze the performance of such a transmission system in this paper.

11. OPTICAL AMPLIFIER

We discuss the performance of trunk network transmitting analog and digital signals in diffcrcnt band simultaneously in a fiber. There are two kinds of optical amplifiers. Onc is semiconductor amplificr, the other is fiber amplifier. All of them c m boost the signals by amplified stimulated emission In additon to amplifying the signals, there are ASF, nosic in the output which may degrade the performance. The noise term after optic$ vmplifiwtion can bc represented as[8]:

6 = 4, + &f + O:i,=*sE + &E=ASE (1)

/Lt = zqn(GP., + s ~ ~ ~ B , , ~ ~ R (a) d L g , ~ s s = 4(RGPtn)(RSnscB) ( 3 )

&E=ASE = RZSasc(2Bopt - B ) R (4)

SASE SE = qqn,,x(G - 1) ( 5 )

where

u : ~ ~ , is the power of shot noisc, R is the bandwidth of pho- tadeteclion circnit , Rapt is the bandwidth of optical signals, G is the gain of apticvl amplifier, P,, is thc optical power of input signals, and SASE is the power spectrum density of ASE. The dominant factor is o:ig=A,sR.

I I we consider only the mast important noise component, the SNR will he

111. ANALYSIS OP THE W I D E B A N D TRUNK NRTWORK

A System architecture

The system architccturc of this trunk network is shown in Fig.1. We modulate thc optical carrier by an external modu- lator. We transmit the analog T V signals in sequentid chan- nels with a channel spacing of 6 MHs. Simullimcously, we can transmit the digital signals in a single channel whose bartd- width is 311 MHz. The centcr frequency of the digital chan- nel is 844 MHz. The digital signals are in the same farm as SONET(0C-3). We can use cither OOK or BPSK to modu- late the digital subcarrier. The frequency band arrangement is shown in Fig.2.

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340

When light propagates down the trunk network, each head- end absorbs some optical power. The power will further decay because of the fiber attenuation. Therefore, the optical power in the trunk network will decay as thc transmission distance is long. Ib overcome this degradation, we must employ OA's to boost the optical power during transmission. However, the

Therefore, we must analyze the system performance carcfully

Let us consider the simple case where the paramcters in each section are the same. Then

(1 - D ) ~ - ' Z P ~ (14) , i i - I 10-n,r./io, n-o, .!"'/IO pk = (aG)

And a t the last headend of the kth section,

ASE introduced by OA will also degrade the performance.

bcfore implementation. , = I

B Performance analysis

Assume the optical power of lransmitter is Po, and

h--2

$sa = &[(G - 1)X(Ga)" ' - ' + (C ~ I)]

r : , n - U / ' . " I ' ~ J O - O " l ' O

Ca[l- GO^)^-'] 1 - G a = Ea(C- I ) [ + 11

(15) z lo-u , r . ~ / l o l o - o ~ / l o ,

Po = Rr.ii(h - It!,), (7)

where Ib is th r d.c. bias current of laser diode and Ithis the

where L , is the fiber length between optical amplifier and headend.

threshold current. We employ external modulation technique ,v, T , ~ ~ ~ DISTOKI'ION ANALYSIS OF in this system so that the output optical power of transmitter can be represented as[lZ]

hM-VSHISONE'1' SYSTEM

po( t ) = Ri,n(Ia - I t h ) ( l + S i n s ( t ) ) (8) A The 3rd order distortion induced by three analog channels

where d ( t ) is thc SCM signal term. From the master headend to the iV - th headend, the light signal will go throuth M optical ampilfiers. The total distance is L km. Therefore the received optical pawer at the N - th headend can be repre- scnted as

In this section, we will investigate the 3rd order nonlinear dis- tortion noise in such an external intensity modulation trans- mission system. From [la], we know that the 2nd order distor- tion c m be nulled out. The dominant distortion term is the 3rd order distortion noise produced by the nonlinear effect of

p = G M ~ ( I - z ) N - l l O - - a = N / l O 1 n - - a i L / l O p ~ (9) the external intersit" modulator.

where D is the coupling ratio ol the coupler, ac is the coupling loss coeflcent (in dB), C is the gain of optical amplifier (in dU), , and aj is the loss coefficent of the fiber. Define

i = l

, then the received optical power at the r-th headend of the k-th section is

7-1

x f l ( 1 - " ! X ) ) Z ! ~ ) P , (11) ;=I

where L!"is the distance between the Mth OA and the (k l ) t h hendend. The ASE noise can be represented as[8]

The 3rd order distortion can be dividcd into four types far convenience. The first typc is the analog band 3rd order nois- es produced by the analog channels. The second type is the analog band 3rd order noises produced jointly by the digital and the analog channels. The third type is the digital band 3rd order noises produced by the analog channels. The 4th type is the digital band 3rd order noises produced jointly by the digital and the analog channels. From [IO], the speclrum of the 3rd order distortion is equal to the convolution of threc spectrums of the baseband signals. If BA represcnts the band- width of analog channels and BD is the bandwidth of digital channel. The bandwidths of the 1st and 3rd types of 3rd order distortion noise will both be 3Ba. The bandwidth of the 2nd and 4th types are both 2Bn +Bo. According to [Ill and [13], the 3rd order distortion noise induced by the analog signal channels can be represented as:

IMP3 = h a 1 1 2 K n p ~ / 3 2 (16)

where

KA = N ~ ( N A + 1)/4 + ((Nn - 3)2 - 5)/4 (17) k--2 k-1

sy;;) = E,[C(G~ - 1) G , ~ , + -1)la', (12) , P A is the modulation index k t h c analog channels, I is the reccived d.c. photo-current, Nn is the number of analog chan- nels. and

,=I ,=$+I

s_", S,(f) * sj(f) * sii(f)lfIBP(f)\'df where E, = hfn,,x, a: is the coupling ratio of that headend. Therefore, the SNR can be obtained as

ha1 = (18) S _ " , S , ( f ) * S , ( f ) * S h ( f ) 4

( I 3 ) where H D p ( f ) is the transfer function of the band pass filter of a single analog channel.

(RPx)' u:h + 4R2PhSy;i)B'

S N R =

Hence, we can estimate the RER of the digital signals and the SNR of the analog T V signals according to the above results.

The dominant term of the previously mcntioned first type of the 3rd order distortion noise is f,+ f 3 - f 7 . In the first case,

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341

we assume that the nonlinear intermodulation components are let 11.1 < n? < n3. Let v i 1 +nz+nS = n = b- [2fm,n/A f1, k > located in the k , ~ , channcl. N n . Because nz < n3, we have nl > n - 2n3. Case 1: l 'hc first ~ a s r wc will consider is k 5 Na. Let If 3 5 n - 183 5 N A or n N A 5 5 n - a) and f a = f">,,,+nlAf, fj = fm,,+iizAf, and f k = fTni,,+naAf 0 5 n - 2ns 5 N n (or & % n3 5 ;) then 7~~ + n2 = where 1 < - n 1 , n 2 , n 3 5 N n , AI is tho frcqncncy separation (n-2n3+1)+(n3-1) = ... = (n-n3-I ) /2~+~((n-n3)+I) /2 j . of (.WO v.djvcent analog channels, and V L I , ~ ~ , n3 are integers. According to tlic above equation, n-2ns+l < [ ( ~ i - n ~ - 1 ) / 2 ] The11 nl - m a = k - TLZ, (or ng 2 (n + 3)/3) . T h r number of the 3rd order dist,ortion

noise terms in t,his case is L(n - n:i - 1)/21 - (n - 2n1). N

" > = I 3rd order distortion nvise terms in this case is L(n - 713 - l ) / Z ] For the case of 2Nn - 1 2 n - n3 > Nn (or n - N A > 'n3 2 + 5 ( N n - n z + k ) n - 2Na + I ) , we know that i < n - 2n3 5 N A . Therefore,

nl+nz = ( n - Z n 3 + 1 ) + ( n ~ + l ) = ... = (7z-na-1) /2]+[( (~~- = N a ( N a - 3112 na) + 11/21, Hcnce. The number of the 3rd w d c r distortion

n.=ktl

. . . . + k ( N - k + 1 ) (19) noise lerms in this case is also [(n - ns - 1)/21 - ( n - Z B ~ )

We can conclude that

min(n-3,L"J N , ) In th i scase , s incen l -ns = k - n z i s t h e s a m e a s n - n 3 = k - n l , eq. (18) should be inultiplied by 1/72, Considering the case n3 = n2, thcre arc N n - 1 tcrms because n2 # k. Considering the c u e n1 = n2, it can be written ;IS 2nl - n3 = k . Then n = ( k + n3)/2 when b + n3 is even. 'Thus there arc about ( N n - 2) /2 terms. Therefore, the number for nl # n2 # ng # k c m be written m:

Ea K A D l b =

.xs=maz( r + 1 . r + i , n - 2 ~ a + 3 )

( [ (n - 7 ~ 3 - I)/?,] - (n - %a)) '

min(n-3,N,)

+ K n =

- [ N A ( N A - : 3 ) / 2 + 5 ( N - k + I )

( N a - 1) - ( N A - 2)/21/2 = k ( N - k + l ) / 2 + ( ( N A - 5)/4. (20)

where N n A f + f m i n 5 k A f + f m i n 5 ( 3 N , - 3 ) A f + 3 f m i n (or Na 'l'his is the numbcr of thc first term of the 3rd order distrotion

noise. Case 2: The oreviauslv mculioncd 3rd tvue of t h e 3rd ordcr

li ~ (3Nn 3) + T ) , zfmlli

This noise power can be represented as ". distortion noises can be divided into 2 cases. Thcy arc f,+ fj- IMP?' = h D I I Z ( I < A D 1 a + 1 < , 4 D l b ) P i / 3 2 (23) fr and f t + f, + f?. The digital band is separated into many slices for convenience. And each slice hils Lhc bandwidth, A f . In the first case, we assume that thc nonlinear intermodidation components ace located in the k , ~ , slice. We now consider the

where

J_", .%(SI * .%(I) Sk(f)IHDF(f)l2G

~ ~ ~ S i ( f ) * S , ( f ) * S ~ ( f j ~ f h D 1 = (24) iwisc falling in the digital b m d . This means fu- 5 kAj+

J m j m 5 fo + % (Or hf 5 5 h, 1. In and H B p ( f ) is the transfer function of the bandpm filter of this case, nl -n3 = 5 - n 2 > 0. However, 1 5 n1-m 5 Nn-1 and 1 5 7 ~ 2 5 Nn. Considering the intersection of the previous

fD-*-fmin fD-*+fmin

single analog cllannel,

Lwri inoqnillities, we have nz = k - N n + 1, ..., N n . B The 3rd order distortion induced by 2 analog channels and the digital chan-

Because k > N n and # 111, the number of the cme n2 = nz is 0. -

If n1 = n2, then 2n1 = 113 + k . Following the samc tecli- ne1 and falling in the analog band niques of the above sitnation, the number of nl = 31.2 is ( 2 N A - k - 2 ) / 2 . The total number of thc 3rd ardcr distortion uoise components in this c a x c m be represented as:

N.4

The previous 2nd type of thc 3rd ordcr distortion noisc in- cludes 3 components in the form of fo + f, - s,, fo - f, - f,, f, + f, - so wherc f o is the center frequency of the digitnl channel. All the other components do not hl l into thc hcqiico- cy bands of interest. We will consider this kind of nonlinear distortion noise in the analog band at first.

I<.nDla = :[/a[ ( N A - k +712)

ns = k - N , + I

- (2Nn - k ) / 2 ] = I /Z l (Nn - k ) (ZNn - k ) + ( N A ( N A + I) Case 1. fo + f, - f, . ..

Let A f be the frequency separiition between two adjacent analog channels and f ? - f, = nAf . Thcii the ccntcr frquency

- ( k - N n ) ( k - N a + l ) ) / 2 - ( 2 N n - k ) / 2 ]

= ' / z [ ( N A - k ) ( 2 N n k, + b / 2 ( 2 N A - k) l = (2Nn - k)'/4

of this noise is fr = j~ - nAf. Let the lowest and highcst frequency of analog band be fmin and fin,., + N n A f , rcspcc- t i d y . There will be noise component locating in the analog band if

(21)

where N n 5 k < 2Na. Now we will discuss the effect of f$+fj+f, terms. For ni #

n2 # mg and avoiding the repeated noisc lcrms in this case, we fmln 5 f D - nAf - (2Bn + B D ) / ~ < fmr,, + N A A ~ (25)

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or Let n = n,+n, and 1 5 n,, n j 5 NA. The number of nonlinear distortions locating at the same frequency is [(n - 1)/2J if n < NA where n satisfies 1351 or 136). This is because n = fmm 5 f D - n A f + (2Ba + B D ) / ~ < fm:n + NAAf ( 2 6 ) - . , , I + (n - 1) = 2 + (n - 2) = ... = L(n - l ) / 2J + [(n + 1)/2]. If n > Na, then the number is NA - [(n + l) /21 + 1. This is because n = NA + (n - NA) = (NA - 1) + (n - NA + 1) =

with > 0. The above two inequalities can be modified as

f D - ( 2 8 ~ + B L J ) / ~ - fmin - N ~ ) < max(0, A f ... = (I(. + 11/21) + (n - [(n + 1)/21),

or Then the noise term falling in the r-th channel is

' (2s) f~ + ( ~ B A + B D ) / ~ - fmin

Af 5

The number of the nonlinear distortions located at the same frequency is Na-n where n satisfies the upper inequality. The r e a s o n i s n = ( n + l ) - l = ( n + 2 ) - 2 = . , . = Na-(Na-n). For example, the term for n = 1 consists of fi - f2 , f2 - f 3 , . . . 2 f N ~ - I - f N ~ .

and

Then the noise power in the r-th channel is

) 5 n where OD is the modulation index of the digital channel, PA is the modulation index of the analog channel, kman is the maximal value of k according to (29), k,,, is the minimal

f~ + (2Ba + B D ) / ~ - fmin

AS max(0,

f D + ( ~ B A + B D ) / ~ - fmin + Na) (41)

AS value of k according to (as), and < max(0,

where S D ( ~ ) is the power spectrum of the digital signal. Case 2. f D - f; - f, Let f, + f, = 2fmin + nAf. Then f r = f~ - f i - f, = f~ - 2fmin - nAf . Similar to Case 1, we can obtain

f m i n 5 f D - 2 f d n - nAf - ( ~ B A t B D ) / ~ < fmin + N a A f (33)

or

fmcn 5 fo - 2fmin - nAf + (2Ba + 8 ~ ) / 2 < fmin + NaAf

with n 2 0. The above two inequalites can be modified as (34)

- NA) < n

fo - ( ~ B A + B D ) / ~ - 3fmin A f

f D - (2Ba + B D ) / ~ - 3fmin

A f max(0,

(35) 5

The number of nonlinear distortions locating at the same frquency is L(n - 1)/2J where n satisfies (41) or (42). It is because n = 1 + (n - 1) = 2 t (n - 2) = ... = L(n - 1)/2] + [(n+l)/21, I f n > NA then thenumberis N~-[(n+1)/21+1. This isbecausen=Nat(n-Nn) = ( N a - l ) + ( n - N n t l ) = ... = (I(. + 1)/21) + (n - I(.+ 1)Pl) .

Then, the noise power falling in the r-th channel is

min(kmo=,r tnn)

1 t NA)) fmrn - f D

ha2 [(I - u ( k - 1 k=moz[k,;. , r - n n )

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C The 3rd order distortion induced by 2 analog channels and the digital chan-

where , U ( . ) is the step fnnction, imd

s_",s,(/) *s,(f) .s lJ(f) l l fnp(f)12df

s_", s * ( f ) * s ~ ( f ) * , s D ( f ) d f ne1 and falling in the digital band I 1 D 2 = ( 5 5 )

The previously-mcntioned 4th type of the 3rd ordcr distortion noise can be divided into 3 components that are in the farms of fo + f i + f,, fi, - ft - fj, f D + f. - f, wllerr fo i s the center frequency of t l x digithl channel. Case 1. J D + fi + f,. 'rile cumporm,ts of the nonlinear distortion of this form arc located in the digital band if

,

case 2. f,, - f( - f,, 'rhe components of the iionlincar cIistortirm of this form arc

located in the digital band if

fu - R D / ~ 5 f D - 2f,,,,,, - nAf - ( ~ R A + n D ) / ?

5 fi, + A,,/2 (56)

f i , - 8 u / 2 5 f D + 2 f m m + a A f - (?Ha + A D ) / 2 or 5 f D +no/? (45)

f D - n D / 2 5 fl) - 2fmin - n A f + (2BA + R U ) / 2 UT 5 f D + / J D / ~ . (57)

fi, - B D / ~ 5 f D + 2fmin + nA f + (?BA + Bn) /2 Let BA < f m i n , then 5 f~ + RD/? . (46)

( 5 8 ) BA - 2r,,.,, + B~

Af Thrn 3 < n 5

) < n

Ha - 2 b t n + B o Thisis becausc rz = I+(n-I) = 2+(11,-2) = ,,. = [ ( ~ ~ - 1 ) / 2 j + [(n+l)/21. I f n > N n , t,hen theniirnhcris Nn-[(7~-1-1)/21-t-I.

5 Af (47) This i shecansen=Arn+(n -Na) = ( N n - l ) + ( 7 ~ - N ~ + l ) =

B A - 2fmin

A f T M Z ( 0 ,

or ... = (I(. + 1)/21) + (71 - l ( 7 1 + 1)/21). Lct

). (48) Hn - 2fm,.

J AS

= l f l ( f D - R A - f l l > / a )

3 5 n 5 moz(0,

A f Let Dn < f n Z t n , then

arrrbL7. (49) = -1-J-71+nn

Af nr B A - 2 fm,n + IJD 351L5

The number of the nonlinear distortions locating a l thc same frequency is L(n - I)/?] with n satisfies the upper ineqodity. This is because n = l + ( n - l ) = ?+(n-2) = ... = L(n-l)/ZJ t [ ( n + I ) / Z l , I f n > N n t hen t l~enumhcr i sNn- [ (~1+1) /2 j+ I . 'l'liisis because n = N a + ( n - N n ) = ( N , . - - l ) + ( n - N ~ + l ) = bm,,, = - ~ ( R A + Ro)/AfJ + T L A (61)

...=(l ( n + l ) / ? l ) + i n - T ( n . + 1 ) / 2 1 ) .

= nAf - fl - l2 fmin/A/] . (59)

(6") lima, = -12frL;.,/AfJ + nn - 3

Then, the noise power falling in tlie r-th slice is We considcr the digital band to be sliced as B number of

sequential sub-bands. Each sub-band has a bandwidth A/. mr4r,,,, ,rtn,1 2fm,.,

Af Le1 h D 2 [ U ( k 7LA + 1-1 + N A )

k=mor(k,,, , ~ - n ~ j

[(.A - L(Zfmn)/Af] - k - 1) /2 j

+ ( I - IL(k - nA + 1-1 + N n ) ) i f~ - ( f ~ - Bn - B O P )

A f Bo/2 + An + ? f w n

b = l

= l = n a f + n + 12fn~t~l/ASJ (50)

(51)

2frni" + nJ A f Af

( N n + l - [(.A - p= J - f i + 1)/21)18:,P:. ( 6 2 ) whcrc A f

Case 3. f o + f, - f,. J . B D / ~ + B A n , = l Ap

kmaz = [ ( B A + . B U ) / A f ] +' lzA (52) In this case, we cansidcr two symmetric cases, J i > f, and f, < f j . At first we will discuss the C ~ S P of f, > fj. IC,,, = 12fmln/AfJ + n a + 3. The relavant frequency can be reprcscntcd BS f n + nAf. 'rhr components of the nonlincar distortion nf this frequency arc locatcd in the digital hand if

(53) Then, the noise power falling in the r-th slice is

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The number of the nonlinear distortions locating a t the same frequency is Na - n where n satisfies the above inequality.

Let

= n a + n (6'3)

= ~ ( B A + D D ) / A ~ ] + VLA (67)

kmt7, = j B n / A f l + n a (68)

and

Then, the noise power falling in the r-th slice can be written as

mln(k*,, ,?+"A)

hi12 ( N n - k + n a ) P i P h . (69)

The other case is the same as the above because of the sym- metric property. The relavant freqnency can be represented as f o - nAf. The components of the nonlinear distortion of this frequency are located in the digital band if

k=mai(k, , , ,.-.A)

f D - BD/2 5 f D - nAf - (2BA + 8 D ) j a

5 f D + Bn/2 (70)

the modulator, we use a low pass filter to truncate the side- lobe of the spectrum of signals to reduce the interference to the analog band. Now we must consider the nonlinear distortion noise due to

the external intensity modulation. If we use OOK, then the DER can be repesented as

If we use BPSK, then

The number of the nonlinear distortions locating a t the same fiqaency is also N a - n where n satisfies the above inequality.

d = ( d h o t + u%2 + & I N ) B A

+ hniI2I<aiP:P;/32 + hnz121<azPi/32

- - na - n (73) ut,bot = 2qIt(Pk + SASEB,~) ( 8 6 )

and U ? i y = ~ s ~ = 4 ( R p k ) ( R , ~ A s B R A ) ( 8 7 ) u ? I , y E = , s ~ : = R z S i s ~ ( 2 D o p t - DA)UA (88)

kmaz = -[Bn/Afl + n A (74) where B A is the bandwidth of a single analog channel and kmin = - [ ( B A + B D ) / a f l + na (75) KA = N n ( N a + l ) / 4 + ( ( N A - 3)2 - 6)/4. (89)

?'hen, the noise power falling in the r-th channel is For convcnicnce, we can rewrite (86) as

noise = X a + y,p:p; + ..pi. (90) mln(k,,, ,?+"A)

The optimal madnliLtiun index of the analog channels can h ~ 2 2 ( N A + k - n A ) P b P : . (76)

be obtained by k=mar(k,,,

(91) ~- - 0. a C N R

V. THE TRANSMISSION PERFORMANCE OF DIGITAL a p A

-7 SONET SIGNALS AND ANALOG TV SIGNALS where

(92) P i C N R o( x n + y.s:a; +..Pi Now we analyze the performance of transmitting OC-3 dig-

ital signal and analog TV signals in this system. The analog T V signals are A K V S B and placed from 50 to 550 MHz. We transmit the OC-3 dipital signal using OOK or BPSK modu-

a single carrier. Before sending the digital baseband signal to

Lct P D = T ~ A , the optimal modulation index o€ analog channels obtained as

lation and assign the channel to be in 850 to 1000 MHz using BA = + z.) )1/6, (93)

Page 7: Broadband hybrid analog/digital CATV trunk network

VI. NUMERICAL RESULTS AND n l S C U S S I O N S

Assume there is an OA between two headends and the in- terval disl,ancc is 50 km. Other important system parameters are lislcd in Table 1.:

Tablc 1

X 1.3 pm wavelengtli of light N, 70 the number of analog clianncls 11 O.SA/W The responsivity of phatodiude Id 10 nA dark current in photodiode FUN -165dU/FIa coefficient of RIN noise Rapt IOI IZ bandwidt,li of optical signal iy O.ldFl coupling loss caefficcnt

D A GMHz bandwidth of one analog channel AD 311MIIz bandwidth of digital channel mi 0.4dB/km fiber loss coellicent I , 60km lengtli of a section of this network I t h 2SmA threshold current of laser diode l a 200mA bias current of laser diode

X 0.2 coupling ratio

__ Wc sut the gain of tlic optical amplifiers to be ZBfl(24.5 dB) and 350(25.4 dB), respec t idy . T h e results of simulation are shown in l“ig.3 to Fig.4. All of the figures show that the syystcm perforrnarice at each licadend satisfies the standard. ‘The CNR’s of the ana,log chnnnels are better than 50 d H and the UER of digital channcl is below IO-’.

V I I . CONCLUSION

In t,his paper, wr have presented an analysis of thc 3rd urtlcr nonlinear distortion mise in an optical fiber AM- VSBjSON1,Yl’ transmission system.

From thc rcsults of the previous sections, we c m conclnde that tlir performance of this trnnk transmission syslem can be maintained by cmploying optical amplification in thc net- work. We may providc additional digital network services in this network for downlink transmission. From thc nnmerical result, LIE C N K of the analog diilnnelr is bcttcr than 49.5 dR at all 1Iradcnds.

’l‘he performance reqirment an the digital channels can also be satisfied. According to the rcsnlts of our simulation, BER of digital channel is less than IO-’ for all heudends. Therefore, we c m properly clloose the digit,zl modnliLtion index to meal the performance requirment of digital transmission.

References ‘I.X, Darcia, “Subcarrier multiplexing for lightwave networks and video dis t r ibut ion systems,” IEEE Journal o n Selected Areas in Communications. , vol. 8, no. 7, p p 1240-1248, 1990.

J A C h i d d i x , H . Loar , D.M. Pan- grac, L.U. Willi;lmson, a n d H .W. wolfe ,“AM video on fiber CATV systems: need a n d implementat ion,” IEEE Journa l on Selecded Areas i n Communicntions. , vol. 8, no. 7 , pi). 1229-1239, 1990.

[IO] Y.-H. Lce ct al., “The impac t of laser phasc noise on t h e colicrent subcarr ier multiplexing systems,” IERE J. Lzgh,lzuniie Teclmul., vol. 9. no. 3, pp. 347-355, 1991.

[Il l Y.-€1. Lee, I.‘,. Lai a n d C.-T. Hsich, “Performance analysis of cellular mobile communications over mul- t i s ta r ring fiber-optic/ coaxial CATV net,works,” Mi- crowaue and optical t echndogy le%ters., vol.10, no. 6 , pp . 353-357, Dec. 1995.

[I21 M . Nnearathy, J . Berger, A.J. Lcy, I . M . Levi, andY. Kagan,”Progress in external ly modulated AM CA’lV transmission systerns,” IIClCF; J. Lightwave Technol., VOLII, no. I , pp. 82.104, I C J ~ ~ .

[13] Mnhsmrnand Tahe r Abnelma’at t i , “Carrier-to- intermodulat ion performance oC multiple FM/FDM carriers ‘I’hrongh a C a A l A s hetrojiinction lascr diode,” IEEE trims. on Communicat iuns. , vol. com- 33, no. 3, pp . 248-248 , 1985.

14s

N. I ianno a n d I C . I to , “Fiber-Optic snbcarr ier multi- plexing video t ranspor t employing inultilcvcl &AM,” IEEE Journal on Selected Areas i n Communzcations. , vol. 8 , no. 7, pp. 1313-1319, 1990.

P.M.HiI1 a n d R.Olshansky,“A 20-channel opticxl coin- rnunication system using subcarr ier innltiplexing for t h c transmission of digi ta l video signals,” 16/3E J. Lightwave Technol., vol. 8. no.4,pp.564-560 , 1990.

M . K Liu a n d P.C. Modes ton ,“ Mnlt,ilcvel signaling a n d pulsc shaping for spec t rum eficicncy in subcarrier multiplexing ,” IEEE J . Lightrunve Technol. , vol. 12. no. 7, pp. 1239-1246, 1994.

A.A.M.Saleh,“Fnndarnental lintit on number of chan- nels i n CKI‘V systems ,” Electrozncs Letters., ~ 0 1 . 2 5 , no.12,pp.776-777, 1989.

N.J.bligo, M.R. Phillips, and G.E. Bodeep,“Clipping dis tor t ion in lightwave CATV systems :models, simu- lations, a n d measnrcmcnt ,” IEEE J . Lightwave Tech- nol., vol. 11. no. I , pp . 138-146, 1993.

John Powers, “Fiber Optics Systems,” 2nd edit,iorr, 1997.

R. Gross a n d R. Olshansky, “Multichannel coherent FSK expcriments using subcarr ier mnltiplcxing tech- niques. ,’’ IEEE J. Lzghlwave ‘Ibchnul. ., vol. 8, no. 3, pp. 406-415, 1990.

Page 8: Broadband hybrid analog/digital CATV trunk network

Po

Fig , 1 .a The system diagram with the parameters.

xl x2 0

Master Headenc'

Fig . 1 .b The system diagram of the trunk network.

Headend Headend 0

Uplink channel ANALOG CHANNEL SONET

Fig.2 . Frequency arrangement of the hybrid TV/SONET

transmission system.

CHANNEL

Page 9: Broadband hybrid analog/digital CATV trunk network

Fig. 3: CNH and RER V.S. n-th lieadend .G=280

Fig. 4: CNR and RER Y . S . nth heudcnd ,G=350