3. C´ alculo de tama˜ nos de prueba para comparaci´ on de distri-
3.5. Ejemplos
The BER was measured as a function o f the decision threshold for different channel spacing AT, and the Q-factor was obtained by the interpolation described in section 5.1.1. Both channels were modulated with independent lOGbit/s PRBS sequences with 2 ’^-l length and the receiver input power was set to -35dBm . An increase o f the pattern length from 2^-1 to 2^’-l caused a power penalty o f approximately IdB in the transmission experiments. This was due to the pattern dependence o f the receiver confirmed in back-to-back measurements.
M easuring BER versus AA,: The BER was measured as a function o f AT over the range 0.4nm to 2nm using 13dBm/channel launch power and a 2^^-l PRBS pattern at lOGbit/s. Since the 2 channels in this experiment had independent bit-pattem s from 2 different outputs o f the pattern generator, the decorrelating fibre was omitted and only the SSMF span was used. The system was optimised for single channel transmission by increasing the channel spacing to AT=2nm where XPM distortion was negligible. The timing and voltage level o f the
Chapter 5: Q-factor measurements 133
decision threshold were adjusted to the lowest BER determined by SPM distortion, ASE noise and dispersion. In the following, A l was varied resulting in additional XPM distortion for narrow ls.X. The Q-factor was determined for a given AT using the decision threshold method. The BER measurements are shown as a function o f the decision threshold in Fig. 5.5.
‘I ’-level: The slope o f the ' T-level BER measurement indicates ai><To because there is additional signal-ASE beating noise for the ‘ 1 ’-level and not for the ‘O’-level. The ‘ 1 ’- level is also more affected by XPM than the ‘O’-level as it is clearly shifted towards the ‘O’-level with decreasing AT. For narrow channel spacing, AT=0.4nm, the BER changed by one order when the decision voltage was varied by approximately 12mV whilst this interval was reduced to »8mV for AT=2nm. However, for all values o f AT error-free transmission was obtained. For AT=2nm, when only SPM distortion and ASE noise were present, the error-free interval extended over approximately 0.5V but decreased to about O.IV for AT=0.4nm.
‘O’-level: The BER varied by about one order o f magnitude when the decision voltage was changed by only Im V for all AT, indicating a stationary ‘O’-level with little broadening. The data set representing the ‘O’-level was shifted by up to 0.2V for values with BER<10^ when the AT was increased from 0.4nm to 2nm. The slight broadening o f the ‘O’-level may be due to XPM-induced pulse broadening leading to ISI from adjacent ‘ 1 ’ bits. This broadening is less significant than the broadening o f the ‘ 1 ’-level which is also affected by nonlinear distortion.
IE-3 ‘O’-level ‘ I ’-level 1E-5 ex □ AA,=2nm ex 1E-7 1E-9 0.00 0.25 0.50 0.75 Fig. 5.5 d e c is io n v o lta g e (V)
BER vs. decision threshold D measured for different AA, 63km SSM F, IBdBm/channel, lOGbit/s PRBS, 2 ’^-l bit sequence, for ( □ ); 2nm, (X ): Q.6nm, (O ): 0.4nm
Chapter 5: Q-factor measurements 134
C alcu latin g Q -factor: The results o f Fig. 5.5 were used to calculate the Q-factor and the results are shown in Fig. 5.6(a). For A/l=0.4nm the Q-factor decreased to Q »6, corresponding to BER=10‘^. For wide channel spacing, AA>lnm, the total variation was AQ<0.5, in agreement with previous pump-probe measurements in chapter 4 investigating XPM distortion versus AZ for the same SSMF link. In Fig. 4.8 it was shown that XPM-induced distortion was negligible for AA>lnm and, therefore, the Q-factor was only determined by SPM, dispersion and ASE noise. In Fig. 5.6(b) the results are shown as a function o f 1/AÀ and the Q-factor was found to depend linearly on the inverse channel spacing over the entire wavelength range. Fig. 5.6 AX 8.5 7.5 O 6.5 5.5 0 0.5 1 1.5 2 8.5 8 7.5 O 7 6.5 6 5.5 (b) penalty due to XPM 0.5 1.5 MAX 2.5
Q -factor obtained from BER m easurem ents for SSM F link, (♦) experimental data, line: interpolation, 10Gbit/s PRBS modulation, 2 '^-l sequence, 13dBm/channel, (a) as a function o f A/l, (b) for 1/AÀ, receiver power: R% = -34dBm
In addition the contribution o f XPM distortion, axpu, was investigated in pump-probe experiments using the same fibre link. In this case, the pump was PRBS-modulated and the probe was in CW mode. In Fig. 5.7(a) the m easured distribution o f Oxpm is shown as a function o f AZ and was found to be proportional to 1/AÂ The histograms in the inset o f Fig. 5.7(a) for A>l=0.4nm and 2nm indicate that the ‘1’-level is broadened for narrow channel spacing due to XPM -induced distortion o f the probe. In addition, Oxpm was determined in
simulations for orthogonal and parallel polarisation o f pump and probe.
For a single span o f SSMF, the results obtained for ctxpm were compared to the wavelength- dependent Q-factor measurements shown in Fig. 5.6. Initially, the Q-factor was calculated for A^=2nm using the BER data presented in Fig. 5.5. The parameters //,, /^ , ob and O] were determined according to section (5.1.1) assuming negligible XPM with cr,(A,l=2nm)« In the following, the experimental results for Cxpm shown in Fig. 5.7(a) were used to calculate ai(AZ) in the interval A /l=0.4...2nm and it was assumed that only cf\ was affected by XPM-
C hapter 5: Q-factor m easurem ents 135
induced distortion. Therefore, the decrease of the Q-factor with 1/AT was calculated using
(Ti( A / 1 ) and the parameters /a, f-h and ctq determined for AA.=2nm. In Fig. 5.7(b) the calculated
Q-factor is compared with the Q-factor determined in direct BER measurements. For AT>0.8nm, these two graphs agree well, however, for small AT the pump-probe experiment underestimates the reduction of the Q-factor by up to 13%. This is due to the variation of the polarisation between pump and probe as shown by the calculation of A g for orthogonal and parallel polarisation. The values for the Q-factor given by the measurement o f cjxpm are within the interval determined by the calculated Q-factor for both states of polarisation.
Fig. 5 .7 (a ) F ig. 5 .7 (b )
0.12
G a u s sia n fit, ' I '-le v e l b r o a d e n in g A ,\=2nm% 0 . 0 8 -
0.04 -
0.00
A /.= 0.4nm v o lta g e [a.u. v o lta g e [a.u .] O0.5
1.0
1.5
2.0
AT [nm]E x p e rim e n ta l n o rm a lis e d X P M d isto rtio n m e a s u re d fo r lin k use d in Q -fa c to r m e a s u re m e n ts o f Fig. 5 .6 , 1 3 d B m /c h a n n e l: cTxpst vs. AA at lO G b it/s, ( O ) : p u m p -p ro b e e x p e rim e n t, d a s h e d line: p a ra lle l p o la risa tio n , d o tte d line: o rth o g o n a l p o la ris a tio n , in s e t: h isto g ra m s sh o w in g b r o a d e n in g o f ' 1 ’-lev el o f th e C W p ro b e d u e to X P M fo r sm all AA, sa m e b in siz e.
o
à
8 7 6 0.5 1.0 1.5 2.0 2.5 1 /AA [ nm' ]C o m p a ris o n o f Q -fa c to rs vs. I/A A, lO G b it/s w ith 2 ’^-l P R B S m o d u la tio n , sin g le sp a n o f 6 3 k m S S M F , 1 3 d B m /c h a n n e l, ( O ) : c a lc u la te d u sin g (Xvm fro m p u m p -p ro b e e x p e rim e n t, (■ ): d ire c tly m e a s u re d Q -fa c to r, d a s h e d line: p a ra lle l p o la risa tio n , d o tte d line: o rth o g o n a l p o la risa tio n
Chapter 5: Q-factor measurements 136
In section 5.3.3 the Q-factor reduction due to XPM as a function o f distance and A/l is estimated using the results o f pump-probe experiments and analytically calculated XPM distortion for up to 12 post-compensated spans.