364 CHAPTER 8. MULTICHANNEL SYSTEMS
Figure 8.22: Crosstalk power penalty at four different values of the BER for a FP filter of finesse
F=100. (After Ref. [149];©c1990 IEEE; reprinted with permission.)
where the powers correspond to their on-state values. If the peak power is assumed
to be the same for all channels, the crosstalk penalty becomes power independent.
Further, if the photodetector responsivity is nearly the same for all channels (Rm≈Rn),
δXis well approximated by
δX≈10 log 10 ( 1 +X), (8.3.4)whereX=∑Nn =mTmnis a measure of the out-of-band crosstalk; it represents the fraction
of total power leaked into a specific channel from all other channels. The numerical
value ofXdepends on the transmission characteristics of the specific optical filter. For
a FP filter,Xcan be obtained in a closed form [149].
The preceding analysis of crosstalk penalty is based on the eye closure rather than
the bit-error rate (BER). One can obtain an expression for the BER ifIXis treated as a
random variable in Eq. (8.3.1). For a given value ofIX, the BER is obtained by using
the analysis of Section 4.5.1. In particular, the BER is given by Eq. (4.5.6) with the
on- and off-state currents given byI 1 =Ich+IXandI 0 =IXif we assume thatIch= 0
in the off-state. The decision threshold is set atID=Ich( 1 +X)/2, which corresponds
to the worst-case situation in which all neighboring channels are in the on state. The
final BER is obtained by averaging over the distribution of the random variableIX. The