4.6. SENSITIVITY DEGRADATION 173
Figure 4.22: Power penalty versus the timing jitter parameterBτj.By using Eqs. (4.6.12) and (4.6.18) and noting thatI 1 = 2 RP ̄rec, whereRis the respon-
sivity, the receiver sensitivity is given by
P ̄rec(b)=(
σTQ
R)
1 −b/ 2
( 1 −b/ 2 )^2 −b^2 Q^2 / 2. (4.6.19)
The power penalty, defined as the increase inP ̄rec, is given by
δj=10 log 10( ̄
Prec(b)
P ̄rec( 0 ))
=10 log 10(
1 −b/ 2
( 1 −b/ 2 )^2 −b^2 Q^2 / 2)
. (4.6.20)
Figure 4.22 shows how the power penalty varies with the parameterBτj, which has
the physical significance of the fraction of the bit period over which the decision time
fluctuates (one standard deviation). The power penalty is negligible forBτj< 0 .1but
increases rapidly beyondBτj= 0 .1. A 2-dB penalty occurs forBτj= 0 .16. Similar
to the case of intensity noise, the jitter-induced penalty becomes infinite beyondBτj=
0 .2. The exact value ofBτjat which the penalty becomes infinite depends on the model
used to calculate the jitter-induced power penalty. Equation (4.6.20) is obtained by
using a specific pulse shape and a specific jitter distribution. It is also based on the use
of Eqs. (4.5.10) and (4.6.12), which assumes Gaussian statistics for the receiver current.
As evident from Eq. (4.6.16), jitter-induced current fluctuations are not Gaussian in
nature. A more accurate calculation shows that Eq. (4.6.20) underestimates the power
penalty [94]. The qualitative behavior, however, remains the same. In general, the
RMS value of the timing jitter should be below 10% of the bit period for a negligible
power penalty. A similar conclusion holds for APD receivers, for which the penalty is
generally larger [95].