494 CHAPTER 10. COHERENT LIGHTWAVE SYSTEMS
Figure 10.7: Bit-error-rate curves for various modulation formats. The solid and dashed lines
correspond to the cases of synchronous and asynchronous demodulation, respectively.
envelope detector is used (see Fig. 10.5). The reason can be understood from Eq.
(10.3.4), which shows the signal received by the decision circuit. In the case of an
ideal ASK heterodyne receiver without phase fluctuations,φcan be set to zero so that
(subscriptdis dropped for simplicity of notation)
I=[(Ip+ic)^2 +i^2 s]^1 /^2. (10.4.12)Even though bothIp+icandisare Gaussian random variables, the probability density
function (PDF) ofIis not Gaussian. It can be calculated by using a standard tech-
nique [38] and is found to be given by [39]
p(I,Ip)=I
σ^2
exp(
−
I^2 +Ip^2
2 σ^2)
I 0
(
IpI
σ^2)
, (10.4.13)
whereI 0 represents the modified Bessel function of the first kind. Bothicandisare
assumed to have a Gaussian PDF with zero mean and the same standard deviationσ,
whereσis the RMS noise current. The PDF given by Eq. (10.4.13) is known as the
Rice distribution[39]. Note thatIvaries in the range 0 to∞, since the output of an
envelope detector can have only positive values. WhenIp=0, the Rice distribution
reduces to theRayleigh distribution, well known in statistical optics [38].
The BER calculation follows the analysis of Section 4.5.1 with the only difference
that the Rice distribution needs to be used in place of the Gaussian distribution. The
BER is given by Eq. (4.5.2) or by
BER=^12 [P( 0 / 1 )+P( 1 / 0 )], (10.4.14)