170 CHAPTER 4. OPTICAL RECEIVERS
of photocurrent statistics [91]. A simple approach consists of adding a third term to the
current variance given by Eq. (4.4.10), so that
σ^2 =σs^2 +σT^2 +σI^2 , (4.6.5)where
σI=R〈(∆Pin^2 )〉^1 /^2 =RPinrI. (4.6.6)
The parameterrI, defined asrI=〈(∆Pin^2 )〉^1 /^2 /Pin, is a measure of the noise level
of the incident optical signal. It is related to therelative intensity noise(RIN) of the
transmitter as
r^2 I=1
2 π∫∞−∞RIN(ω)dω, (4.6.7)where RIN(ω) is given by Eq. (3.5.32). As discussed in Section 3.5.4,rIis simply the
inverse of the SNR of light emitted by the transmitter. Typically, the transmitter SNR
is better than 20 dB, andrI< 0 .01.
As a result of the dependence ofσ 0 andσ 1 on the parameterrI, the parameterQin
Eq. (4.5.11) is reduced in the presence of intensity noise, SinceQshould be maintained
to the same value to maintain the BER, it is necessary to increase the received power.
This is the origin of the power penalty induced by intensity noise. To simplify the
following analysis, the extinction ratio is assumed to be zero, so thatI 0 =0 andσ 0 =
σT. By usingI 1 =RP 1 = 2 RP ̄recand Eq. (4.6.5) forσ 1 ,Qis given by
Q=
2 RP ̄rec
(σT^2 +σs^2 +σI^2 )^1 /^2 +σT, (4.6.8)
where
σs=( 4 qRP ̄rec∆f)^1 /^2 , σI= 2 rIRP ̄rec, (4.6.9)
andσTis given by Eq. (4.4.9). Equation (4.6.8) is easily solved to obtain the following
expression for the receiver sensitivity:
P ̄rec(rI)=QσT+Q(^2) q∆f
R( 1 −r^2 IQ^2 )
. (4.6.10)
The power penalty, defined as the increase inP ̄recwhenrI=0, is given by
δI=10 log 10 [P ̄rec(rI)/P ̄rec( 0 )]=−10 log 10 ( 1 −r^2 IQ^2 ). (4.6.11)Figure 4.21 shows the power penalty as a function ofrIfor maintainingQ=6 cor-
responding to a BER of 10−^9. The penalty is negligible forrI< 0 .01 asδIis below
0.02 dB. Since this is the case for most optical transmitters, the effect of transmitter
noise is negligible in practice. The power penalty is almost 2 dB forrI= 0 .1 and
becomes infinite whenrI=Q−^1 = 0 .167. An infinite power penalty implies that the
receiver cannot operate at the specific BER even if the received optical power is in-
creased indefinitely. In the BER diagram shown in Fig. 4.19, an infinite power penalty
corresponds to a saturation of the BER curve above the 10−^9 level, a feature referred to
as the BER floor. In this respect, the effect of intensity noise is qualitatively different