4.5. RECEIVER SENSITIVITY 165
Figure 4.19: Bit-error rate versus theQparameter.whereP ̄recis the average received power defined asP ̄rec=(P 1 +P 0 )/2. The APD
gainMis included in Eq. (4.5.12) for generality. The case ofp–i–nreceivers can be
considered by settingM=1.
The RMS noise currentsσ 1 andσ 0 include the contributions of both shot noise and
thermal noise and can be written as
σ 1 =(σs^2 +σT^2 )^1 /^2 and σ 0 =σT, (4.5.13)whereσs^2 andσT^2 are given by Eqs. (4.4.17) and (4.4.9), respectively. Neglecting the
contribution of dark current, the noise variances become
σs^2 = 2 qM^2 FAR( 2 P ̄rec)∆f, (4.5.14)
σT^2 =( 4 kBT/RL)Fn∆f. (4.5.15)By using Eqs. (4.5.11)–(4.5.13), theQparameter is given by
Q=
I 1
σ 1 +σ 0=
2 MRP ̄rec
(σs^2 +σT^2 )^1 /^2 +σT. (4.5.16)
For a specified value of BER,Qis determined from Eq. (4.5.10) and the receiver sensi-
tivityP ̄recis found from Eq. (4.5.16). A simple analytic expression forP ̄recis obtained
by solving Eq. (4.5.16) for a given value ofQand is given by [3]
P ̄rec=Q
R(
qFAQ∆f+σT
M