6.5. SYSTEM APPLICATIONS 263
useR=ηq/hνand Eq. (6.1.19), and write Eqs. (6.5.7)–(6.5.9) in terms of the amplifier
noise figureFnas
σs^2 = 2 q^2 ηGPs∆f/hν, (6.5.12)
σsig^2 −sp= 2 (qηG)^2 FnPs∆f/hν, (6.5.13)
σsp^2 −sp=(qηGFn)^2 ∆νopt∆f, (6.5.14)where theRPspterm was neglected in Eq. (6.5.7) as it contributes negligibly to the shot
noise. A comparison of Eqs. (6.5.12) and (6.5.13) shows thatσs^2 can be neglected in
comparison withσsig^2 −spas it is smaller by a large factorηGFn. The thermal noiseσT^2
can also be neglected in comparison with the dominant terms. The noise currentsσ 1
andσ 0 are thus well approximated by
σ 1 =(σsig^2 −sp+σsp^2 −sp)^1 /^2 , σ 0 =σsp−sp. (6.5.15)The receiver sensitivity is obtained by substituting Eq. (6.5.15) in Eq. (6.5.11),
using Eqs. (6.5.13) and (6.5.14) withPs= 2 P ̄rec, and solving forP ̄rec. The result is
P ̄rec=hνFn∆f[Q^2 +Q(∆νopt/∆f)^1 /^2 ]. (6.5.16)The receiver sensitivity can also be written in terms of the average number of pho-
tons/bit,N ̄p, by usingP ̄rec=N ̄phνB. Taking∆f=B/2 as a typical value of the receiver
bandwidth,N ̄pis given by
N ̄p=^12 Fn[Q^2 +Q( 2 ∆νopt/B)^1 /^2 ]. (6.5.17)Equation (6.5.17) is a remarkably simple expression for the receiver sensitivity. It
shows clearly why amplifiers with a small noise figure must be used; the receiver sen-
sitivity degrades asFnincreases. It also shows how optical filters can improve the re-
ceiver sensitivity by reducing∆νopt. Figure 6.20 showsN ̄pas a function of∆νopt/Bfor
several values of the noise figureFnby usingQ=6, a value required to achieve a BER
of 10−^9. The minimum optical bandwidth is equal to the bit rate to avoid blocking the
signal. The minimum value ofFnis 2 for an ideal amplifier (see Section 8.1.3). Thus,
by usingQ=6, the best receiver sensitivity from Eq. (6.5.17) isN ̄p= 44 .5 photons/bit.
This value should be compared withN ̄p=10 for an ideal receiver (see Section 4.5.3)
operating in the quantum-noise limit. Of course,N ̄p=10 is never realized in practice
because of thermal noise; typically,N ̄pexceeds 1000 forp–i–nreceivers without opti-
cal amplifiers. The analysis of this section shows thatN ̄p<100 can be realized when
optical amplifiers are used to preamplify the signal received despite the degradation
caused by spontaneous-emission noise. The effect of a finite laser linewidth on the
receiver sensitivity has also been included with similar conclusions [114].
Improvements in the receiver sensitivity, realized with an EDFA acting as a pream-
plifier, can be used to increase the transmission distance of point-to-point fiber links
used for intercity and interisland communications. Another EDFA acting as a power
booster is often used to increase the launched power to levels as high as 100 mW. In
a 1992 experiment, a 2.5-Gb/s signal was transmitted over 318 km by such a tech-
nique [115]. Bit rate was later increased to 5 Gb/s in an experiment [116] that used two