482 CHAPTER 10. COHERENT LIGHTWAVE SYSTEMS
The SNR is obtained by dividing the average signal power by the average noise
power. In the heterodyne case, it is given by
SNR=
〈I^2 ac〉
σ^2=
2 R^2 P ̄sPLO
2 q(RPLO+Id)∆f+σT^2. (10.1.11)
In the homodyne case, the SNR is larger by a factor of 2 if we assume thatφs=φLOin
Eq. (10.1.5). The main advantage of coherent detection can be seen from Eq. (10.1.11).
Since the local-oscillator powerPLOcan be controlled at the receiver, it can be made
large enough that the receiver noise is dominated by shot noise. More specifically,
σs^2 σT^2 when
PLOσT^2 /( 2 qR∆f). (10.1.12)Under the same conditions, the dark-current contribution to the shot noise is negligible
(Id RPLO). The SNR is then given by
SNR≈
RP ̄s
q∆f=
ηP ̄s
hν∆f, (10.1.13)
whereR=ηq/hνwas used from Eq. (4.1.3). The use of coherent detection allows one
to achieve the shot-noise limit even forp–i–nreceivers whose performance is generally
limited by thermal noise. Moreover, in contrast with the case of avalanche photodiode
(APD) receivers, this limit is realized without adding any excess shot noise.
It is useful to express the SNR in terms of the number of photons,Np, received
within a single bit. At the bit rateB, the signal powerP ̄sis related toNpasP ̄s=NphνB.
Typically,∆f≈B/2. By using these values ofP ̄sand∆fin Eq. (10.1.13), the SNR is
given by a simple expression
SNR= 2 ηNp. (10.1.14)In the case of homodyne detection, SNR is larger by a factor of 2 and is given by
SNR= 4 ηNp. Section 10.4 discusses the dependence of the BER on SNR and shows
how receiver sensitivity is improved by the use of coherent detection.
10.2 Modulation Formats
As discussed in Section 10.1, an important advantage of using the coherent detection
techniques is that both the amplitude and the phase of the received optical signal can
be detected and measured. This feature opens up the possibility of sending information
by modulating either the amplitude, or the phase, or the frequency of an optical carrier.
In the case of digital communication systems, the three possibilities give rise to three
modulation formats known as amplitude-shift keying (ASK), phase-shift keying (PSK),
and frequency-shift keying (FSK) [1]–[6]. Figure 10.2 shows schematically the three
modulation formats for a specific bit pattern. In the following subsections we consider
each format separately and discuss its implementation in practical lightwave systems.