508 CHAPTER 10. COHERENT LIGHTWAVE SYSTEMS
DPSK and FSK schemes through numerical models that include the effects of phase
noise and the preamplifier noise [121]–[125].
Asynchronous heterodyne schemes have also been used for long-haul coherent sys-
tems using in-line optical amplifiers for increasing the transmission distance. A 1991
experiment realized a transmission distance of 2223 km at 2.5 Gb/s by using 25 erbium-
doped fiber amplifiers at approximately 80-km intervals [126]. The performance of
long-haul coherent systems is affected by the amplifier noise as well as by the non-
linear effects in optical fibers. Their design requires optimization of many operating
parameters, such as amplifier spacing, launch power, laser linewidth, IF bandwidth,
and decision threshold [127]–[129]. In the case of WDM systems, the use of DPSK
can reduce the XPM-induced interaction among channels and improve the system per-
formance [130].
10.6.2 Synchronous Heterodyne Systems
As discussed in Section 10.4, synchronous heterodyne receivers are more sensitive than
asynchronous receivers. They are also more difficult to implement as the microwave
carrier must be recovered from the received data for synchronous demodulation. Since
the sensitivity advantage is minimal (less than 0.5 dB) for ASK and FSK formats (com-
pare Tables 10.1 and 10.2), most of the laboratory experiments have focused on the
PSK format [131]–[135] for which the receiver sensitivity is only 18 photons/bit. A
problem with the PSK format is that the carrier is suppressed when the phase shift
between 1 and 0 bits is exactly 180◦because the transmitted power is then entirely
contained in the modulation sidebands. This feature poses a problem for carrier re-
covery. A solution is offered by the pilot-carrier scheme in which the phase shift is
reduced below 180◦(typically 150–160◦) so that a few percent of the power remains in
the carrier and can be used for synchronous demodulation at the receiver.
Phase noise is a serious problem for synchronous heterodyne receivers. As dis-
cussed in Section 10.5.1, the ratio∆ν/Bmust be less than 5× 10 −^3 , where∆ν=
∆νT+∆νLOis the IF linewidth. For bit rates below 1 Gb/s, the laser linewidth should
be less than 2 MHz. External-cavity semiconductor lasers are often used in the syn-
chronous experiments, as they can provide linewidths below 0.1 MHz. Several exper-
iments have been performed using diode-pumped Nd:YAG lasers [131]–[133], which
operate at a fixed wavelength near 1.32μm but provide linewidths as small as 1 kHz.
In one experiment, the bit rate was 4 Gb/s, but the receiver sensitivity of 631 pho-
tons/bit was 15.4 dB away from the quantum limit of 18 photons/bit, mainly because
of the residual thermal noise and the intensity noise as a balanced configuration was not
used [133]. The receiver sensitivity could be improved to 235 photons/bit at a lower
bit rate of 2 Gb/s. This sensitivity is still not as good as that obtained for asynchronous
heterodyne receivers. The performance of multichannel heterodyne systems has also
been analyzed [134].
10.6.3 Homodyne Systems
As seen in Table 10.1, homodyne systems with the PSK format offer the best re-
ceiver sensitivity as they require, in principle, only 9 photons/bit. Implementation