Page 516 - Fiber Optic Communications Fund

11

Digital Signal Processing

11.1 Introduction

The key component that revived coherent fiber communications in the mid-2000 was high-speed digital signal
processing. In the 1990s, coherent receivers used optical phase-locked loops (OPLL) to align the phases and
dynamic polarization controllers to match the polarization of the received signal with that of the LO. However,
dynamic polarization controllers are bulky and expensive [1], and each channel of a WDM system needs a
separate polarization controller. Phase locking in the optical domain using OPLL is difficult as well. With
the advances in high-speed DSP, phase alignment and polarization management can be done in the electrical
domain, as discussed in Sections 11.5 and 11.7, respectively. Linear impairments such as chromatic dispersion
(CD) and polarization mode dispersion can be compensated using equalizers, as discussed in Sections 11.6
and 11.7, respectively. It is also possible to compensate for the interplay between dispersion and nonlinearity
by using digital back propagation (DBP), in which the nonlinear Schrödinger equation is solved for a virtual
fiber whose signs of dispersion, loss, and nonlinear coefficients are opposite to those of the transmission fiber.
DBP is discussed in Section 11.8.

11.2 Coherent Receiver
Fig. 11.1 shows a schematic of the coherent IQ receiver with digital signal processing. The in-phase and
quadrature components of the received signal can be written as (see Chapter 5, Eqs. (5.114) and (5.118))
y = RA A Re{s(t) exp [−i( t +Δ)]}∕2, (11.1)
IF
r LO
I
y = RA A Im{s(t) exp [−i( t +Δ)]}∕2, (11.2)
r LO
Q
IF
where s(t) is the transmitted data:
∑
s(t)= a g(t − mT ), (11.3)
m s
m
T is the symbol period, and g(t) represents the pulse shape. Eqs. (11.1) and (11.2) have to be modified to take
s
∘
into account the noise and delays due to 90 hybrids:
y = KRe{s(t − ) exp [−i(2f (t − )+Δ)] + n(t)}, (11.4)
I
I
IF
I
y = KIm{s(t − ) exp [−i(2f (t − )+Δ)] + n(t)}, (11.5)
Q
Q
Q
IF
Fiber Optic Communications: Fundamentals and Applications, First Edition. Shiva Kumar and M. Jamal Deen.
© 2014 John Wiley & Sons, Ltd. Published 2014 by John Wiley & Sons, Ltd.