2023年12月2日发(作者：m14步枪)

Digital filters for coherent optical receivers

Seb J. Savory

Optical Networks Group, Dept. of Electronic & Electrical Engineering,

University College London., Torrington Place, London WC1E 7JE,UK

ssavory@

Abstract: Digital filters underpin the performance of coherent optical

receivers which exploit digital signal processing (DSP) to mitigate

transmission impairments. We outline the principles of such receivers and

review our experimental investigations into compensation of polarization

mode dispersion. We then consider the details of the digital filtering

employed and present an analytical solution to the design of a chromatic

dispersion compensating filter. Using the analytical solution an upper bound

on the number of taps required to compensate chromatic dispersion is

obtained, with simulation revealing an improved bound of 2.2 taps per

1000ps/nm for 10.7GBaud data. Finally the principles of digital polarization

tracking are outlined and through simulation, it is demonstrated that

100krad/s polarization rotations could be tracked using DSP with a clock

frequency of less than 500MHz.

©2008 Optical Society of Americas

OCIS codes: (060.1660) Coherent communications; (060.4510) Optical communications;

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#87192 - $15.00 USDReceived 4 Sep 2007; revised 14 Nov 2007; accepted 14 Nov 2007; published 9 Jan 2008(C) 2008 OSA21 January 2008 / Vol. 16, No. 2 / OPTICS EXPRESS 80415. S.J. Savory, V. Mikhailov, R.I. Killey, P. Bayvel, “Digital coherent receivers for uncompensated 42.8Gbit/s

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1. Introduction

Prior to the advent of dispersion compensating fiber (DCF), chromatic dispersion was

considered to be one of the key limitations for optical communications systems[1]. Although

current systems use DCF this increases the complexity and cost of the system with an

alternative approach being to compensate the chromatic dispersion entirely in the electrical

domain either at the transmitter or receiver. Of the options considered for electronic chromatic

dispersion compensation, one of the most promising is a phase and polarisation diverse digital

coherent receiver[2].

While coherent detection was experimentally demonstrated as early as 1979[3], its use in

commercial systems has been hindered by the additional complexity, due to the need to track

the phase and the polarization of the incoming signal. In a digital coherent receiver these

functions are implemented in the electrical domain leading to a dramatic reduction in

complexity. Furthermore since coherent detection maps the entire optical field within the

receiver bandwidth into the electrical domain it maximizes the efficacy of the signal

processing. This allows impairments which have traditionally limited 40Gbit/s systems to be

overcome, since both chromatic dispersion and polarization mode dispersion (PMD) may be

compensated adaptively using linear digital filters[4-15].

This paper consists of three parts. Firstly we outline the principles of a digital coherent

receiver and demonstrate its ability to compensate large values of PMD. We then present a

new method for the design of the chromatic dispersion compensating filter, which allows

bounds to be obtained on the performance of such a filter. Finally we consider the dynamical

behavior of the receiver, in order to estimate the speed at which polarization rotations could

be tracked. While the focus of this paper will be 40Gbit/s systems the principles described are

equally applicable to higher data rates such as 100Gbit/s and beyond.

2. Principles of digital coherent receivers

2.1 Receiver architecture

Digital coherent receivers utilize a phase and polarization diverse architecture to map the

optical field into the electrical domain. Once digitized, digital signal processing (DSP), is used

#87192 - $15.00 USDReceived 4 Sep 2007; revised 14 Nov 2007; accepted 14 Nov 2007; published 9 Jan 2008(C) 2008 OSA21 January 2008 / Vol. 16, No. 2 / OPTICS EXPRESS 805to track both the phase and polarization of the signal, allowing for a considerable reduction in

complexity compared to an optical homodyne receiver. The functionality of the phase and

polarization diverse coherent receiver is to map in the optical field into four electrical signals,

corresponding to the in-phase and quadrature field components for the two polarizations. This

may be achieved practically using a number of options, ranging from more complex options

such as the passive quadrature hybrid with balanced detectors to fused fiber couplers with

single ended photodiodes as illustrated in Fig. 1.

(Ex,Ey)Polarization beam splitter

Photodiode

Photodiode

I/Q coupler

Re(Ex)Im(Ex)Input optical

signal

Polarization controller

Optical

local

oscillator

Photodiode

Polarization controller

Photodiode

Re(Ey)Im(Ey)Elo

Fig. 1. Schematic of a phase and polarization diverse receiver where Ex, Ey and Elo are the

electric fields associated with the horizontal and vertical polarization components of the input

optical signal and local oscillator respectively

The exact details of architecture chosen to implement the phase and polarization diverse

receiver will have little bearing on the subsequent DSP. Therefore without loss of generality,

as in our previous experimental work[8], we consider the architecture illustrated in Fig. 1, in

which asymmetric 3x3 fiber couplers are employed as 90° hybrids, such that the four

electrical signal are given by

22*⎛⎞2E+2E⎛⎞ReExEloxlo⎛i1⎞⎜⎟⎜⎟⎜⎟22*⎜4Ex+Elo⎟

1⎜i2⎟2⎜ImExElo⎟⎜⎟⎜i⎟=5⎜ReEE*⎟+10⎜2E2+2E2⎟ylo⎟ylo⎜⎜3⎟⎜⎟*2⎜i⎟⎜ImEE⎟⎜4Ey+Elo2⎟ylo⎠⎝4⎠⎝⎝⎠