Frequency domain chromatic dispersion estimation

Abstract

The low complexity, robust, and precise algorithm solely employs a simplified autocorrelation function of the signal spectrum for blind chromatic dispersion estimation to adapt frequency domain compensation functions in digital coherent receivers.

Full text

Frequency Domain Chromatic Dispersion Estimation
F.N. Hauske1, C. Xie1, Z. Zhang2, C. Li2, L. Li3, Q. Xiong3
1: Huawei Technologies Duesseldorf GmbH, European Research Center, Riesstrasse 25,
D-80992 Munich, Germany, e-mail: fabian.hauske@huawei.com, 2: Huawei Technologies
Canada., Ltd., Ottawa R&D Centre, Ottawa, Canada, 3: Huawei Technologies Co., Ltd.,
Optical Network Technology Research, Shenzhen, China
Abstract: The low complexity, robust, and precise algorithm solely employs a simplified auto-
correlation function of the signal spectrum for blind chromatic dispersion estimation to adapt fre-
quency domain compensation functions in digital coherent receivers.
c
2010 Optical Society of America
OCIS codes: (060.1660) Coherent communications; (060.2330) Fiber optics communications
1. Introduction
Coherent detection receivers with digital equalization allow full compensation of all linear channel impairments of a
linear or weakly nonlinear optical fiber channel [1]. This allows for uncompensated transmission with digital equal-
ization of chromatic dispersion (CD) instead of optical compensation by means of dispersion compensating fibers
(DCF). It has been proposed by [2] to employ a low-complexity frequency domain (FD) filter to compensate for
static CD and to use a time-domain (TD) 2x2 muli-input multi-output (MIMO) finite impulse response (FIR) filter
stage with fast update for tracking time-varying effects like polarization-mode dispersion (PMD) and rotation of the
state of polarization (SOP). Although the value of CD does not change largely during transmission, in switched net-
works, a fast and reliable initialization of the CD filter is required.
Digital CD compensation has been demonstrated, where either the filtering function has been known and pre-set
[3], a training sequence has been applied for filter update [4] or the adaptation algorithm has been not disclosed [5].
Blind filter adaptation by use of a modified constant modulus algorithm (CMA) has been demonstrated in [6], [7].
We present a blind (non-data aided) FD CD estimation algorithm for adaptive equalizers solely based on the dig-
ital spectra of the signal. In contrast to [6], [7], this allows for continuous monitoring of CD and for a low speed esti-
mation routine initializing the equalizer in a side process independent from the modulation format. Robust estimation
over a wide range of CD within a fixed adaptation length is demonstrated for 112 Gbit/s polarization-division multi-
plex (PDM) quaternary phase-shift keying (QPSK) with combined channel impairments.
2. Frequency Domain Chromatic Dispersion Estimation
After the polarization-diverse 90◦-hybrid, and analog/digital conversion (ADC), overlapping blocks of the signal
sequence are transferred into the FD by a fast Fourier transform (FFT). Copies of those data blocks Sx,in,k[m]and
Sy,in,k [m]from both polarizations xand yare used in a low speed side processor to estimate and monitor the param-
eter of CD (see Fig. 1). The data blocks indexed kare not necessarily adjacent. The index m=−M/2 + 1, ..., M/2
denotes discrete frequencies within a block length M(even number) with the direct current (DC) frequency centered
at m= 0. The frequency resolution ∆f=Rs/M of each FFT block is defined by the sampling rate Rsin the ADC.
D (f)
-1
ADC
ADC
optical
90°hybrid
x-pol.
y-pol.
LO
PBS
ADC
ADC
clockrecovery
s/pconversion
carrierrecovery
detection
blockwiseFFT
ADC
ADC
blockwiseIFFT
p/sconversion
TD2x2MIMOFIR
Re
Im
j
Re
Im
j
D[m]
FDCDestimation
Fig. 1. Optical front-end with polarization diverse 90◦-hybrid, ADC and digital
equalization including FD CD compensation.
impairment distribution parameter
PMD Maxwellian mean 25 ps
PDL linear [0:10] dB
CD linear [-30:30] ns/nm
LOFO linear [-1.5:1.5] GHz
θlinear [0:2π]
ϕlinear [0:2π]
OSNR constant 14 dB
Tab. 1. Table of random channel impairments including
the statistical distribution.
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-2.5 -2 -1.5 -1 -0.5 0 0.5
x104
0
0.2
0.4
0.6
0.8
1
1.2
1.4
di[ ]ps/nm
Jnorm
mean
min
standard
deviation
0500 1000 1500 2000 2500 3000 3500 4000 4500 5000
0.1
0.2
0.3
0.4
0.5
0
4
8
12
16
20
#FFT blocks
stdof Jnorm
trial
Fig. 2. Example of normalized error criterion Jnorm (left) and standard deviation of Jnorm for each channel realization with the required number
of FFT blocks for averaging (right).
To mitigate polarization effects, we apply the signal Sin,k[m] = Sx,in,k [m] + Sy,in,k [m]to tentative filtering func-
tions Di[m] = exp(−jm2∆f2δiπλ2/c)with the speed of light c, the carrier wavelength λand the CD parameter δi
leading to filtered blocks Sout,k,i[m] = Sin,k [m]·Di[m][6]. The values of CD vary by δi=δmin + (i−1)∆δup to
δmax. A modified, discrete, circular auto-correlation
Uk,i[n] = 1
M
M/2
∑
m=−M/2+1
sign (ℜ{cshift(Sout,k,i[m], n)})·S∗
out,k,i[m]
+jsign (ℑ{cshift(Sout,k,i[m], n)})·S∗
out,k,i[m](1)
is applied for each FFT block kand each CD filtering function Diwith a circular shift cshift(Sout,k,i[m], n)of the
signal Sout,k,i[m]by n∈melements. In a hardware implementation, the sign sign of the according real part ℜand
imaginary part ℑrespectively just adds on the sign of the complex conjugate S∗
out,k,i[m], reducing the processing
complexity significantly to a few additions. The shift ndoes not necessarily cover all possible shifting values of m.
We define an error criterion
J[i] = ∑
k
∑
n
|Uk,i[n]|2(2)
averaging over the absolute values of the correlation functions of several FFT blocks. In principle, this FD criterion
can be derived from the CMA criterion applied in the TD [6]. The argument of the minimum error criterion delivers
the estimated CD parameter
δest =δmin + ∆δ(arg(min
iJ[i]) −1) ,(3)
which is delivered to update the CD compensation function D[m].
To judge on the reliability of the estimation and to evaluate the necessary number of FFT blocks for averaging,
we introduce a normalized error criterion Jnorm, which is scaled to a unity mean value and a minimum at zero as de-
picted in Fig. 2, left. The standard deviation of Jnorm indicates the distance of the minimum value from the diver-
gence of the error criterion. Low values of the standard deviation indicate a reliable estimation, large values close to
one indicate weak estimations.
3. Estimation Performance
We tested the estimation performance on random data of 112 Gbit/s PDM-QPSK in a single channel, single span
simulation with random channel conditions and concentrated noise loading at the receiver. The random variations
and the according distributions of CD, PMD, polarization-dependent loss (PDL), local oscillator frequency offset
(LOFO), optical signal-to-noise ratio (OSNR), polarization phase ϕand polarization angle θare listed in Tab. 1. In
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10-0.9 10-0.7 10-0.5 10-0.3
100
101
102
103
104
105
standarddeviationof Jnorm
|derr| [ps/nm]
erroneous
estimations
detected
goodestimations
detectedas
erroneous
-400 -300 -200 -100 0 100 200 300 400
100
101
102
103
derr [ps/nm]
incidents
Fig. 3. Estimation error |δerr|versus standard deviation of normalized error criterion Jnorm (left) and histogram of estimation error |δerr|(right).
total, 5000 independent trials have been realized. After the optical front-end (compare [1]), the signal is digitized by
ADC with Rs= 2 samples per symbol. Overlapping FFT-blocks of M= 1024 samples are transferred into the FD.
The tentative filtering functions have been scanned from δmin =−32000 ps/nm in steps of ∆δ= 200 ps/nm up to
δmax =−32000 ps/nm. The correlation function has been applied in a range from n=−0.7M/2, ...,+0.7M/2.
Initially averaging over a minimum of 4 FFT-blocks, the number of blocks is consecutively increased until the
normalized error criterion reaches a value of Jnorm ≤0.25 with a maximum number of 20 FFT blocks. The required
number of FFT blocks for each channel realization is given in Fig. 2, right. About 7.5% of all trials require more than
4 blocks, less than 0.9% would require more than 20 blocks. All those trials that do not satisfy the condition Jnorm ≤
0.25 are marked as potential erroneous estimations.
We evaluate the estimation performance by the estimation error δerr =CD −δestim. From Fig. 3, left, we can
see that the indication of potential erroneous estimations correctly detected all corrupt estimations (0.2%) but also
marked 0.6% of correct estimation as erroneous. In Fig. 3, right, the histogram of the estimation error proves a zero
mean value with a standard deviation of the estimation error of 103 ps/nm and a maximum deviation of 400 ps/nm.
This refers to a maximum deviation of two CD estimation steps ∆δ. It should be noted that about 57 ps/nm of the
standard deviation result from the finite resolution of ∆δ. A step width below ∆δ= 200ps/nm would further reduce
the estimation error. As the estimation error has a zero mean value, a long-term average could reduce the estimation
error close to zero. Increasing the OSNR to higher values clearly improves the estimation precision, while even lower
OSNR values require more averaging. Similarly, shorter FFT-blocks require more averaging and longer blocks vice
versa.
4. Conclusion
We demonstrated a low complexity, pure FD CD estimation algorithm with a high robustness against any combina-
tion of channel impairments, any polarization effect in particular. The estimation method is independent from the
modulation format and from the line rate. Given a maximum estimation error of 400 ps/nm, a subsequent TD FIR
filter with only 5 taps would be sufficient to compensate the remaining CD in 112 Gbit/s PDM-QPSK systems.
References
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