IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 25, NO. 21, NOVEMBER 1, 2013 2137

Differential Phase Frame Synchronizationfor Coherent Transponders

Vincent A. J. M. Sleiffer, Student Member, IEEE, Maxim Kuschnerov,Roy G. H. van Uden, Student Member, IEEE, and Huug de Waardt, Member, IEEE

Abstract— Future optical transmission systems usingmultimode fibers as a transmission medium require data-aidedbased coherent receivers for stable and fast convergence, as blindestimation does not guarantee convergence and the convergencetime significantly increases with respect to data-aided estimation.The problem with data-aided digital signal processing is thatthe training sequence should be found inside the receivedsignal, which may be heavily distorted. We present an overheadefficient algorithm based on differential phase correlation tofind the start of the training sequence and show its robustnesstoward linear transmission impairments and local oscillatoroffset in single mode fiber.

Index Terms— Coherent detection, phase modulation, digitalsignal processing (DSP).

I. INTRODUCTION

IN ORDER to meet the growing demand for internetbandwidth with traffic growth rates around 40-50% per

year, telecommunication component providers face the task ofincreasing the spectral efficiency of fiber utilization [1]. After10Gbit/s systems became successful in the 1990’s, solutionsfor 40Gbit/s and 100Gbit/s became available in the last years[2], [3]. To cope with future capacity demands, research isleaving the single-mode fiber as transmission medium andis now focused on the development of transmission systemsusing space-division multiplexing in multi-mode or multi-corefibers [4]–[10]. Multi-mode transmission paves the way forvirtually unlimited transmission capacity by transmitting infor-mation over a multitude of available fiber modes. Recently anew record was obtained, transmitting 73.7 Tb/s over 119kmof few-mode fiber [7], underlining the great potential of thistechnology.

The change in transmission medium from single-mode fiberto multi-mode fiber also means a change in digital signalprocessing (DSP). During transmission the modes mix andcannot be anymore received separately without significantperformance penalty. Therefore the well-known 2×2 multipleinput multiple output (MIMO) has to be extended to N×N

Manuscript received May 28, 2013; revised August 14, 2013; acceptedSeptember 15, 2013. Date of publication September 17, 2013; date of currentversion October 9, 2013.

V. A. J. M. Sleiffer, R. G. H. van Uden, and H. de Waardtare with the COBRA Institute, Eindhoven University of Technol-ogy, Eindhoven 5612AZ, The Netherlands (e-mail: v.a.j.m.sleiffer@tue.nl;r.g.h.v.uden@tue.nl; h.d.waardt@tue.nl).

M. Kuschnerov is with Coriant Research and Development GmbH, Munich81541, Germany (e-mail: maxim.kuschnerov@coriant.com).

Color versions of one or more of the figures in this letter are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LPT.2013.2282336

MIMO, where N equals the number of spatial and polarizationmodes.

Whereas for single-mode transmission blind DSP was oftenused to de-multiplex the polarizations and undo linear trans-mission impairments, this is becoming more complex whenconsidering more modes and assuring all sent signals arerecovered with degenerate solutions of the equalizer, althoughpossible as shown in [4]. Therefore the better approach is toemploy data-aided DSP to assure convergence and recovery ofall the separate signals [11]. A problem faced here however isto detect the start of the training sequence, used as referenceto adapt the filter taps to the channel impulse response. Thisbecomes even more complicated when the number of modesis growing and mode-mixing is present.

Here we present an algorithm to find the start of a trainingsequence assuming the fundamental mode (LP01) is receivedwith enough extinction ratio compared to the higher ordermodes, as is the case for phase-plate based mode multiplexersand de-multiplexers [10]. This algorithm was successfully usedin [7], [8] and proposed before for use in wireless technologyfor the same purpose [12]. Furthermore we analyze the robust-ness of the algorithm to linear transmission impairments andlocal oscillator offset in the single-mode transmission domain.

II. FINDING START OF A TRAINING SEQUENCE

A. Framing Function

Linear channel distortions are mitigated in the receivereither by directly or indirectly estimating the channel transferfunction and applying an equalization function that reversesthe channel impairments while at the same time minimizingnoise enhancement. In general the estimation of the transferfunction of the transmission link can be done in two ways:

• Blind: the receiver only uses the received signal andknowledge of the received signal statistics and modulationformat to estimate the transfer function [13].

• Data aided: known training sequences (TS) are trans-mitted and by recovering them, the transfer functionis known [11]. A well-known approach is the use ofCAZAC sequences [14].

Data aided methods are dominantly used in wireless channelsthat suffer from severe impairments and recently have foundtheir way into coherent optic applications. They offer a stableand fast convergence, where on the contrary using blindestimation, the convergence cannot be guaranteed by designand the convergence time is significantly larger than for data-aided methods [11].

1041-1135 © 2013 IEEE

2138 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 25, NO. 21, NOVEMBER 1, 2013

Fig. 1. a) Find start using two repetitions of the training sequence, b) bruteforce searching for start by seeing if the output error decreased, i.e. theequalizer converged, c) performing blind DSP and correlate output sequencewith known training sequence to determine start, d) using differential phaseinformation, i.e. correlate received differential phase information with knowntraining sequence differential phase information.

Data-aided channel acquisition requires a framing func-tion, meaning that the start of the training sequence has tobe found before the actual equalization. This can becomequite complex if the channel distortions are severe or severalchannels are transmitted at the same time using multipleinput multiple output (MIMO) transmission, where severalchannels are sent over one single frequency using spatialmultiplexing. Designing training sequences that include theframing functionality inherently increases the overhead usedfor training sequences and thus leads to a less than effectiveuse of the limited spectrum.

B. Approaches

Two common approaches exist for finding the beginning ofthe training sequence in MIMO channels. The first one is basedon a repetition of the training sequence to find a repeatingdistortion pattern (Fig. 1a) [15]. This approach means thatthe overhead used for training sequences is doubled. Given aconstant spectrum for a channel, this leads to a reduction ofthe forward error correction (FEC) overhead, which decreasesthe reach and system margin of such a system. Moreover, thisapproach is vulnerable to a frequency offset that might beintroduced by a mismatch between the transmitter laser andthe local oscillator at the receiver.

The second approach (Fig. 1b) includes a brute-force searchof the training sequence, where the receiver tries to lockfor the training sequence in defined steps going through acomplete received frame. This approach not only increasesthe convergence time by at least a factor of hundred, but alsothe convergence is prone to errors and does not guarantee a100% finding of the training sequence.

Fig. 2. Differential phase regions decision lines and assigned values andtypical correlation plot for the start of the frame at position 1000 in a 32768symbol long sequence (no impairments) and considering 512 TS symbols.

A third approach is depicted in Fig. 1c. The approach istrying to converge to a solution using blind digital signalprocessing (DSP) and after convergence of (at least one of)the channels, the start is found by correlating the expectedsequence with the converged signal [16]. This approach willrequire a large start up time of the system, and convergenceis not assured.

C. Differential Phase Correlation

The approach applied in our experiments is based on analgorithm described in [12]. This method only works when thesignal is phase-modulated. The method is based on correlatingthe differential phase information of the sent and receivedtraining sequence (Fig. 1d). In case the two match, a high peakwill be observed and the beginning of the TS is found. Thisbrings the direct advantage that the training sequence does nothave to be repeated, reducing the required training sequenceoverhead by a factor of two compared to the first method.Since the approach is based on the phase difference betweentwo symbols, it can also inherently tolerate frequency offsetsby the local oscillator. Although in principle 16QAM symbolscan be used for this method since it is a phase-modulatedas well as amplitude modulated format, the efficiency usingQPSK or BPSK symbols will be higher due to a lowerprobability of a QPSK/BPSK symbol crossing a boundary. Inthis letter QPSK TSs are assumed.

III. DESCRIPTION OF THE ALGORITHM

The algorithm was implemented as follows. Both the differ-ential phase information for the training sequence and receiveddata are calculated. Correlating these results without applyingan additional step will result in non-optimal performance.Correlating a phase shift of 0 with 0 will yield 0, where alarge value is preferred in case the phase shifts match. Thesame holds for a ½π phase shift, where a full correlationwill only result in a ¼π2, compared to π2 when the phaseshifts are both π . Therefore every phase shift is first assignedtwo corresponding values of either 1 of −1, such that all

SLEIFFER et al.: DIFFERENTIAL PHASE FRAME SYNCHRONIZATION 2139

Fig. 3. Simulation setup.

full correlations yielded the same results, and opposite phasechanges result in a negative correlation. These values aredepicted in Fig. 2. The resulting two column matrices forboth the TS and received signal are used for calculating thecorrelation. Please note these decision lines can also be usedwhen using either BPSK (regions 2 and 3 can be seen as alower reliability zone and give lower correlation as such) or16QAM TSs (correlation on most significant bit). A typicalresult without transmission impairments is also depicted inFig. 2, which shows a very sharp peak at the start of theframe. The resilience of this algorithm to linear transmissioneffects was tested using simulations.

IV. SIMULATION SETUP

The setup used in the simulations is depicted in Fig. 3.The light from a laser was splitted into two equally poweredtributaries which are both 28 GBaud QPSK-modulated usingan IQ-modulator, driven by an ideal DAC running at 2 samplesper symbol, after which they are combined again using apolarization beam combiner (PBC). The signals driving theIQ-modulators were randomly generated 32768 symbols longbinary streams of which the pattern was stored for correlationafterwards, creating completely uncorrelated signals on bothpolarizations. The resulting 28-Gbaud DP-QPSK modulatedsignal was first filtered using a Gaussian 4th order optical bandpass filter with a 45-GHz 3-dB bandwidth and subsequentlysent into a totally linear fiber to emulate chromatic dispersion(CD), polarization-mode dispersion (PMD) and polarizationdependent loss (PDL). At the receiver side the signal isfiltered using a Gaussian 4th order optical band pass filter ofwhich the filter bandwidth was varied. Afterwards, the stateof polarization was changed, additive white gaussian noise(AWGN) was loaded and a frequency offset between local-oscillator (LO) and signal as well as laser line width wasemulated. After regular coherent detection and resampling,a two sample per symbol signal was obtained on which theproposed algorithm was performed to determine the start of thesent symbols using 512 symbols in the sent sequence as TS.

Fig. 4. Normalized correlation value (contours) of (a) CD [ps/nm] vs.OSNR [dB/0.1nm], (b) Frequency offset [MHz] vs. OSNR [dB/0.1nm] and(c) CD[ps/nm] vs. Frequency offset [MHz].

V. RESULTS AND DISCUSSION

In first instance a single polarization is analyzed for perfor-mance of the algorithm, in which all parameters are consideredideal and only two of them are varied. Per setting onehundred realizations were analyzed. The optical filter beforethe receiver was set to a 45-GHz 3-dB bandwidth. Fig. 4adepicts a contour plot in which the CD [ps/nm] is sweptversus OSNR [dB/0.1nm]. The contours show the normalizedcorrelation value (ncv) obtained, where 0 means no correlationand 1 full correlation, between the TS and the start of the TSin the received signal. It can be observed that the algorithm isquite sensitive to CD compared to OSNR. Beyond ±200 ps/nmthe reliability quickly drops. Therefore in [7], [8] prior todetermining the start, blind CD compensation was employedwhich is standard for state of the art coherent receivers [17].Another way to mitigate this problem is reducing the symbolrate of the TS. At an OSNR of 10 dB/0.1 nm the algorithmstill proves to be very reliable (ncv >0.7).

Fig. 4b shows the tolerance of the algorithm in frequencyoffset between LO and signal [MHz] vs. OSNR [dB/0.1nm].Since the algorithm is based on a differential phase correlation

2140 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 25, NO. 21, NOVEMBER 1, 2013

TABLE I

SIMULATION PARAMETERS

Fig. 5. Normalized correlation value vs. probability density (PDF) withsimulation parameters in Tab. I. Red: without CD, PMD and PDL, Blue: withCD, PMD and PDL.

it is expected to be very tolerant to a frequency offset, as alsoobserved from Fig. 4b. Assuming no noise, the algorithm isexpected to malfunction at a boundary of 3500 MHz for a28 GBaud QPSK signal, in which a 1/4 π shift is obtainedbetween two consecutive symbols.

In the last contour plot, Fig. 4c, the frequency offset betweenLO and signal [MHz] vs. CD [ps/nm] is depicted. This figureunderlines the previous observed behavior, a large toleranceto frequency offset and sensitivity to CD.

As a last reliability test, simulations (using polarization-multiplexing) were carried out with the parameters listed inTab. 1. In Fig. 5 the probability density functions of thenormalized correlation value obtained are plotted for the caseswith (blue) and without (red) CD, PMD and PDL. Withoutthe transmission effects a mean ncv of ~0.7 with a standarddeviation 0.1 is obtained. For comparison, in case randomdata without the TS was tested for finding the start, a meancorrelation of 0 was obtained with a standard deviation of~0.1. For this case with all realizations the correct start wasdetermined.

With transmission effects obviously the percentage of cor-relation drops, but still the mean ncv is >0.4. The standarddeviation did not change substantially and is ∼0.1. The startwas determined correctly in >94% of the cases (574 wrongdecisions), where a single symbol offset was considered tobe correct, as it is still within the MIMO equalizer’s windowwhich is normal for state of the art coherent receivers [17]. Thereliability could easily be increased by using more symbols(for 1024 symbols the start was determined correctly for allcases), by averaging over more frames for correlation, or byusing a special pattern TS.

VI. CONCLUSION

In this letter we showed that the position of a trainingsequence in received data suffering from linear transmissionimpairments, AWGN as well as laser phase noise and LOfrequency offset, can be very reliably estimated using a corre-lation between the received data differential phase informationand the differential phase information of the known senttraining sequence. This method was successfully used in themode-division multiplexed experiments to find the start on theLP01 modes in the references [7] and [8].

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