Adaptive digital equalization in the presence of chromatic dispersion ...

Adaptive Digital Equalization in the Presence of Chromatic Dispersion, PMD, and Phase Noise in Coherent Fiber Optic Systems Diego E. Crivelli

Hugo S. Carrer

Mario R. Hueda

Digital Communications Research Laboratory - National University of Cordoba - Argentina Av. Vélez Sarsfield 1611 - Córdoba (X5016GCA) - Argentina - Email: [email protected] Abstract— Chromatic dispersion (CD) and polarization mode dispersion (PMD) severely limit the performance of optical transmission systems operating at data rates of 10 Gb/s and beyond. Electrical equalization techniques have been proposed to compensate dispersion in both coherent and intensity modulation/directdetection (IM/DD) systems. The former benefit from the fact that a complete compensation with zero penalty is possible, at least in principle, whereas in the latter the loss of phase information caused by the direct detection process results in a nonzero dispersion penalty even when optimal equalizers are used. In this paper, we investigate the combined adaptive digital equalization of all-order PMD, CD, and laser phase noise in highspeed coherent optical transmission systems. Although electrical equalization in coherent optical transmission systems has been addressed by previous literature [1]–[3], equalization of the combined effects of CD, PMD, and laser phase noise has not been reported so far. Simultaneous equalization of these impairments is particularly important in modulation systems that exploit polarization to increase the modulation efficiency, such as the joint polarization modulation and M-ary differential phase shift keying (JPMDPSK) system described in [4]. We propose a novel 4-dimensional equalizer structure for JPMDPSK systems. The specific example considered in this paper is 40 Gb/s transmission with a 10 GBaud symbol rate, using DQPSK modulation on each axis of polarization. Our results show that the new fourdimensional equalizer can compensate channel dispersion of up to 1000 km of standard single-mode fiber, with less than 3 dB penalty in signal to noise ratio (SNR). This is a dramatic improvement over 40 Gb/s IM/DD systems, even when they use electrical [5] or optical [6] equalization. The feasibility of the very large scale integration (VLSI) of coherent receivers in current technology is also discussed.

I. I NTRODUCTION Chromatic dispersion (CD) and polarization mode dispersion (PMD) severely impact the performance of high-speed optical fiber transmission systems (10-40 Gb/s and beyond). Although simple equalization techniques such as linear (LE) or decision-feedback equalization (DFE) have been proposed to compensate CD and PMD in intensity modulation/direct detection (IM/DD) receivers, their effectiveness in single-mode fibers is limited as a result of the nonlinear behavior of these channels [7]. Fiber impairments may be efficiently mitigated using elaborate equalization techniques such as maximum likelihood sequence estimation (MLSE) [8]–[10]. However, nonzero penalty is incurred in IM/DD receivers even with the optimal detector, owing to the loss of phase information caused by the optical to electrical conversion. IEEE Communications Society Globecom 2004

Unlike in IM/DD schemes, in coherent detection receivers it is possible to completely compensate CD and PMD with zero penalty by means of electronic equalization techniques. CD [11] and PMD [12] can also be compensated with zero penalty in the optical domain. However, adaptation schemes for optical equalizers are rather complicated because the error signal is obtained from the electrical domain after direct detection, a process that inherently eliminates phase information. In addition, techniques working entirely in the electrical domain may be simpler to implement and they lend themselves better to cost-effective VLSI integration than those based on optical signal processing. Electronic equalization techniques using microwave and millimeter wave technology have been reported in [1], [2]. These techniques are difficult to implement and they are not adaptive. A more elaborate scheme introduced in [3] utilizes an analog fractionally spaced equalizer (FSE) and exploits the advantages of analog techniques proposed in [13] to provide adaptivity. One of the most important shortcomings of the coherent equalization schemes described in the previous literature is that they ignore polarization effects in the channel and the received signal. This is acceptable when polarization is not exploited by the transmission system to carry information. In these situations, polarization diversity receivers can be used to compensate the random variations that normally occur in the state of polarization of the received signal [14], and the equalizer only needs to deal with the phase and magnitude information. However, in transmission systems using joint polarization and phase modulation, the received signal must be treated as a four-dimensional vector, and the equalizer structure must compensate effects such as the random exchanges of energy between the two states of polarization that occur in normal fibers and possibly independent dispersion effects for each polarization, as might happen in high order PMD. In this paper we introduce a four-dimensional equalizer structure that can effectively compensate high order PMD, as well as CD and effects such as polarization-dependent loss. It can also partially compensate the phase noise of the transmitter and the local oscillator. A polarization diversity receiver would normally add the two polarization components after demodulation and detection. In the receiver described in this work, the phase and polarization components are

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kept separate and processed as a four-dimensional vector (or, equivalently, a two-dimensional complex vector) by the equalizer. We investigate the relative merits of different types of equalizers, such as linear and decision-feedback, baud rate sampled or fractionally-spaced, etc., for the problem of interest in this work, and assess the performance of the preferred structure by computer simulation. We show that our scheme can compensate CD and PMD of a 1000 km standard singlemode fiber with less than 3 dB of penalty in signal to noise ratio (SNR) in a 40 Gb/s transmission system based on joint polarization and DQPSK modulation (JPDQPSK) with a symbol rate of 10 GBaud, similar to the one described in [4]. This is a dramatic improvement over 40 Gb/s IM/DD systems, even when they use electrical [5] or optical [6] equalization. We also investigate the feasibility of a very large scale integration (VLSI) in current CMOS technology of the receiver studied in this paper. Based on the performance results reported in Section V and the feasibility studies of a CMOS VLSI implementation of Section VI, we conclude that digital adaptive equalization techniques will become an efficient and cost-effective way to compensate fiber optic impairments in high-speed coherent transmission systems. The rest of the paper is organized as follows. In Section II the channel and receiver schemes are described. Techniques to equalize the optical channel are presented and analyzed in Section III. In Section IV the fractionally spaced equalizer is investigated. Simulation results are presented in Section V. Implementation is discussed in Section VI. Finally, our conclusions are summarized in Section VII. II. C HANNEL AND R ECEIVER D ESCRIPTION Fig. 1 shows a simplified model of the system under consideration. The transmitted bits externally modulate the intensity and/or phase of the transmitter laser (TL). The optical fiber introduces chromatic and polarization mode dispersion, as well as attenuation. Optical amplifiers (OA) deployed periodically along the fiber compensate the attenuation and introduce ASE noise. The received signal is optically filtered and applied to the receiver front-end (RFE). Then, the optical signal is mixed with a local oscillator (LO) laser and demodulated to baseband. In this paper we assume homodyne detection. The RFE is similar to the one of an 8-branch double balanced phase and polarization diversity receiver [14], with the exception that the four diversity branches are not immediately combined. Instead, they are treated as a four-dimensional vector to be processed by the equalizer described in Section III. The four components of the demodulated signal are sampled either one or multiple times per symbol period, depending on whether a baud-rate sampled or a fractionally-spaced equalizer is used, and fed into a digital signal processor (DSP) for subsequent equalization and detection. The electrical field component (EFC) of the electromagnetic wave at the output of the external modulator (EM) can be written as → − → → x + Ey (t)− y E (t) = Ex (t)− (1) → − → = (e (t) + je (t)) x + (e (t) + je (t))− y, 1

2

IEEE Communications Society Globecom 2004

3

4

Optical Channel Transmitted bits EM

Fiber

Fiber

Received bits OF

RFE

DSP

OA TL

LO

Fig. 1. System model. EM, external modulator; TL, transmitter laser; OA, optical amplifier; OF, optical filter; RFE, receiver front-end; LO, local oscillator; DSP, digital signal processor.

TIA HY LO

PBS

r1 TIA

r2

Sampled signal

r3 Fiber

TIA

PBS

r4

HY TIA

Fig. 2. Receiver front end. LO = local oscillator; PBS = polarization beam splitter; HY = four-port optical hybrid; TIA = trans-impedance amplifier.

where e1 (t) and e2 (t) are the in-phase and quadrature com→ ponents of the − x -aligned EFC Ex (t), while e3 (t) and e4 (t) → are the corresponding components of the − y -aligned EFC → − → − Ey (t). x and y are unit vectors along the orthogonal axes → − of polarization. Notice that E (t) can be treated either as a 4-dimensional real vector or as a 2-dimensional complex vector. We adopt the latter notation because it facilitates the description of the equalizer of Section III. ˜ Let E(ω) = [Ex (ω) Ey (ω)]T r be the Fourier transform → − of vector E (t) ((·)T r means transpose). Then, ignoring the nonlinear effects and polarization dependent loss (PDL), the fiber propagation equation that takes into account all order PMD, chromatic dispersion, and attenuation is given by [4]: ˆx (ω) E −αL −jβ(ω)L ˜ e JE(ω) ˆy (ω) = e E (2) u(ω) v(ω) Ex (ω) −αL −jβ(ω)L =e e −v ∗ (ω) u∗ (ω) Ey (ω) where (·)∗ means complex conjugate. In (2), J is the well-known Jones matrix [15]. Parameter β(ω), which accounts for chromatic dispersion, is obtained by averaging the propagation constants of the two principal states of polarization β(ω) = (βx (ω) + βy (ω))/2. Parameter α is the fiber loss. In practical systems, it can be assumed to be a constant within the signal bandwidth (in this work, we set α = 0). Finally, L is the fiber length. Fig. 2 shows a simplified diagram of the RFE. The received field polarization components are separated by means of a polarization beam splitter and combined with the corresponding polarization components of the local oscillator (which is linearly polarized at π/4 with respect to the receiver reference

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d(k)

φˆ(k)

Slicer

∆φˆ(k) d(k)

T

Slicer

∆φˆ(k)

(d(k−1) )∗

(a)

(b)

Fig. 3. Two detection techniques for DPSK. (a) Synchrodyne. (b) Differential. r(t)

Lowpass filter r(t) G

Matched Filter (a)

Fig. 4.

are modeled as white complex Gaussian processes. h11 (t), h12 (t), h21 (t), and h22 (t), constitute the baseband equivalent channel model, defined by h (t) h12 (t) H(t) = 11 , (4) h21 (t) h22 (t)

Equalizer

h11 (t) = F −1 e−jβ(ω)L u(ω) , h12 (t) = F −1 e−jβ(ω)L v(ω) , h21 (t) = F −1 −e−jβ(ω)L v ∗ (ω) , h22 (t) = F −1 e−jβ(ω)L u∗ (ω) ,

C

(b)

(a) Sampled matched filter. (b) Practical implementation.

axes), using two four-port optical hybrids. The EFCs at the output of the hybrids are detected by means of balanced photodiodes. Note that this balanced architecture has the advantage of suppressing the relative intensity noise (RIN) [14]. Signals r1 and r2 are the in-phase and quadrature components of the ˆx (t). In a similar way, signals r3 and r4 are received EFC E the in-phase and quadrature components of the received EFC ˆy (t). These signals are sampled at the symbol period T , or E at a fraction of T in the case of fractionally spaced processing. The noise sources present in the system are amplified spontaneous emission (ASE), shot, thermal, and phase noise. ASE noise is introduced by optical amplifiers and can be modeled as additive white Gaussian noise (AWGN) in each polarization. Shot noise has a Poisson distribution, but for large numbers of incident photons its distribution can be closely approximated as a Gaussian [16]. Thermal noise from the analog front-end of the receiver is modeled as a Gaussian variable. Phase noise is also present in the signal, as a result of phase fluctuations in the transmit and local oscillator lasers. t It is usually characterized ˙ )dτ , where the time as a Wiener process, φ(t) 0 φ(τ ˙ derivative φ(t) is a zero-mean white Gaussian process with a power spectral density Sφ˙ (ω) = 2π∆v ([16]–[18]), and ∆v is defined as the laser linewidth parameter. Lasers diodes with ∆v ≈ 1 − 5 MHz are available today. The problem of phase noise can be reduced using differential PSK (DPSK), where the information is encoded by changes in phase, ∆φ(k) , from one symbol to the next [19]. Fig. 3 shows two DPSK decoder architectures: (a) synchrodyne detection, and (b) differential detection. Synchrodyne detection, which is adopted in this work, results in a lower penalty than differential detection, but it requires that the phase of the signal be tracked. As we shall show later, a simple digital algorithm similar to carrier recovery can be used to track the phase of the signal. Based on (2), the baseband received signal-plus-noise terms for each axis of polarization can be written as

and F −1 represents the inverse Fourier transform operator. The front-end matched filter (MF) based receiver is shown in Fig. 4(a). In our model, MF is defined by matrix HH (−t) ((·)H means transpose and conjugate). From (3), it is possible to verify that MF completely eliminates the channel dispersion, and no further signal processing is needed prior to detection. In real situations, MF is hard to synthesize because of (i) the complexity of the channel response and (ii) its nonstationary nature owing to PMD. An alternative structure for the receiver front-end consists in using a lowpass filter followed by an equalizer in the discrete time domain, as shown in Fig. 4(b). A fractionally-spaced equalizer automatically synthesizes the MF response [19]. We model the discrete time oversampled channel by N subchannels, where N denotes the oversampling factor. The (m) m-th (m = 0, . . . , N − 1) subchannel column vector hij (i, j = 1, 2) is obtained by sampling the continuous time model given by (5) at t = k + m N T (where k ∈ Z is the baud-rate sample index). Fig. 5 shows the discrete time model of the entire sys(·) tem. At the transmitter, the MDPSK symbols ai ∈ A = j2πν/M e |ν ∈ {0, 1, · · · , M − 1} are differentially encoded. (k) (k) (k−1) The resulting MPSK symbols are bi = ai bi , with i = x, y. The discrete-time received signal for the m-th subchannel can be expressed as: (m)

rx(k,m) =

(h11 (t)⊗Ex (t)+h12 (t)⊗Ey (t))+nx (t)

jφy (t)

ry (t) = e

(h21 (t)⊗Ex (t)+h22 (t)⊗Ey (t))+ny (t),

(3)

where φx (t) and φy (t) are the phase noise components on each polarization, and ⊗ denotes convolution. In (3), the power of each LO component has been normalized to unity. ASE, shot, and thermal noise are represented by nx (t) and ny (t), and they IEEE Communications Society Globecom 2004

Lh

jφ(k,m) x

e

−1

n=0

(n,m) (k−n) bx

h11

(n,m) (k−n) by

+ h12

+n(k,m) x (m)

Lh

(k,m)

ry(k,m) = ejφy

−1

n=0

(n,m) (k−n) bx

h21

(n,m) (k−n) by

+ h22

(6)

+n(k,m) , y

jφx (t)

rx (t) = e

(5)

(m)

(n,m)

are, respectively, the channel truncawhere Lh and hij tion length and the n-th sample of the m-th subchannel. Continuing with Fig. 5, after the equalizer the samples are (k) (k) rotated by the estimated angles φˆx and φˆy and applied to the slicer. Note that after equalizer, the samples are baud-spaced, so we have dropped index m from all signals.

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Receiver model DPSK encoder

(k,m)

ejφx

T (k)

ax

(k) ay

(k)

ˆ e−j φx

Discrete time channel model

ˆb(k) x

(k)

dx

(k,m)

(k)

a ˆx

nx

Equalizer (k,m)

(k)

(k)

rx

bx

H

(k) by

C

(k) qy ˆ(k) −j φ y

(k,m)

ejφy

(k)

ˆb(k) y

(k)

(k,m)

dy

ny

ˆb∗(k−1) x

ex

e

T

(·)∗

T

qx

(k,m) ry

(k)

a ˆy T

(·)∗

ˆb∗(k−1) y

(k)

ey

Fig. 5.

Discrete time transmission model with DPSK synchrodyne detection.

The slicer output is used to estimate the transmitted sequence as follows ˆ(k)ˆ∗(k−1) , a ˆ(k) x = bx bx

ˆ(k)ˆ∗(k−1) . a ˆ(k) y = by by

(7)

To track the signal phase, we use the following estimation algorithm (k+1) (k) (k) ∗(k) = φî + δ di ˆbi φî , (8) where i can be either x or y, means measured angle, and δ, 0 ≤ δ ≤ 1, is the algorithm step size. III. S TRUCTURE OF THE E QUALIZER This section analyzes different equalization structures for the receiver described previously. Toward this end, we consider two possible schemes: linear equalization (using a feedforward FIR filter) and decision feedback equalization (using feedforward and feedback FIR filters). Both techniques have been studied in detail in the literature [20]. In this paper, we focus on selecting the best one for optical coherent transmission systems using joint phase and polarization modulation. The structures under consideration are the following: • Linear equalizer (LE) with a baud-spaced FIR (baudspaced equalizer, BSE) • LE with a fractionally spaced FIR (fractional-spaced equalizer, FSE) • Decision feedback equalizer (DFE) with baud-spaced single sided forward filter, and • DFE with baud-space doubled sided forward filter. The most suitable equalizer structure for the receiver analyzed in this paper must be chosen based on the nature of the fiber channel impairments. From previous analysis, discounting a flat attenuation and neglecting for the moment polarization dependent loss (PDL), it can be noted that the optical channel affects the phase and polarization of the signal but not its amplitude. This “all-pass” nature of the coherent optical channel must be taken into account when selecting a BSE or an FSE. The FSE can equalize the fiber channel without noise enhancement. On the other hand, a BSE may cause noise amplification in receivers with significant excess bandwidth IEEE Communications Society Globecom 2004

(this is common when Gaussian transmitted pulse shapes are used). Although this is a well known limitation of BSE, in our application it has an additional undesirable implication: it negates the inherent advantage of the previously mentioned “all-pass” nature of the coherent channel. For this reason we choose an FSE structure. A baud spaced DFE could be adopted to reduce the noise enhancement effect. Two types of DFE may be used: with a single sided (i.e., with purely noncausal taps) forward filter (DFE-SSF), or with a double sided (i.e., with both causal and noncausal taps) forward filter (DFE-DSF). These schemes have different behavior when they are used in optical fiber channels. According to [21], the DFE-SSF does not perform as well as the conventional FSE in the presence of delay distortions, since the forward equalization section of the DFE-SSF may cause amplitude distortion and noise enhancement. Although, the DFE-DSF can achieve better performance than the DFESSF, according to the same reference its forward filter section requires about twice the time span of the conventional FSE. This longer time span degrades performance in the presence of phase noise, even for the currently available lasers with a linewidth of only 1 − 5 MHz. From the above discussion, we conclude that linear equalization with fractional spaced filters (LE-FSE) is the best choice for coherent receivers, based on current laser technology. Although LE-FSE requires higher sampling rate than other equalizer schemes, it can be implemented in current VLSI technology using parallel processing (Section VI). IV. A DAPTIVE F RACTIONALLY S PACED E QUALIZATION Signal equalization with a LE-FSE can be achieved with four FIR filters, as we show in Fig. 6. The equalized samples are given by (k) T r qx (k) R(k) , (9) q = (k) = C(k) qy r(k) (k) (k) where R(k) = rx(k) , rx and ry are the Lc -dimensional y

column vectors whose components are the fractionally spaced

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c11

(k,m)

ry

SNR [dB] @BER=10−6

18

(k,m)

rx

(k,m)

qx

c21 c12

(k,m) qy

c22 FIR filters

Fig. 6.

received samples at instant k. C(k) =

16.5 16 15.5 15 100

(k)

(k)

(k)

(k)

c11 c12 c21 c22

Fig. 7.

ˆ(k)

ej φx 0

0

ˆ(k)

ej φy

is a diagonal matrix with the

estimated phase of each polarization state, and ρ is the step size parameter. V. S IMULATION R ESULTS In this section we analyze the performance of the previously developed receiver (N = 2). We use two polarization multiplexed QDPSK constellations, which enable a 40 Gb/s data rate with a 10 GBaud symbol rate. The transmitted pulse shape has an unchirped Gaussian envelope exp(−t2 /2T02 ) with T0 = 36 ps [22]. We present results for a typical single mode fiber as specified by the ITU G.652 Recommendation [23] used in the third telecommunication window (1550 nm), which leads to a dispersion parameter D √ = 17 ps/km/nm. PMD was set to the worst case of 10 ps/ km. The fiber is modeled using the coarse step method [24], with more than 100 sections of IEEE Communications Society Globecom 2004

200

250

300

350

Required SNR vs channel length. Phase noise is set to zero.

(k)

with cij

Then, the well-known stochastic gradient algorithm is used to adapt the filter coefficients, that is, ∗ T r ˆ (k) , e(k) C(k+1) = C(k) + ρ R(k) (11) Φ

150

Fiber span [km]

being Lc -dimensional column vectors whose components are the coefficients of the fractionally spaced equalizer at instant k. If reflected in the equalizer structure, the unitary nature of the Jones matrix would place constraints on the values of (k) cij . By removing those constraints we enable the equalizer to compensate effects such as polarization dependent loss (PDL). Two criteria may be used to find the coefficients of the equalizer. The peak distortion criterion completely eliminates the dispersion effect by inverting the channel response. Noise amplification may occur using this criterion. The minimum mean squared error (MMSE) criterion reduces noise enhancement [20] and better performance can be achieved. Based on these considerations, in the following we focus on adaptive equalization using the MMSE criterion. From Fig. 5, the instantaneous error at the slicer can be written as (k) (k) ˆb(k) ex x − dx (k) . (10) e = (k) = (k) ˆby − d(k) ey y

ˆ (k) = where Φ

17

Block diagram of the equalization filter stage.

15 taps 10 taps 8 taps

17.5

birefringent fiber. This adequately models first- and higher order PMD as well as CD. We present results for only one of the two polarization multiplexed channels. The signal-to-noise ratio (SNR) for such a channel is defined as: E [dB], (12) SNR = 10 log10 N0 where N0 is the double sided noise power given by the sum of ASE, shot, and thermal noise powers. E is the noise free signal power. The phase noise parameter is ∆vT with ∆v and T previously defined. Fig. 7 shows the SNR required for a constant bit error rate (BER) of 10−6 for the proposed receiver as a function of the fiber length. Each plot corresponds to a different equalizer length. For the purpose of this simulation the phase noise parameter was set to zero. It can be seen that an 8-tap equalizer is sufficient to compensate up to 200 km of fiber with about 1 dB penalty. A 10-tap equalizer can reach 300 km, and a 15-tap equalizer can compensate more than 350 km. It should be noted that, with a sufficient number of taps, an unlimited fiber length can be compensated when phase noise is not present. But, as we shall see next, a penalty is induced by phase noise. This penalty is responsible for the limitation as to the maximum length of fiber that can be compensated. Fig. 8 shows the SNR required for a constant bit error rate (BER) of 10−6 for the proposed receiver as a function of the phase noise parameter, with a channel length of 300 km and a 15-tap equalizer. It can be seen that the proposed system can handle up to 20 MHz of laser phase noise with a penalty of less than 3 dB. In Fig. 9 we investigate the performance limit for an unconstrained complexity equalizer (i.e. assuming there is no limit in the number of taps) and for a phase noise parameter of 0.001. It can be seen that the proposed receiver can compensate up to 1000 km of fiber with less than 3 dB penalty. Monte-Carlo simulation results are shown in Fig. 10 for a 300 km fiber channel. For a fully coherent QPSK demodulation scheme when no phase noise is present and parameter δ = 0, perfect equalization can be achieved by the proposed architecture (note that the solid line shows the theoretical limit for QPSK). The remaining curves correspond to DPSK with a parameter δ = 0.6 (which works well in every case), and for different phase noise parameters. From Fig. 10 we observe

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Channel Coefficients (Module)

SNR [dB] @BER=10−6

19 18 17 16 15

0

0.0005

0.001

0.0015

0.002

0.5 5

0.4

4

0.3

6 7

0.2

9

8

0.1 0

3

2

0

∆vT

5 10 15 Number of sample at baud-rate (×104 )

20

5 10 15 Number of sample at baud-rate (×104 )

20

10

Required SNR vs phase noise parameter. δ = 0.6. MSE @20dB

Fig. 8. SNR [dB] @BER=10−6

22 21 20

1

0.1

19 0.01

18 17 16

0

200

400

600

800

1000

Fig. 11. Variation of the equalizer coefficients (top) and the corresponding MSE (bottom) for a time varying channel. The labels in the upper figure corresponds to the coefficient index number.

1200

Fiber span [km]

Fig. 9. Required SNR vs channel length, with an unconstrained complexity equalizer and phase noise parameter ∆vT = 0.001. δ = 0.6.

that the main loss is intrinsic to the differential demodulation (DPSK). The degradation caused by phase noise matches the one shown in Fig. 8. Fig. 11 shows the equalizer performance under channel variations owing to the nonstationary nature of PMD. In real systems, the channel variation is a very slow process. It could take hours or even days to accumulate an appreciable change in the response. For practicality of the simulations, we model the channel variations at a higher than normal rate and by means of small random rotations of the axes of each birefringent fiber segment in the simulation model of the whole fiber. In Fig. 11 the module of the representative coefficients of the c11 filter (top) and the corresponding observed MSE (bottom) are shown. A 250 km fiber and a 10-taps equalizer were used. The initial convergence of the equalizer can be seen in this figure. After initial convergence, the MSE remains −1 Theory w/o PN w/o PN, δ = 0.6 ∆vT = 0.001 ∆vT = 0.0015

−2

log10 (BER)

−3 −4 −5 −6 −7 −8 −9 −10

5

10

15

20

25

30

SNR [dB] Fig. 10. Bit error rate versus signal-to-noise ratio for fractionally spaced equalization. PN, phase noise; w/o, without.


0

constant while the channel changes with time. At sample number 100000, a large and sudden channel variation was introduced. The equalizer quickly recovers from the transient returning to the original MSE level, while the coefficients track the channel variation. VI. I MPLEMENTATION C ONSIDERATIONS Although the main purpose of this paper is to investigate equalizer structures for coherent receivers using joint phase and polarization modulation, it is useful to consider some implementation issues based on current technology. We focus on transmission systems with a signaling rate of 10 GBaud and modulation efficiency of 4 bits per symbol. Semiconductor laser linewidth directly impacts system performance. Old lasers had linewidths as large as 50 MHz (i.e., ∆vT ≈ 0.01), therefore constellations such as QPSK were not viable. Nowadays, InGaAsP MQW-DFB laser diodes with linewidth of 1-5 MHz (i.e., ∆vT ≤ 0.001) are commercially available. This performance makes them suitable for the application considered in this work. For future optical telecommunications systems, verticalcavity surface-emitting lasers (VCSEL) should be considered owing to their low-cost [25], [26]. Furthermore, recent work has demonstrated a good linewidth performance of VCSELs [27]. However, VCSELs with wavelengths around 1550 nm are not commercially available today. Semiconductor photonic integrated circuits (PICs) [28] appear to be the best choice for coherent receiver front-end integration. Integrated coherent receivers have been demonstrated in [29]–[32]. In particular, [32] showed a polarization insensitive heterodyne receiver which could be used (with minor changes) for integration of the receiver front-end described in this paper.

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The implementation that can make this technology most viable commercially is a digital monolithic integrated circuit in CMOS technology. The main challenges to the design of such a receiver are the analog to digital converter (ADC) and the implementations of high speed FIR filters. Interleaved ADCs can be used to increase the effective sampling rate [33]–[35] whereas parallel FIR filter architectures can be used for high speed FIR implementations. In [36] these themes are treated in the context of direct detection optical receivers, but the discussion can be extended to the case of concern to us. VII. C ONCLUSIONS In this paper we have proposed a coherent receiver for highspeed optical fiber systems using joint phase and polarization modulation. The specific example considered uses two polarization multiplexed QDPSK signals, which allows 40 Gb/s at a signaling rate of 10 GBaud. We have derived a new equalizer structure that adaptively compensates the combined effect of PMD, CD, and laser phase noise. We have evaluated the system performance on standard single mode fiber channels. Our results have shown the excellent performance of coherent detection receivers operating in the presence of the phase noise levels present in commercially available lasers. Additionally, the feasibility of a very large scale integration (VLSI) of the receiver in current technology has been addressed in this paper. Our results show that digital adaptive equalization techniques will be able to efficiently compensate fiber optic impairments in high-speed optical transmission systems. R EFERENCES [1] N. Takachio and K. Iwashita, “Compensation of fiber chromatic dispersion in optical heterodyne detection,” IEEE Electron. Lett., pp. 108–109, Jan. 1988. [2] J. H. Winters, “Equalization in coherent lightwave systems using microwave waveguides,” J. Lightwave Technol., vol. 7, pp. 813–815, May 1989. [3] ——, “Equalization in coherent lightwave systems using a fractionally spaced equalizer,” J. Lightwave Technol., vol. 8, no. 10, pp. 1487–1491, Oct. 1990. [4] S. Betti, F. Curti, G. D. Marchis, and E. Iannone, “A novel multilevel coherent optical system: 4-quadrature signaling,” J. Lightwave Technol., vol. 9, no. 4, pp. 514–523, Apr. 1991. [5] M. Nakamura, H. Nosaka, M. Ida, K. Kurishima, and M. Tokumitsu, “Electrical PMD equalizer ICs for a 40-Gbit/s transmission,” in Proc. of the Optical Fiber Communication Conference and Exhibit (OFC), vol. TuG4, 2004. [6] M. Bohn et al., “Experimental verification of combined adaptive PMD and GVD compensation in a 40Gb/s transmission using integrated optical FIR-filters and spectrum monitoring,” in Proc. of the Optical Fiber Communication Conference and Exhibit (OFC), vol. TuG3, 2004. [7] O. E. Agazzi and V. Gopinathan, “The impact of nonlinearity on electronic dispersion compensation of optical channels,” in Proc. of the Optical Fiber Communication Conference and Exhibit (OFC), Feb. 2004. [8] O. E. Agazzi, D. E. Crivelli, and H. S. Carrer, “Maximum likelihood sequence estimation in the presence of chromatic and polarization mode dispersion in intensity modulation/direct detection optical channels,” in IEEE Proc. of the International Conference on Communications (ICC), vol. 5, pp. 2787–2793. [9] W. Sauer-Greff, A. Dittrich, R. Urbansky, and H. Haunstein, “Maximumlikelihood sequence estimation in nonlinear optical transmission systems,” Lasers and Electro-Optics Society (LEOS 2003). The 16th Annual Meeting of the IEEE, vol. 1, pp. 167–168, Oct. 2003.


[10] H. F. Haunstein, K. Sticht, A. Dittrich, W. Sauer-Greff, and R. Urbansky, “Design of near optimum electrical equalizers for optical transmission in the presence of PMD,” in Proc. of the Optical Fiber Communication Conference and Exhibit (OFC), vol. 3, 2001, pp. 558–560. [11] M. Secondini, E. Forestieri, and G. Prati, “Adaptive minimum MSE controlled PLC optical equalizer for chromatic dispersion compensation,” J. Lightwave Technol., vol. 21, no. 10, pp. 2322–2331, Oct. 2003. [12] E. Forestieri, G. Colavolpe, and G. Prati, “Novel MSE adaptive control of optical PMD compensators,” J. Lightwave Technol., vol. 20, no. 12, pp. 1997–2003, Dec. 2002. [13] J. H. Winters and R. D. Gitlin, “Electrical signal processing techniques in long-haul fiber-optic systems,” IEEE Trans. Commun., vol. 38, no. 9, pp. 1439–1453, Sept. 1990. [14] W. van Etten and J. van der Plaats, Fundamentals of Optical Fiber Communications. Prentice Hall, 1991. [15] J. P. Gordon and H. Kogelnick, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Nat. Acad. Sci., vol. 97, no. 9, pp. 4541–4550, Apr. 2000. [16] J. R. Barry and E. A. Lee, “Performance of coherent optical receivers,” Proceedings of the IEEE, vol. 78, no. 8, pp. 1369–1394, Aug. 1990. [17] L. G. Kazovsky, “Phase-and-polarization-diversity coherent optical techniques,” J. Lightwave Technol., vol. 7, no. 2, pp. 279–292, Feb. 1989. [18] G. J. Foschini, L. J. Greenstein, and G. Vannucci, “Noncoherent detection of coherent lightwave signals corrupted by phase noise,” IEEE Trans. Commun., vol. 34, no. 6, pp. 1437–1448, Nov. 1988. [19] J. R. Barry, E. A. Lee, and D. G. Messerschmitt, Digital Communication, 3rd ed. KAP, 2004. [20] J. G. Proakis, Digital Communications, 3rd ed. McGraw-Hill, 1995. [21] J. A. C. Bingham, The theory and practice of modem design. WileyInterscience, 1988. [22] G. P. Agrawal, Fiber-Optic Communication Systems. WileyInterscience, 1997. [23] Characteristics of Single-Mode Optical Fibre and Cable, International Telecommunications Union ITU-T Recommendation G.652, Mar. 2003. [24] T. Merker, N. Hahnenkamp, and P. Meissner, “Comparison of PMDcompensation techniques at 10 Gbit/s using an optical first-order compensator and electrical transversal filter,” Opt. Commun., pp. 135–141, Aug. 2000. [25] J. S. Harris, “Tunable long-wavelength vertical-cavity lasers: The engine of next generation optical networks?” IEEE J. Select. Topics Quantum Electron., vol. 6, no. 6, pp. 1145–1160, Nov./Dec. 2000. [26] C. J. Chang-Hasnain, “Progress and prospects of long-wavelength VCSELs,” IEEE Commun. Mag., vol. 41, no. 2, pp. 530–534, Feb. 2003. [27] P. Signoret et al., “3.6-MHz linewidth 1.55-µm monomode verticalcavity surface-emitting laser,” IEEE Photon. Technol. Lett., vol. 13, no. 4, pp. 269–271, Apr. 2001. [28] T. L. Koch and U. Koren, “Semiconductor photonic integrated circuits,” IEEE J. Quantum Electron., vol. 27, no. 3, pp. 641–653, Mar. 1991. [29] T. L. Koch et al., “GaInAs / GaInAsP multiple-quantum-well integrated heterodyne receiver,” Electron. Lett., vol. 25, no. 24, pp. 1621–1623, Nov. 1989. [30] H. Takeuchi, K. Kasaya, Y. Kondo, H. Yasaka, K. Oe, and Y. Imamura, “Monolithic integrated coherent receiver on InP substrate,” IEEE Photon. Technol. Lett., vol. 1, no. 11, pp. 398–400, Nov. 1989. [31] R. Kaiser et al., “Monolithically integrated polarization diversity heterodyne receivers on GaInAsP / InP,” Electron. Lett., vol. 30, no. 7, pp. 1446–1447, Aug. 1994. [32] R. Kaiser, D. Trommer, H. Heidrich, F. Fidorra, and M. Hamacher, “Heterodyne receiver PICs as the first monolithically integrated tunable receivers for OFDM system applications,” Optical and Quantum Electronics, vol. 28, pp. 565–573, 1996. [33] W. C. Black and D. A. Hodges, “Time-interleaved converter arrays,” IEEE J. Solid-State Circuits, vol. 15, no. 6, pp. 1022–1029, Dec. 1980. [34] A. Petraglia and S. K. Mitra, “Analysis of mismatch effects among A/D converters in a time-interleaved waveform digitizer,” IEEE Trans. Instrum. Meas., vol. 40, no. 5, pp. 831–835, Oct. 1991. [35] D. Fu, K. C. Dyer, S. H. Lewis, and P. J. Hurst, “A digital background calibration technique for time-interleaved analog-to-digital converters,” IEEE J. Solid-State Circuits, vol. 33, no. 12, pp. 1904–1911, Dec. 1998. [36] O. E. Agazzi, V. Gopinathan, K. Parhi, K. Kota, and A. Phanse, “DSP based equalization for optical channels - feasibility of a VLSI implementation,” IEEE 802.3ae Task Force, New Orleans., Sept. 2000. [Online]. Available: http://grouper.ieee.org/groups/802/3/ae/public/sep00/agazzi 1 0900.pdf

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