SPM mitigation in 16-ary amplitude-and-differential-phase shift keying long-haul optical transmission systems

Dung Dai Tran; Arthur J. Lowery

doi:10.1364/OE.18.007790

1. Introduction

Spectral efficiency is becoming an important consideration for optical communications systems. 16-level amplitude-and-differential-phase-shift keying (16-ADPSK) [1] is a high spectral efficiency format that uses a combination of quadrature-amplitude-shift-keying (QASK) and differential-quadrature-phase-shift-keying (DQPSK) modulation in each optical symbol, so can increase the channel bit rate or equivalently the spectral efficiency by 4-times compared with binary modulation formats.

This increase in spectral efficiency, however, comes at a cost of a reduction in transmission distance for a given amplifier spacing, as multi-bit per symbol transmission formats require a higher OSNR for a given BER. The high OSNR, in turn, requires higher transmission powers, making the system susceptible to fiber nonlinearity. To get the most benefit of 16-ADPSK, the effect of fiber nonlinearity must be minimized. This can be achieved by nonlinearity compensation which, depending on the location, can be classified into pre-compensation and post-compensation. Pre-compensation introduces distortion to the signals before transmission, which is compensated by fiber during signal propagation. Killey [2], Essiambre et al. [3], Roberts et al. [4] obtained the fiber model by backward propagating of signals from the receiver to the transmitter and used this model for pre-distortion of the signals. However this technique requires a precise knowledge of the system dispersion map, the fiber nonlinearity, the distance-dependent signal power, and extensive computing efforts. To simplify the process of fiber modeling, Liu and Fishman [5] derived a fast algorithm for pre-distortion of the signal, that avoids the need of detailed knowledge of the signal power evolution and the need to solve the NLSE within fiber, thus it dramatically reduces the computation time. Xu et al. [6] simply added to the signals an extra phase shift, proportional to the power of the transmitted bits and the fiber nonlinearity coefficient, to compensate the self-phase-modulation (SPM) in the fiber. Goeger [7] assigned a constant optical phase shift to each RZ bit dependent on the two previous bits.

Post-compensation compensates the nonlinear phase shift at the receiver. Xia and Rosenkranz [8] proposed a nonlinear feed-forward/decision-feedback equalizer (FFE/DFE) at the receiver that increases the nonlinear threshold by 4.5 dB for a 1-dB eye-opening penalty for a 43 Gbit/s RZ, 8 × 80-km system. Xu and Liu [9] used a phase modulator driven by the received signal intensity to compensate the nonlinear phase shift for a DPSK signal. Ho and Kahn [10] analyzed the nonlinearity mechanism and defined the optimal amount of phase to be post-compensated for a quadrature-phase-shift-keying (QPSK) system. Kikuchi et al. [11] applied an angular rotation, equal to the phase shift caused by the fiber nonlinearity but with opposite sign, to each signal points at the receiver of the 16-ADPSK and 32-ADPSK signals for mitigating the fiber nonlinearity effect. Oda et al. [12] proposed a method using cascaded digital signal processing (DSP) blocks that facilitates a 2-dB Q-improvement for a 112-Gbit/s 1200-km coherent DP-QPSK system. Millar et al. [13] reported a method modified from [12] that allows an increase of optimum launch power by 1 dB for 42.7-Gbit/s 7780-km and 85.4-Gbit/s 6095-km coherent PDM-QPSK systems. Pre- and post-compensation were also implemented in combination by Lowery [14] for adaptively compensating the fiber nonlinearity in long-haul optical orthogonal-frequency-division-multiplexing (OFDM) systems.

In this paper, we report a method for mitigating the effect of SPM in 16-ADPSK systems, using pre-compensation of the nonlinearity. This allows these systems to be operated at higher optical powers. The method has a much simpler hardware structure and requires much less computation compared with the pre-compensation methods in [2–4]. Although it cannot follow the fast (within a symbol) signal power changes in the optical link as the post-compensation methods in [8,9,12–14] it provides useful improvements in performance. Furthermore, we show that the differential detection in the receiver automatically compensates for the nonlinear phase shift due to the mean power of the Amplified Spontaneous Emission (ASE) from the optical amplifiers.

2. Theory

Figure 1 shows an optical transmission system using the 16-ADPSK signal model proposed by Sekine et al. [1]. In the transmitter which is based on a dual-drive Mach-Zehnder modulator (DDMZM) and works in the polar-coordinate modulation mode [15,16], each four bits of the transmitted data [D ₃ D ₂ D ₁ D ₀] are encoded into two voltages v ₁(t) and v ₂(t) for driving the amplitude-and-phase modulator (APM) when SPM pre-compensation is not used. When it is used, a voltage ΔV from the ΔV block is added to v ₁(t) and v ₂(t) to create two driving voltages v ₃(t) and v ₄(t). More details about the compensation mechanism are given in the end of this section. The NRZ 16-ADPSK pulses produced by the APM are then created by the pulse carver (PC), which is also based on a DDMZM, into 66%-RZ pulses to minimize the effects of inter-symbol interference. The direct detection receiver comprises an amplitude demodulator (AD) for detecting the D ₂ and D ₃ bits, and two differential phase demodulators (PD) based on Mach-Zehnder delay interferometers (MZDIs) for detecting the D ₀ and D ₁ bits.

Fig. 1 16-ADPSK optical transmission system, top, with details of the transmitter, bottom left, and receiver, bottom right.

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Figure 2a shows the transmitted signal constellation in the complex plane, with ${\vec{E}}_{i}, i = 0, 1, ..., 15$ , representing the optical field of one of the 16 optical symbols coded by 4 bits [D ₃ D ₂ D ₁ D ₀]. To guarantee the balanced error probabilities between the constellation points, the ratios of the powers of the different symbols are set to P ₁ = 2.47P ₀, P ₂ = 4.56P _0, P ₃ = 7.26P ₀, where P ₀ is the power of the inner-most symbols. Figure 2b shows the signal constellation at point A in Fig. 1 and the phase change of the optical symbols caused by the fiber nonlinearity.

Fig. 2 Typical 16-ADPSK signal constellations: (a) transmitted and (b) received showing the effect of self-phase modulation (SPM).

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For an optical symbol with the optical field ${\vec{E}}_{i}$ and the ASE noise ${\vec{n}}_{k}$ contributed by the k-th optical amplifier (OA), the nonlinear phase changes ϕ_NL,i caused by the symbol at the end of s spans is given by the summation [10,17]:

φ_{N L, i} = γ L_{e f f} {{| {\vec{E}}_{i} + {\vec{n}}_{1} |}^{2} + {| {\vec{E}}_{i} + {\vec{n}}_{1} + {\vec{n}}_{2} |}^{2} + ... + {| {\vec{E}}_{i} + {\vec{n}}_{1} + {\vec{n}}_{2} ... + {\vec{n}}_{s} |}^{2}}

where:

γ = 2 π n_{2} / (λ_{0} A_{e f f})

is the fiber nonlinear coefficient, n ₂ is the material nonlinear index, A_eff is the fiber core effective area, λ ₀ is the central wavelength, L_eff is the fiber effective nonlinear length per span, and

{\vec{E}}_{i}

takes one of 16 values as described in Fig. 2a. The mean value of

φ_{N L, i}

,

〈 φ_{N L, i} 〉

, depends on the powers

{| {\vec{E}}_{i} |}^{2}

and is [10]:

〈 φ_{N L, i} 〉 = s γ L_{e f f} ({| {\vec{E}}_{i} |}^{2} + (s + 1) σ_{A S E}^{2})

where

σ_{A S E}^{2}

is the variance of the optical field due to the ASE noise of one span. Equation (2) shows that the signal and noise powers both contribute to the mean phase changes <ϕ_NL,i>.

The phase demodulator at the receiver differentiates the received phase to estimate the value of a symbol. This avoids the need for an optical phase reference, such as a local oscillator. For two consecutive optical symbols with complex envelopes ${\vec{E}}_{i}$ and ${\vec{E}}_{j}$ , the phase error of the differential phase has a mean value <Δϕ_NL,ijdemod>:

〈 Δ φ_{N L, i j demod} 〉 = 〈 φ_{N L, i} 〉 - 〈 φ_{N L, j} 〉 = s γ L_{e f f} ({| {\vec{E}}_{i} |}^{2} - {| {\vec{E}}_{j} |}^{2})

This shows that the effect of the ASE’s power (proportional to its variance) is cancelled by the differential detection. Of course there will be instantaneous phase errors due to the random field of the ASE, which cannot be cancelled using differential detection.

The effect of the phase error on the performance of the DQPSK signal component in the 16-ADPSK signal will be minimized when <Δϕ_NL,ijdemod> is minimized. This can be achieved by nonlinearity pre-compensation with the working principle described in Fig. 3 : the arrow 1 shows the pre-distortion of the signal phases at the transmitter. The arrow 2 shows the phase compensation by the fiber nonlinearity that results in the minimization of the phase error <Δϕ_NL,ijdemod>.

Fig. 3 Pre-distortion and compensation of phases (1) which compensates for the SPM in the fiber (2).

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The pre-distortion of phases is applied using compensating voltages ΔV_i and ΔV_j which are calculated based on the mean phase shifts <ϕ_NL,i> and <ϕ_NL,j> in Eq. (2) and added to the driving voltages v ₁(t) and v ₂(t) of the amplitude-and-phase modulator (APM):

Δ V_{i} = \frac{q 〈 φ_{N L, i} 〉 V_{π}}{π}

where: V_π is a voltage required to provide a π -radian phase shift of the carrier in each optical, upper and lower, paths of the APM; the factor q defines the percentage of the compensation. The pre-compensation functionalities are shown in Fig. 1: the ΔV block calculates the compensating voltages using s, γ, L_eff, and the power of optical symbols extracted from the transmitted data, and the two adder blocks add the compensating voltages ΔV to the voltages v ₁(t) and v ₂(t).

3. 16-ADPSK system simulations

Two chromatic dispersion (CD) compensation schemes were simulated, with dispersion maps and channel power profiles shown in Fig. 4 where DL is the residual chromatic dispersion, P is the signal power along the fiber length, and P_in is the signal power input to the fiber. The first scheme, called the double-stage OA scheme, uses 80-km SMF, 17-km DCF, and a double-stage OA with 5.61-dB and 16-dB gains in each 80-km amplified span. The attenuation coefficients of the SMF and DCF are 0.2 dB/km and 0.33 dB/km; the dispersion coefficients are 17 ps/nm/km and −80 ps/nm/km; the fiber nonlinearities are 2.6 × 10⁻²⁰ m²/W and 4.0 × 10⁻²⁰ m²/W; the fiber core effective areas are 80 μm² and 30 μm². The second scheme, called the single-stage OA scheme, uses 54-km SMF and 27-km negative dispersion fiber (NDF) [18,19] and a 16.57-dB gain single-stage OA in each 81-km amplified span; the attenuation coefficients of the SMF and NDF are 0.187 dB/km and 0.24 dB/km; the dispersion coefficients are 18.5 ps/nm/km and −37 ps/nm/km; the fiber nonlinearities are 2.3 × 10⁻²⁰ and 2.6 × 10⁻²⁰ m²/W; the fiber core effective are: 101 μm² and 27 μm². Other parameters are: 8 WDM channels, 6-dB OA noise figure, 60-Gbit/s/channel, 37.5-GHz channel spacing. The signal constellation is monitored in optical domain at the input of the optical receiver, point A, as shown in Fig. 1. All simulations used VPItransmissionMaker^TM 7.6.

Fig. 4 (a) Dispersion map and channel power profile of the double-stage OA scheme and (b) single-stage OA scheme.

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4. Results and discussion

The effect of SPM, and its mitigation, can be seen through the dependence of the quality of signal, the $Q_{e f f}$ parameter, on the channel input power:

Q_{e f f}, d B \equiv 20 \log_{10} (\sqrt{2} {erfc}^{- 1} (2 B E R))

where erfc⁻¹(.) denotes the inverse of the complementary error function, BER is bit-error-ratio of the signal under investigation. For example, a BER of 3 × 10⁻³, corresponding to the limit of a forward error correction (FEC) [4] gives a Q_eff of 8.78 dB.

Figure 5a shows Q_eff versus channel input power for a single-wavelength system using pre-compensation with different values of the q factor: the optimum for q is 0.8 indicating partial compensation is best. This is because pulse spreading due to chromatic dispersion has reduced the peak power of the optical symbols so that the actual nonlinear phase changes are less than the phase changes given by Eq. (1). Figure 5b shows Q_eff versus channel input power for a single-wavelength system and an 8-channel WDM system for the case q = 0.8. Two signal constellations shown in the insets for the single-channel system without and with pre-compensation indicate that the pre-compensation scheme has minimized the mean phase error <Δϕ_NL,ijdemod>. At low powers Q_eff increases with dB-for-dB with optical power, as this is the noise-limited region of operation. At higher powers, nonlinearity becomes dominant, and Q_eff decreases rapidly with increasing optical power. Pre-compensation moves the power for an optimum Q_eff upwards. This improvement is seen for the single-channel and the WDM systems, indicating that the dominant degradation in the WDM system is SPM. In both systems, the peak value of Q_eff is increased by over 1-dB. This should allow transmission over longer distances.

Fig. 5 (a) Signal quality versus channel input power and compensation factor for a single-channel system showing the effect of the compensation factor, q; (b) Signal quality versus channel input power for single-channel and WDM systems for optimum q.

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To find the maximum transmission distance of the 16-ADPSK systems, the optical noise and nonlinearity limits are constructed for Q_eff = 8.78 dB at different distances as shown in Fig. 6 where the x axis represents the transmission distance (on a log scale) and the y axis represents the channel power. The optical noise and nonlinearity limits show the signal power required to maintain the signal quality at Q_eff = 8.78 at the corresponding transmission distances. Q_eff = 8.78 is a typical limit (corresponding to BER = 3 × 10⁻³) higher than which a FEC still works effectively [4]. The areas bounded by these limits show the signal power required to achieve a target transmission distance with Q_eff >8.78. The difference of the power levels between the two limits at a given transmission distance shows the range of powers over which the system would operate satisfactorily. The point where the two limits cross shows the maximally achievable transmission distance for Q_eff = 8.78 and the corresponding power.

Fig. 6 (a) Noise and nonlinearity limits to 60-Gbit/s double-stage OA systems and (b) to 60-Gbit/s single-stage OA systems. c) Chromatic dispersion limits to 60-Gbit/s double-stage OA system and (b) to 60-Gbit/s single-stage OA systems.

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Figure 6a shows the noise and nonlinearity limits for the single-channel and WDM systems with the double-stage OA scheme. For the WDM system, the transmission distance has been increased from 700 km without compensation, to 1010 km with compensation. For the single-channel system, the transmission distance has increased from 740 km to 1150 km. The increase in the nonlinearity limited distance with compensation is less for the WDM system than for the single-channel system. This is expected as the WDM systems also suffers from cross-phase modulation (XPM), which is not compensated for.

Figure 6b shows the noise and nonlinearity limits for the systems using the single-stage OA scheme. With pre-compensation, the maximum transmission distance was increased from 980 km and 900 km to 1460 km and 1320 km for the single-channel and WDM systems, respectively. Compared with the double-stage OA systems, the single-stage OA systems have longer transmission distances and distances at 3-dB power dynamic range. This is due to the fact that the single-stage OA systems require lower OSNRs for a given BER compared with the double-stage OA systems and the dispersion compensation occurs within fiber that is contributing to the transmission distance. The figure also shows that the single-stage OA systems are poorer at compensation than the double-stage OA systems. This can be explained by the fact that the single-stage OA systems experience less nonlinearity than the double-stage systems (see the fiber parameters of the two types of systems in the system setup section) so the compensation cannot be as effective. An analogue can be found in Fig. 5a and 5b where the effect of compensation in the linear and weakly nonlinear region (low power region) is practically nil or very low compared with the effect of compensation in the nonlinear region (high power region). Like the double-stage OA WDM system, the single-stage OA WDM system also suffers from XPM. However, the power and distance penalties due to XPM for both types of WDM systems are small compared with the single-channel systems (<2 dB and 140 km). This indicates that the SPM pre-compensation works effectively and independently from XPM, which reduces the system design complexity.

Figure 6c and 6d show the degrading effect of chromatic dispersion together with the fiber nonlinearity to the signal quality of the single channel double-stage and single-stage OA systems. The criteria for defining the dispersion maximally allowed for effective operation of SPM compensation is an 1-dB decrease of Q_eff (from 9.78 dB to 8.78 dB), which is equivalent to 1-dB power or OSNR penalty, when the residual chromatic dispersion DL increases from 0 ps/nm. From the figures, it can be seen that the maximally allowed chromatic dispersion is within around [-110 125] ps/nm and [-130 135] ps/nm for 960-km double-stage and 1296-km single-stage OA systems, respectively. These ranges increase to around [-120 135] ps/nm and [-140 155] ps/nm when the transmission distances decrease to 320 km and 324 km.

5. Conclusions

We have shown that a simple pre-compensation scheme can be used to mitigate the effects of self-phase modulation in 16-ADPSK systems. Simulations show that the scheme works effectively for both single-channel and WDM systems, and help to increase the transmission distance by a factor of 1.5.

Acknowledgement

We express our thanks to VPIphotonics (www.vpiphotonics.com) for the use of their simulator, VPItransmissionMaker 7.6.

References and links

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SPM mitigation in 16-ary amplitude-and-differential-phase shift keying long-haul optical transmission systems

Abstract

1. Introduction

2. Theory

3. 16-ADPSK system simulations

4. Results and discussion

5. Conclusions

Acknowledgement

References and links

Cited By

Figures (6)

Equations (6)

Optics Express