Nonlinearity Mitigation of Intensity Modulation and Coherent Detection Systems JINLONG WEI,1* NEBOJŠA STOJANOVIC,1 CHANGSONG XIE1 1Huawei
Technologies Düsseldorf GmbH, European Research Center, Riesstrasse 25, 80992 München, Germany. *Corresponding author:
[email protected] Received XX Month XXXX; revised XX Month, XXXX; accepted XX Month XXXX; posted XX Month XXXX (Doc. ID XXXXX); published XX Month XXXX
Coherent optical communication systems are still too expensive for metro and short reach networks in the near future. Coherent detection with intensity modulator replacing costly dual-polarization I/Q modulator could offer a good trade-off between cost and performance for metro networks. The major performance limit of such systems is the nonlinearity. To our best knowledge, this paper offers the first known investigation on nonlinearity of a high speed intensity modulation and coherent detection system using an integrated laser and electroabsorption modulator. Advanced nonlinearity mitigation digital signal processing (DSP) are proposed including a 2 × 1 multiple-input single-output complex transversal Volterra FFE filter, a first proposed post-FFE noise cancellation filter taking into account both pre- and postcursor noise correlations based on a simple autocorrelation coefficient calculation, and a maximum likelihood sequence estimator. The receiver DSP needs no carrier and phase recovery that is required by a conventional coherent receiver DSP. Results show that, compared to a simple linear FFE equalization, the proposed nonlinear DSP enables over 8-dB and 4-dB improvement in OSNR sensitivity at 7% overhead harddecision feedforward error correction (FEC) and 20% overhead soft-decision FEC threshold BERs, respectively, for a 56-Gb/s intensity modulation and coherent detection system. To our best knowledge, record 18-dB OSNR sensitivity at hard-decision FEC threshold BER of 3.8 × 10-3 is also achieved. © 2018 Optical Society of America OCIS codes: (060.2330) Fiber optics communications; (060.4080) Modulation. http://dx.doi.org/10.1364/OL.99.099999
Coherent optical communication systems offer high spectral efficiency and reliable performance but high cost transceiver photonic hardware and advanced complex digital signal processing (DSP) are unavoidable. Therefore, its main applications are commonly restricted to high capacity long-haul transmission links. For metro and short reach applications where the capacity
requirement is less stringent as compared to long-haul links, coherent transceivers are not yet a cost effective solution. This raises the demand for tailoring coherent system by simplifying hardware and DSP-based optical receiver to offer a better trade-off between cost and performance. The major transceiver cost of a coherent system is in the transmitter’s laser and dual-polarization in-phase and quadrature (I/Q) modulator. Consequently, intensive research efforts have been made to replace the coherent transmitter with a simple intensity modulator such as directly modulated laser (DML) [1], vertical-cavity surface-emitting laser (VCSEL) [2], or electro-absorption-integrated modulated laser (EML) [3,4]. This significantly relaxes the requirement on the transceiver lasers and thus simplifies the DSP by eliminating the need for a carrier and phase recovery (CPR) [2,3]. The drawback of such a system is its relatively low optical signal to noise ratio (OSNR) sensitivity due to the system nonlinearity, which is partly from components and optical fiber link. In addition, due to the lack of CPR, frequency offset upon coherent detection also brings about noise correlation as will be shown later, which further degrade system performance. Although the OSNR sensitivity can be significantly improved by leveraging the chirp of an intensity modulator, it requires a CPR in the receiver’s DSP and the transmitter chirp must be large enough by properly applying a high RF driving voltage [1], which requires specially designed lasers otherwise it may significantly shorten existing commercial lasers’ lifetime. To our best knowledge, this work offers the first known contribution on mitigating nonlinearities of an intensity modulation coherent detection system and advanced receiver nonlinear DSP without receiver CPR is proposed which enables significant improvement of system OSNR sensitivity. In this paper, a nonlinear 2 × 1 multiple-input single-output (MISO) complex transversal Volterra feed-forward equalizer (FFE) equalizer in association with a following noise cancellation (NC) filter, as well as a maximum likelihood sequence estimator (MLSE) is proposed to alleviate the system nonlinearity of an EML-based transmitter and coherent detection system without CPR. The postFFE NC filter is implemented with a simple autoregressive coefficient acquisition algorithm. Results show that a 4-dB improvement in OSNR performance can be achieved at 20% overhead soft-decision feed-forward error correction (SD-FEC) threshold BER by using nonlinear DSP in a 56-Gb/s Duobinary
intensity modulation and coherent detection transmission system over 320-km single-mode fiber (SMF). The nonlinear DSP also enables record 18-dB OSNR sensitivity with 7% overhead harddecision FEC (HD-FEC) threshold BER of 3.8×10-3.
port of the last EDFA to measure the OSNR. After passing through an optical band-pass filter (OBPF) with a 3-dB bandwidth of 80-GHz, emulating a de-multiplexer that removes the out-of-band ASE noise, the optical signal is fed into a 20-GHz integrated coherent receiver (ICR). An external cavity laser (ECL) is used as a local oscillator. The four RF outputs of the ICR representing the I/Q channels of X and Y polarizations are injected into a 33-GHz real-time oscilloscope operated at 80 GS/s. The digitized signal is then processed offline. The offline DSP in the receiver consists of chromatic dispersion (CD) estimation and compensation, timing recovery, a complex Volterra 2 × 1 MISO equalizer which targets to a Duobinary output signal with three intensity levels, a NC filter, a 2-state MLSE and a bit error rate (BER) calculator. Mueller-Mueller algorithm was used for timing recovery. Due to the bandwidth limitation of the transceiver, Duobinary detection is an efficient solution. The 2 × 1 MISO equalizer is based on the single phase-least mean error square (SPLMS) concept [3] at the beginning and then transits to a decision directed mode when it is stable. The symbol spaced complex transversal Volterra MISO equalizer is expressed by
R t
M 1
a
x ,i
i 0
N 1
i 0, j i , k 0 N 1
i 0, j i , k 0
Rx t i a y ,i Ry t i
(ax ,i , j , k Rx t i Rx t j Rx* t k ) (1)
( a y ,i , j , k Ry t i Ry t j Ry * t k )
where (.)* represents the complex conjugate of (.), M and N are the sample count considered for the linear and the 3rd order kernels [5, 6], respectively. t is discrete time index. Rx and Ry represent the X and Y polarization input complex samples, respectively, while R is the output sample of the equalizer. The linear and nonlinear FFE tap coefficients for the X and Y polarizations are defined by ax ,i and Fig. 1. (a) Experimental setup of the 56-Gb/s Duobinary system. (b) the diagram of the NC filter structure.
Fig. 1(a) depicts the setup for the considered 56-Gb/s Doubinary transmission system. At the transmitter’s offline DSP, a pseudorandom bit sequence with length of 129024 was 2-fold upsampled by inserting a zero every second sample and then filtered by a square-root raised cosine pulse shaping (with an identified optimum roll-off coefficient of 0.75). The signal was then resampled such as to match the 84-GSa/s DAC sampling rate. After removing the DC from the re-sampled output, the signal was clipped to reduce the peak to average power ratio to 10 dB and quantized with 8 bits. The generated signal is then loaded into a 16-GHz DAC operating at 84 GS/s and followed by a 30-GHz driver. The RF signal drives a 30-G EML which produces the output signal as shown in the inset eye diagrams of Fig. 1. The eye diagram clearly shows inter symbol interference (ISI) which is due to the limited bandwidth of the transmitter components. The EML is fully driven in order to achieve a high extinction ratio. The optical data signal is combined with an ASE noise signal generated by an Erbium-doped fiber amplifier (EDFA). Note that the EML output signal was attenuated before being launched into fiber, which can alleviate fiber nonlinearity. The launched optical signal propagates through a SMF link with 4 spans, each consisting of 80-km SMF and an EDFA. An optical spectrum analyzer (OSA) is connected to the monitoring
ax ,i , j , k , a y ,i and a y ,i , j , k , respectively. Fig. 1 (b) illustrates the diagram of the proposed post-FFE NC filter. The NC filter is denoted as
R '[n] R[n]
K
c k
(2)
nk
k K , k 0
where R and R’ are the input and output samples of the NC filter, respectively. 2K taps are considered for the NC filter. Actually not all taps are needed and taps with much less weights can be discarded. n k in Eq. (2) corresponds to the noise of the (n+k)-th symbol which is obtained by k R[k ] R[k ] where R[k ] is the symbol obtained from R[k] after hard decision and the former’s phase is set to be identical to that of the latter. The NC filter tap coefficient ck are usually calculated at the beginning of the communication, which is given by
ck
1 Lk
Lk
R i R *[i k ], and c
k
i 1
ck* , for k 0. (3)
L is the number of symbols of FFE output used to calculate the NC filter tap coefficients. Note that ck is further normalized to c0 . The proposed NC filter is efficient to cancel correlative noise. Although conventional Arburg algorithm [7, 8] approach was used
frequently, the proposed NC filter tap coefficient calculation approach has the following significant advantages: It takes into account the correlated noise from both pre- and post-cursor symbols as indicated in Fig. 1(b) thus is more efficient Much less complexity since it does not require to continuously solve Yule-Walker equations as Arburg algorithm does [9] Since the 2 ×1 MISO equalizer adopts a Duobinary equalization, a simple 2-state MLSE after the NC filter is efficient for symbol sequence detection under a channel with memory.
Fig. 2. BER versus OSNR for different 2 ×1 MISO FFE tap configurations. The linear tap count is fixed at 21.
The OSNR can be further improved by adding 3rd-order Volterra nonlinear kernels into the 2 ×1 MISO equalizer. The more nonlinear coefficient taps used, the larger improvement in OSNR can be obtained. The optimum nonlinear kernel was identified to be N = 5 (corresponding to 75 taps), which brings about 3-dB improvement in OSNR sensitivity at SD-FEC threshold BER compared to linear FFE case. For longer equalizers beyond N = 5 very little improvement in OSNR sensitivity at BER of 2 × 10-2 was observed. In addition, the nonlinear 2 × 1 MISO equalizer also enables the adoption of a HD-FEC as the error floor is significantly reduced. Note that the nonlinear tap number can be significantly reduced by ignoring taps with low-weighted coefficient values [5]. For N = 5 case, as shown in Fig. 2 where simplified FFE can achieve almost identical performance compared to un-simplified FFE. The simplified FFE takes into account only about one third of the nonlinear taps by discarding the other taps whose absolute coefficient values are less than the average. Having identified the optimum 3rd-order Volterra nonlinear kernels for the 2 ×1 MISO FFE, Fig. 3 presents the results by further incorporating the proposed NC filter and a MLSE. The NC filter enables a significant 5-dB improvement in OSNR sensitivity at HDFEC threshold BER compared to using a nonlinear 2 × 1 MISO FFE only. No improvement is observed at the SD-FEC. A further 3-dB improvement in OSNR sensitivity at HD-FEC threshold BER is obtained by using a 2-state MLSE, which is well designed to recover a Duobinary signal. To our best knowledge, a record 18-dB OSNR sensitivity at HD-FEC threshold BER has been obtained here for a 56-Gb/s intensity modulation and coherent detection system without incorporating CPRs in receiver DSPs. In addition, about 4dB improvement in OSNR sensitivity relative to linear FFE case observed at SD-FEC threshold BER. A theoretical benchmark performance is also presented in Fig. 3 by considering a carrier to signal power ratio (CSPR) of 0 dB. The detailed theoretical performance analysis can be found in [13].
Fig. 3. BER versus OSNR for cases of MISO FFE only, MISO FFE with NC, as well as MISO FFE with NC and MLSE.
In order to evaluate the performance of the nonlinear 2 × 1 MISO equalizer, Fig. 2 shows the BER versus OSNR performance subject to various offline equalizer tap configurations for a 320-km SMF transmission. Note that only the linear and the 3rd-order nonlinear kernels are considered here because the 2nd-order kernels were found to have very little influence on the system performance. This is different from direct detection systems where the 2nd-order nonlinearity dominates due to the strong signalsignal beating interference attributed to square-law detection [1012]. The equalizer consists of M=21 linear taps and (N3+N2)/2 3rdorder nonlinear taps. When the receiver DSP only adopts the linear FFE taps in the 2 × 1 MISO equalizer, the system can achieve an OSNR sensitivity of about 18 dB at BER of 2×10-2 allowing for a 20% SD-FEC. However, the strong error floor makes it fail to support HDFEC that requires a threshold BER of 3.8 × 10-3.
Fig. 4. Representative constellation diagrams for signals obtained from linear 2 × 1 MISO FFE without nonlinear terms, FFE with 3rd-order terms, and Volterra FFE plus NC filter, respectively, corresponding to marked measurement points in Fig. 3. The corresponding histograms are also presented.
The OSNR improvement enabled by nonlinear DSPs is a direct result of strong reduction of error floor. Fig. 4 illustrates the representative signal constellation diagrams corresponding to the marked measurement points in Fig. 3. The constellation taking into account only linear equalizer terms shows strong distortion, which can be alleviated by the nonlinear equalizer resulting in a better separation between amplitude levels. NC filter further improves the constellation quality. A corresponding histogram comparison of the three constellations is also presented, which shows a straightforward statistical amplitude distribution for each case and the use of nonlinear equalization and NC filter reduce significantly the frequency of amplitude levels in the threshold regime, leading to reduced error on the hard thresholding.
sensitivity were obtained at HD-FEC and SD-FEC threshold BERs, respectively, for a 56-Gb/s intensity modulation and coherent detection system. To our best knowledge, a record 18-dB OSNR sensitivity at HD-FEC threshold BER of 3.8 × 10-3 was also achieved without using CPR in receiver DSP.
Fig. 6. NC coefficients obtained via Arburg algorithm and the proposed approach for (a) optical back to back and (b) 320 km SMF cases.
Fig. 5. The power spectral density of (a) signal and (b) estimated noise before and after NC filter for 320 km SMF transmission. The spectra after NC is artificially downshifted to distinguish with those before NC.
In order to understand the underpinning physics of the excellent performance of NC filter, Fig. 5 indicates the signal power spectrum density (PSD) for the received signal and its estimated noise before and after the NC filter. The signal PSD shows little change by applying the NC filter. Whilst the noise PSD comparison shows that the NC filter enables more white noise at high frequency region. Moreover, a significant suppression of the PSD peaks around the carrier occurs, which is mainly attributed to the frequency offset of the coherent detection. This indicates that although a CPR is avoided in receiver DSP, frequency offset does introduce noise correlation to the signal and the NC filter is very efficient to alleviate its effect. The NC filter consists of 10 taps with its tap coefficient absolute values shown in Fig. 6. It implies the effectiveness of the proposed NC filter tap coefficient calculation approach which brings about similar coefficient values to those obtained by conventional Arburg algorithm albeit slight fluctuation is observed for both optical back to back and 320-km SMF transmission cases. Similar OSNR performance was also observed between the two approaches. In summary, investigation of nonlinearity mitigation in an intensity modulation and coherent detection system has been undertaken in this paper. Advanced nonlinear DSP were proposed, for the first time, including a simplified 2 ×1 MISO Volterra complex FFE filter, a post-FFE NC filter and a MLSE without CPR. Based on the nonlinear DSP, over 8-dB and 4-dB improvements in OSNR
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