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40 Gb/s CAP32 System With DD-LMS Equalizer for Short Reach Optical Transmissions Li Tao, Yiguang Wang, Yuliang Gao, Alan Pak Tao Lau, Nan Chi, and Chao Lu
Abstract— Carrierless amplitude and phase (CAP) modulation is a promising candidate for short reach optical communications. In this letter, we propose the use of decision-directed least mean square (DD-LMS) adaptive equalization algorithm for high-order CAP transmission systems. The optimal length of taps and step size of DD-LMS algorithm is investigated for 30 Gb/s and 40 Gb/s CAP32 systems. A hybrid equalization technique that consists of DD-LMS and its aided two-stage pre-convergence is proposed that allows experimental transmission of 40 Gb/s CAP32 40 km standard single mode fiber (SSMF). Index Terms— Carrierless amplitude and phase, adaptive equalization, DD-LMS.
I. I NTRODUCTION
F
UTURE short reach communication systems, such as data center interconnects require higher capacity data transmission at low cost. Carrier-less amplitude and phase (CAP) modulation is generating increasing interest because it allows relatively high data rate to be transmitted using optical components of limited bandwidth. It is generated by combining the output of two filters, which are utilized to shape the in-phase and quadrature signals respectively. The impulse responses of two filters form a Hilbert pair. It is a variant of quadrature amplitude modulation (QAM) because the two filters take the place of the carriers in QAM modulation [1]–[5]. Comparing with QAM and orthogonal frequency division multiplexing (OFDM), complex mixers and radio frequency (RF) sources or optical IQ modulator is not necessary. Neither does it require the discrete Fourier transform (DFT) utilized in OFDM signal generation and demodulation.
Manuscript received August 24, 2013; revised October 3, 2013; accepted October 18, 2013. Date of publication October 28, 2013; date of current version November 6, 2013. This work was supported in part by G-UA44 of the Hong Kong Polytechnic University, NHTRDP (973 Program) of China under Grant 2010CB328300, in part by the NNSF of China under Grants 61250018 and 61177071, and in part by the Key Program of Shanghai Science and Technology Association under Grant 12dz1143000. L. Tao is with the Department of Communication Science and Engineering, Fudan University, Shanghai 200433, China, and also with the Photonics Research Center, Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hong Kong (e-mail:
[email protected]). Y. Wang and N. Chi are with the Department of Communication Science and Engineering, Fudan University, Shanghai 200433, China (e-mail:
[email protected];
[email protected]). Y. Gao and A. P. T. Lau are with the Photonics Research Center, Department of Electrical Engineering, The Hong Kong Polytechnic University, Hong Kong (e-mail:
[email protected];
[email protected]). C. Lu is with the Photonics Research Center, Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hong Kong (e-mail:
[email protected]). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LPT.2013.2287529
Higher order modulation can also be used in CAP system [2], such as CAP16, CAP32. From this point of view, the complexity of computation and system structure of short reach data communication systems are reduced considerably through the use of CAP modulation. Recently, many CAP systems with large capacity have been reported. Ref. [1] presents a CAP16 system with bit rate up to 40 Gb/s. The system capacity is extended to 100 Gb/s by using multi-subbands [2]. However, CAP-based system is very sensitive to symbol timing offsets and jitters and the quality of acquisition of the symbol timing could significantly affect the overall system performance. It has been shown that about 4 dB power penalty is incurred when timing jitter is 1 ps for 100 Gb/s CAP16 system [3]. In addition, another significant drawback of CAP system is that it requires a flat channel frequency response. The non-flat in-band frequency response of the transmission system will significantly degrade the system performance. Therefore, adaptive equalizers are often necessary in mitigating such impairments and the synchronization process can be considered to be implicitly done through the blind adaptive equalization. We have demonstrated a 10 Gb/s and 20 Gb/s CAP16 system over 40 km single mode fiber with the help of cascaded multi-modulus algorithm (CMMA) [4] and modified CMMA scheme respectively [5]. Another well-known approach for blind adaptive equalization is to use constant modulus algorithm (CMA) to perform pre-convergence and then switch to decision-directed least mean square algorithm (DD-LMS) once the error rate has dropped to a sufficiently low level [8]–[10]. Usually the BER after the pre-convergence is around 1e-2. This scheme can obtain good performance because DD-LMS does not depend on the statistics of symbols but rely on the symbol decisions. In this letter, DD-LMS is proposed for the equalization of optical CAP32 system for the first time. The effectiveness of different adaptive equalization techniques is investigated experimentally for a 30 Gb/s CAP32 system. Then a novel hybrid scheme that consists of DD-LMS and its aided twostage pre-convergence is proposed to realize a 30 Gb/s and 40 Gb/s CAP32 experiment system over 40 km standard single mode fiber (SSMF). II. O PERATING P RINCIPLE The signal shaping process at the transmitter in a CAP transmission system will introduce intersymbol interference (ISI). It can be eliminated if exact sampling time is found in CAP demodulation process. However, this requires accurate timing synchronization, or large samples per symbol to help
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TAO et al.: 40 Gb/s CAP32 SYSTEM WITH DD-LMS EQUALIZER
Fig. 1.
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Structure of adaptive equalizer in CAP system.
choosing the best sampling points. The sampling time offsets will lead to subsequent signals being seriously distorted. Also, the distortions caused by the transmission channel are unknown and therefore an adaptive equalizer is needed to recover the CAP signal. In long haul coherent optical transmission systems, DD-LMS with CMA-based pre-convergence has been used extensively because of its better convergence performance comparing with the simple CMA algorithm. In contrast to CMA and its other derived forms, which depend on the statistics of symbols, the DD-LMS scheme computes the difference between the signal before and after the decision directly. Fig. 1 shows the structure of a DD-LMS equalizer with N taps. The objective is to find the coefficient of each filter tap, H (k) = {h 0 (k), h 1 (k), . . . h N−1 (k)}, to match as closely as possible to the inverse response of transmission system. The initialization is performed by setting the coefficient of the center tap to 1 and other taps coefficients to 0 before update. The update of coefficients depend on the difference between y(k) and the output of symbol decision d(k). The error signal calculation and coefficient update for each tap is expressed as e (k) = d (k) − y (k) H (k + 1) = H (k) + 2µ · e (k) X ∗ (k) .
(1) (2)
Here, d(k) is the output after symbol decision, u is the step size, X ∗ (k) is the complex conjugate of input sequence X (k) = {x(k), x(k − 1), x(k − N + 1)}. DD-LMS is suitable for highorder CAP signal once the reliable symbol decision can be made. Like in long haul transmission systems, preconvergence is also required in CAP system, because the hard decision of the received CAP signal in DD-LMS scheme is more likely to be incorrect and the convergence of the equalizer may not be achieved. Since CMA relies on the statistics of the signal instead of hard decisions, it can be also used in CAP system to compute the tap update term when symbols lie farther away from constellation points. However, the output of conventional CMA scheme may produce phase rotation because all the symbols are converged into the referenced ring. The resulting phase rotation will increase the decision errors in the following DD-LMS scheme [4]. In order to utilize DD-LMS scheme without extra phase rotation, the cost function of the CMA scheme can be separated into inphase and quadrature component and take advantage of the symbol statistics of square constellations [11], so the output square constellation makes it unnecessary for the phase rotation. In the following experimental study, the performance of
Fig. 2. Experiment setup of CAP32 transmission system, Inset A: electrical spectrum of received 40 Gb/s CAP32 signal after PD with and without linear pre-emphasis, ECL: external cavity laser, IM: intensity modulator, EA: electrical amplifier, AWG: arbitrary waveform generator.
DD-LMS with aided pre-convergence is investigated and a hybrid scheme is proposed for 40 Gb/s CAP32 transmission system. III. E XPERIMENTAL S ETUP AND R ESULTS Fig. 2 shows the experiment setup of a CAP32 system. Firstly, the original data sequence is mapped into 5 levels and up-sampled by a factor of 3. Then the separated signal is sent into two shaping filters with 32 taps. The impulse responses of two filters form a Hilbert pair. The square-root raisedcosine function is used as the baseband impulse response with roll-off coefficient of 0.1. An arbitrary waveform generator (AWG, Tektronix 7122C) is used to produce the RF signal. The sample rate of AWG is set to 18 GSa/s and 24 GSa/s to generate 30 Gb/s and 40 Gb/s CAP32 signal respectively. In order to reduce the chromatic dispersion induced power penalty, the tunable external cavity laser is set to 1530 nm as the signal source. The output power from laser is 12 dBm. The output amplitude after the electrical amplifier is 5-Vpp and is used to drive the 10GHz intensity modulator (IM) (Vpi=5 V). The fiber launch power is set to 2 dBm. After the fiber link, the signal is detected by a photo detector (PD) with a responsivity of 0.65 A/W. Then the CAP32 signal is sampled by an oscilloscope at a sampling rate of 40 GSa/s and is processed offline. The spectrum of 40 Gb/s CAP32 signal after PD (blue) is shown in the Inset A in Fig. 2. It can be found that high frequency components have large power attenuation. The bandwidth limitation from AWG and frequency fading induced by chromatic dispersion are believed to be the two main reasons for this large power attenuation. It will degrade the system performance heavily. Therefore, electrical domain pre-emphasis is utilized in our experiment. The conventional
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Fig. 4. Comparison of different equalization schemes for 30 Gb/s CAP32 system with back-to-back transmission.
Fig. 3. Optimal number of taps and step size of LMS scheme in (a) 30 Gb/s CAP32 system, (b) 40 Gb/s CAP32 system, u indicates the step size of DD-LMS based equalizer.
pre-emphasis scheme needs to send a training signal to calculate the system’s exact transfer function. Then the data signal is emphasized according to the transfer function. In our experiment, only the power attenuation of the high frequency components is estimated and a linear transfer function is utilized to approximate the exact transfer function (indicated by the black dashed line of Inset A in Fig. 2). It is feasible because the utilization of equalizer at the transmitter can equalize the distortion caused by the approximate linear transfer function. The spectrum with pre-emphasis scheme after PD (red) is also shown in the Inset A in Fig. 2. For the offline processing, the sampled signal is first resampled and sent into two matched filters with 32 taps, which are the time-reversed version of the corresponding shaping filters, so the in-phase and quadrature signals are separated. After down-sampling, the DD-LMS based equalizer is used and followed by the signal demapping. Finally, bit error counting for CAP32 signal is performed over 2 × 105 bits. The optimal number of taps and step size for DD-LMS is investigated and are shown in Fig. 3. The optimal step size of 30 Gb/s and 40 Gb/s CAP32 system is from 1e-7 to 1e-5. The minimum number of taps for the 40 Gb/s CAP32 system is 60, which is higher than the 30 Gb/s CAP32 system. As the linear pre-emphasis is not as perfect as the one using transfer function and the distortions caused by ISI are related to more
symbols in the higher baud rate system, the higher baud rate system requires more taps when DD-LMS scheme is used. Small step size and long filter taps require more convergence time duration. Therefore, for the practical system, the proper step size and taps can be chosen from Fig. 3 to get a tradeoff between convergence time duration and performance. Fig. 4 indicates the performance comparison of different equalization schemes in 30 Gb/s CAP32 system with backto-back transmission. Compared with CMMA and modified CMMA, DD-LMS scheme offers significant performance improvement. Moreover, we present a hybrid scheme where the modified CMMA is added into the pre-convergence process. It is considered as the second stage of preconvergence for the following DD-LMS scheme. Further improvement in system’s performance is observed. In this hybrid scheme, the modified CMMA can provide better preconvergence performance because it is multi-modulus based which is suitable for high order modulation signal. Therefore, the following DD-LMS scheme has more reliable symbol decision during the tap update process. On the other hand, there are multiple impedance mismatches between electrical components. The DD-LMS based adaptive filter with long taps can mitigate some low-frequency/narrow-band distortion that may occur at the transmitter and the receiver [12]. Therefore it can be concluded that DD-LMS scheme is feasible in high order CAP transmission system. The BER performance of 30 Gb/s and 40 Gb/s CAP32 system over 40 km fiber link is then studied. Using the hybrid adaptive equalization scheme discussed above, the BER performance is improved significantly as indicated by the inserted constellations in Fig. 5. A 3dB power penalty is observed at BER of 3.8 × 10−3 when the system bit rate is increased from 30 Gb/s to 40 Gb/s. More serious power attenuation of higher baud rate signal caused by AWG and chromatic dispersion induced channel fading is believed to be the cause for this large penalty. The computational complexity of an ideal system to generate and demodulate CAP signals is directly related to the number of taps of the shaping and matched filters. Different adaptive equalizers are employed to compensate the distortion from timing offsets and channel frequency response.
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aided pre-convergence is proposed and it can further improve system performance. The experimental study shows that the hybrid equalization scheme allows the realization of 30 Gb/s and 40 Gb/s CAP32 transmission over 40 km SSMF. R EFERENCES
Fig. 5. BER performance of 30 Gb/s and 40 Gb/s CAP32 system over 40 km SSMF.
DD-LMS scheme outperforms other equalization schemes but also increases the receiver computational complexity to some extent. For a practical implementation, a tradeoff will be made between complexity and performance. IV. C ONCLUSION In this letter, we demonstrate the feasibility of DD-LMS with aided pre-convergence scheme for high order optical CAP transmission system through the experiment. The optimal length of taps and step size of DD-LMS scheme for 30 Gb/s and 40 Gb/s CAP32 transmission system is investigated. Compared with CMMA and modified CMMA, DD-LMS offers better performance. Then a novel hybrid adaptive equalization technique that consists of DD-LMS and modified CMMA
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