## Abstract

In this paper, we verify the effectiveness of the last-stage long memory filter (LMF) in mitigating the long-memory response (LMR) of hardware, i.e. the transmitter and receiver. Based on the experimental results, we draw the following conclusions: 1) LMF can effectively mitigate the LMR impact, such as transmitter reflections, and its efficiency is more significant for high-order QAM signals. 2) Using LMF, a partially-correlated pattern exhibits similar performance to that of an uncorrelated pattern both in back-to-back and after 320-km standard single mode fiber (SSMF) transmission. Moreover, a simple solution to the computational complexity of LMF, effective-tap (ET) LMF, is proposed and demonstrated.

© 2013 OSA

## 1. Introduction

Future high-speed transmission is expected to reply on the use of high-order quadrature-amplitude modulation (QAM) format [1–5]. A common issue of the high-order QAM (order ≥ 16) generation is the accompanied large implementation penalty caused by the increased requirement for device quality (such as linearity and bandwidth) due to the greatly reduced symbol spacing. To reduce this penalty, the first long-memory filtering (LMF) technique, based on a polarization-dependent (2x2), 801-tap, and Ts/2-spaced adaptive filter (where Ts is the symbol duration) with least-mean-square (LMS) algorithm, is introduced for 4000-km transmission of 10x494-Gb/s polarization-division-multiplexing (PDM) −64QAM [2]. Later in [4, 5] a LMF, based on polarization-independent, 801-tap, and Ts-spaced adaptive filter with LMS, is used to compensate for the transmitter’s reflections yielding an ~0.9-dB gain at BER = 2.4e-2 (soft-decision forward error correction, SD-FEC, threshold [6]). In these reports [2, 4, 5], the use of LMF is claimed to mitigate the long-memory response (LMR) of hardware, i.e. transmitter and receiver. However, that claim has not been confirmed and whether this gain, totally or in part, would result from the neighboring correlated symbols within the long memory-length of LMF is unclear. In addition, the previous LMF [2, 4, 5] utilizes a long tap-length (801 taps) for LMR mitigation, which might result in remarkable computation issue. Therefore, it would be necessary to verify the LMF gain to confirm its effectiveness for a real system in which the data symbols are likely to be independent (in the absence of forward error correction coding, FEC) and offer a more realistic solution to the complexity issue of the previous long tap-length LMF.

In this paper, by using an uncorrelated data pattern, we demonstrate that the last-stage LMF can compensate for the hardware LMR impact such as reflections, and thus reduce the implementation penalty for high-order QAM signals. We also verify that, when using LMF, the partially-correlated data pattern, broadly used under laboratory conditions, exhibits similar performance to that of an uncorrelated pattern both in back-to-back and after 320-km SSMF transmission. Finally, aiming to solve the complexity issue of LMF, we propose and demonstrate the effective-tap (ET) -LMF solution, which identifies and only utilizes the more-effective taps for equalization, therefore leading to a computational-saving realization.

## 2. Working principle

In a typical single-carrier equalizer, the signal processing is mainly composed of, listed in sequence, CD compensation, polarization separation, and carrier recovery. The carrier recovery usually is considered as the end of the equalization and its output is sent to the FEC decoding to correct the error bits improving system performance. The introduced LMF is inserted right after the carrier recovery processing. Its working principle is basically the same as the conventional adaptive finite impulse response (FIR) filter with a feature of long memory-length to mitigate the hardware LMR. The benefit of locating after the carrier recovery is that the phase noise would not disturb the LMF’s coefficients, which may allow better equalization efficiency. The architecture of a LMF is depicted in Fig. 1(a) and the relation between its inputs and outputs are given below:

where*y*is the output of LMF,

_{k}*k*is the discrete-time sample,

*N*is the tap length of LMF,

_{t}*C*is the tap weights or coefficients, and

_{k}*s*is the input to LMF. The tap coefficients

_{k}*C*are adaptively adjusted by the error vector between the filter output

_{k}*y*and the filter input

_{k}*s*via, for instance, the LMS algorithm [7].

_{k}Previously, the LMF utilizes all the taps (termed as full-tap LMF) within the long memory-length of LMF which results in a huge computational effort. Essentially, the required computation for full-tap LMF (FT-LMF) is in proportion to its tap length: for instance, if we apply one Ts-spaced FT-LMF for each polarization, one output sample will cost *N _{t}* complex multiplications. Since the memory length of LMR would last over one hundred-symbol duration, the computational cost and consumed power would be too high to be affordable for the receiver digital signal processors. Although such a long tap-length filter could be realized in the frequency domain to reduce the required computations, adaptivity would remain an issue that cannot easily be accommodated in a frequency-domain filter. As a matter of fact, since the LMR results from the hardware which should be relatively stable, only specific taps that correspond to the LMR would really take effect during LMF equalization. Hence, we propose an ET-LMF for LMR equalization, of which the concept is depicted in Fig. 1(b). The ET-LMF identifies and only utilizes the “effective taps” for equalization, where the effective taps are selected if their tap amplitudes after equalization are higher than a predefined threshold, γ. To determine which taps are effective to be used, one possible approach is to perform an offline identification that firstly uses an adaptive FT-LMF and, after convergence, pick up the taps with amplitudes greater than γ for the on-line ET-LMFoperation. Obviously, the effective tap number will be a function of γ and decrease with the increase of γ. Since the LMR would occur only at some specific timing, rather than distributing over the time domain, the required tap number (only the effective ones) of ET-LMF could be much fewer than that of previous FT-LMF, thus greatly saving the required computations. Notably, the ET-LMF would still have a long memory length (but with fewer taps), which is determined by the maximum temporal spacing between any two effective taps. As can be expected, there exists a trade-off between the required tap number and the LMF gain, which will be observed in Section 4.

Unless specified otherwise, hereafter “LMF” refers to the previous FT-LMF and “ET-LMF” refers to the proposed effective-tap LMF.

## 3. Experimental setup

Figure 2 shows the experimental setup and post processing for studying LMF gain, for which 11.2-GBd PDM-64QAM is selected as the signal source. At the transmitter, the output of an external cavity laser (ECL, linewidth <100 kHz) is modulated to an 11.2-GBd 64QAM signal with an optical I/Q modulator, which is driven with two electrical eight-level signals, i.e. the in-phase and quadrature-phase signals, from an arbitrary waveform generator (AWG). The required eight-level signals are synthesized in Matlab beforehand by multiple copies of a 2^{15}−1 pseudo-random binary sequence (PRBS) with different delays. The synthesization is depicted in Fig. 3(a), where D1, D2 and D3 are integers representing bit delays. In this paper, we discuss two data patterns: i) an uncorrelated pattern (UCP) with D1 = 4096, D2 = 8192, and D3 = 16384, and ii) a partially-correlated pattern (PCP) with D1 = 169, D2 = 96, D3 = 69. In the first pattern, any pair of correlated symbols is spaced at least 4096 symbols, which is longer than the memory length of LMF (≤ 801Ts) in this paper. Therefore, we define the first pattern as an uncorrelated pattern since all symbols within the LMF memory are supposed to be uncorrelated. As to the second pattern, it has multiple correlated symbols within the memory length of LMF due to the relatively shorter delays among PRBSs (which, notably, are still longer than the length of a conventional adaptive equalizer, such as the constant-modulus-algorithm (CMA)-based equalizer in this paper) and, thus, is defined as a partially-correlated pattern. In fact, the partially-correlated pattern has earlier been demonstrated in our 41.4-GBd PMD-64QAM demonstration [4]. Notably, for Fig. 5 the synthesized eight-level signal would extra go through a digital reflection emulator with a Z-transform of (1 + 0.05z^{−200}), where the amplitude and delay of this reflection are 0.05 and 200Ts, respectively. The optical spectra (20-MHz resolution) of the output single-polarized 11.2-GBd 64QAM signals are given in Fig. 3(b) with both UCP and PCP. With PCP, high-density ripples can be found under the envelope of the power spectrum, caused by the relatively shorter delays among PRBSs. After the I/Q modulator, the single-polarized 64QAM signal is sent to a PDM emulator, which splits the input signal equally, delaying one copy by 291Ts, and recombines it at the output, is used to emulate the target 11.2-GBd PDM-64QAM (line rate = 134 Gb/s). The signal is fed to the transmission link consisting of 4 spans of 80-km SSMF (span loss ≈17 dB) with hybrid Raman and EDF amplification. The average on-off Raman gain is ~12 dB in each span.

At the receiver, an optical amplifier is used to enhance the signal power and an optical band-pass filter (OBPF) with 30-GHz 3-dB bandwidth is utilized to remove the out-of-band noise. The received signal is then detected by a polarization-diversity intradyne receiver, which includes an optical hybrid and four balanced photodiodes. The local oscillator (LO) is performed by another ECL with <100-kHz linewidth and its central wavelength is tuned to the transmitter wavelength for semi-homodyne detection. The four outputs from the balanced photodiodes, the real and imaginary parts of both polarizations, are recorded by two cooperated 32-GHz, 80-GS/s real-time sampling scopes. The stored data with a length of 2-million sampling points are processed offline in a desktop computer.

The configuration of the offline processing can be found in Fig. 1 and is described in detail as follows: (i) deskew and orthogonalization. (ii) Digital filtering with (0.6/Ts) 3-dB bandwidth. (iii) Resampling, two samples per symbol. (iv) Chromatic dispersion compensation in frequency domain. (v) Clock recovery, for which we oversample the signal and extract the tone at the symbol rate from the spectrum of the magnitude-squared signal. Samples are re-taken at the time where the phase of the extracted tone equal 0 and π. (vi) polarization-dependent, 31-tap, Ts/2-spaced adaptive butterfly FIR filter with CMA for pre-convergence. (vii) Polarization-dependent, 31-tap, Ts/2-spaced adaptive FIR filter with radius-directed algorithm (RDA [8],) for steady-state operation. 8) polarization-dependent, feed-forward blind phase search method with a block size of ~40 [9]. (viii) (Option) polarization-independent, 801-tap (for single-polarized signals) or 401-tap (for PDM signals), Ts-spaced LMF with LMS algorithm. It is worth noting that whenever PCP is applied, the LMF taps that correspond to the correlated symbols (and its neighboring two) are nulled in order not to use the correlated symbols for equalization.

## 4. Results and discussions

Throughout this paper the OSNR values are presented with a noise bandwidth of 0.1 nm and the LMF, whenever applied, adopts 801 taps for single-polarized signals and 401 taps for PDM signals with center-spike initialization. ET-LMF is applied only for the results in Fig. 7.

First of all we show that the LMF is more beneficial to higher-order QAM signals. In Fig. 4(a) we depict BER as a function of OSNR for 4, 16 and 64QAM signals with and without LMF. Only a single-polarized signal at 11.2 GBd is investigated here. For the 4QAM generation, we use two equal 2^{15}−1 PRBSs as the I- and Q- branch signals with a relative delay of 16384Ts; while for the 16QAM generation, the required four-level driving signal is first synthesized by two equal 2^{15}−1 PRBSs with a relative delay of 8192Ts and this four-level signal is later split into two copies with a relative delay of 16384Ts, which serve respectively as the I and Q-branch signals resulting in a 16QAM signal. As to the 64QAM, the model given in Fig. 3(a) with UCP is applied. Since the delays in all three signal generations are made longer than the LMF length of 801Ts, the LMF should not utilize any correlated symbol for equalization. Figure 4(a) shows the LMF gain is larger for high-order QAM format: at 4QAM, the LMF gain is negligible over a wide range of BERs; while at 16 and 64QAM, this gain is enhanced for lower BERs and is more significant at 64QAM. This demonstrates the effectiveness of LMF in mitigating the LMR impact, especially for high QAM signals. The recovered constellations (OSNR > 40 dB) with and without LMF are depicted in the upper row of Fig. 4(b). The absolute values of the LMF tap coefficients (|*C _{k}*|), after equalization, as a function of tap index (ranging from −400 to 400) are shown in the bottom of Fig. 4(b). The tap coefficients, which stand for the inherent LMR of system, are found to be similar for all three QAM formats (4, 16, and 64): clustered side-peaks surrounding the central main peak (index = 0), and one clear side peak showing up at tap index ≈ + 300. This reveals that the LMF gain comes indeed from its mitigation in the LMR of hardware, rather than any partially-correlated symbol.

We subsequently emphasize the LMF’s ability in LMR mitigation. In Fig. 5, we deliberately add the digital reflection at the transmitter to the 64QAM signal to demonstrate that the LMF can compensate for the transmitter reflection. The reflection is introduced numerically in Matlab as the model given in Fig. 3(a). Only the single-polarized 64QAM signal at11.2 GBd is considered here, and both UCP and PCP are studied. We first focus on the UCP: in the absence of digital reflection, the LMF compensates for the inherent LMR impact of hardware offering an < 1-dB gain at BER = 4e-3, the hard-decision forward-error-correction (HD-FEC) threshold [10]. In the presence of digital reflection, this gain is enhanced to be > 3 dB with a penalty of only ~0.2 dB relative to the case of without digital reflection. This clearly illustrates LMF’s ability in LMR mitigation. Meanwhile we also depict the PCP resultswith 801-tap LMF in the presence of digital reflection. Its performance is found to be similar to that of UCP, which reveals that the PCP, even if the LMF is incorporated, would not induce any unreasonable gain over the UCP.

In Fig. 6 we further study the LMF gain after 320-km SSMF transmission. The signal quality is represented by Q factor derived directly from the BER. In this study PDM-64QAM at 11.2 GBd is considered with both the UCP and PCP. In order to keep the UCP still “uncorrelated”, for PDM signals the LMF length is reduced to 401 taps covering symbols from −200Ts to + 200Ts which shall exclude the closest correlated symbol (291Ts) from the other polarization. In the case of UCP, with no LMF an ~1.3-dB margin is found from the SD-FEC threshold at the optimum launch power of –7 dBm; while with LMF this margin is enhanced to ~2.1 dB showing that ~0.7 dB gain is achieved by LMF. On the other hand, the PCP with LMF is found to exhibit similar performance to that of UCP over a broad range of launch powers and therefore, taking this finding together with the results of Fig. 5, weconclude that the PCP may be applied to represent the system performance of UCP. This result may be useful for laboratory evaluations since in most cases the truly random patterns, or uncorrelated patterns, are difficult to generate.

Here we demonstrate the proposed ET-LMF to reduce the tap length with least harm to the LMF gain. The 11.2-GBd PDM-64QAM signal in Fig. 6, with UCP at the −7-dBm launch power, is used for this demonstration. In Fig. 7(a), we first present the tap amplitudes of LMF (|*C _{k}*|) after full-tap (401 taps) equalization. To determine the effective taps we define a threshold γ for which the taps are defined as effective and to be used for ET-LMF if |

*C*| ≥ γ. This method will exclude those ineffective taps for equalization, therefore greatly reducing the tap number while sacrificing limitedly the LMF gain. The ET-LMF gain vs. γ is given in Fig. 7(b), and the required tap number for each polarization is also depicted. We find that the ET-LMF gain is > 0.6 dB with a required tap number of ~66 (at γ = 1.25e-3), and still > 0.5 dB with a tap number of only ~31 (at γ = 2.5e-3). This clearly illustrates the complexity reduction achieved by the proposed ET-LMF.

_{k}At last, we conduct simulations to verify the reliability of UCP, which has been emulated as a true random pattern and served as a pattern reference throughout this paper. In simulations, 11.2-GBd single-polarized 64QAM signals are run with three different patterns: two of which are UCP and PCP, and the third pattern is generated by the “randint” function of Matlab software. Laser phase noise, transmission line, and LMR are ignored to focus on the pattern effect on LMF, and the equalizer is the same one as used in our experiment. The simulation results of BER vs. OSNR are given in Fig. 8. We‘ve found that all three patterns exhibit similar performance irrespective of the use of 801-tap LMF. This clearly indicates that 1) UCP does not induce any unreasonable gain (over the Matlab pattern) when using the 801-tap LMF, 2) LMF provides no gain in the absence of LMR. Therefore, we conclude that UCP should be qualified to be used to represent correctly the system performance when applying the LMF.

## 5. Conclusion

We have studied the effectiveness of LMF in mitigating the LMR impact and showed that its efficiency is more significant for high-order QAM signals. At the SD-FEC threshold, the LMF gains in back-to-back and after 320-km transmission are found to be ~0.5 and ~0.9 dB, respectively. We’ve also found that, when using the LMF, the partially-correlated pattern, which has been employed in an earlier demonstration [4], yields similar performance to that of the uncorrelated pattern both in back-to-back and after transmission. This information would be helpful for laboratory evaluations where uncorrelated patterns may be difficult to generate. Finally, we have proposed and demonstrated an ET-LMF approach to mitigate the complexity issue with LMF.

Since long memory or buffer is required to implement the LMF, the size of transceiver would be difficult to be reduced. Thus, the downsizing of transceiver with the LMF would be a new challenge which is out of the scope of this paper.

## Acknowledgment

This work was partly supported by the National Institute of Information and Communications Technology (NICT), Japan.

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