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Abstract
Chromatic dispersion, which introduces pattern-dependent inter-symbol interference (ISI), appears to be a long-standing performance limiting problem in optical intensity modulation direct detection (IM/DD) transmission systems. In this paper, we propose a multiplier-free maximum likelihood sequence estimation (MLSE) equalizer for C-band double-sideband IM/DD transmission. It models the IM/DD channel with dispersion-induced ISI and Gaussian noise. A look-up table is applied to record ISI for transition probability calculation and the Viterbi algorithm for decision sequence acquisition. Specifically, to reduce the number of multipliers, a refined construction of Viterbi algorithm based on tentative path decisions is adopted, which compresses the complexity of branch metric calculation to less than 1/4 for PAM-4 format. Moreover, approximation calculation is employed to realize multiplier-free hardware implementation, which greatly reduces the hardware consumption. The proposed MLSE equalizer offers superior performance and lower complexity over conventional equalizers. In the experimental verification, we experimentally demonstrate a C-band 56-Gb/s double-sideband 4-level pulse amplitude modulation (PAM-4) IM/DD transmission over 40-km standard single mode fiber exploiting the proposed refined MLSE without any optical amplifier, filter or dispersion managed modules at the receiver end, achieving a bit-error-ratio of 2.65×10−4, which is 2.28 orders of magnitude lower than the scheme using Volterra nonlinear equalizer.
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1. Introduction
With the development of 5G mobile fronthaul and data center interconnection (DCI), the capacity demand of short distance optical interconnection is growing rapidly [1]. Owing to its simplicity and low cost, intensity modulation direct detection (IM/DD) has become a mainstream solution in short-reach interconnections [2–5]. At the range of ZR and ZR+ in DCI applications, chromatic dispersion-induced power fading effect at C-band restricts the transmission capacity and reaches. Single side-band transmission is an effective solution for anti-dispersion [6–9]. However, it requires optical band-pass filter (OBPF) or dual-drive Mach-Zehnder modulator (MZM), which increase the cost and system complexity. Therefore, for the double-sideband (DSB) transmission, various linear and nonlinear channel equalizers have been investigated to mitigate the impact of power fading, and among which Volterra nonlinear equalizer (VNLE), decision feedback equalizer (DFE) and maximum likelihood sequence estimation (MLSE) are the most widely adopted ones in IM/DD systems. A 28-GBaud 4-level pulse amplitude modulation (PAM-4) transmission 50-km in a DML-based IM/DD system using an effective hybrid equalizer with FFE and truncated Volterra filter has been demonstrated [10]. To achieve the bit-error-ratio (BER) of $4.7 \times {10^{ - 3}}$, the number of Volterra filter’s taps is up to 275. The phase chirp and bandwidth limit of DML helps to mitigate the impact of power fading. In [11], a record C-band 64-Gbit/s optical on-off keying (OOK) transmission system over 100-km is presented incorporating polynomial nonlinear equalizer (PNLE), DFE and MLSE. Nevertheless, it includes an MLSE with the memory length of 14 and a 413-taps PNLE, which requires a huge number of multiplier resources. Among the aforementioned channel equalizers, MLSE has the best performance. It is widely used in the optical IM/DD system equalization [12,13]. The common MLSE based on finite impulse response (FIR) channel model is particularly effective in partial response channel equalization. However, due to the dispersion-induced inter-symbol interference (ISI), high-baud-rate IM/DD channel has a long memory length, which leads to unacceptable complexity for MLSE.
A practical method to reduce the complexity of MLSE is to use partial response equalizer to truncate the system response before performing MLSE. The partial response equalizer can be composed of feed forward equalization (FFE) or VNLE. But, for the systems with large dispersive distortion, long system response and high-order PAM, FFE and VNLE are not efficient enough to reduce the complexity for hardware realization. Another MLSE for effectively equalizing dispersion channels is based on ISI channel model [14,15]. It uses look-up table (LUT) to record ISI of different waveforms and uses probability density function (PDF) to calculate branch metrics. PDF is generally obtained through histogram or the method of moments. Using the ISI-based MLSE for channels with complex nonlinear effects, the dispersion channel can be equalized with a short memory length. However, as the key part of MLSE, Viterbi algorithm’s (VA) complexity is exponentially related to PAM order and memory length. It is generally only used for dispersion equalization of OOK and 10-Gbps IM/DD systems.
In this paper, we make the following improvements to the MLSE equalizer in three folds mentioned in [14] for IM/DD systems: Firstly, on the assumption that the channel noise performs a Gaussian-like distribution, the branch metrics can be easily calculated without statistics. We present a path-decision-assisted VA, which reduces the branch metric calculation over 75% for PAM-4 format. In this way, the complexity of MLSE with high-order PAM and long memory length is controlled in an acceptable range. Secondly, a recursive least squares (RLS) algorithm is applied to establish and update the LUT-storing ISI for the non-stationary channel. Moreover, we adopt an approximation calculation scheme to realize multiplier-free in hardware implementation, which greatly reduces the required hardware resources. Compared with conventional FIR-based MLSE, DFE and VNLE, the proposed scheme reveals better performance on dispersion equalization and requires much less multipliers. We experimentally demonstrate an effective, low complexity and multiplier-free MLSE equalizer in a 56-Gb/s PAM-4 system. It achieves a BER of $2.65 \times {10^{ - 4}}$ after 40-km standard single mode fiber (SSMF) C-band transmission with the received optical power of −1 dBm.
2. Principle
Basic equalization scheme of this work is built mainly upon a simplified version of the MLSE scheme mentioned in [14,15]. As is shown in Fig. 1, the proposed scheme is constructed by three components: look-up table, probability calculation and Viterbi algorithm. Firstly, the look-up table records ISI of the channel. Secondly, according to the ISI channel model, the likelihood probability of each possible sequence is calculated. Thirdly, VA selects the decision sequence with the highest probability. Key improvement of our scheme lies in the probability calculation and VA.
2.1 Channel model and LUT construction
In conventional FIR-based MLSE, as is mentioned in [16,17], the channel is modeled using impulse response as:
where ${s_k}$ and ${r_k}$ are the $k$-th symbols of the sequence before and after channel transmission, $\; {n_k}$ is random noise, and ${f_i}$ are the FIR taps ($L$ is the memory length of the channel). If ${n_k}$ is a Gaussian noise, the probability of the sequence (${s_1}, \ldots ,{s_N}$) can be calculated by:
Fig. 2. (a) First-order taps of the Volttera filter estimating the channel memory length; (b) Amplitude distribution of main symbols of a 5-length pattern ($- 3,1,1, - 3, - 1$) and a 3-length pattern ($1,1, - 3$) after 40-km transmission. (c) Gaussian distribution fit curve
Although the random noise distribution has been physically and theoretically discussed in [20] under an ideal situation, which is strongly non-Gaussian, it is still worthy to discuss it in the non-ideal memory-length-limited model in practice. Since the memory length of ISI model that we use to fit the channel response is much shorter than the actual channel, when establishing the probability distribution of the main symbols of a specific pattern, the ISI of symbols outside the pattern act as a component of noise ${n_k}$ in Eq. (3). Therefore, the noise term ${n_k}$ contains two parts: one is the random noise introduced by optical and electric components, such as ASE noise of the optical amplifier, thermal noise and shot noise of the photodiode; the other one is the ISI component of symbols outside the pattern. We collect the statistics on the amplitude distribution of main symbols of a 5-length pattern ($- 3,\; 1,\; 1,\; - 3,\; - 1)$ and a 3-length pattern ($1,1, - 3$) after 40-km transmission, and its histogram is shown in the Fig. 2(b) (the mean value is moved to 0). As the memory-length increases, the variance of the noise ${n_k}$ grows larger, which means noise ${n_k}$ contains ISI components. The distribution is complex and difficult to describe in a mathematical form, and is normally obtained using histogram method or method of moments. However, for simplification, we use experimental statistics and simplification scheme to construct the noise model. Gaussian distributed noise model is a very simple and general model to calculate for MLSE. As is shown in the Fig. 2(c), the distribution of noise ${n_k}$ fits with a Gaussian curve well. Although the noise distribution of each pattern is different, it is beneficial to simplify the probability calculation by using the same Gaussian distribution instead, which is very important for the hardware implementation of MLSE with a large number of states. In this case, the branch metric can be calculated by a simple square operation (described in Sec. 2.2). Therefore, the mean value of the Gaussian random process ${r_k}$ is $({s_k} + {A_k})$, and the variance is determined by $\; {n_k}$.
In short and medium reach IM/DD transmission system, affected by various factors such as the polarization mode dispersion (PMD) and power variety of the transmitter, the change of the channel is subtle, but still cannot be ignored. Therefore, updating the LUT is essential for nonstationary channel equalization.
$L$ consecutive transmitted symbols have ${M^L}$ states for PAM-$M$ format. Each pattern ${{\boldsymbol S}_k}$ corresponds to a unique entry address ${I_m}$ in the LUT, where ${I_m} \in {\boldsymbol I}$ and ${\boldsymbol I} = \{{{I_1},{\boldsymbol \; }{I_1}, \ldots ,{I_{{M^L}}}} \}$. In order to update the distortion value ${A_{{I_m}}}$ when channel changed, RLS is adopted in updating the LUT. According to the least squares principle, the cost function can be expressed as:
By reforming Eq. (6) in an iterative form, the LUT building/update mechanism can be achieved as shown in Fig. 3. When building the LUT, the pattern ${{\boldsymbol S}_k}$ is obtained using a training sequence. It is obtained using decisions by VA when updating the LUT. With a L-length window sliding, the amplitude value of the ${I_m}$’s main symbol ${r_{i,m}}$ is accumulated with weight in the corresponding LUT entry, which is denoted as $LUT({{I_m}} )$. The LUT counter $C({{I_m}} )$ is used to track the update times of each specific entry. The ISI distortion value ${A_{{I_m}}}$ is:
The tracking capability, accuracy and stability of RLS algorithm depends on the forgetting factor $\mu $. When building the LUT, the forgetting factor $\mu $ can be set as 1 for quicker convergence. When updating the LUT in transmission, it can be set as a value less than but close to 1 for tracking capability. Besides, the least mean square (LMS) algorithm can also be applied as the adaptive algorithm to estimate the channel, as is mentioned in [21].
Using the transmission characteristics of the channel, all hypothetical possible sending sequences are compared with the actual received sequences, and the decision sequence with the highest probability is selected as the output. Let $({{{\hat{s}}_1}, \ldots ,{{\hat{s}}_N}} )$ denote the decision sequence, and $({{r_1}, \ldots ,{r_N}} )$ denote the actual received samples. As the Gaussian noise assumption, the N-length decision sequence is given by:
2.2 Path-decision-assisted Viterbi algorithm
The MLSE requires searching a decision sequence with maximum likelihood probability from all possible sequences. Viterbi algorithm is a good strategy to obtain it without traversing all possible sequences, which reduces the complexity. VA of the proposed MLSE scheme includes the following steps:
- 1) Construct the state transition trellis. Each node represents a state of several adjacent symbols of the sequence, and each branch between two nodes represents a state transition.
- 3) For the current node, add the connected branch metric to the cumulative branch metric of the survival path recorded by related nodes in the upper layer and select the shortest one as the new survivor path. Then record the new survival path and cumulative branch metric to the current state node;
- 4) After N symbols, trace back and output the symbol sequence $({{{\hat{s}}_1}, \ldots ,{{\hat{s}}_N}} )$ with the shortest path metric in the nodes of current layer;
- 5) Update the LUT according to the output symbol sequence.
For channels with a long memory length, the complexity of the VA is high. Many techniques have been proposed to reduce the VA’s complexity, such as partitioning and per-survivor processing [22,23]. In this paper, we propose the path-decision-assisted (PDA) VA to improve the performance of a short-memory-length MLSE without increasing the state number and computational complexity. It also retains the classical structure of MLSE to preserve ease of hardware implementation. For simplicity, we call the VA with a $P$-memory-length state transition as “$P$-length VA” in the following.
Firstly, we construct an $L$-length LUT as is introduced in Section 2.1. Then, same with the conventional VA, we construct state transition trellis with a shorter memory length of ${\; }P$, which has ${M^{P - 1}}\; $ nodes and ${M^P}\; $ branches in each layer. But when calculating the branch metric using the corresponding $P$-length pattern, we trace back the last $L - P$ tentative decisions of the survival path recorded by related nodes in the upper layer and extend the pattern to L symbols. In this way, the pattern can be used to look up $L$-length table. It allows applying an L-memory-length ISI model to $P$-length VA. For instance, as shown in Fig. 4(a) and (b) ($\; P = 3,\; \; L = 5,\; \; $PAM-4), when calculating the branch metric between the state $({{s_1},\; {s_2}} )$ and $({{s_2},\; {s_3}} )$, the conventional VA is supposed to use the pattern $({{s_1},\; {s_2},\; {s_3}} )$ to look up the table. However, in the proposed PDA-VA, the node $({{s_1},\; {s_2}} )$ has stored the tentative survival path:${\; }( \ldots {\hat{s}_{ - 1}},\; {\hat{s}_0},\; {\hat{s}_1},\; {\hat{s}_2}$). Using these tentative decisions, the pattern can be extended to $({{{\hat{s}}_{ - 1}},\; {{\hat{s}}_0},\; {s_1},\; {s_2},\; {s_3}} )$, which means we can use a 5-memory-length model with only 43 branch metrics for calculation.
Fig. 4. The path-decision-assisted Viterbi algorithm ($L = 5,\; P = 3$): (a) functional block diagram (b) example of a partial state transition trellis for PAM-4.
The memory length of the actual channel is fixed. However, when we use a limited-length model to fit the actual channel response, a longer length model will have a response with higher resolution, and that fits the actual channel better. It is the same with conventional FFE equalizer. Besides, as is mentioned in Section 2.1, the ISI of symbols outside the pattern act as a component of noise when the memory length of ISI model is shorter than the actual channel. Extending model length also reduces ISI component in noise, which improves the performance of MLSE. Compared with the conventional $P$-length VA based on $P$-memory-length ISI model, our PDA scheme using a $L$-memory-length ISI model introduces a performance improvement with the same number of states.
However, using the tentative decisions may cause error propagation. Our scheme has a slighter performance penalty compared with the conventional $L$-length VA based on $L$-memory-length ISI model. As the branch metric calculation depends on the amplitude of the main symbol, in order to suppress the error propagation, the tentative decisions in the pattern are supposed to not include the main symbol, as Eq. (9) shows. When $\; L = 5$, P should be 3 or 4. In Section 4, we verify the performance of the PDA schemes with different P and L, and compare them with the conventional VA.
Table 1 compares the resource requirement of the $L$-length two VAs. For high-order modulation format and channel with a large memory length, the proposed path-decision-assisted VA can significantly cut down the hardware resource consumption.
Table 1. Complexity comparison of Conventional and Path-decision-assisted ${\boldsymbol L}$-length Viterbi Algorithm
In [24], a simplified FIR-based MLSE scheme for branch metric calculation is proposed. It uses the absolute value of the distance instead of the Euclidean distance. This paper extends it to LUT-based MLSE and realizes a multiplier-free MLSE. In addition, we found that the absolute value distance scheme has an obvious performance degradation for the proposed MLSE in transmission experiment. Therefore, we propose a segmented linear absolute value distance replacement, which results in much slighter performance degradation. The performance difference between the two schemes will be compared in Section 4. According to Eq. (9), one multiplier serving for the square operation is required for each transition state. For this only one multiplier, we replace it in branch metric calculation approximately by:
The above equations can be realized with only adders and bit operations. Therefore, the entire proposed MLSE equalizer is multiplier-free, except for LUT building and updating. The complexity is reduced from ${M^P}$ multipliers per symbol to 0.
3. Experiment setup
Experimental setup of the 56-Gbps IM/DD transmission system is shown in Fig. 5. At the transmitter, the binary sequence is mapped into PAM-4 format. Considering the electrical bandwidth limitation, PAM-4 signal is first processed with 31-taps FIR filter for pre-emphasis, and then with another 128-tap root-raised cosine (RRC) filter with roll-off factor of 0.5 for pulse shaping. The generated signal is loaded into an arbitrary waveform generator (AWG, Keysight M8196A) with 3-dB bandwidth of 30 GHz. The AWG sampling rate is 84 GS/s. The oversampling ratio of PAM-4 signal is set at 3, thus the signal baud rate becomes 28 GBaud. After electrical amplification, the output electrical signal is fed into an MZM with 32-GHz bandwidth. We use a 1550 nm continuous-wave (CW) laser with 100-kHz linewidth as the optical source. The launching power after MZM into the fiber link is fixed at 8.5 dBm. After 40 km SSMF transmission, the received optical power (ROP) into the receiver is controlled by a variable optical attenuator (VOA). The ROP changes from $- 8$ to $- 1$ dBm. Then the optical signal is directly detected by a 40-GHz bandwidth photodiode (PD). An oscilloscope (Lecroy LabMaster 10-36Zi-A) with 36-GHz electrical bandwidth at 80-GSa/s sample rate is used to sample the electrical PAM-4 signal. The DSP in the receiver includes clock data recovery (CDR), RRC filter, MLSE, PAM-4 de-mapping and BER counter. The initial look-up table is established by using a training sequence of 163840 PAM-4 symbols.
Fig. 5. (a) Experimental setup of the 56-Gbps IM/DD transmission system; (b) Optical spectrum at the transmitter end; (c) Electrical spectrum at the receiver end.
4. Results
The performance of MLSE algorithm mainly depends on the accuracy of channel model. FIR-based MLSE is the optimal performance receiver only when the channel is a partial impulse response channel. When the channel response is more complex, considering dispersion, polarization mode dispersion, Kerr effects and nonlinearity of modulator and receiver, a desired impulse response model is not suitable for characterization. Using a more general ISI model will lead to better performance. To evaluate the capability of the ISI channel model for describing a dispersion-limited channel, we apply LUT correction and VNLE [25] in the 40-km C-band SSMF IM/DD transmission system at the ROP of $- 1$ dBm. The LUT correction mitigates the pattern-dependent ISI distortion $\; {A_k}$ with a trained LUT according to Eq. (3). Usually, the patterns are obtained from received symbols with decision. In this experiment, to avoid ISI model being affected by decision-induced symbol errors, we use another known symbol sequence to ensure the correctness of all patterns. The memory length of LUT is set as 5. The VNLE is based on third-order Volterra series. The tap numbers of its first, second and third kernels are 71, 21 and 5, respectively. In Fig. 6, the $Q_{dB}^2\textrm{ - factor}$ is:
Fig. 6. (a) (d) The scatter plots, (b) (e) histograms and (c) (f) spectrums of the signals (1 sample per symbol) after VNLE (left) or LUT correction (right).
Figure 6 shows the scatter plots, histograms and spectrums of the signals processed by VNLE and LUT correction. As is shown in Fig. 6(a) and (d), the $Q_{dB}^2\textrm{ - factor}$ of the LUT correction scheme is 8.9 dB higher than that using VNLE, which means the ISI channel model can better describe the response of the channel. In an IM/DD system, dispersion caused power-fading effect would bring in some notches in the spectrum. The notch in the main lobe of the signal will cause serious distortion of the waveform. Channel equalizers could help to mitigate such influence. As is shown in Fig. 6(c) and (f), both equalizers can effectively enhance the high frequency part of the spectrum and flatten the frequency response. However, applying VNLE, the spectrum notch and signal distortion still exist. FIR filter or Volterra series filter with limited memory length can barely construct appropriate channel response to compensate notches. The ISI compensation based on LUT can smooth out the notch and eliminate the signal distortion caused by power fading with a short memory length. This is because the ISI model uses statistics to record the interference of the surrounding symbols to the main symbol in patterns, which is equivalent to a Volterra series filter setting a set of taps for each pattern. Therefore, ISI-based MLSE has better dispersion equalization ability than FIR-based MLSE and VNLE.
In order to verify the channel tracking ability of adaptive RLS-LUT scheme, we respectively apply the fixed and RLS-LUT correction to the received signal data collected in a single transmission experiment at the ROP of $- 4$ dBm. The Fig. 7 shows the $Q_{dB}^2\textrm{ - factor}$ versus time curves. The forgetting factor of RLS-LUT is 0.96. Due to the same trained initial table value, the performances of the two correction schemes are basically the same at the beginning. After 50000 symbols, because of instability of the channel, the $Q_{dB}^2\textrm{ - factor}$ of RLS-LUT correction becomes significantly greater than that of fixed LUT. The RLS adaptive scheme results in ∼0.2-dB $Q_{dB}^2\textrm{ - factor}$ overall increase for this time window.
To evaluate the performance of our proposed MLSE in IM/DD systems, we compare the proposed MLSE schemes using conventional and path-decision assisted VA with the other three common nonlinear equalizers: FIR-based MLSE, FFE-DFE [26] and VNLE. As is shown in Table 2, the memory lengths of both the proposed and FIR-based MLSE are set as 5. All the traceback length of VA is 13. VNLE is the same one in the above-mentioned experiment. The tap numbers of FFE and DFE are 31 and 11. As the major contributor of complexity, number of multipliers per symbol is also provided in Table 2. It shows that, complexity of our proposed MLSE with path-decision-assisted VA is the lowest among the schemes in comparison.
Table 2. Parameters of the Four Equalizers
Figure 8(a) shows the BER versus ROP curves of the three equalizers in comparison. The BER performance of our scheme is below 7% FEC threshold after 40km SSMF IM/DD transmission. When ROP is $- 1$ dBm, the proposed scheme achieves a BER of 2.65×10−4 after transmission, which is 2.28 orders of magnitude lower than VNLE, and 1.37 orders of magnitude lower than FIR-based MLSE. The FFE-DFE & VNLE is an effective nonlinear channel equalizer for IM/DD system. However, because of the error propagation problem at high BER situations, its performance remains just similar to the VNLE. Its BER is 2.18 orders of magnitude higher than the proposed scheme. Therefore, the proposed scheme outperforms the conventional equalizers for dispersion-limited channels without any hardware multiplier.
Fig. 8. BER versus ROP curves of (a) four equalizers, (b) ISI-based MLSE with different memory lengths and path-decision-assisted (PDA)/conventional VA.
Figure 8(b) demonstrates the performance gap between the ISI-based MLSE with path-decision-assisted/conventional VA and different memory lengths. It applies a fixed LUT and no approximation algorithm. The performance of 5-memory-length ISI-based MLSE using 3-length PDA-VA is slightly weaker than that with the 5-memory-length conventional VA. The PDA leads to a performance penalty of only 0.7-dB ROP, but the complexity is reduced from 1024 branches per symbol to 64 branches per symbol. It achieves a BER of 2.6×10−4 after transmission at −1-dBm ROP. Moreover, compared to the 3-memory-length conventional VA, with the same branch number, using path-decision to support a 5-memory-length ISI model leads to a great improvement of performance. The accuracy of channel model based on ISI is dependent on the memory length. We can observe that increasing the L value of PDA-VA ISI-based MLSE from 5 symbols to 7 symbols can bring in a 1.0-dB ROP performance improvement. The 3-memory-length model is too short to fit the actual channel model. A longer memory length model is conducive to fit the actual channel more accurate. However, when the memory length increases, the scale of LUT training sequence will increase geometrically, leading to a longer training sequence length. For high-order modulation formats, the complexity of conventional VA is related to ${M^L}$, while the complexity of path-decision-assisted VA is only related to ${M^P}$.
The number of the path decisions we use in branch metric calculation determines the accuracy of probability calculation, and traceback length determines the correctness of path selection. This inevitably leads to a trade-off between the performance and hardware storage. We test the performance of the proposed MLSE with five symbols with varying P value and traceback lengths at the ROP of $- 4$ dBm. As is shown in Fig. 9(a), when ${\; }P = 2$, the main symbol of the pattern is obtained from tentative survival path, which leads to serious error propagation. Considering complexity and performance, the P value is recommended to be set as ${\; }({L + 1} )/2$. Figure 9(b) presents the curve of BER vs. traceback length. The performance is saturated when the traceback length becomes larger than 13.
Fig. 9. (a) BER vs. P value ($\textrm{traceback\; length} = 13$); (b) BER vs. Traceback length ($P = 3$).
The performance of RLS algorithms depends on the forgetting factor, which leads to a trade-off between the accuracy and stability. For the same sample sequence, we update LUT using different forgetting factors and apply the proposed MLSE. In Fig. 10(a), an optimal forgetting factor of 0.96 is found for the proposed MLSE at $- 4$-dBm ROP. The BER at this optimal forgetting factor is 1.1×10−3 lower than that of the fixed LUT scheme.
Fig. 10. (a) BER vs. Forgetting Factor at −4-dBm ROP. (b) Performance penalty of the multiplier-free approximation calculation.
In addition, we evaluate the performance penalty of the approximation calculation for the proposed MLSE scheme. Figure 10(b) shows the results of the MLSE with and without approximation calculation, of which the RLS forgetting factor is 0.96. The multiplier-free approximation algorithm has almost no BER penalty, which could greatly reduce the cost and power consumption of application specific integrated circuit (ASIC). Compared with accurate calculation with Euclidean distance, our segmented linear scheme has much less performance penalty than the absolute value distance scheme in [24]. The BER of the proposed scheme is 2×10−3 lower than the absolute value scheme and almost the same with the Euclidean distance scheme at the ROP of $- 4$ dBm.
5. Conclusion
In this paper, we propose a multiplier-free MLSE equalizer and experimentally demonstrate a C-band 56-Gb/s PAM-4 IM/DD transmission over 40-km SSMF without any optical amplifier, filter or optical dispersion compensation at the receiver end. It achieves a BER of 2.65×10−4 after 40-km SSMF transmission with the ROP of $- 1$ dBm, which is much lower than the FIR-based MLSE and VNLE. To reduce the complexity for hardware realization, the VA is assisted with path-decision. Compared with the conventional 5-memory length VA, it significantly reduces the computational complexity to 1/16, inducing only a trivial performance penalty of 0.7-dB ROP. In addition, using segmented linear approximation calculation can realize multiplier-free hardware implementation with almost no performance penalty.
Funding
Science and Technology Planning Project of Shenzhen Municipality (JCYJ20200109142010888); National Key Research and Development Program of China (2018YFB1801300); Innovation Fund of WNLO.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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