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Abstract
An intensity-sloped optical code with an optical chip-pulse stream generated by Si-based ODFT suffers from crosstalk and signal-to-noise (SNR) degradation. To mitigate these problems related to code-orthogonality reduction, we propose a simple intensity-discrepancy-compensation scheme that involves adjusting the chip-level intensity in the digital-domain. We numerically show a 0.1 dB SNR improvement for 40 Gb/s quadrature phase-shift keying (QPSK) Fourier-encoded synchronized optical code division multiplexing (FE-SOCDM) signal when multiplexing 1 dB/chip intensity-sloped optical codes. A proof-of-principle experiment achieves a 0.3 dB received power improvement using intensity-discrepancy compensation for two optical code multiplexing signals with 1.5 dB/chip.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Time- and wavelength-division multiplexing passive optical networks (TWDM-PON) with 10 Gb/s signals at each of 4 different wavelengths have become standardized and are widely studied [1,2]. Increasing power budgets in future long-reach PON systems will significantly impact both capital expenditure (CAPEX) and operating expenditure (OPEX). A coherent PON system, involving multilevel optical phases and amplitudes can achieve a high receiver sensitivity [3,4]. However, 10Gb/s-based coherent PON systems, using a QPSK format, have also displayed a higher receiver sensitivity [5].
As an alternative to wavelength multiplexing, OCDM can open new possibilities [6–8]. Within the “internet of things” (IoT) context, an OCDM system can handle various signals independently, using their respective optical codes (OC) in a conventionally utilized bandwidth without hampering the legacy system. Numerous experiments have been performed on OCDM systems, involving intensity modulation and direct detection (IM/DD) [9,10].
In previous QPSK-OCDM experiments, we demonstrated the simultaneous detection of a 4-channel (4ch) Fourier-encoded signal by combining a coherent receiver and digital signal processing (DSP) [11]. Multiple OCs were generated and processed in the optical domain simultaneously using a silica-based multi-port optical en/decoder [12]. To scale the device size, we proposed a 4ch silicon optical waveguide-based optical discrete Fourier transform (Si-ODFT) device comprising a cascaded asymmetric Mach-Zehnder interferometer (CAMZI) that can simultaneously generate and process multiple OCs [13].
If the intensity at each chip in the cascaded CAMZI is incorrectly designed or adjusted, the code orthogonality becomes degraded as a result of an inter-chip intensity-discrepancy in a single OC. The degraded performance of the decoded signal occurs while the different signals are decoded simultaneously in the uplink FE-SOCDM system. This inter-chip intensity discrepancy can be compensated optically by means of an inter-chip intensity equalizing method using optical attenuators. However, such as optical-domain inter-chip equalization is effective only on the expected optical attenuation value, and the received signal-to-noise ratio (SNR) is degraded by chip-intensity attenuation.
In the present paper, we propose a digital-domain inter-chip intensity-discrepancy compensation (IC-IDC) scheme, that can collectively compensate an inter-chip intensity-sloped 4ch FE-SOCDM signal. The proposed scheme can be used without depending on the number of channels and chips. To calculate the accurate average intensity of each chip, we should select the number of samples for which the influence of noise is negligible in the averaging process in IC-IDC. The amount of calculation for estimating the average intensity increases as the multi-level value of the modulation format increases. To the best of our knowledge, that is the first collective compensation applied to an inter-chip intensity-sloped 4ch FE-SOCDM signal. A numerical validation of the method confirms an improvement of better than 0.1 dB to the SNR for 1 dB/chip intensity-sloped four-OC multiplexed signals. We experimentally demonstrate a 0.3 dB improvement in the received power, for 1.5 dB/chip intensity-sloped two-OC multiplexed signals.
2. Performance degradation and compensation
2.1 Principle of intensity-sloped OC generation and the digital-domain decoder
Figure 1(a) outlines the overall architecture of an upstream FE-SOCDM system involving a 4ch Si-based ODFT encoder and a digital-domain 4-point DFT decoder. The schematic diagram in Fig. 1(b) shows a prototyped 4ch Si-based ODFT with a two-stage CAMZI configuration. A short pulse-shaped QPSK signal with a symbol rate Rs is fed into a 4ch ODFT and generates multiple OCs from its output port.
Fig. 1 FE-SOCDM system (a) system configuration (b) conceptual diagram of the prototype 4ch Si-based ODFT, (c) Si-based ODFT with CAMZI, (d) temporal OC waveform.
Figure 1(c) shows the configuration of the CAMZI structured Si waveguide. The input optical single or twin pulse becomes split into two separate signals at each stage of the MZI structured Si waveguide. The chip intensity becomes degraded by the optical delay line in the upper branches. The waveguide output thus causes an inter-chip intensity discrepancy. Previous experiments confirmed that a 1 dB/chip intensity discrepancy occurs in a single OC that was generated by our prototyped 4ch ODFT, as shown in Fig. 1(d) [13]. The Fourier-coded signal with the inter-chip intensity discrepancy is expressed as
where are the attenuation coefficients for each chip, ordered according to .We next describe the underlying principle of the decoding procedure for the 4ch FE-SOCDM signal. Let be a discrete complex signal that equals the sum of the I and Q signals, obtained by phase diversity homodyne detection of the FE-SOCDM signal and the reference light:
The transposed and arranged matrix for ODFT signal is thenThe 4-point DFT associated with , as expressed in Eq. (3), isHere, is the inverse matrix of when and shown in Eq. (5).Each element of Eq. (5) is constructed from which the Fourier matrix of Eq. (1). In the case of synchronous transmission, it is not necessary to perform inter-channel carrier phase synchronization across all channels. The FE-SOCDM signal can thus be decoded collectively by digital-domain DFT.2.2 Code orthogonality degradation
We here evaluate the code orthogonality degradation that arises from the inter-chip intensity-sloped OCs. In the example considered, the digital-domain 4-point DFT is processed for OC#1 only.
Figure 2 shows optical spectra for ideal and intensity-sloped OCs. The extinction ratio is defined as the ratio between the main-lobe peak power of OC#1 and the null point power of OC#2, as indicated in Figs. 2(a) and 2(b). The extinction ratio between adjacent OCs in the ideal and inter-chip intensity-discrepancy cases are 60 and 20 dB, respectively. Crosstalk between adjacent OCs, due to inter-chip intensity-discrepancy, becomes stronger.
Figure 3(a) shows digital-domain 4-point DFT processed constellation maps for OC#1 to #4, in the ideal case where there is no inter-chip intensity discrepancy. Since the code number is matched between the encoder and decoder, the desired signal is obtained from the output port. On the other hand, in the case of an unmatched code number between the encoder and decoder, the output signal becomes zero. Therefore, code orthogonality is perfectly maintained and the channel can be clearly identified.
Fig. 3 DFT processed constellation maps from OC#1 to #4 (a) ideal case, (b) 1 dB/chip intensity discrepancy case.
Figure 3(b) shows the corresponding results for a real case, involving an inter-chip intensity discrepancy. The power of the desired signal is here reduced relative to the ideal case. Also, the undesired signal generated from the DFT output port is not zero.
Figure 4 shows the discrete sampling points of each chip in multiplexing inter-chip intensity sloped OCs. Whereas the sampling points for chip#1 coincide with those associated with the absence of inter-chip intensity sloped OCs, we can confirm that the power-level of sampling points from chip #2 to #4 is lower than the ideal symbol points, owing to the inter-chip intensity discrepancy. It can be confirmed that all the chips display a 4-level and 25-symbol point constellation. Importantly, the effect of an inter-chip intensity discrepancy is apparent only in the intensity domain, not phase domain. Therefore, to overcome the inter-code orthogonality reduction caused by an inter-chip intensity discrepancy, we consider that the inter-chip intensity equalization is effective for the multiplexed OCs.
2.3 Inter-chip intensity discrepancy compensation for multiplexed OCs
Figure 5 shows the configuration of the proposed IC-IDC scheme for blind-based DSP. Each chip intensity is aligned to the intensity of chip #1. The choice of reference chip, however, is arbitrary.
The coherently detected signal is converted to a sampled discrete digital signal at the sampling rate of the chip by an analog-to-digital converter (ADC). The sampled signal is split according to the chip number by a serial-to-parallel converter (S/P). IC-IDC is then performed. Each chip intensity with a complex value is averaged over multiple samples using a moving averaging filter (MAF). The average intensity value of each chip approaches to the expected value with increasing sampling number. Therefore, it is possible to estimate the pseudo-ideal coefficients from multiplied OCs in order to align all the chip intensities to that of the chip #1. Each coefficient calculator (CC) generates the coefficient, which is calculated from the average intensity of each chip. By multiplying the intensity of each input chip by the estimated coefficients, the intensity value from each output of the compensation block becomes the expected value intensity of chip #1. The output signal from the compensation block is decoded by the digital-domain 4-point DFT. Collective decoding is then performed.
3. Numerical validation
3.1 Simulation model
Figure 6 shows the simulation model of the 4ch FE-SOCDM system with IC-IDC. An optical pulse is generated by a laser diode (LD) and modulated into a QPSK signal by an IQ modulator (IQM). The optical pulse stream in each channel is optically coded and multiplexed by 4ch ODFT. In the transmission line, random noise is collectively added to OC multiplexed signal. The received OC multiplexed signal is divided into I and Q components by a coherent receiver and converted to a digitally sampled signal by the ADC. Then, the sampling signal for each chip is split by the S/P converter and fed into the IC-IDC system to equalize the chip intensities. Finally, digital collective decoding is performed by 4-Point DFT. Table 1 lists the simulation parameters.
Table 1. Simulation parameters
3.2 Results for uniformed inter-chip intensity sloped OCs
We calculated the number of MAF taps required to yield the expected intensities for each chip. Figure 7 plots the variance of the compensation coefficient as a function of the number of taps, confirming that the calculated average intensity for each chip converges after 50 taps. We thus set the tap number of MAF to 50. Figure 8 plots the “bit error ratio” (BER) performance as a function of the SNR, as the intensity discrepancy varies from 0 to 2 dB/chip. Here, the described SNR is determined before IC-IDC. By applying IC-IDC, the code orthogonality is improved. However, the SNR after IC-IDC is surely reduced as compared with the SNR before IC-IDC when multiplying by the coefficient value for each chip that causes performance degradation. In that case, the performance is not ideal.
We compare the SNR value required to achieve a BER = 10−3 between the cases without compensation and with IC-IDC. As shown in Fig. 9, the required improvements in SNR for intensity discrepancies of 1, 1.5, and 2 dB/chip are 0.3, 1.0, and 2.4 dB, respectively. Notably, for intensity discrepancies in excess of 0.5 dB/chip, the SNR vs. BER performance is degraded because the noise power is enhanced more strongly than the inter-code orthogonality improvement.
3.3 Results for varied inter-chip intensity sloped OCs
In Section 3.2, the simulation results are summarized when the inter-chip intensity discrepancies across all OCs are aligned, but the inter-chip intensity discrepancy is slightly different across all OCs owing to a manufacturing error of the 4ch ODFT. We consider three different inter-chip intensity-discrepancy cases when the inter-chip intensity discrepancy of each OCs was changed from 0 to 2 dB. The required SNR difference ΔSNR at BER = 10−3 for the cases without compensation and with IC-IDC is calculated using the average BERs of all the OCs. Figures 10 show a color map of ΔSNR as a function of performance improvement. As in Section 3.2, the performance of the intensity discrepancy over a 0.5 dB/chip increases because the code orthogonality improvement exceeds noise enhancement.
Fig. 10 BER improvement value by IC-IDC (a) ch1 = 0dB, ch2 = 0dB, (b) ch1 = 0dB, ch2 = 0.5dB, (c) ch1 = 0dB, ch2 = 1dB, (d) ch1 = 0.5dB, ch2 = 0dB, (e) ch1 = ch2 = 0.5dB, (f) ch1 = 0.5dB, ch2 = 1dB, (g) ch1 = 1dB, ch2 = 0dB, (h) ch1 = 1dB, ch2 = 0.5dB, (i) ch1 = ch2 = 1dB.
Moreover, we also numerically evaluated the performance improvement in the case of inter-chip intensity discrepancies across chips due to the delay and the split loss in CAMZI. Figures 11 show the simulation model to evaluate when the intensity-discrepancy differs between chip #1-#2 and chip #2-#3. Figures 12 show the results when 1 dB/chip and 2 dB/chip are referenced, and IC-IDC can compensate for all cases of slight discrepancies between chip #1-#2 and chip #2-#3.
Fig. 11 Simulation model of inter-chip intensity discrepancies across chip (a) 1 dB/chip, (b) 2 dB/chip.
4. Proof-of-principle experiment
4.1 Experimental setup
Figure 13 outlines the experimental setup of 2 OCs with a symbol rate of 2.5-GSymbol/s, the FE-SOCDM system with IC-IDC, emulating inter-chip intensity sloped OC generating/processing. As a proof-of-principle experiment, we assumed the effectiveness of IC-IDC for simultaneously generating and detecting for two inter-chip intensity-sloped OCs by an arbitrary waveform generator (AWG: Tektronix, 7122C) and a digital storage oscilloscope (DSO: Tektronix, 6154C). The optical spectrum of both OCs is shown in Fig. 14.
A single LD generated a continuous wave (CW) with a central wavelength of 1550 nm. A polarization-maintained 3 dB optical coupler splits the CW, and the outputs were fed separately into the IQM or the coherent receiver. One of the CW outputs was modulated to 2ch FE-SOCDM signal, and it was launched into a coherent receiver. The 2-ch FE-SOCDM signal controlled the received power via an optical tunable attenuator (ATT) and was fed into the coherent receiver. The maximum LO power was set to 10 dBm, the required power for the input of balanced-photodiodes. In the coherent receiver, the polarization-controlled CW and the FE-SOCDM signal were multiplexed and split into I and Q components in the optical domain. The received FE-SOCDM signal waveform was measured using a DSO. We conducted an offline DSP for the DSO output. The DSP consists of S/P, IC-IDC, 4-point DFT, and carrier-phase recovery (CPR).
4.2 Experimental results
Figures 15(a) and 15(b) show the constellation of two OC multiplexed signals with a 1dB/chip discrepancy at the DSO output, without and with the application of IC-IDC. The encoded signal is a 9-point constellation with different occurrence rates like nine 9-QAM. These figures evidently confirm that the use of IC-IDC reduces signal variation on the constellation map.
Figures 16 plots the dependence on the received power of the average BERs of 2ch FE-SOCDM signal with intensity discrepancies of 0, 1, and 1.5 dB/chip. Here, the inter-chip intensity discrepancies between two OCs were set to the same value. By experiment, we observed that the BER performance of a 2ch FE-SOCDM signal was degraded by 1.2 dB for BER = 10−3 by a 1 dB/chip intensity discrepancy. Without compensation of the 1 and 1.5 dB/chip intensity sloped OCs, the required powers were −31.1 and −30.3 dBm. When IC-IDC was applied, the required power increased to −31.2 and −30.6 dBm, respectively. The performance improvement of the proposed method was 0.1 and 0.3 dB, respectively. Figures 17 plot the calculated BER performance as a function of the SNR under the same experimental condition. We can confirm that the performance improvement between experiment and simulation is almost same in the case of same slope value.
To effectively achieve the performance improvement by the proposed method, we should consider the effective number of bit (ENOB) of DSO so that quantization error does not occur. In the case of four-chip OC, the minimum required ENOB is 2-bit resolution corresponding to four-level quantization. Here, the ENOB of DSO was 8-bit resolution in the case of 20 GSa/s. Therefore, the error value of intensity-discrepancy can be ignored.
5. Conclusions
We have proposed and demonstrated a 4ch FE-SOCDM system using IC-IDC that can simultaneously equalize overall intensity level for all multiplexed OCs at the latter stage of the receiver-side DSP. Numerical simulation indicates an improvement of more than 0.1 dB in the SNR of four 1 dB/chip intensity-sloped OCs. We experimentally showed that the proposed IC-IDC reduces crosstalk and yields a 0.3 dB received power improvement for two 1.5 dB/chip intensity-sloped OCs.
Funding
Japan Society for the Promotion of Science (16K06345); Ministry of Education, Culture, Sports, Science and Technology.
Acknowledgments
The authors would like to thank M. Hossen of Khulna University of Engineering and Technology, Bangladesh. This research was supported by the Ministry of Education, Culture, Sports, Science, and Technology of Japan under the “Leading Initiative for Excellent Young Researchers (LEADER).” This work was partly supported by JSPS KAKENHI Grant Number 16K06345. We would like to thank Editage (www.editage.jp) for English language editing.
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