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Abstract
We propose and demonstrate the asymmetric direct detection (ADD) of polarization division multiplexed single-sideband (PDM-SSB) signals with orthogonal offset carriers. ADD exploits the photocurrent difference to eliminate the Y-Pol interference in the X-Pol, and the X-Pol signal intensity to eliminate the X-Pol interference in the Y-Pol without resorting to iterative algorithms. This enables not only low-complexity signal linearization but also a simplified receiver front-end composed of a single optical filter, two single-ended photodiodes and two analog-to-digital converters (ADC). In the experiment, we first perform a parametric study of the proposed scheme at 40 Gbaud in the back-to-back configuration (B2B) to evaluate the performance impact of different system parameters including the carrier to signal power ratio (CSPR), the matched filter roll-off, and the filter guard band. Next, we demonstrate the transmission of 416 Gbit/s PDM 16-QAM signal over 80 km single-mode fiber (SMF) below the soft-decision forward error correction (SD-FEC) threshold of 2×10−2. We also numerically study the effectiveness of a 2×2 multiple-input-multiple-output MIMO equalizer in alleviating the inter-polarization linear crosstalk resulting from the non-orthogonal PDM-SSB signals due to polarization-dependent loss (PDL), which is not negligible for potential on-chip implementation of ADD.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The massive growth of the network traffic has been driven by the rapid development of information processing electronics that scales up following the Moore’s law. Cisco forecasts [1] that the global IP traffic, which reached 1.5 Zettabyte in 2017, will more than triple by 2022, of which 33% will stay within the Metro network. Coherent transmission is a high throughput high spectral efficiency technology inclusive of Metro and inter-datacenter distances. At lesser throughputs and spectral efficiencies in the 40 km to 80 km reach range, direct detection (DD) transmission schemes can generally provide cost-effective, power-efficient and compact footprint transceivers [2–4]. Compared with dual-polarization coherent, DD schemes require fewer photodiodes (PDs) and analog to digital converters (ADCs) at the receiver. Moreover, DD schemes have no carrier recovery or frequency offset compensation algorithms in the receiver DSP, which can allow for more compact and lower power-consumption ASICs.
Intensity modulation direct detection (IMDD) schemes suffer from chromatic dispersion (CD) induced power fading in the C band [5,6], which can be relaxed by transmitting a single-sideband (SSB) signal with higher optical spectral efficiency [7–9]. Polarization-division multiplexing (PDM) doubles the spectral efficiency such that fewer colors are required to reach the same aggregate capacity when PDM and wavelength-division multiplexing (WDM) are used simultaneously. Thus, a category of PDM-SSB schemes has been reported previously which involves the use of Stokes vector receivers (SVRs) [10–13]. In [10], Antonelli et al. propose a scheme that incorporates Kramers-Kronig (KK) detection [14] with PDM-SSB-SVR to retrieve the field information of X-Pol based on |X|2 obtained from the Stokes parameters S0 and S1. The field of Y-Pol is obtained by dividing the field of X-Pol from the beating term XY* derived from S2 and S3. [11,12] proposed another scheme that cascades KK after polarization de-rotation to recover the PDM-SSB signal using the intensities |X|2 and |Y|2. Later in [13], the SSB signal at the Y-Pol in [10] is replaced by a complex double sideband (DSB) signal to improve the spectral efficiency. However, the hardware cost-saving of the PDM-SSB-SVR schemes is marginal and an extra overhead is incurred to obtain and track a de-rotation matrix that incurs both increased overhead and extra delay. Another category of schemes relies on the use of a local oscillator to demultiplex the PDM-SSB signals at the expense of increased operational cost due to the remote wavelength management as well as extra pilot symbols for the polarization tracking [15,16]. [17] reported a filter-based alternative for PDM-SSB signal that employs a pair of filters, PDs, and ADCs at the receiver. That scheme uses a pair of sharp edge filters (800 dB/nm) and iterative DSP to mitigate the inter-polarization signal-signal beating interference (SSBI) which incurs delay.
We propose the asymmetric direct detection (ADD) for PDM-SSB signals, which enables a reduced complexity receiver front-end comprising a single optical filter (125 dB/nm), two single-ended PDs and two ADC channels. ADD improves the spectral efficiency compared to [17] by assigning a guard band only for the X-Pol as opposed to a guard band for each state of polarization (SOP). In addition, the DSP developed to linearize the received PDM-SSB signal does not require an iterative algorithm, thereby reducing the delay. At the receiver, the signal is split into two copies with one copy being filtered before direct detection, while the other copy is detected without filtering. The Y-Pol interference in the X-Pol is removed by exploiting the PD current difference, while the X-Pol SSBI in the Y-Pol is removed by the non-iterative estimate based on the intensity of the recovered X-Pol signal. The Y-Pol signal can subsequently be reconstructed by KK recovery. We first study the impact of system parameters on the performance of ADD at 40 Gbaud in back to back (B2B). We then demonstrate the transmission of a 52 Gbaud PDM 16-QAM signal with a BER below the soft-decision forward error correction (SD-FEC) threshold of 2×10−2, which corresponds to a throughput of 346 Gbit/s (raw data rate 416 Gbit/s). We also conduct a numerical study of the effectiveness of a $2 \times 2$ multiple-input-multiple-output MIMO equalizer in mitigating the linear crosstalk resulting from the non-orthogonal PDM-SSB signals induced by the polarization-dependent-loss (PDL), which is often not negligible for potential on-chip implementation of ADD [18–20].
The rest of the paper is organized as follows. Section 2 details the working principle of the proposed scheme. Section 3 describes the experimental set-up and DSP. The experimental results including the parametric study and the demonstration of the 52 Gbaud transmission over 80-km SSMF are presented and discussed in section 4. Finally, section 5 concludes the paper.
2. Principle of ADD for PDM-SSB signal
The working principle of ADD is illustrated through a spectrum block diagram in Fig. 1. Figure 1(a) shows the optical spectrum of the transmitted PDM-SSB signal with orthogonal offset carriers assigned on the opposite edges of the signal similar to [17]. The signal as well as the carrier can be all digitally generated via a dual-pol IQ modulator (IQM) driven by the amplified RF signals from a four-channel arbitrary waveform generator (AWG) as in [12,17,21,22]. Yet, it is worth mentioning that the digital carrier generation could incur a higher requirement on the effective number of bits (ENOB) and the bandwidth of the AWG. Compared with [17], the spectral efficiency of the PDM-SSB signal for ADD is improved, since a guard band is assigned only in the X-Pol between the signal and the carrier as opposed to a guard band for each polarization. The generated signal is split into two copies at the receiver, where one copy is optically filtered to attenuate the X-Pol side carrier, while the other copy is detected without filtering as is depicted in Figs. 1(c) and 1(b), respectively. When the X-Pol carrier power is negligibly low after filtering, the baseband spectra after square-law detection are shown in Figs. 1(d) and 1(e), respectively. The subtraction of the photocurrent between Fig. 1(d) and Fig. 1(e) helps remove the interference from the Y-Pol, retaining only the linear term of the X-pol signal as shown in Fig. 1(g). Figure 1(g) is used to recover the X-Pol signal as well as estimate the X-pol SSBI shown in Fig. 1(f). Then Fig. 1(f) is removed from Fig. 1(e) to create the signal containing only the intensity of the Y-Pol signal shown in Fig. 1(h), which can be recovered by the KK method.
Fig. 1. The transmitted signal spectrum and the Rx signal spectrum evolution in the linearization DSP.
To best describe the feasibility of the scheme, we formulate the transmitted signal as,
The Y-pol signal recovery DSP depends on the sharpness of the optical filter. When a sharp optical filter is used, the linearization DSP can be further simplified with $\alpha $ set to zero such that the X-Pol SSBI can be estimated using the recovered X-Pol signal and then removed in Eq. (3) for subsequent KK recovery of ${E_Y}$. Note that the scaling factor for the X-Pol SSBI is $1\textrm{/}({2{T_X}} )$ in this scenario, where the estimate of ${T_X}$ can be obtained from the average of (4). Whereas when a slow roll-off filter is employed, $\alpha $ needs to be optimized to estimate the undesired linear crosstalk term $2\alpha {T_X}{\mathop{\rm Re}\nolimits} ({({{E_X} + {n_X}} ){e^{ - j{w_X}t}}} )$ in Eq. (3). Moreover, the overall signal-to-noise ratio (SNR) of the PDM-SSB signal degrades as $\alpha $ increases. This is due to the decreased linear term of ${E_X}$ relative to the dominant PD and ADC noise ${n_{Th3}}$ in Eq. (4); this leads to a reduced SNR for the recovered ${E_X}$ signal. The SNR of ${E_Y}$ is reduced as well since the estimate of the X-Pol SSBI ${|{{E_X} + {n_X}} |^2}$ in Eq. (3) relies on the SNR of ${E_X}$.
The impact of the distributed component PDL is often not negligible if ADD were to be implemented on a silicon photonics (SiPh) chip, since the orthogonal transverse electric (TE) and transverse magnetic (TM) modes are subjected to different propagation losses and insertion losses due to the asymmetric silicon waveguide cross-section [18–20]. The presence of nontrivial PDL depolarizes the PDM-SSB signals, thus penalizing the performance. The non-orthogonal PDM-SSB signal can be expressed as
By denoting ${E_X} + \cos (\theta )({T{ _Y}{e^{j( - w{ _Y}t)}} + {E_Y}} )$ as ${E^{\prime}_X}$, Eq. (5) can be reformulated as
3. Experimental set-up and DSP
The digital generation of the offset carriers requires the perfect match of the signal amplitude and phase between the I and Q channels at the carrier frequency, which is over 30 GHz in the experiment. Otherwise, the presence of the image carriers creates extra interference terms that degrade the SNR. Due to the limited transmitter bandwidth of 14 GHz in our set-up, the suppression of image carriers beyond 30 GHz is hard to tune due to the imbalanced loss and phase difference with the RF chains and child MZMs at higher frequencies. We follow [17] to use separate lasers to generate the offset carriers in the experiment. Figure 2 shows the experimental set-up and the DSP with the polarization-maintaining components shown in blue including the patch cord, power splitter, and power combiner. The IQ MZM biased at null point is driven by the linearly amplified RF signals from two channels of an 8-bit AWG to modulate the 1550.12 nm optical carrier from an external cavity laser (ECL). An EDFA follows to boost the signal power for CSPR control. Next, the SOP of the signal is aligned with the SOP of two separate lasers that generate the orthogonal offset carriers using a polarization controller (PC). The PDM signal is created through a polarization emulator comprising a power splitter, a variable optical delay line (VODL), a variable optical attenuator (VOA) and a polarization beam combiner (PBC). The decorrelation delay between the orthogonal SOPs is tuned to correspond to equal an integer number of symbol duration. After transmission, a pre-amplifier and a VOA are used to optimize the received optical power before electrical to optical conversion. At the receiver, the signal is split into two branches by a 50/50 power splitter. The signal in the upper branch is filtered by a Santec OTF-350 filter with a 125 dB/nm edge roll-off and then detected by a 50 GHz 3-dB bandwidth single-ended PD without a trans-impedance amplifier (TIA). The signal in the lower branch is attenuated by the same amount of power equivalent to the insertion loss of the filter in the upper branch. Note that the digital calibration of the power of the two branches can also be performed at first by setting the filter as an all-pass filter. The calibration coefficient can be saved and used to obtain finer magnitude alignment when the filter is set to reject the side carrier later. Finally, the waveforms are sampled and stored by a 160 GSa/s 8-bit real-time oscilloscope (RTO) with 63 GHz bandwidth for offline DSP processing.
The Tx DSP generates 16-QAM symbols which are upsampled to the AWG sampling rate of 88 GSa/s for pulse shaping via a root-raised cosine (RRC) filter. Then a pair of pre-emphasis filters are applied to compensate for the low-pass filtering of the transmitter for both quadrature channels. Next, modulator non-linearity is compensated before the signal is quantized and sent to the AWG memory for digital to analog conversion.
At the receiver, the sampled waveforms are resampled to 3 samples per symbol. Next, the PDM-SSB signal is linearized jointly following the process described in section 2, downconverted to the baseband and resampled to 2 samples per symbol. After compensating for CD, the frequency offset (FO) is compensated based on the 4th-power method [23]. The signal is then matched-filtered and synchronized for time-domain equalization. A phase-locked loop (PLL) interleaved single-input and single-output (SISO) feedforward equalizer (FFE) is employed to compensate for the ISI and the phase noise simultaneously. The equalizer filter contains 71 T/2-spaced taps, where T is the symbol duration. Finally, the symbols are determined and decoded for BER counting.
4. Results and discussion
4.1 Parametric study at 40 Gbaud B2B
We first conduct a parametric study at 40 Gbaud in B2B on the impact of system parameters including the CSPR of each SOP, the roll-off factor of the RRC filter, and the guard band size. First, the CSPR is swept for each SOP with the roll-off factor and the signal-carrier guard band set to 0.1 and 13 GHz, respectively. Herein the CSPR is defined as the carrier power to signal power ratio per polarization. The optical filter is tuned to attenuate only the X-Pol carrier as much as possible without filtering the X-Pol signal. This helps improve the signal SNR as discussed before. The optical spectrum before and after filtering is shown in Fig. 3(a), where substantial attenuation of the X-Pol carrier is observed. Figs. 3(b)-(d) shows the BER as a function of the Y-Pol CSPR when the X-Pol CSPR takes 11.85 dB, 14.24 dB, 16.39 dB, respectively. It is consistently found that the X-Pol BER increases with the Y-Pol CSPR, which is due to the increased inter-polarization crosstalk in the X-Pol due to the limited polarization extinction ratio of the PBC. By comparison, the Y-Pol BER reduces as the Y-Pol CSPR increases due to improved satisfaction of the minimum phase criterion for KK recovery. Despite the divergence of the X-Pol and Y-Pol BER curves, the average BER is the figure of merit to be kept below the FEC threshold for error-free decoding when the bits of the two polarizations are interleaved and decoded together using one FEC decoder. Otherwise, both the X-Pol and Y-Pol BER should be kept below the FEC threshold for simplified interleaver design. Among the three different X-Pol CSPR values, it is found that 14.24 dB corresponds to the minimum average BER. A lower X-Pol CSPR causes the X-Pol signal more vulnerable to the Y-Pol crosstalk, whereas a higher X-Pol CSPR degrades the signal SNR because of the decreased signal power after optical amplification due to larger proportion of the carrier power.
Fig. 3. (a) signal spectrum before and after optical filtering, (b) (c) (d) BER as a function of the Y-Pol CSPR when X-Pol CSPR equals to 11.85 dB, 14.24 dB, and 16,39 dB, respectively.
With the X pol CSPR and Y pol CSPRs set to 14.24 dB and 10.47 dB, respectively, we measure the BER change versus RRC with the X-Pol carrier set away from the zero frequency by 35 GHz. Figure 4 plots the BER as a function of the RRC filter roll-off factor. It can be observed that as the roll-off factor of the RRC filter increases, the average BER increases and the X-Pol BER and Y-Pol BER diverge. This is caused by the increased filtering of the signal when the roll-off factor increases. Since the signal consumes larger bandwidth, and thus more vulnerable to optical filtering. This not only detrimentally affects the effectiveness of the Y-Pol interference removal through the subtraction of the PD photocurrents but also degrades the X-Pol SSBI estimate. Hence, it is desirable to select a small roll-off for ADD and we proceed with a roll-off factor of 0.1 for the remainder of the following study.
Next, we study the tolerance of the system performance to a narrow guard band. Figure 5 plots the average PDM signal BER as a function of the guard band size. The two curves in the figure correspond to the coefficient $\alpha $ in Eq. (4) set to zero and an optimized value, respectively. For both cases, the average BER drops with an enlarging guard band, since the X-Pol carrier is more suppressed, and the undesired signal filtering is relaxed. A steep BER decrease is observed when the guard band increases from 1 GHz to 8 GHz. For guard band over 13 GHz, the BER levels off. It can also be observed that the average BER with optimized $\alpha $ is slightly smaller compared with $\alpha $ at zero, which is attributable to the removal of the linear X-Pol crosstalk in addition to the X-Pol SSBI while recovering the Y-Pol signal. However, the BER improvement is negligible with optimized $\alpha $ indicating the X-Pol SSBI is the dominant crosstalk in this experiment. This means that $\alpha $ can be set to zero with trivial penalty which simplifies the DSP.
Fig. 5. Average BER versus the guard band size when $\alpha $ is set to either zero or an optimized value.
The pre-amplifier and VOA are then used to find the optimum incident optical power (IOP) to the single-ended PD in B2B. Figure 6(a) plots the BER as a function of the PD IOP of the unfiltered branch in B2B. It is shown in the figure that as the PD IOP increases, the BER decreases with more converged performance between two polarizations. This is ascribed to the more dominant signal power relative to the power of the electrical noise produced by the PD and ADC, which improves the signal SNR. As a result, the IOP is selected as 7.4 dBm for the remainder of the following study.
Next, a transmission experiment is carried out over 80 km SSMF to optimize the launch power. Figure 6(b) plots the BER as a function of the launch power. As shown in the figure, the lowest average BER is obtained at a launch power of 8 dBm. Higher launch power will exacerbate the fiber nonlinear effects, while lower launch power will undesirably increase the noise from the EDFA. Therefore, 8 dBm is chosen as the optimum launch power.
4.2 Maximizing the system throughput over 80 km SSMF
In this subsection, we scale up the baud to explore the maximum throughput of ADD over 80 km SSMF using our set-up. The X-Pol carrier is set to 35 GHz in the baseband for all the symbol rates. Higher X-Pol carrier frequency is not achievable due to the 63-GHz bandwidth limitation of the RTO. Otherwise, at higher bauds beyond 52 Gbaud, the signal cannot be entirely received. The matched filter roll-off is 0.1, and the CSPRs of X-Pol and Y-Pol are fine-tuned around 14.24 dB and 10.47 dB respectively to achieve the minimum average BER with the optimized IOP and launch power.
Figure 7 plots the BER as a function of the symbol rate. As the symbol rate increases from 20 Gbaud to 55 Gbaud with a roll-off factor of 0.1, the guard band decreases from 24 GHz to 4.75 GHz, which introduces extra SNR penalty at higher symbol rates. By using an interleaved FEC encoder, the system with ADD can operate up to 52 Gbaud over 80 km SSMF with the average BER below the SD-FEC threshold of 2×10−2, corresponding to a throughput of 346.6 Gbit/s (raw bit rate 416 Gbit/s) after removing the 20% overhead.
We also perform a numerical study of a 2×2 MIMO equalizer in mitigating the linear crosstalk resulting from the non-orthogonal PDM-SSB signals induced by PDL. The MIMO equalizer is used to mitigate the inter-polarization linear crosstalk in the received PDM-SSB signal. Since two additional lasers are used to generate the orthogonal offset carriers in the proof-of-concept experiment, the FO of the inter-polarization interference is different from that of the signal itself and thus is not compensated after the compensation of the signal FO. Herein a lumped PDL emulator with constant PDL value is used in the simulation at 40 Gbaud in B2B. Figure 8(a) plots the angle deviation from 90o as a function of the PDL value when the angle $\theta $ between the SOPs and the main axis of the emulator equals to 0o, 15o, 45o. Since the angle deviation from 90o for a specific PDL is symmetric over $\theta = {45^o}$, the curves with $\theta $ larger than 45o are not plotted in the figure. In addition, $\theta = {45^o}$ corresponds to the largest angle deviation from 90o. Figure 8(b) plots the aggregate PDM signal SNR after SISO/MIMO equalization as a function of the angle deviation from 90o. It can be observed that the signal SNRs decrease with enlarging angle deviation for both SISO and MIMO equalization, but the MIMO equalization leads to higher signal SNR over the SISO counterpart with more than 6 dB SNR gain for angle deviations over 50o. This demonstrates the effectiveness of the 2×2 MIMO in mitigating the linear crosstalk for a single carrier PDM SSB signal. Taking the constant PDL as the worst PDL instance with an occurrence probability of 10−5, the MIMO and the SISO equalizer have the 1 dB SNR penalty tolerance to mean PDL of 1.33 dB and 1.02 dB, respectively [24].
Fig. 8. (a) Angle deviation from 90o versus PDL. (b) Aggregate SNR versus X-Y angle deviation from 90o.
5. Conclusions
We propose ADD for PDM-SSB signals which features a receiver front-end with reduced hardware comprising a single filter, two single-ended PDs, and two ADC channels. We also developed a low-complexity algorithm based on ADD to linearize the signal by exploiting the PD current difference to remove the unwanted inter-polarization interference. The feasibility of the scheme is verified by a proof-of-concept experiment where 416 Gb/s (346.6 Gb/s net rate) transmission over 80 km SSMF is achieved with the aggregate BER below the SD-FEC threshold of 2×10−2. It is also revealed by a detailed parametric study that the coefficient $\alpha $ linked to the X-Pol SSBI estimation can be set to zero with negligible SNR penalty, which further reduces the complexity of the linearization DSP. Finally, it is found that a 2×2 MIMO equalizer can improve the system performance by mitigating the PDL induced linear crosstalk.
Disclosures
The authors declare no conflicts of interest.
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