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Abstract
The bandwidth upgrade required in short-reach optical communications has prompted the need for detection schemes that combine field reconstruction with a cost-effective subsystem architecture. Here we propose an asymmetric self-coherent detection (ASCD) scheme for the field reconstruction of self-coherent (SC) complex double-sideband (DSB) signals based on a direct-detection (DD) receiver with two reception paths. Each reception path consists of a photodiode (PD) and an analog-to-digital converter for the detection of a part of the received optical signal that experiences a different optical transfer function via the configuration of an optical filter. We derive an analytical solution to reconstructing the signal field and show the optimal filter response in optimizing the signal SNR. Further, we numerically characterize the theoretical performance of a specific ASCD scheme based on a chromatic dispersion filter and validate the principle of the ASCD scheme in a proof-of-concept experiment. The ASCD scheme approaches the electrical spectral efficiency of coherent detection with a cost-effective DD receiver, which shows the potential for high-speed short-reach links required by edge cloud communications and mobile X-haul systems.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical modulation encodes information via the physical dimensions of optical carriers. Intensity modulation and direct detection (IMDD) schemes extract the square of the field amplitude and consequently are restricted to signaling schemes utilizing one real dimension [1]. As a phase diverse scheme, coherent detection exploits an additional degree of freedom, thus yielding a complex modulation dimension [2]. The combination of field recovery allowed by coherent detection with the high-speed very-large-scale integration (VLSI) circuits enables digital compensation of various transmission impairments including polarization-mode dispersion (PMD) and chromatic dispersion (CD). This advantage removes the need for complex analog compensation techniques either by optics or electronics [3,4]. As such, the last decade has witnessed the rapid advancement of digital coherent optical transceivers in long-haul optical communications following an ever-increasing demand for bandwidth upgrades [5,6].
Though coherent detection has been entertained for short-reach optical communications recently, IMDD is still dominantly employed due to the cost-effectiveness of this approach. Nevertheless, the capacity of IMDD systems is constrained by CD and one-dimension modulation, thus requiring more parallel lanes to be integrated into a small form factor in order to scale throughput and thus is less suitable due to a tight power constraint imposed on short-reach transceivers. Self-coherent detection (SCD) has attracted extensive interest in recent years because of the ability to combine field reconstruction with digital signal processing (DSP) found in coherent detection schemes alongside the cost-effectiveness of direct detection [7–15]. SCD schemes inject a continuous-wave (CW) tone at the transmitter which co-propagates with the signal and subsequently beats with the signal via direct detection. This configuration eliminates the need for a local oscillator (LO) at the receiver, which not only relaxes the requirement for laser stabilization but also leads to complexity reduction in DSP. To date, there are numerous SCD schemes reported for the detection of single sideband (SSB) signals using a single-ended photodiode (PD). The main challenge of SSB-SCD is to remove the signal-signal beating interference (SSBI), which could appear within the signal band and compromise the transmission performance. A widely used approach utilizes a guard band as wide as the information-carrying signal to accommodate the SSBI [13] at the expense of a low electrical spectral efficiency (ESE), defined as the ratio between the signal throughput per unit electrical bandwidth (bit/s/Hz). Note that ESE is used here instead of optical spectral efficiency in order to characterize the efficiency of the use of the electrical bandwidth. A reduced guard band can be applied by removing the SSBI in an iterative manner [14–15]. The recent proposal of Kramers-Kronig (KK) coherent detection removes the SSBI via the KK relation and therefore eliminates the guard band provided that the SC-SSB signal is minimum phase [16–17]. Hence, SSB-SCD can down-convert the full optical information to the electrical baseband allowing for digital compensation of CD for extended transmission reach [18–20]. Nonetheless, these SSB-SCD schemes have an intrinsic capacity limit since the CW tone is placed at the edge of the signal spectrum and no information is loaded onto the image sideband, which constrains the achievable ESE.
Doubling the ESE without substantially increasing the complexity of both the DSP and the hardware is thus an appealing objective that requires the design of the system architecture and algorithms for the field recovery of SC complex double sideband (DSB) signals [21–24]. Otherwise, more optical lanes are required for SSB-SCD systems to achieve the same throughput at a given electrical bandwidth. In [21], a time-domain interleaved scheme allocates the CW-tone and signal to different time slots and relies on two matched signal copies and a conventional coherent detection receiver to extract the in-phase and quadrature components of the electric field. However, the ESE is not improved compared to SSB-SCD, because only half of the time-domain waveform is loaded with signal. In [22,23], the authors propose carrier-assisted differential detection (CADD), which restores the signal field by adding an extra PD to the receiver structure in [21] in order to detect the intensity of a delayed signal copy. However, the ESE improvement is achieved at the expense of five PDs (2 BPDs and 1 PD) and three analog-to-digital converters (ADC), which increases the hardware complexity. Another alternative utilizes two band rejection filters to reject the opposite sidebands of a DSB signal such that two PDs at the receiver detect an SC-SSB signal, respectively [24]. However, schemes based on band-rejection filters are sensitive to the laser drift, thus requiring more precise wavelength stabilization. Moreover, band rejection filters with a sharp filter edge are both costly and difficult to realize in current filter technologies.
In this paper, we propose a novel SCD scheme for SC-DSB signals, which we refer to as asymmetric self-coherent detection (ASCD). The ASCD scheme doubles the ESE compared to SSB-SCD schemes using only two single-ended PDs and ADCs. The incoming signal is split in two. Each PD subsequently detects a different part of the received optical signal as a function of different optical transfer functions. This is implemented using an optical filter with a configurable response. Based on this general architecture, we derive an analytical solution to reconstructing the electric field of the incident DSB signal. We found from the field solution that no information can be loaded at 0 GHz due to the presence of a singularity. Nonetheless, the impact of this singularity can be effectively mitigated using a moderate guard band provided that the filter response is properly designed. In addition, we show that the optimal filter has an all-pass amplitude response and a phase response whose even part possesses a notch at 0 GHz. We found that chromatic dispersion (CD) is a quadratic approximation of the optimal filter response and conduct a parametric study of this CD-based ASCD scheme in order to analyze the theoretical performance. Next, we experimentally validate the principle of the ASCD scheme via this specific instance based on a CD filter. Since the field reconstruction is implemented based on an analytical solution derived in the paper, thousands of iterations are not required due to the Gerchberg-Saxton (GS) algorithm adopted in [25,26] for the detection of carrier-less DSB signals and the electrical noise from the PDs and the ADCs does not need to be zero due to the finite difference approximation in [27]. We also note that our analysis and results can serve as a guideline to design optical filters that maximize the SNR of the reconstructed signal.
2. Principle
2.1 Analytical solution to the field reconstruction of complex DSB signals
The general architecture of the ASCD scheme is depicted in Fig. 1. The incident optical signal is first split in two. Each PD subsequently detects a different part of the received optical signal. An optical filter (OF) with a configurable response is utilized so that the two detected signal parts experience different optical transfer functions. As we will show later, field reconstruction can be achieved via various filter responses in the ASCD scheme. An intuitive description of the working principle is the auxiliary information extracted from the filtered branch to complement the information of the unfiltered branch acquired via direct detection. Thus, the key to ASCD is the appropriate design of the filter transfer function bounded by the inherent limits of the ASCD scheme, e.g. the 0 GHz singularity as will be shown later.
The photocurrents after square-law detection are p1(t) and p2(t), which are expressed as follows:
Note that ${A_O}(0 )= {\Phi _O}(0 )= 0$ due to the property of odd functions. Without loss of generality, we set $\Phi (0 )= 0$. Then, we insert (5) into (4) and derive the following expression without showing the entire simplification process:
Based on (3) and (6), we derive the analytical solution to reconstructing the field of the received DSB signal with the real and imaginary parts expressed in the frequency domain as follows:
We note that (9) and (10) apply to the field reconstruction of self-coherent DSB signals based on the ASCD scheme with no constraints on the frequency response of the filter. However, observing that ${S_Q}(\omega )$ recovered based on (10) is impaired by a noise term as a function of $U(\omega )$ and $V(\omega )$, the filter frequency response should be optimized to maximize the signal SNR. In addition, despite our analysis of the ASCD scheme in a single-polarization configuration, the scheme can be extended to detect polarization-division multiplexed (PDM) SC-DSB signals by use of a controllable polarization rotator concatenated with a polarization beam splitter (PBS), which ensures that the CW tone is equally split between the two output ports of the PBS. There are also other ways to realize a PDM-ASCD scheme, which is beyond the scope of our discussion and we will focus here on the ASCD scheme in a single-polarization configuration.
Figure 2 depicts a schematic diagram of the SSBI mitigation process based on a recursive feedback algorithm. During a first field recovery based on (9) and (10), the SSBIs R1(ω) and R2(ω) are set to zero. The restored signal field S(ω) is utilized to estimate R1(ω) and R2(ω), which are fed back, and removed from the photocurrents P1 and P2 as in (9) and (10) for a second estimate of S(ω) with improved SNR due to the mitigated SSBI. This process can be implemented iteratively until the impact of SSBI is marginal compared to other penalty sources. As will be shown later, often fewer than 4 iterations are sufficient for the SSBI mitigation.
2.2 Optimal filter frequency response
We note that our previous paper [28] is a specific realization of the proposed ASCD architecture, whose filter response is taken as a step function as follows when reconstructing the signal field
This filter response requires a sharp filter edge which is costly to realize and is not optimal in achieving the maximum signal SNR. Moreover, it can be verified from (8) that $V(\omega )= 0$ at $\omega = 0$ regardless of the design of the filter transfer function. This indicates that the imaginary part of the reconstructed signal based on the ASCD scheme cannot carry any information at $\omega = 0$ due to a singularity of (10). Thus, a guard band is required for the transmitted signal in order to alleviate the performance degradation induced by this singularity. In practice, a moderately sized guard band is sufficient without significantly reducing the ESE provided that the filter frequency response is appropriately designed. For frequency components at $\omega \ne 0$, the power spectral density (PSD) of the noise term on the left-hand side of (10) is
where the PSD of N1 and N2 are taken as ${N_0}\textrm{/2}$. To minimize $F(\omega )$ is equivalent to minimizing $\frac{{({{{|{U(\omega )} |}^2} + 1} )}}{{{{|{V(\omega )} |}^2}}}$, which is denoted as $G(\omega )$ and expanded as followsThough (13) appears to be complicated, the odd-even decomposition beforehand simplifies the following analysis. A first observation is that $G(\omega )$ is not affected by the odd part of the phase response, i.e. only the even part of the phase response should be attended to when designing the filter frequency response. In addition, it can be readily shown via simple partition of (13) that ${A_E}(0 )= 1$ minimizes $G(\omega )$ for $\omega \ne 0$, which suggests that it is desirable to have an amplitude response of the filter that does not attenuate the CW-tone. We found that $G(\omega )$ has a lower bound of 1 as shown in the appendix. This lower bound is attained if and only if
2.3 ASCD scheme with a chromatic dispersion filter
Based on the analysis above, it is desirable to design an optical filter having an ideal ${\Phi _E}(\omega )$ with a notch at $\omega = 0$ as in (15). However, practical filters have smooth phase responses and can only approximate the sharp phase variation at $\omega = 0$. For such filters, ${\Phi _E}(\omega )$ can be expanded in the Maclaurin series as follows
Note that the second-order term is associated with the group delay dispersion, i.e. the chromatic dispersion (CD) induced by the optical filter. This indicates that a truncated second-order approximation of the ideal response could be used for the field reconstruction of SC-DSB signals. In this case, $U(\omega )= \cos ({{\Phi ^{(2 )}}(0 ){\omega^2}/2} )$, $V(\omega )= \sin ({{\Phi ^{(2 )}}(0 ){\omega^2}/2} )$ in (10) with $\textrm{exp} ({j{\Phi _O}(\omega )} )$ set to 0 without loss of generality. Note that $V(\omega )$ based on CD has multiple null points, which results in singularities in the retrieved imaginary signal part following the distribution ${\pm} \sqrt {2k\pi /{\Phi ^{(2)}}(0 )} $, where k takes any integers. No information can be encoded at these singularities due to the enhancement of the noise and the SSBI. We will evaluate the performance impact of these singularities depending on CD in the next section. Since the field recovery is realized using the analytical solution derived above such that thousands of iterations are not required as in [25,26] and there is no need to set the electrical noise from the PD and the ADC to zero due to the finite difference approximation approach adopted in [27]. In addition, CD filters can be realized by various optical components including different types of fibers, and grating structures with relatively low loss. Also notable is a relatively constant CD achievable in the C-band such that a compatible WDM architecture can be realized as depicted in Fig. 3, where the CD filter disperses multiple parallel lanes simultaneously.
3. Results
In section 2, our analysis leads to the analytical solution to the field reconstruction of SC-DSB signals based on the ASCD scheme, the derivation of the optimal filter frequency response, and the CD-based ASCD scheme compatible with a WDM architecture. Next, we will numerically evaluate the theoretical performance of the ASCD scheme and experimentally validate its feasibility in a proof-of-concept experiment.
3.1 Theoretical performance of the ASCD scheme
The numerical analysis is carried out based on the following configuration: a self-coherent DSB signal is pulse-shaped via a 0.1 raised-cosine (RC) filter and transmitted over 80 km of single-mode fiber (SMF). The fiber channel is assumed linear, lossless with a CD coefficient of 17 ps/nm/km. AWGN is linearly added to the signal to simulate the amplified spontaneous emission (ASE) noise in order to investigate the theoretical performance of the ASCD scheme. In addition, the electrical bandwidth of the PD and ADC is simulated using a brick-wall filter for which a minimum bandwidth is chosen to pass only the tone-signal beating and reject the out-of-band noise and interferences. The postprocessing DSP includes signal field recovery, CD compensation, synchronization, linear equalization, and BER counting. Note that the CD compensation is carried out by multiplying the inverse CD response of the fiber to $S(\omega )$ obtained from (9) and (10) and thus does not depends on the CD filter used in the receiver for the field reconstruction. Since the ASCD scheme has a singularity at 0 GHz, the self-coherent DSB signal in the numerical analysis is composed of two independent sidebands, each having a guard band from 0 GHz. In addition, each sideband carries a 28 Gbaud SSB PAM 4 signal, which leads to an aggregate 56 Gbaud PAM 4 signal.
Figure 4 plots the BER as a function of OSNR for the CD-based ASCD systems with the CD set to different values. We also include the BER performance of the ASCD system based on the optimal filter frequency response, i.e. an all-pass filter with a phase notch. Note that the power of the CW-tone is considered as part of the ‘signal power’ when calculating the OSNR. The CSPR and guard band are set to 11 dB and 2 GHz, respectively, and 4 iterations are performed to mitigate the SSBI. It is seen from the figure that lower BER is achieved for the ASCD system based on the optimal filter compared to CD-based ASCD systems. In addition, the BER of the CD-based ASCD scheme only depends on the absolute value of CD, and the lowest BER is achieved at an absolute CD of 350 ps/nm. The performance difference at varied CDs is due to the changed profile of the noise and the SSBI which are enhanced by multiple singularities of $1/V(\omega )$ due to the CD filter. To visualize this more clearly, we show in Fig. 5 the noise-SSBI spectra of the reconstructed signal based on (9) and (10) at two absolute CD values of 200 ps/nm and 500 ps/nm.
Fig. 4. Simulated BER as a function of the OSNR at varied CD for the CD filter-based ASCD. The performance of the optimal filter is also included as a reference.
It is seen from Fig. 5 that the CD-based ASCD scheme has multiple singularities, which is consistent with our analysis in 2.3. Consequently, the noise and the SSBI are enhanced at multiple singularities as opposed to the optimal case where only a single singularity exists at 0 GHz. Furthermore, at a higher absolute CD of 500 ps/nm compared to 200 ps/nm, the separations between the singularities reduce and the enhanced noise and SSBI become less pronounced around the 0 GHz singularity. Thus, at an absolute CD higher than the optimal value, e.g. 400 ps/nm used in Fig. 4, the second-order singularities moves within the signal bands and enhances the noise and the SSBI, whereas at an absolute CD lower than optimal, e.g. 300 ps/nm, the enhanced noise and SSBI around 0 GHz are more pronounced, which also leads to deteriorated performance. Due to the above reason, the absolute CD should be optimized to properly accommodate the signal bands within the frequency intervals separated by the singularities in order to minimize the noise-SSBI enhancement. Note that the requirement of an optimal CD can be relaxed by sending an SC-DSB signal with multiple digital subcarriers, each loaded with an appropriate information rate. This modulation format offers more flexibility such that the frequency intervals at higher frequency can be utilized, which is advantageous for achieving a higher aggregate symbol rate.
As described in section 2, SSBI is removed iteratively. Since fewer iterations are more favorable to the implementation of DSP circuits, it is important to determine the minimum number of iterations required to effectively mitigate the SSBI. In Fig. 6, we plot BER versus the iteration number at varied OSNRs. It is seen in the figure that the BER curves first decrease and then level off when greater than 4 iterations are performed. More specifically, as the OSNR decreases from 33 dB to 27 dB, the iteration number required to reach the BER floor decreases from 4 to 2. This is attributed to a stronger ASE noise power at a lower OSNR such that the impact of the residual SSBI on the system performance becomes relatively marginal after fewer iterations
The effectiveness of the iterative SSBI cancellation algorithm can also be visualized from Fig. 7, where the spectra of the noise and the SSBI with and without 4 iterations of cancellation are plotted. The noise-SSBI spectra show a significant power reduction after 4 iterations of SSBI cancellation. Furthermore, as the OSNR increases, the noise-SSBI spectra are reduced to a greater extent, which is in agreement with the results shown in Fig. 6.
Fig. 7. Simulated noise-SSBI spectra with and without 4-iteration of SSBI cancellation at different OSNRs.
Next, we characterize the performance impact of the guard band and CSPR with the iteration number and CD accordingly optimized. Figure 8 shows the change of the BER as a function of the CSPR at an OSNR of 30 dB with the guard band varied from 1 to 3 GHz. As shown in the figure, all the curves are convex, each having an optimal CSPR. The explanation is that at an excessively lower CSPR the SSBI cancellation algorithm is less effective due to distorted SSBI estimates. However, when an overly higher CSPR is used, the effective OSNR, i.e. the ratio between the signal power and the ASE noise power is lower at a given OSNR. In addition, we find that by increasing the guard band, the transmission performance can be significantly improved, which is due to the alleviated impact of the enhanced noise and SSBI near the 0 GHz singularity.
The parametric analysis above prepares us to jointly optimize the system parameters and compare the OSNR sensitivity of the CD-based ASCD scheme versus other SCD schemes. Figure 9 shows the BER as a function of the OSNR for the CD-based ASCD scheme at varied guard bands over 80 km of SMF. The CSPR is optimized at each OSNR due to the trade-off between the SSBI mitigation and the impact of the tone-ASE noise beating. The CD is optimized accordingly at each guard band and CSPR to achieve the best BER performance. We also include a BER curve of the KK scheme in the figure. For fairness of comparison, the KK scheme detects an SSB PAM-4 signal at an identical symbol rate of 56 Gbaud as the ASCD scheme and the CSPR is also optimized at each OSNR. In order to relax the requirement for the remote wavelength control, no optical filter is assumed for the rejection of the out-of-band ASE noise for both schemes. ASCD scheme operates at a sampling rate of 56 GSample/s, whereas the KK scheme operates at a higher sampling rate of 84 GSample/s due to its requirement of a higher upsampling rate because of the spectrum broadening induced by nonlinear operations. In addition, brick wall filters are used to simulate the limited electrical bandwidth of the receiver front-end and are configured to pass only the signal-tone beating component of the down-converted signal for both the ASCD and the KK scheme. As seen from the figure, the BER of the CD-based ASCD scheme decreases with an increasing guard band. In particular, with guard bands of 2 GHz and 3 GHz, the ASCD scheme performs better than the KK scheme. The worse performance of the KK scheme is attributed to the ASE noise from the image sideband in addition to the in-band ASE noise [29]. By contrast, the down-converted signal in the ASCD scheme only has in-band ASE noise. We also note that the ASCD scheme reduces the required electrical bandwidth by nearly a factor of two compared to the KK scheme. In addition, we plot in the figure a BER curve of the optimal filter-based ASCD scheme for a 56 Gbaud SSB PAM-4 signal with the CSPR optimized at each OSNR and a BER curve of a 28-Gbaud 16-QAM signal detected using the theoretical homodyne coherent detection scheme, which considers an OSNR penalty induced by the corresponding CSPR that is added to help determine the distortion incurred by the ASCD scheme. The reference OSNR of the homodyne coherent detection scheme with CSPR-induced penalty is obtained by multiplying the original OSNR by a factor of $1 + CSPR$. It is seen from the figure that these two BER curves completely overlap, which indicates that the performance of the optimal filter-based ASCD scheme is only affected by the AWGN noise similar to the homodyne coherent detection scheme.
Fig. 9. Simulated BER versus OSNR for CD filter-based ASCD, ideal phase notch filter-based ASCD, and the KK receiver over 80 km of SMF.
3.2 Experimental validation
In this section, we experimentally validate the principle of asymmetric self-coherent detection using the CD-based ASCD scheme. Figure 10 depicts the experimental setup and the DSP blocks of the transmitter and receiver. The SC DSB signal is generated from a dual-drive Mach-Zehnder modulator (DDMZM) with a 3 dB E-O bandwidth of 30 GHz. The DDMZM is biased at the intensity quadrature such that a CW-tone is produced and co-propagates with the signal. Two channels of an arbitrary waveform generator (AWG) operating at 88 GSa/s are used to provide the in-phase and quadrature driving signals. After propagation over 80 km of single-mode fiber, the optical signal is pre-amplified by an EDFA before impinging upon the CD-based ASCD scheme. We use a tunable dispersion compensation module (DCM) with a 2.5 dB insertion loss in the proof-of-concept experiment to conveniently tune and optimize the CD. CD filters with lower loss can be realized with specifically customized DCMs or dispersion compensating fiber. Note that wo PDs with trans-impedance amplifiers having a 3-dB bandwidth of 35 GHz are used to detect the two parts of the split optical signal, respectively, which are subsequently sampled by 62-GHz ADCs with a sampling rate of 160 GSa/s. A brick-wall filter with a 17.4 GHz bandwidth is used to limit the electrical bandwidth of the receiver for a 56 Gbaud PAM-4 signal with a 2 GHz guard band per sideband. The two variable optical attenuators (VOAs) are used to adjust the launch power and the incident optical power to the receiver, respectively. In the transmitter DSP deck, two independent PAM 4 signals are pulse-shaped via an RC filter with a roll-off factor of 0.1, converted into SSB PAM-4 signals, and subsequently up-converted to an intermediate frequency to accommodate the guard bands. Pre-compensation of the modulator nonlinearity is performed [30] and followed by a pe-emphasis filter to flatten the response of the transmitter RF chain. In the receiver postprocessing DSP deck, the field reconstruction is implemented using the aforementioned method. After synchronization, MIMO equalization is performed to remove the ISI and linear crosstalk due to imbalanced PD responses or a residual time-skew between the two branches.
Note that the DDMZM nonlinearity needs to be carefully handled; otherwise, the transmission performance will be significantly compromised. In order to generate a SC-DSB signal of the form $a(t )\textrm{exp} ({j\varphi (t )} )$, the driving RF signals V1 and V2 that pre-compensates the nonlinear transfer function of the DDMZM are expressed as
respectively, where ${V_\pi }$ is the voltage to induce a $\pi $ phase shift in one DDMZM arm, a(t) is the amplitude of the signal and $\varphi (t )$ is the phase of the signal. Since the AC-coupled driving signals in our setup has a limited swing, a relatively high CSPR of 17 dB is needed in order to invert the nonlinear transfer function of the modulator based on (17) and (18). Note that the CSPR can be reduced by use of driver amplifiers with a higher gain or the transmitter structure in [23] where an IQ-MZM with moderate nonlinearity is utilized. However, since a single EDFA is used in the proof-of-concept experiment, the performance impact of the ASE noise is marginal despite a relatively high CSPR. The launch power, filter CD, incident optical power to the PDs are optimized to 6.2 dBm, -320 ps/nm, and -1 dBm, respectively. Figure 11 shows the BER change versus the iteration number to mitigate the SSBI for a 56 Gbaud PAM-4 signal with a 2 GHz guard band per sideband in the back-to-back configuration. As seen in the figure, only 1 iteration is sufficient in alleviating the impact of the SSBI, achieving a net 112 Gb/s data rate with a pre-forward error correction (FEC) BER below the hard decision (HD)-FEC threshold of 3.8×10−3. The small iteration number could benefit the high-speed parallel implementation of the field recovery DSP.Figure 12 shows the change of the BER as a function of the incident optical power to the PDs with or without the transmitter nonlinear pre-compensation (NLPC). The figure shows that NLPC is required in order to attain a pre-FEC BER below the HD-FEC threshold of 3.8×10−3 in our setup. Furthermore, it is found that the enhanced noise and residual SSBI can be effectively mitigated for SSB PAM 4 signals by use of a post-filter (PF) combined with a maximum likelihood sequence estimator (MLSE), which leads to significantly lower BER.
4. Discussion and conclusion
In addition to a high ESE, another distinct advantage of the ASCD scheme is a simple DD receiver subsystem required for the detection of SC-DSB signals. From our perspective, the bandwidth and number of PDs and ADCs used in the receiver, the need for LOs are the determining cost metrics to evaluate the hardware complexity of different coherent detection schemes due to the following reason: high-speed PDs and ADCs are expensive; apart from higher cost, using more PDs and ADCs requires a higher received optical power to counteract the receiver noise and higher electrical power to operate the extra hardware; the need for a LO imposes more stringent laser stabilization and the carrier phase recovery DSP. Table 1 shows the hardware complexity of different detection schemes in a single polarization configuration assuming the reception of a signal with the same bandwidth B and information rate.
Table 1. Hardware complexity of different detection schemes in a single-polarization configuration.
The table shows that the KK system requires the highest electrical bandwidth B among all schemes due to an unused image sideband. Otherwise, at an electrical bandwidth B/2, the KK system requires two optical wavelengths to achieve the same aggregate throughput, thereby doubling the number of lasers, modulators, and DSP chips. The additional components needed not only make it more challenging for the design of compact optical modules but also incur a yield problem since more lasers and modulators are integrated on a photonic chip. The CADD scheme reduces the electrical bandwidth of the PDs and the ADCs by a factor of 2, yet requiring an additional optical hybrid, two more ADCs, and 4 more PDs (2 BPDs), which increases the receiver complexity and requires higher received optical power.
By comparison, the ASCD scheme uses 2 PDs and 2 ADCs with a bandwidth close to B/2, while still being able to detect signals with the same bandwidth and information rate. A special realization of the ASCD scheme characterized in this paper uses CD as the optical filter response. A merit of this specific scheme is the exploitation of optical components, e.g. fibers or grating structures, which are based on established processes and can provide a wideband CD with a low optical loss [31–32]. In addition, the compatibility with a WDM architecture further reduces the cost of the filter.
To summarize, we propose the ASCD scheme that increases the ESE of SSB-SCD schemes by a factor of 2 using two single-ended PDs and two ADCs. The key to the field reconstruction lies in the different optical transfer functions between the two optical detection branches by means of an optical filter. We derive the analytical solution to the received optical field, discuss the inherent characteristics of the ASCD scheme, and identify the optimal filter transfer function to optimize the signal SNR. In addition, we characterize the theoretical performance of the ASCD scheme and experimentally validate its working principle by transmitting a net 112 Gb/s PAM-4 signal over 80 km below the 3.8×10−3 HD-FEC threshold. The combination of the high ESE of coherent detection and the cost-effectiveness of direct detection shows the potential of the ASCD scheme for short-reach optical links required in the edge cloud communications and mobile X-haul systems.
Appendix
Proving that
From the definition of the amplitude response, we have the following inequality at $\omega \ne 0$
Due to the property of even and odd functions, (20) is equivalent to
The addition and multiplication of (19) and (21) leads to the following conditions:
Thus, $J(\omega )\ge - ({A_E^2(\omega )- A_O^2(\omega )} )+ 1 \ge 0$ and $G(\omega )$ is lower bounded by 1. The equality is achieved when $\cos ({2{\Phi _E}(\omega )} )={-} 1$, $A_E^2(\omega )= 1$, and $A_O^2(\omega )= 0$, which leads to the optimal filter response given in (14) and (15).
Disclosures
The authors declare no conflicts of interest.
Data availability
All data underlying the results presented in this paper are available upon request from the corresponding author.
References
1. K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. P. T. Lau, “Digital Signal Processing for Short-Reach Optical Communications: A Review of Current Technologies and Future Trends,” J. Lightwave Technol. 36(2), 377–400 (2018). [CrossRef]
2. P. J. Winzer and R.-J. Essiambre, “Advanced optical modulation formats,” in Optical Fiber Telecommunications VB, I. Kaminow and T. Li, eds. Academic, New York2008, pp. 232–304
3. Seb J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express 15(5), 2120–2126 (2007). [CrossRef]
4. E. M. Ip and J. M. Kahn, “Fiber Impairment Compensation Using Coherent Detection and Digital Signal Processing,” J. Lightwave Technol. 28(4), 502–519 (2010). [CrossRef]
5. F. Buchali, V. Aref, M. Chagnon, K. Schuh, H. Hettrich, A. Bielik, L. Altenhain, M. Guntermann, R. Schmid, and M. Moller, “1.52 Tb/s single carrier transmission supported by a 128 GSa/s SiGe DAC,” in Optical Fiber Communication Conference Postdeadline Papers 2020, (Optical Society of America, 2020), paper Th4C.2.
6. M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photonics Technol. Lett. 20(9), 670–672 (2008). [CrossRef]
7. S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. Winzer, “100-Gb/s discrete-multitone transmission over 80-km SSMF using single-sideband modulation with novel interference-cancellation scheme,” 2015 European Conference on Optical Communication (ECOC), Valencia, 1-3, (2015).
8. X. Liu, S. Chandrasekhar, and A. Leven, “Digital self-coherent detection,” Opt. Express 16(2), 792–803 (2008). [CrossRef]
9. D. Che, Q. Hu, and W. Shieh, “Linearization of Direct Detection Optical Channels Using Self-Coherent Subsystems,” J. Lightwave Technol. 34(2), 516–524 (2016). [CrossRef]
10. D. Che, C. Sun, and W. Shieh, “Optical Field Recovery in Stokes Space,” J. Lightwave Technol. 37(2), 451–460 (2019). [CrossRef]
11. X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, J. Sinsky, A. Mecozzi, M. Shtaif, and P. Winzer, “218-Gb/s Single-Wavelength, Single-Polarization, Single-Photodiode Transmission Over 125-km of Standard Singlemode Fiber Using Kramers-Kronig Detection,” in Optical Fiber Communication Conference Postdeadline Papers, OSA Technical Digest (online) (Optical Society of America, 2017), paper Th5B.6.
12. S. T. Le, K. Schuh, M. Chagnon, F. Buchali, R. Dischler, V. Aref, H. Buelow, and K. M. Engenhardt, “1.72-Tb/s Virtual-Carrier-Assisted Direct-Detection Transmission Over 200 km,” J. Lightwave Technol. 36(6), 1347–1353 (2018). [CrossRef]
13. B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Experimental Demonstrations of Electronic Dispersion Compensation for Long-Haul Transmission Using Direct-Detection Optical OFDM,” J. Lightwave Technol. 26(1), 196–203 (2008). [CrossRef]
14. W. R. Peng, X. Wu, K. Feng, V. R. Arbab, B. Shamee, J. Yang, L. C. Christen, A. E. Willner, and S. Chi, “Spectrally efficient direct-detected OFDM transmission employing an iterative estimation and cancellation technique,” Opt. Express 17(11), 9099–9111 (2009). [CrossRef]
15. Z. Li, M. Sezer Erkılınç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “SSBI Mitigation and the Kramers–Kronig Scheme in Single-Sideband Direct-Detection Transmission With Receiver-Based Electronic Dispersion Compensation,” J. Lightwave Technol. 35(10), 1887–1893 (2017). [CrossRef]
16. A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers–Kronig receivers,” Adv. Opt. Photon. 11(3), 480–517 (2019). [CrossRef]
17. A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers–Kronig coherent receiver,” Optica 3(11), 1220–1227 (2016). [CrossRef]
18. X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, A. Mecozzi, M. Shtaif, and P. Winzer, “Kramers–Kronig Receivers for 100-km Datacenter Interconnects,” J. Lightwave Technol. 36(1), 79–89 (2018). [CrossRef]
19. T. Bo and H. Kim, “Kramers-Kronig receiver operable without digital upsampling,” Opt. Express 26(11), 13810–13818 (2018). [CrossRef]
20. L. Blech, C. Antonelli, A. Mecozzi, Y. C. Eldar, and M. Shtaif, “Enhancing the Kramers–Kronig receiver via dispersion-based spatial diversity,” Opt. Lett. 45(13), 3494–3497 (2020). [CrossRef]
21. X. Chen, D. Che, A. Li, J. He, and W. Shieh, “Signal-carrier interleaved optical OFDM for direct detection optical communication,” Opt. Express 21(26), 32501–32507 (2013). [CrossRef]
22. W. Shieh, C. Sun, and H. Ji, “Carrier-assisted differential detection,” Light Sci Appl 9(1), 18 (2020). [CrossRef]
23. C. Sun, T. Ji, H. Ji, Z. Xu, and W. Shieh, “Experimental Demonstration of Complex-Valued DSB Signal Field Recovery via Direct Detection,” IEEE Photon. Technol. Lett. 32(10), 585–588 (2020). [CrossRef]
24. L. Zhang, T. Zuo, Q. Zhang, J. Zhou, E. Zhou, and G. N. Liu, “150-Gb/s DMT over 80-km SMF transmission based on Spectrally Efficient SSBI cancellation using guard-band Twin- SSB Technique,” ECOC 2016; 42nd European Conference on Optical Communication, Dusseldorf, Germany, 1-3, 2016.
25. H. Chen, N. K. Fontaine, J. M. Gene, R. Ryf, D. T. Neilson, and G. Raybon, “Dual Polarization Full-Field Signal Waveform Reconstruction Using Intensity Only Measurements for Coherent Communications,” J. Lightwave Technol. 38(9), 2587–2597 (2020). [CrossRef]
26. H. Chen, H. Huang, N. K. Fontaine, and R. Ryf, “Phase retrieval with fast convergence employing parallel alternative projections and phase reset for coherent communications,” Opt. Lett. 45(5), 1188–1191 (2020). [CrossRef]
27. M. Matsumoto, “Optical Signal Phase Reconstruction Based on Temporal Transport-of-Intensity Equation,” J. Lightwave Technol. 38(17), 4722–4729 (2020). [CrossRef]
28. X. Li, M. Zhu, Z. Xing, M. O’Sullivan, and D. V. Plant, “Asymmetric direct detection of twin-SSB signals,” Opt. Lett. 45(4), 844–847 (2020). [CrossRef]
29. X. Chen X, S. Chandrasekhar, and P. Winzer, Self-coherent systems for short reach transmission[C]//2018 European Conference on Optical Communication (ECOC). IEEE: 1–3 (2018).
30. Y. Zhang, M. O’Sullivan, and R. Hui, “Theoretical and experimental investigation of compatible SSB modulation for single channel long-distance optical OFDM transmission,” Opt. Express 18(16), 16751–16764 (2010). [CrossRef]
31. Y. Painchaud, A. Mailloux, H. Chotard, É. Pelletier, and M. Guy, “Multi-channel fiber Bragg gratings for dispersion and slope compensation,” in Optical Fiber Communications Conference, A. Sawchuk, ed., Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, 2002), paper ThAA5.
32. Y. Painchaud, M. Lapointe, F. Trépanier, R. L. Lachance, C. Paquet, and M. Guy, “Recent progress on FBG-based tunable dispersion compensators for 40 Gb/s applications,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OThP3.
