1. Introduction

Optical equalization of fiber dispersion in communications systems has been used since the 1990s; e.g. by adding dispersion compensating modules (DCMs) containing dispersion compensating fiber at regular intervals along the link [1]. Alternative proposals included using fiber Bragg gratings (FBGs), including apodized FBGs [2], chirped FBGs, sampled FBGs to provide compensation at multiple wavelengths [3], thermally tuned FBGs [4,5], mechanically tuned FBGs [6], etalons [7], and bulk optics with micro-electromechanical systems (MEMS) [8]. Integrated devices have included ring resonator structures [9], cascaded unbalanced Mach-Zehnder interferometers [10], virtual-imaged phased arrays [11], arrayed-waveguide grating routers [12], and photonic integrated circuit Bragg gratings [13].

Due to advances in processing speed, coupled with full optical field recovery using coherent or single-sideband receivers, digital signal processing (DSP) has now replaced the DCMs [14,15]; being adaptive, DSP can also support optically-switched networks. One of the only downsides to DSPs is that their chipsets consume several watts of power per wavelength channel. This is in contrast to the optical DCMs that they have replaced, which can ‘process’ 10-100’s of wavelength channels simultaneously in the optical domain, and only require a single optical amplifier [16], consuming a few watts of electrical power for all of the channels [17]. The minimum number of wavelength channels where optical signal processing (OSP) becomes more efficient than DSP is dependent on many parameters, which themselves depend on the evolving state-of-the-arts in DSP and OSP [18]. For example, for PIC dispersion compensators, the waveguide, fiber-coupling should decrease with time, leaving the intrinsic losses due to splitting/combining in the FIR filter; thus, reducing the number of wavelength channels where they could become advantageous over DSP.

Adaptive optical equalization could give the best of both worlds: a large processing bandwidth together with adaptive operation. A traditional equalizer for wireless systems is the least-mean squares finite-impulse response (LMS-FIR) equalizer. In earlier work, we have shown that the LMS-FIR equalizer, implemented in DSP, is able to select and optimize a channel in a multi-subcarrier system [19]. Our aim in the follow-up work is to transfer the majority of the DSP into the optical domain, so we can potentially reduce power consumption and increase the processing bandwidth. Using simulations, we previously presented an optical LMS-FIR equalizer that implements an electro-optic feedback loop, with the mixing properties of a square-law photodetector to derive signals that can be used to update the tap weights of the filter [20]. This was complex and required pilot tones to be transmitted to aid processing. However, the simulations demonstrated adaptive equalization of chromatic dispersion (CD), which had degraded quadrature phase shift keying (QPSK) signals. This showed that the optical LMS-FIR equalizer converges to optimal weights to compensate CD.

In this contribution, we use a photonic integrated circuit (PIC) that implements a 4-tap finite impulse response (FIR) filter to demonstrate that OSP could be used in conjunction with DSP to equalize CD. The chip used in this work is based on our previously reported self-calibrating PIC FIR filter [21], which is able to provide a “dialed up” phase and amplitude response [22]. In this proof-of-concept, the chip can be used in two ways: (1) as a static dispersion compensator with its tuning coefficients set by a knowledge of the dispersion; (2) as an adaptive dispersion compensator with its tuning coefficients adapted using a digital LMS algorithm. The idea is that once adaptation has taken place, the processing load on the DSP will be reduced, and because DSP is usually implemented in CMOS, the power consumption will decrease. The adaptive method uses backpropagation-like calculations to remove the need for additional analog-to-digital converters and receivers. The chip has a free-spectral range (FSR) of 28 GHz, and could compensate several wavelength channels simultaneously, which has the potential to reduce the overall power consumption in a WDM system. As this is a proof of concept and the number of taps in the chip’s FIR filter was limited, we use simulations to show that the dispersion compensating characteristics could be improved by implementing additional taps and a greater range of delays.

2. PIC-based FIR filter

The self-calibration feature of our PIC [22] enables it to accurately implement a desired frequency and phase response, which we will use to create a static dispersion equalizer. The self-calibration feature can also be disabled, so the PIC can be used as a conventional FIR filter trained in a feedback loop [20].

Our photonic integrated circuit was fabricated on the silicon nitride loaded thin-film lithium niobate (Si₃N₄/LNOI) platform [23,24]. This PIC platform was used since it makes use of the strong electro-optic property of LiNbO₃ with Si₃N₄ being used as the optical loading material for low-propagation loss. It is also a relatively mature fabrication process in our group, which was evidenced by the first prototype of the chip working as expected, albeit with slightly mistuned grating couplers. Its self-calibration feature is based on the fractional delay reference method, which adds a reference path with a delay of one-half the incremental delays between the FIR-filter’s paths, which enables a measurement of the resulting power response to provide both the amplitudes and phases of every path in the FIR filter [21,22]. As shown in Fig. 1(a), it comprises: an array of tunable 2 $\times$ 2 Mach-Zehnder interferometers (MZIs) with equal arm lengths loaded with a heater on one arm to tune the power splitting ratio; an array of S-shaped spiral delay lines with a delay time of $(2n-1)\Delta T$ between the $n$th tap and the reference arm; tunable phase shifters equipped on each tap except the reference arm; and an array of 3-dB directional couplers to combine/interfere the different taps. Grating couplers were used to interface the PIC to optical fibers with a working wavelength of around 1575 nm. All the waveguide components and grating couplers were designed to work for TE mode. Each heater for the tuning element has a resistance of approximately 125 $\Omega$.

 

Fig. 1. (a) Schematic and (b) microscope image of the 4-tap FIR filter with a half-tap delayed reference path.

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3. Experimental setup

Figure 2 shows the experimental setup for optical equalizers using the static or adaptive techniques in a coherent optical fiber communication system and Fig. 3 shows the DSP flow. Because we are using DSP to fine-tune the equalization and compensate for the non-flat amplitude response of the optical equalizer, strictly it should be called a hybrid equalizer. That is, it uses a combination of equalization in the optical domain and equalization in the digital domain.

 

Fig. 2. Experimental setup for a static optical equalizer with on-chip calibration (Option A) and an adaptive optical LMS equalizer (Option B). AWG: arbitrary waveform generator, EDFA: erbium-doped fiber amplifier, PC: polarization controller, PBS: polarizing beam splitter.

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Fig. 3. DSP flow for the equalizers. The flow for the adaptive equalizer includes extra functions (dotted border) to adaptively tune the optical FIR filter at every iteration, in preparation for the next signal capture.

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For the live system, a 14-Gbd QPSK signal with pulse shaping (roll-off factor of 0.025) is generated by an arbitrary waveform generator (Keysight M8195A) operating at 64 GSa/s. The electrical signal is modulated onto the optical carrier by a dual-polarization IQ modulator with a tunable laser source (Keysight N7714A) operating at 1575.066 nm. The signal is transmitted along a 30-km S-SMF. The launch power is set to be 3 dBm to avoid fiber nonlinearity. The PIC is placed at the end of the transmission channel using an EDFA (Gain = 18 dB) before the PIC for loss compensation and a PC together with a PBS for polarization control. Only the TE-mode is enabled to be processed in the system, by nulling the TM output of the PBS. After transmission, the signal is amplified by a second EDFA with an output power of +4 dBm and then detected by a coherent receiver (Finisar CPRV1220A) with the insertion of a local oscillator (Keysight N7714A) operating at 1575.066 nm, then sampled by a 40 GSa/s oscilloscope (Agilent Technologies DSO-X 92804A).

3.1 Static equalizer

When the PIC acts as a static optical equalizer (Option A), the calibration circuit using an on-chip reference path in the top half of Fig. 2 is enabled, to calibrate the filter taps [22].

This demonstration of the static optical equalizer contains two steps:

(1) The values of tap weights of a 4-tap FIR filter that are required to compensate chromatic dispersion introduced by a standard single-mode fiber (S-SMF) with a known length are first calculated; then, the PIC is calibrated using Cal In and Cal Out connected to the LUNA 2-port OVA to measure its frequency response, to determine the tap weights. The tap weights are adjusted over several measurement iterations, until the inverse of the fiber’s chromatic dispersion is implemented. The tunable laser is then turned off.

(2) The received signal is fed into calibrated 4-tap signal processing core, which is now accessed by using Signal In. The compensated signal appears at Signal Out, and is fed to a coherent receiver connected to a real-time digital oscilloscope. The digitalized signal is processed using offline DSP. The signal is first orthogonalized for in-phase and quadrature components and then resampled to 2 samples per symbol, followed by frequency offset compensation. The algorithm used for frequency offset estimation is the 4th-order spectral peak search algorithm. A root-raised cosine (RRC) filter with a roll-off factor of 0.025 is used for matched filtering, which is the same as that in the transmitter-side DSP. Frame synchronization is implemented to synchronize the processed signal and the training sequence used for the LMS algorithm. After frame synchronization, a DSP LMS equalizer is implemented to digitally fine-tune the compensation; we shall show that the PIC compensates for the majority of the fiber dispersion, but also adds some amplitude ripple due to it only having 4 taps. This is followed by frame synchronization and phase compensation. Specifically, training-based maximum likelihood phase estimation is used. The BER and Q-factor are calculated to show the system performance. The BER is calculated by comparing the received bits in a frame to the transmitted sequence of bits and counting the number of errors. The Q-factor is extracted from error vector magnitude (EVM), which is directly proportional to signal SNR assuming Gaussian noise statistics [25].

3.2 Adaptive equalizer

When the PIC acts as an adaptive optical LMS equalizer (Option B), a feedback control loop is operated in DSP to update the tap weights of the PIC iteratively. The initial tap weights of PIC in the adaptive version were set to be uniform, that is, with no dispersion compensation, by using the fractional reference delay method. Thus, the equalizer has to adapt to the dispersion of the fiber, without a knowledge of the fiber.

This control algorithm has three steps:

(1) In DSP, the received signal is first orthogonalized to balance the in-phase and quadrature components and then resampled to 2 samples per symbol, this is followed by frequency offset compensation. A root-raised cosine (RRC) filter with a roll-off factor of 0.025 is used for matched filtering, which is the same as that in the transmitter-side DSP.

(2) This signal as the optical equalizer’s output is then synchronized with the training sequence used for error-signal calculation. The error signal is calculated by comparing the training sequence and the optical equalizer’s output. In addition, a FIR filter that has the inverse frequency response of the optical filter is implemented, the purpose of which is to obtain an approximation of the unequalized (raw) signal, which is similar to that at the optical equalizer’s input. Such a raw signal is required for the calculation of the weight updates. After synchronizing the optical equalizer’s input and the error signal, the updated tap weights are updated based on the LMS algorithm that is used to adapt the OSP. They are then converted to the electrical powers for the tunable components of the 4-tap optical FIR filter, using knowledge of the sensitivities and bias points of the MZIs and phase shifters, which was gained in the calibration stage. However, these power updates only need to be approximate as the FIR filter is within the LMS feedback loop. The communication to the programmable power supply is generated by MATLAB. These processes close the feedback loop based on the LMS algorithm.

(3) In DSP, the signal as the equalizer’s output is followed by frame synchronization and phase compensation. The BER and Q-factor are calculated to show the system performance. This whole process is done iteratively to operate the adaption based on LMS algorithm and to show the system performance at each iteration.

4. Results

4.1 Static equalizer

The 4-tap signal processing core of the PIC was designed to compensate chromatic dispersion introduced by a 30-km S-SMF (with D = 19 ps/nm/km near 1575 nm) for a 14-Gbd QPSK signal. Such an equalizer is designed as a fractional-spaced equalizer to process 2 samples per symbol as the FSR of the 4-tap optical FIR filter is 28 GHz.

The tap weights of the static optical equalizer are listed in Table 1.

Table 1. Tap weights of the static optical equalizer

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The tap weights of the 4-tap signal processing core were first set by using the calibration system including the on-chip reference path to provide the desired frequency response, which should be the inverse frequency response of a 30-km S-SMF. The calibration algorithm enables the individual update of filter taps, by minimizing the amplitude and phase errors of each tap weight [22]. Each run to update the tap weights of the optical equalizer is called an iteration, and each iteration takes 16.5 seconds. The calibration process runs for 30 iterations to ensure that the signal processing core converges to provide the desired frequency response. For a stable convergence, the update factors used for the amplitudes and phases of tap weights are chosen as follows: (1) $\mu ^{}_{\text {MZI}}$ = 0.5 for the first 10 iterations; $\mu ^{}_{\text {PS}}$ = 0); (2) $\mu ^{}_{\text {MZI}}$ = $\mu ^{}_{\text {PS}}$ = 0.5 after 10 iterations; (3) $\mu ^{}_{\text {MZI}}$ = $\mu ^{}_{\text {PS}}$ = 0.3 after a further 20 iterations.

Figure 4(a) and (b) show the frequency responses of the 4-tap optical FIR filter after calibration, which were experimentally measured by the LUNA 2-port OVA using the Signal In and Signal Out ports of the PIC. The 4-tap calibrated optical FIR filter provides an inverse parabolic phase response within the signal’s bandwidth; however, the magnitude response of the optical filter is not flat, which is a result of the limited number of taps. The simulated ideal frequency response provided by a 4-tap FIR filter shows a similar magnitude response to the experiment.

 

Fig. 4. Frequency responses of (a-b) the 4-tap calibrated static optical equalizer, (c-d) the converged digital LMS equalizer, and (e-f) the overall system.

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Figure 4(c) and (d) show the frequency responses of the final digital LMS equalizer when converged in the system using the static optical equalizer. The digital LMS equalizer acts as a fractional-spaced equalizer processing 2 samples per symbol. For the digital LMS equalizer parameters, the number of taps is set to 41 to achieve near-ideal compensation, and the step size is chosen to be 5e-4 to achieve a stable convergence. The data sequence used for training is 10000-samples long. The tap weights mostly converge within 2000 one-sample iterations. It is noted that the longer the training sequence is, the better performance of the equalizer it can give; however, there is a trade-off between equalizer performance and computational complexity.

Figure 4(e) and (f) show the frequency responses of the overall system. The performance of the static optical equalizer on the signal can be assessed by comparing the tap weights of the final digital equalizer in the 30-km transmission system. The final digital equalizer settles to a flat phase response. This indicates that most of the chromatic dispersion has been compensated in the optical domain by the static optical equalizer. It is also noted that the digital equalizer has a non-flat magnitude response, as it is trying to compensate in magnitude response. This is because the magnitude response given by the 4-tap static optical equalizer is not ideal for dispersion compensation.

4.2 Adaptive equalizer

The 4-tap optical FIR filter on the PIC, using the Signal In and Signal Out ports, was employed in a 30-km transmission system using a DSP-based feedback control loop to realize automatic adaption.

In the DSP-based feedback control loop, after processing the signal by an inverse optical FIR filter, the 200-sample sequence is fed into the optical LMS algorithm, in which the step size is chosen to be 1e-4 to achieve stable convergence. This long sequence (compared with sample-by-sample updates in many LMS equalizers) means that the update information is more accurate at each iteration, so fewer iterations are required.

Each iteration takes 4.6 seconds, which comprises: (a) DSP to calculate the updated tap weights of the optical equalizer, (b) communication delays between the PC and the programmable power supply, and (c) DSP to calculate the quality metrics for optical signals. It is noted that the signal processing in the optical domain is real-time while the signal is also processed in offline DSP, which records a block of the waveforms and processes, and then updates the weights for the next block, so the updates are slow and it may have a long latency due to the oscilloscope. Note that this interval allows the heaters to stabilize between iterations, and also the thermal crosstalk to settle. Some improvements can be made by speeding up the iteration rate, such as reducing the length of the DSP-processed signal.

Figure 5 shows the Q-factor of the received signal during iterations in the system using different equalizers. It is shown that the system converges in a monotonic fashion from this initial condition, which indicates that the feedback loop is stable. The Q-factor has converged after 7 iterations for the adaptive optical LMS equalizer. The speed of convergence is dependent on the optical LMS algorithm’s processed sequence length and the step size, which contributes to the update values of tap weights.

 

Fig. 5. Q-factor of the received signal during iterations in the system using different equalizers.

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5. Discussion

The calibration algorithm for filter taps is based on the criteria to minimize amplitude errors and phase errors for each tap individually.

Figure 6 shows signal constellation diagrams in the system using the static optical equalizer before the digital equalization, after the digital equalization and after clock phase recovery. The phase compensation by the static optical equalizer cannot be quantified in Fig. 6(a); however, Fig. 4 shows that the optical equalizer provides chromatic dispersion compensation. Figure 6(b) shows the signal after the amplitude response of the OSP has been equalized by the digital LMS equalizer; there is a phase wander caused by the linewidths of the transmitter laser and receiver local oscillator. The optical equalizer has reduced the amplitude fluctuations at the sampling points of the symbols, by reducing intersymbol interference. The DSP then implements phase recovery, resulting in the near-perfect constellation of Fig. 6(c). The Q-factor is 18.01 dB. This is a proof of concept that the system with static OSP can give as good a performance as the system without OSP, that is, a system with only DSP, provided the fiber’s dispersion-length product is known. Of course, given enough processing power, and full knowledge of the optical signal such as can be obtained from a polarization-diverse optical receiver, we should expect that DSP (without OSP), would give the ultimate performance.

 

Fig. 6. Signal constellation diagrams in the system using the static optical equalizer (a) before the digital equalization, (b) after the digital equalization and (c) after clock phase recovery.

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Figure 7 shows the signal constellation diagrams before and after adaptive optical equalization. The initial state of the optical equalizer was set to correspond to zero dispersion. During convergence, the Q-factor improves from 9.48 dB to 17.97 dB. This is a similar performance as the static optical equalizer (Q = 18.01 dB), but with the advantage that the equalizer need not know the length and dispersion of the transmission fiber. Because the system aims for optimal signal quality, it would be able to correct for changes in the fiber plant, optical routers, or even changes in the transceivers.

 

Fig. 7. Signal constellation diagrams for the adaptive equalizer: (a) initial state, (b) after convergence (20 iterations).

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In this proof of concept, the limited number of taps caused significant amplitude distortion, which had to be compensated for by DSP; the improvement in the dispersion compensating characteristics by implementing additional taps will now be investigated by simulations.

The simulation aims to compensate chromatic dispersion introduced by 30-km S-SMF within a bandwidth of 14 GHz. The FIR filter has a FWHM pass-band width of 28 GHz.

Figure 8 shows the frequency responses of the optical FIR filter with different numbers of taps. Optical filters with more taps give flatter magnitude responses. An 8-tap optical FIR filter can give a relatively flat magnitude response with ripples less than 1-dB peak-to-peak. Thus, with an 8-tap optical FIR filter for dispersion compensation, the signal suffers lower magnitude distortion. Compared with the performance of a 12-tap optical FIR filter, it can be seen that 8 taps are adequate to compensate chromatic dispersion introduced by 30-km S-SMF.

 

Fig. 8. Frequency responses of optical FIR filters with different numbers of taps.

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6. Conclusion

We have provided proof-of-concept demonstrations of dispersion compensation using both static and adaptive equalizers based on a self-calibrating FIR photonic chip design. The chip’s periodic response is suitable for compensating several wavelength channels. The static equalizer relies on the chip’s ability to accurately provide a desired phase response, with the desired phase response being determined from estimates of the fiber’s dispersion. The adaptive equalizer finds its optimal tuning based on measurements of the errors between the received signal and the training data.

The current design of PIC implements on 4 taps, which causes undesirable amplitude ripples. We showed that using more taps can improve the response, which reduces the amplitude equalization required of the DSP, and also enables a larger fraction of a wavelength channel to be occupied.

In conclusion, we have presented experimental results for static and adaptive equalizers using optical signal processing provided by a self-calibrating chip. For the first time, an adaptive feedback loop has been provided with the goal of minimizing intersymbol interference due to chromatic dispersion. Because the signal processing is partially in the optical domain, it is able to operate on the optical phase of the signal, which would be lost if directly detected (unless a single sideband is transmitted, which would require a more complicated ‘complex’ optical modulator). We showed that the optical equalizer with random initial coefficients adapted itself successfully for one length of fiber, though there is no intrinsic reason why it should not work for different lengths of fiber. Future work will aim to study the equalizer’s capability and versatility to be adapted to multiple fiber lengths.