Journal & Conference Publications

Abstract:
The impairments arising from the Kerr nonlinearity in optical fibers limit the achievable information rates in fiber-optic communication. Unlike linear effects, such as chromatic dispersion and polarization-mode dispersion, which can be compensated via relatively simple linear equalization at the receiver, the computational complexity of the conventional nonlinearity mitigation techniques, such as the digital backpropagation, can be substantial. Neural networks have recently attracted attention, in this context, for low-complexity nonlinearity mitigation in fiber-optic communications. This Ph.D. dissertation deals with investigating the recurrent neural networks to efficiently compensate for the nonlinear channel impairments in dual-polarization long-haul fiber-optic transmission. We present a hybrid convolutional recurrent neural network (CRNN) architecture, comprising a convolutional neural network (CNN) -based encoder followed by a recurrent layer working in tandem. The CNN-based encoder represents the shortterm channel memory arising from the chromatic dispersion efficiently, while transitioning the signal to a latent space with fewer relevant features. The subsequent recurrent layer is implemented in the form of a unidirectional vanilla RNN, responsible for capturing the long-range interactions neglected by the CNN encoder. We demonstrate that the proposed CRNN achieves the performance of the state-of-theart equalizers in optical fiber communication, with significantly lower computational complexity depending on the system model. Finally, the performance complexity trade-off is established for a number of models, including multi-layer fully-connected neural networks, CNNs, bidirectional recurrent neural networks, bidirectional long short-term memory (bi-LSTM), bidirectional gated recurrent units, convolutional bi-LSTM models, and the suggested hybrid model.

Abstract:
Bidirectional recurrent neural networks (bi-RNNs), in particular, bidirectional long short term memory (bi-LSTM), bidirectional gated recurrent unit, and convolutional bi-LSTM models have recently attracted attention for nonlinearity mitigation in fiber-optic communication. The recently adopted approaches based on these models, however, incur a high computational complexity which may impede their real-time functioning. In this paper, by addressing the sources of complexity in these methods, we propose a more efficient network architecture, where a convolutional neural network encoder and a unidirectional many-to-one vanilla RNN operate in tandem, each best capturing one set of channel impairments while compensating for the shortcomings of the other. We deploy this model in two different receiver configurations. In one, the neural network is placed after a linear equalization chain and is merely responsible for nonlinearity mitigation; in the other, the neural network is directly placed after the chromatic dispersion compensation and is responsible for joint nonlinearity and polarization mode dispersion compensation. For a 16-QAM 64 GBd dual-polarization optical transmission over 14×80 km standard single-mode fiber, we demonstrate that the proposed hybrid model achieves the bit error probability of the state-of-the-art bi-RNN-based methods with greater than 50% lower complexity, in both receiver configurations.

Abstract:
The impairments arising from the Kerr nonlinearity in optical fiber are a major obstacle in fiber-optic transmission systems. To compensate for these impairments at the receiver, the complexity of the digital signal processing algorithms must be reduced. Deep learning-based equalizers have shown to be promising in this area. However, their efficient implementation in practical systems is still an open problem. In this paper, we propose a low-complexity convolutional recurrent neural network (CNN+RNN) for deep learning of Kerr nonlinearity effects in long-haul optical fiber channels governed by the nonlinear Schrödinger equation. This approach reduces computational complexity by balancing the computational load via capturing short-range temporal features using multi-channel strided convolution layers with ReLU activation, and the long-range temporal features using a unidirectional vanilla recurrent layer. We demonstrate that for a 16-QAM 64 GBd optical transmission system over 1120 km of standard single-mode fiber with 14 spans, the proposed model approaches the performance of digital backpropagation and achieves superior or comparable performance to recently-proposed MLP, CNN+MLP, bi-RNN, bi-GRU, bi-LSTM, and CNN+bi-LSTM-based equalizers in the literature, with substantially fewer floating-point operations (FLOPs) than these models.

Abstract:
Communication systems with the information encoded in the amplitude of the carrier and a receiver based on direct detection are called intensity-modulated and direct detected (IM-DD) systems. For IM-DD systems, the chromatic dispersion (CD) is one of the main impairments operating with single-mode fiber at the frequency region of 1.55 μm. The reason is that the interaction of intensity-modulated signals and the square-law detection of the photodetectors (PD) create nulls in the received signal’s spectrum — severely impacting the system performance. These nulls are known as the power fading effect.

This thesis contributes to the state-of-the-art equalization techniques for IM-DD systems with digital-only, optical-only, and optoelectronic equalizers. For digital-only equalizers, we show original contributions by proposing and studying reservoir computing for IM-DD systems. We point out the advantage in the training process of the algorithm, which can be beneficial for dynamic systems, such as optical communications. Numerical analyses of the reservoir’s memory capacity and equalization performance are given and compared to time-delay neural networks. For optical-only equalization, we show the use of multiple Mach–Zehnder delay interferometer (MZDI) for mitigating the CD in the optical domain, which avoids the power fading effect. The original contribution is training the time delay and the phase shift components that mitigates the CD through an adaptive algorithm that tries to reduce the loss function of the system. For the optoelectronic system, we have proposed two directions. The first is using the same structure used for optical-only equalization for CD mitigation, together with nonlinear equalizers — the original contribution is in the joint training of time delay and phase shift of the optical structure and the nonlinear equalizer. The other direction is
also an original contribution where we propose that the optical signal is divided into smaller subbands (through optical filters), and an individual PD detects each. A nonlinear equalizer is then used to reconstruct the signal and recover the information.

Abstract:
High-symbol-rate coherent optical transceivers suffer more from the critical responses of transceiver components at high frequency, especially when applying a higher order modulation format. Recently, we proposed in [20] a neural network (NN)-based digital pre-distortion (DPD) technique trained to mitigate the transceiver response of a 128~GBaud optical coherent transmission system. In this paper, we further detail this work and assess the NN-based DPD by training it using either a direct learning architecture (DLA) or an indirect learning architecture (ILA), and compare performance against a Volterra series-based DPD and a linear DPD. Furthermore, we willfully increase the transmitter nonlinearity and compare the performance of the three DPDs considered. The proposed NN-based DPD trained using DLA performs the best among the three contenders, providing more than 1~dB signal-to-noise ratio (SNR) gains for uniform 64-quadrature amplitude modulation (QAM) and PCS-256-QAM signals at the output of a conventional coherent receiver DSP. Finally, the NN-based DPD enables achieving a record 1.61~Tb/s net rate transmission on a single channel after 80~km of standard single mode fiber (SSMF).

Abstract:
Nonlinear channel impairments are a major obstacle in fiber-optic communication systems. To facilitate a higher data rate in these systems, the complexity of the underlying digital signal processing algorithms to compensate for these impairments must be reduced. Deep learning-based methods have proven successful in this area. However, the concept of computational complexity remains an open problem. In this paper, a low-complexity convolutional recurrent neural network (CNN + RNN) is considered for deep learning of the long-haul optical fiber communication systems where the channel is governed by the nonlinear Schrodinger equation. This approach reduces the computational complexity via balancing the computational load by capturing short-temporal distance features using strided convolution layers with ReLU activation, and the long-distance features using a many-to-one recurrent layer. We demonstrate that for a 16-QAM 100 G symbol/s system over 2000 km optical-link of 20 spans, the proposed approach achieves the bit-error-rate of the digital back-propagation (DBP) with substantially fewer floating-point operations (FLOPs) than the recently-proposed learned DBP, as well as the non-model-driven deep learning-based equalization methods using end-to-end MLP, CNN, RNN, and bi-RNN models.

Abstract:
The substantial increase in communication throughput driven by the ever-growing machine-to-machine communication within a data center and between data centers is straining the short-reach communication links. To satisfy such demand – while still complying with the strict requirements in terms of energy consumption and latency – several directions are being investigated with a strong focus on equalization techniques for intensity modulation/direct-detection (IM/DD) transmission. In particular, the key challenge equalizers need to address is the inter-symbol interference introduced by the fiber dispersion when making use of the low-loss transmission window at 1550 nm. Standard digital equalizers such as feed-forward equalizers (FFEs) and decision-feedback equalizers (DFEs) can provide only limited compensation. Therefore more complex approaches either relying
on maximum likelihood sequence estimation (MLSE) or using machine-learning tools, such as neural network (NN) based equalizers, are being investigated. Among the different NN architectures, the most promising approaches are based on NNs with memory such as time-delay feedforward NN (TD-FNN), recurrent NN (RNN), and reservoir computing (RC). In this work, we review our recent numerical results on comparing TD-FNN and RC equalizers, and benchmark their performance for 32-GBd on-off keying (OOK) transmission. A special focus will be dedicated to analyzing the memory properties of the reservoir and its impact on the full system performance. Experimental validation of the numerical findings is also provided together with reviewing our recent proposal for a new receiver architecture relying on hybrid optoelectronic processing. By spectrally slicing the received signal, independently detecting the slices and jointly processing them with an NN-based equalizer (wither TD-FNN or RC), significant extension reach is shown both numerically and experimentally.

Abstract:
The cloud edge data center will enable reliable and low latency options for the network, and the interconnection among these data-centers will demand a scalable low-complexity scheme. An intensity-modulated and directed detected transmission system is an attractive solution, but chromatic dispersion is the main limitation for higher symbol rate systems. To overcome this challenge, we have proposed and experimentally demonstrated a receiver with shared-complexity between optical and digital domains that enables 80 km transmission reach below KP4 FEC limit for a 32 GBd on-off keying signal. The optical stage consists of optical filters that slices the signal into smaller sub-bands and each is detected by a photodetector. A feedforward neural network and reservoir computing are compared to reconstruct the full signal from the slices and mitigate the chromatic dispersion. Both equalizers have shown similar performance with the advantage of the reservoir computing requiring fewer inputs and easier training process. In this work, we have compared the linear and nonlinear activation functions in the feedforward neural network to investigate the gain of using a nonlinear equalizer. The maximum transmission reach is reduced almost to half, ≈ 45 km, when using the linear. The performance is also reduced if a reduced number of slices is used in the receiver, as we have demonstrated. In this case, using 2 slices to reduce the complexity of the system, instead of the total 4, we have shown a ≈ 55 km transmission reach below KP4 FEC limit. In this work we have also provided a numerical comparison with 4×8 GBd subcarriers system. The results have shown a 40 km increase in transmission reach compared to the proposed optoelectronic system. The trade-off between performance and complexity should be analyzed for each case, as a different hardware is required in each situation.

Abstract:
Nonlinearity compensation is considered as a key enabler to increase channel transmission rates in the installed optical communication systems. Recently, data-driven approaches – motivated by modern machine learning techniques – have been proposed for optical communications in place of traditional model-based counterparts. In particular, the application of neural networks (NN) allows improving the performance of complex modern fiber-optic systems without relying on any a priori knowledge of their specific parameters. In this work, we introduce a novel design of complex-valued NN for optical systems and examine its performance in standard single mode fiber (SSMF) and large effective-area fiber (LEAF) links operating in relatively high nonlinear regime. First, we present a methodology to design a new type of NN based on the assumption that the channel model is more accurate in the nonlinear regime. Second, we implement a Bayesian optimizer to jointly adapt the size of the NN and its number of input taps depending on the different fiber properties and total length. Finally, the proposed NN is numerically and experimentally validated showing an improvement of 1.7 dB in the linear regime, 2.04 dB at the optimal optical power and 2.61 at the max available power on Q-factor when transmitting a WDM 30 × 200G DP-16QAM signal over a 612 km SSMF legacy link. The results highlight that the NN is able to mitigate not only part of the nonlinear impairments caused by optical fiber propagation but also imperfections resulting from using low-cost legacy transceiver components, such as digital-to-analog converter (DAC) and Mach-Zehnder modulator.

Abstract:

Nonlinear frequency division multiplexing (NFDM) techniques encode information in the so-called nonlinear spectrum which is obtained from the nonlinear Fourier transform (NFT) of a signal. NFDM techniques so far have been applied to the nonlinear Schrödinger equation (NLSE) that models signal propagation in a lossless fiber. Conventionally, the true lossy NLSE is approximated by a lossless NLSE using the path-average approach which makes the propagation model suitable for NFDM. The error of the path-average approximation depends strongly on signal power, bandwidth and the span length. It can degrade the performance of NFDM systems and imposes challenges on designing high data rate NFDM systems. Previously, we proposed the idea of using dispersion decreasing fiber (DDF) for NFDM systems. These DDFs can be modeled by a NLSE with varying-parameters that can be solved with a specialized NFT without approximation errors. We have shown in simulations that complete nonlinearity mitigation can be achieved in lossy fibers by designing an NFDM system with DDF if a properly adapted NFT is used. We reported performance gains by avoiding the aforementioned path-average error in an NFDM system by modulating the discrete part of the nonlinear spectrum. In this paper, we extend the proposed idea to the modulation of continuous spectrum. We compare the performance of NFDM systems designed with dispersion decreasing fiber to that of systems designed with a standard fiber with the path-average model. Next to the conventional path-average model, we furthermore compare the proposed system with an optimized path-average model in which amplifier locations can be adapted. We quantify the improvement in the performance of NFDM systems that use DDF through numerical simulations.

Abstract:

An optical pre-processing structure is used to reduce the burden of digital equalizers and increase transmission reach for a direct detected system impaired by chromatic dispersion. The optical pre-processing consists of the optical signal being sliced into narrow frequency sub-band by an optical filter. Two distinct filters are numerically investigated: an arbitrary waveguide grating (AWG) filter and a series of cascaded Mach-Zehnder delay interferometers (MZDI). Each signal’s spectral slice is detected by a photodetector and used as input for the digital equalizer. Two options are also considered for equalization: a feedforward neural network (NN) equalizer and a recurrent neural network with reservoir computing (RC). The results are analyzed in simulation in terms of signalto-noise penalty at the KP4 forward error correction threshold. The penalty is calculated with respect to a back-toback transmission without equalization. A 32 GBd on-off transmission shows 0 dB penalty at ≈25 km transmission reach with optoelectronic processing with FNN and at ≈40 km with RC.

Abstract:

Chromatic dispersion is one of the key limitations to increasing the transmission distance-rate product for short-reach communication systems relying on intensity modulation and direct detection. The available optical dispersion-compensation techniques have lost favor due to their high impact on the link loss budget. Alternative digital techniques are commonly power-hungry and introduce latency. In this work, we compare different digital, optical and joint hybrid approaches to provide equalization and dispersion compensation for short-reach optical transmission links. Reservoir computing, as a promising technique to provide equalization with memory in an easily trainable fashion, is reviewed and the properties of the reservoir network are directly linked to system performance. Furthermore, we propose a new hybrid method relying on reservoir computing combined with a simple signal pre-conditioning stage directly in the optical domain. The optical pre-processing uses an arrayed waveguide grating to split the received signal into smaller sub-bands. The performance of the proposed scheme is thoroughly characterized both in terms of reservoir properties and appropriate pre-processing. The benefits are numerically demonstrated for 32-GBd on-off keying signal transmission, and show an increase in reach from 10 km to 40 km, corresponding to 400 %, compared with more complex digital-only techniques.

Abstract

In this paper, a machine learning-based tunable optical-digital signal processor is demonstrated for a short-reach optical communication system. The effect of fiber chromatic dispersion after square-law detection is mitigated using a hybrid structure, which shares the complexity between the optical and the digital domain. The optical part mitigates the chromatic dispersion by slicing the signal into small sub-bands and delaying them accordingly, before regrouping the signal again. The optimal delay is calculated in each scenario to minimize the bit error rate. The digital part is a nonlinear equalizer based on a neural network. The results are analyzed in terms of signal-to-noise penalty at the KP4 forward error correction threshold. The penalty is calculated with respect to a back-to-back transmission without equalization. Considering 32 GBd transmission and 0 dB penalty, the proposed hybrid solution shows chromatic dispersion mitigation up to 200 ps/nm (12 km of equivalent standard single-mode fiber length) for stage 1 of the hybrid module and roughly double for the second stage. A simplified version of the optical module is demonstrated with an approximated 1.5 dB penalty compared to the complete two-stage hybrid module. Chromatic dispersion tolerance for a fixed optical structure and a simpler configuration of the nonlinear equalizer is also investigated.

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Journal Articles & Conf. Proceedings