Nonlinear Channel Equalization via Reservoir Computing with Delayed Optical Feedback Semiconductor Nanolasers

Reservoir computing is a machine learning approach that enables us to use recurrent neural networks without involving the complexity of training algorithms and make hardware implementation possible. We present a novel photonic architecture of a reservoir computer that employs a nonlinear node and a resonator to implement a virtual recurrent neural network. This resonator behaves as an echo generator component that substitutes the delay line in delay-based reservoir computers available in the literature. The virtual neural network formed in our implementation is fundamentally different from the delay-based reservoir computers. Different virtual architectures based on the FSR and the Finesse of the resonator are investigated to provide higher performance depending on the task. We test the performance of our proposed reservoir by 3 benchmark tasks, signal classification, nonlinear channel equalization, and memory capacity. Our system enhances the memory capacity of the reservoir compared to the delay-based systems and shows reliable results in signal classification and nonlinear channel equalization.

Photonic reservoir computing has been intensively investigated to solve machine learning tasks effectively. A simple learning procedure of output weights is used for reservoir computing. However, the lack of training of input-node and inter-node connection weights limits the performance of reservoir computing. The use of multiple reservoirs can be a solution to overcome this limitation of reservoir computing. In this study, we investigate parallel and deep configurations of delay-based all-optical reservoir computing using semiconductor lasers with optical feedback by combining multiple reservoirs to improve the performance of reservoir computing. Furthermore, we propose a hybrid configuration to maximize the benefits of parallel and deep reservoirs. We perform the chaotic time-series prediction task, nonlinear channel equalization task, and memory capacity measurement. Then, we compare the performance of single, parallel, deep, and hybrid reservoir configurations. We find that deep reservoirs are suitable for a chaotic time-series prediction task, whereas parallel reservoirs are suitable for a nonlinear channel equalization task. Hybrid reservoirs outperform other configurations for all three tasks. We further optimize the number of reservoirs for each reservoir configuration. Multiple reservoirs show great potential for the improvement of reservoir computing, which in turn can be applied for high-performance edge computing.

Delay-based reservoir computing with temporally multiplexed virtual nodes provides a hardware-efficient platform for photonic implementations, yet parameter selection is often guided by empirical tuning. Here, we report a systematic experimental study of a single-node delay-based photonic reservoir computer that resolves the key physical and dynamical factors governing computational performance using the nonlinear channel equalization (NCE) benchmark. By mapping the bifurcation landscape of the system using port Hamiltonian linear algebra, we establish a direct correspondence between operating regime and NCE performance as well as memory capacity, showing that optimal performance occurs near, but below, the onset of oscillatory and chaotic dynamics. We further provide a unified comparison of temporal optimization strategies, including delay–input period desynchronization and controlled local node coupling, within the same physical platform. At a 16 dB signal-to-noise ratio, the symbol error rate (SER) decreases with node count but saturates beyond N ~ 50, revealing intrinsic dynamical limits to scaling in delay-based architectures. A readout-shifting strategy achieves an SER of 0.003. These results move delay-based photonic reservoir computing toward a predictive, physics-guided design framework for scalable high-speed operation.

We developed a high-speed concurrent support vector machine (CSVM) processor for real-time nonlinear channel equalization. All phases of the recognition process, including kernel computing, learning, and recall of the support vector machine (SVM) are performed on a single chip. The concurrent operation of this CSVM using a parallel architecture of elements allows it to achieve high speed. The hardware-friendly kernel adatron (KA) SVM learning algorithms are embedded on a chip. The results of the nonlinear channel equalization obtained by the KA algorithm are compared with those obtained by the quadratic programming (QP) method. The CSVM using the KA learning algorithm is designed and implemented using the FPGA chip. The CSVM processor performs 20% faster than the existing SVM processors.

A new training scheme for neural networks and application in non-linear channel equalization

An RBF neural network, combined with a Lyapunov adaptation (LA) algorithm is proposed for linear or nonlinear channel equalization. The output observations of the nonlinear channel are regarded as inputs of the RBF neural filter. The weights of the neural network are updated by the LA algorithm that is based on Lyapunov stability theory so that the error between the reference signal and output of the RBF neural filter can converge to zero asymptotically. The stochastic properties of the signals are not required and the stability is guaranteed by the Lyapunov stability theory. The design of the LA algorithm is extremely simplified compared with existing LMS and RLS algorithms. Hence, the proposed scheme possesses distinct advantages of stability, speed of convergence, convergence properties and some key features of RBF neural networks over the conventional linear filter with RLS and LMS for channel equalization.

In this paper we propose a radial basis function (RBF) neural network for nonlinear time-invariant channel equalizer. The RBF network model has a three-layer structure which is comprised of an input layer, a hidden layer and an output layer. The learning algorithm consists of unsupervised learning and supervised learning. The unsupervised learning mainly adjusts the weight among input layer and hidden layer. The supervised learning adjusts the weight among output layer and hidden layer. We will implement RBF by using FPGA. Computer simulation results show that the bit error rates of the RBF equalize using software and hardware implements are close to that of the optimal equalizer.

Nonlinear adaptive channel equalization is a well-documented problem. Equalizers based on the complex decision feedback recurrent neural network (CDFRNN) have been intensively studied to address this problem. However, when trained with conventional training algorithms like the real time recurrent learning (RTRL) technique, the equalizer suffers from low convergence speed, requiring very long training sequence to achieve proper performance. In this work, we propose a new approach to equalize nonlinear channels using genetic algorithms. The proposed Volterra decision feedback genetic algorithm (VDFGA) uses a genetic optimization strategy to estimate Volterra kernels in order to model the inverse of the channel response. Simulation results show very high convergence speed, which allowed to achieve interesting bit error rate (BER) using relatively short training symbols, when considering only 8-bits long coded weights.

An existing non-linear filter like the recursive least square fuzzy adaptive filter (RLS-FAF) is developed for channel equalisation. It makes use of both the linguistic and numerical information in their natural form. It is constructed from a set of changeable fuzzy IF-THEN rules which comes from the human experts. This equaliser has the ability to converge to its optimum decision region in a shorter period. The other advantage of the FAF is that linguistic information from the human experts can be directly incorporated into the filters. However, the RLS-FAF is not without limitations. First, it requires a high computational load and secondly, it requires prior linguistic knowledge or human experts. Therefore, a new architecture, namely the multilayer perceptron fuzzy adaptive filter (MLP-FAF) is implemented for the non-linear adaptive equalisation specifically in a digital communication system. This approach replaces the human experts with a MLP structure. The MLP-FAF described has the added advantage over the RLS-FAF in the reduced computational complexity due to the usage of the LMS algorithm in updating the fuzzy rules.

A systolic architecture dedicated to a piecewise linear fuzzy logic algorithm for a nonlinear channel equalization is presented. The piecewise linear membership function proposed for the inference step is more suitable for a VLSI implementation than the Gaussian function proposed in the literature. Depending on the number of piecewise linear membership functions (m) on the input space, the equalizer can perform for linear or nonlinear channel equalization. The performance evaluation of the systolic architecture is evaluated in terms of speed and area. The latency and throughput of the 16-bits design are respectively (2m+1)f/sub c/ and f/sub c/, where f/sub c/ is the clock frequency. In 0.5 /spl mu/m CMOS technology the f/sub c/ is evaluated at 40 MHz.

A high-speed data-communication over low-voltage power line is currently an active field of broad application. Power-line communication (PLC), based on orthogonal frequency-division multiplexing (OFDM), is developing rapidly. OFDM with an appropriately selected guard interval is considered as one of the most effective ways to eliminate the intersymbol interference of high-rate signal transmission. However, it is unable to deal with the orthogonality degradation between the subchannels due to the time-variant characteristics of the multipath power-line channels, which are known as the interchannel interference problem. It is, therefore, necessary to introduce a nonlinear channel equalizer. In this paper, a multilayer perceptron scheme trained with a mean square error (MSE) criterion is proposed for the design of the nonlinear channel equalizer. The performances of the traditional linear equalizer and the proposed nonlinear one are compared. In order to evaluate the robustness of the proposed approach against the channel distortion, experimental measurements are made in a real PLC network. The effectiveness of the proposed approach is verified via the experiments on the test system.

Non-linear channel equalization using adaptive MPNN

We experimentally demonstrate the possibility to process two tasks in parallel with a photonic reservoir computer based on a vertical-cavity surface-emitting laser (VCSEL) as a physical node with time-delay optical feedback. The two tasks are injected optically by exploiting the polarization dynamics of the VCSEL. We test our reservoir with the very demanding task of nonlinear optical channel equalization as an illustration of the performance of the system and show the recover of two signals simultaneously with an error rate of 0.3% (3%) for a 25 km-fiber distortion (50 km-fiber distortion) at a processing speed of 51.3 Mb/s.

We report on a simple approach of time-delayed reservoir computing (RC) based on a two-element phased laser array for image identification. Here the phased laser array with optical feedback and injection is trained according to the representative characteristics extracted through histograms of oriented gradients. These characteristic vectors are multiplied by a random mask signal to form input data, which are subsequently trained in the reservoir. By optimizing the parameters of the RC, we achieve an identification accuracy of 97.44% on the MNIST dataset and 85.46% on the Fashion-MNIST dataset. These results indicate that our proposed RC indeed allows accurate classification of handwritten digit and fashion production. Moreover, we further forecast an RC scheme based on a larger-scale phased laser array, which is expected to tackle more complex tasks at a high speed. Our work offers a possibility for advanced image processing using highly integrated neuromorphic photonic systems.

During the last decade reservoir computing (RC) has proven to be a powerful machine learning concept using recurrent networks to process sequential information streams [1]. Lately, the concept of RC was drastically simplified to reduce hardware requirements, thus making machine learning concepts more obtainable to apply in actual physical systems [2]. RC has been implemented in photonic configurations and has efficientiy processed analog optical signals following simple schemes and minimal training overhead. Especially the realization using a semiconductor laser with time-delayed optical feedback has shown the potential of all-optical machine learning, utilizing signals with transient states at the GHz regime [3].