Real-valued Neural Network Research Articles

Global Receptive Field Designed Complex-Valued Convolutional Neural Network Equalizer for Optical Fiber Communications

In this paper, an improved complex-valued convolutional neural network (CvCNN) structure to be placed at the received side is proposed for nonlinearity compensation in a coherent optical system. This complex-valued global convolutional kernel-assisted convolutional neural network equalizer (CvGNN) has been verified in terms of Q-factor performance and complexity compared to seven other related nonlinear equalizers based on both the 64 QAM experimental platform and the QPSK numerical platform. The global convolution operation of the proposed CvGNN is more suitable for the calculation process of perturbation coefficients, and the global receptive field can also be more effective at extracting effective information from perturbation feature maps. The introduction of CvCNN can directly focus on the complex-valued perturbation feature maps themselves without separately processing the real and imaginary parts, which is more in line with the waveform-dependent physical characteristics of optical signals. Based on the experimental platform, compared with the real-valued neural network with small convolutional kernel (RvCNNC), the proposed CvGNNC improves the Q-factor by ∼2.95 dB at the optimal transmission power, while reducing the time complexity by ∼44.7%.

Noise equalization scheme based on probabilistic shaping and complex-valued ANN for dual-polarization continuous spectrum NFDM system with high-order modulation formats

In dual-polarization continuous spectrum nonlinear frequency division multiplexing (DP-CS NFDM) systems, the presence of noise destroys the independence between subcarriers in the nonlinear spectral domain (NSD). Additionally, as the modulation order and the number of subcarriers increase, the signal power increases and the effect of noise on the performance of the system becomes more severe. In this paper, we propose a noise equalization scheme based on probabilistic shaping (PS) and complex-valued neural network (c-ANN) for dual-polarization transmission CS NFDM system with high-power signals. The scheme utilizes PS to reduce the distribution probability of high-power constellation points of the signal with high-order modulation format, to decrease the peak-to-average power ratio of the continuous spectrum subcarriers and the average power of the signal, which can achieve the suppression and equalization of the amplifier spontaneous emission (ASE) noise and the processing noise. In addition, the scheme uses the c-ANN to effectively reduce the correlation between subcarriers caused by the noise and improve the system performance. The effectiveness of the proposed scheme is verified in the DP-CS NFDM system, and the simulation results show that the Q-factor gain is enhanced by roughly 1.1 dB and 0.8 dB for the number of subcarriers of 128 and 256, respectively, compared to the classic nonlinear Fourier transform (NFT) scheme. Among them, with different noise figure (NF) and satisfying the 7% forward error correction (FEC) threshold, the 512QAM signal with an entropy of 8 after equalization increase the transmission distance by 80 km longer than that of uniform 256QAM signals for the number of subcarriers of 128. Compared with the joint scheme based on PS and real-valued neural network (r-ANN), this scheme has better equalization performance at the same complexity, and the complexity can be reduced by 50% under the same performance.

Ultrafast Bragg coherent diffraction imaging of epitaxial thin films using deep complex-valued neural networks

Domain wall structures form spontaneously due to epitaxial misfit during thin film growth. Imaging the dynamics of domains and domain walls at ultrafast timescales can provide fundamental clues to features that impact electrical transport in electronic devices. Recently, deep learning based methods showed promising phase retrieval (PR) performance, allowing intensity-only measurements to be transformed into snapshot real space images. While the Fourier imaging model involves complex-valued quantities, most existing deep learning based methods solve the PR problem with real-valued based models, where the connection between amplitude and phase is ignored. To this end, we involve complex numbers operation in the neural network to preserve the amplitude and phase connection. Therefore, we employ the complex-valued neural network for solving the PR problem and evaluate it on Bragg coherent diffraction data streams collected from an epitaxial La2-xSrxCuO4 (LSCO) thin film using an X-ray Free Electron Laser (XFEL). Our proposed complex-valued neural network based approach outperforms the traditional real-valued neural network methods in both supervised and unsupervised learning manner. Phase domains are also observed from the LSCO thin film at an ultrafast timescale using the complex-valued neural network.

Finite-Time Passivity and Synchronization for a Class of Fuzzy Inertial Complex-Valued Neural Networks with Time-Varying Delays

This article investigates finite-time passivity for fuzzy inertial complex-valued neural networks (FICVNNs) with time-varying delays. First, by using the existing passivity theory, several related definitions of finite-time passivity are illustrated. Consequently, by adopting a reduced-order method and dividing complex-valued parameters into real and imaginary parts, the proposed FICVNNs are turned into first-order real-valued neural network systems. Moreover, appropriate controllers and the Lyapunov functional method are established to obtain the finite-time passivity of FICVNNs with time delays. Furthermore, some essential conditions are established to ensure finite-time synchronization for finite-time passive FICVNNs. In the end, corresponding simulations certify the feasibility of the proposed theoretical outcomes.

Enhance Terahertz Image Resolution via Complex-valued convolutional neural networks

Terahertz imaging technology is widely used in nondestructive testing (NDT), human security inspection, far-field imaging systems, and so on. Improving image resolution is always a topic of discussion. For visible image and image super-resolution, the convolutional neural network (CNN) has achieved a better improvement effect than the traditional algorithm. Compared to optics, it is quite feasible to gain both the amplitude and phase information in THz imaging, the Complex-valued convolutional neural network (CV-CNN) is better suited for the field of terahertz imaging than the real-valued neural network. In this paper, A lightweight complex-valued neural network is constructed which enhances terahertz imaging in a vector network analyzer (VNA) imaging system. Compared to CNN, CV-CNN has a better peak signal-to-noise ratio (PSNR) and structural similarity (SSIM), and it is significantly less vulnerable to overfitting. Phase information can be used well at the same time, which is impossible for CNN. The network is trained using the MNIST dataset and verified by using simulated and measured data obtained from a 200Ghz imager.

Real-Valued Neural Network Nonlinear Equalization for Long-Reach PONs Based on SSB Modulation

Real-valued neural network nonlinear equalization for complex-valued signals combined with single sideband (SSB) modulation is proposed to be a promising scheme for long-reach passive optical networks (LR-PONs). With the assist of neural network equalizer (NNE), fiber nonlinearity induced by large launch power can be mitigated. We experimentally demonstrate a transmission of 120 Gbps 16-QAM SSB signal in C-band over an 80-km single mode fiber (SMF) without optical inline amplifier and pre-amplifier.

Complex-Valued Iris Recognition Network.

In this work, we design a fully complex-valued neural network for the task of iris recognition. Unlike the problem of general object recognition, where real-valued neural networks can be used to extract pertinent features, iris recognition depends on the extraction of both phase and magnitude information from the input iris texture in order to better represent its biometric content. This necessitates the extraction and processing of phase information that cannot be effectively handled by a real-valued neural network. In this regard, we design a fully complex-valued neural network that can better capture the multi-scale, multi-resolution, and multi-orientation phase and amplitude features of the iris texture. We show a strong correspondence of the proposed complex-valued iris recognition network with Gabor wavelets that are used to generate the classical IrisCode; however, the proposed method enables a new capability of automatic complex-valued feature learning that is tailored for iris recognition. We conduct experiments on three benchmark datasets - ND-CrossSensor-2013, CASIA-Iris-Thousand and UBIRIS.v2 - and show the benefit of the proposed network for the task of iris recognition. We exploit visualization schemes to convey how the complex-valued network, when compared to standard real-valued networks, extracts fundamentally different features from the iris texture.

Uniform Stability of Complex-Valued Neural Networks of Fractional Order With Linear Impulses and Fixed Time Delays.

As a generation of the real-valued neural network (RVNN), complex-valued neural network (CVNN) is based on the complex-valued (CV) parameters and variables. The fractional-order (FO) CVNN with linear impulses and fixed time delays is discussed. By using the sign function, the Banach fixed point theorem, and two classes of activation functions, some criteria of uniform stability for the solution and existence and uniqueness for equilibrium solution are derived. Finally, three experimental simulations are presented to illustrate the correctness and effectiveness of the obtained results.

A Joint PAPR Reduction and Digital Predistortion Based on Real-Valued Neural Networks for OFDM Systems

The peak-to-average power ratio (PAPR) reduction and linearization techniques are both effective methods to improve the efficiency of the transmitter in digital video broadcasting (DVB) systems. Traditional methods deploy the PAPR reduction model and the linearization model, respectively, without considering their mutual influence. Therefore, the joint optimizations of PAPR reduction and linearization techniques are proposed. However, these methods train the PAPR reduction model and the linearization model based on the time-division training method. It is difficult to meet the requirements of multiple objectives. To address this issue, this paper proposes a joint PAPR reduction and digital predistortion (DPD) method using the real-valued neural network (RVNN) for Orthogonal Frequency Division Multiplexing (OFDM) systems. The proposed method jointly trains the PAPR reduction function and the DPD function with multi-objective optimization, to achieve PAPR reduction and linearization simultaneously. Especially, this method unifies the PAPR reduction function and the DPD function into one model based on RVNN, and no extra processing is required at the receiver. Compared with the traditional methods, the experimental results show that the proposed method has superior performance in PAPR, adjacent channel power ratio (ACPR) and bit error rate (BER), while having lower computational complexity.

Comparison of Real- and Complex-Valued NN Equalizers for Photonics-Aided 90-Gbps D-band PAM-4 Coherent Detection

5G defines below 100 GHz as the millimeter-wave bands, whereas 100 GHz - 3 THz is categorized as THz band in 6G. Deep leraning (DL) is expected to enable a significant paradigm shift in 6G wireless networks. In this paper, D-band 90-Gbps single channel PAM-4 signal generation and transmission over 10-km SMF and 3-m wireless link at 140-GHz can be achieved. A novel complex-valued neural network (CVNN) equalizer using &#x2018;&Copf;ReLU&#x2019; activation function to directly recover PAM-4 signals from received noised signals is demonstrated. There are three DSP options in the experiment. In <i>Opt</i>.1, firstly conducted cascaded multi-modulus algorithm (CMMA) pre-equalization (pre-EQ) at transmitter, then processed via frequency offset estimation (FOE), carrier phase recovery (CPR) and finally real-valued neural network (RVNN) equalization at receiver. Here, the RVNN equalizers include DNN with a softmax output layer, two-step joint-DNN equalizer and LSTM. The experimental results show that LSTM-based equalizer outperforms the other real NN-based equalizers by average 0.5 to 1.5 dB at BER of 10^&#x2212;3 magnitude. Differently from <i>Opt</i>. 1, real-valued CMMA pre-EQ at transmitter is unexpected for CVNN in the other two options. In <i>Opt</i>. 2, we only combine down-conversion and CVNN regarded as &#x2018;pure data-driven&#x2019; training at receiver. This pure data-driven CVNN equalizer improves BER a lot and also has a larger computation burden, especially BER is as low as 1 &#x00D7; 10^&#x2212;4 with <i>n</i>₀ &#x003D; 571 and <i>n</i>₁ &#x003D; 200 training cells and the time complexity reaches 350000 in one iteration. Thanks to the aid of traditional mathematical-oriented models including FOE and CPR, the computation burden of CVNN in <i>Opt</i>. 3 is released significantly. Furthermore, we compare the performance of CVNN and RVNN in terms of BER decision accuracy, time complexity and receiver sensitivity. Followed by the same DSP with the same complexity, the comparison result between DNN and CVNN in the same structure of [371-260-1] with 11000 samples and 300 epochs shows that CVNN performs better due to its reservation of phase information. Therefore, we believe that the joint use of model-based, e.g., FOE, CPR steps and complex DL-based techniques has a potential for the future 6G wireless physical layer algorithms.

Rainfall-runoff modelling using octonion-valued neural networks

ABSTRACT Rainfall-runoff modelling is at the core of any hydrological forecasting system. High spatio-temporal variability of precipitation patterns, complexity of the physical processes, and large quantity of parameters to characterize a watershed make the prediction of runoff rates quite difficult. In this study, a hyper-complex Artificial Neural Network (ANN) in the form of an Octonion-Valued Neural Network (OVNN) is proposed to estimate runoff rates. Evaluation of the proposed model is performed using a rainfall time series from a rain gauge near a Canadian watershed. Results of the AI-generated runoff rates illustrate its capacity to produce more computationally efficient runoff rates when compared to those obtained using a physically-based model. In addition, training the data using the proposed OVNN versus a real-valued neural network shows less space-complexity (1*3*1 vs. 8*10*8, respectively) and more accurate results (0.10% vs. 0.95%, respectively), that accounts for the efficiency of the OVNN model for real-time control applications.

Asymptotic behavior of Clifford-valued dynamic systems with D-operator on time scales

In this paper, a general class of Clifford-valued neutral high-order neural network (HNN) with D-operator on time scales is investigated. In this model, time-varying delays and continuously distributed delays are taken into account. As an extension of the real-valued neural network, the Clifford-valued neural network, which includes a familiar complex-valued neural network and a quaternion-valued neural network as special cases, has been an active research field recently. By utilizing this novel method, which incorporates the differential inequality techniques and the fixed point theorem and time-scale theory of computation, we derive a few sufficient conditions to ensure the existence, uniqueness, and exponential stability of the pseudo almost periodic (PAP) solution of the considered model. The results in this paper are new, even if time scale mathbb{T}=mathbb{R} or mathbb{T}=mathbb{Z}, and complementary to the previously existing works. Furthermore, an example and its numerical simulations are included to demonstrate the validity and advantage of the obtained results.

Neural Cryptography Based on Complex-Valued Neural Network.

Neural cryptography is a public key exchange algorithm based on the principle of neural network synchronization. By using the learning algorithm of a neural network, the two neural networks update their own weight through exchanging output from each other. Once the synchronization is completed, the weights of the two neural networks are the same. The weights of the neural network can be used for the secret key. However, all the existing works are based on the real-valued neural network model. There are seldom works studying the neural cryptography based on a complex-valued neural network model. In this technical note, a neural cryptography based on the complex-valued tree parity machine network (CVTPM) is proposed. The input, output, and weights of CVTPM are a complex value, which can be considered as an extension of TPM. There are two advantages of the CVTPM: 1) the security of CVTPM is higher than that of TPM with the same hidden units, input neurons, and synaptic depths and 2) the two parties with the CVTPM can exchange two group keys in one neural synchronization process. A series of numerical simulation experiments is provided to verify our results.

Real-Valued Neural Networks for Complex-Valued Impairment Compensation Using Digital Up-Conversion

Analog distortion compensation based on digital signal processing methods are widely applied for transmitter or receiver impairments in various digital communication systems. Recently, several neural network methods were developed for distortion compensation. However, while digital communication systems are typically complex-valued, neural networks are mostly designed to work with real-valued inputs. Thus, adaptations of the network architecture or input data should be applied. In this article a method for using a single-input real-valued neural network for digital communication-based complex-valued signals without any modifications to the neural network is proposed. The method transforms the complex-valued signal to a real-valued one by taking the real component of a complex frequency offset applied through digital up-conversion, without affecting the distortion, therefore allowing standard neural network-based functionality with significant reduction in size. The method is tested with a multi-layer perceptron and gated recurrent unit architectures applied over a generic Wiener-Hammerstein model for the case of equalization of a coherent optical system. A reduction of about 7% and 26% in network size is shown for the gated recurrent unit-based and multi-layer perceptron-based architectures respectively, without any significant change in performance. This size reduction capability shows the high potential in applying the proposed method in neural network-based equalization and pre-distortion operations.

Low-Complexity PAPR Reduction Method for OFDM Systems Based on Real-Valued Neural Networks

High peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems is one of the major drawbacks in wireless transmitters. In this letter, a novel low complexity PAPR reduction method based on the real-valued neural network (NN) is proposed. This method first builds the PAPR reduction module using the real-valued NN to achieve the reduction of PAPR. To reconstruct the transmission signal, the PAPR decompression module is introduced into the receiving end to recover the signal in order to minimize the bit error rate (BER) of the systems. The PAPR reduction module and the PAPR decompression module can be jointly trained offline, therefore, the reduction of PAPR and the minimization of BER can be achieved simultaneously. To reduce the process rate of the PAPR reduction, the trained model uses multiple parallel processing links to achieve the reduction of the PAPR. The extensive simulations indicate that the proposed method outperforms previously available methods in terms of PAPR and BER, while having low complexity.

Concurrent Dual-Band Receiver Based on the Multi-Port Correlator for Wireless Applications

A concurrent dual-band receiver based on a single multiport correlator is proposed in this brief to down-convert dual-band radio frequency signals. The system configuration, output power, as well as its spectrum analysis are discussed, and then a generalized baseband signal recovery theory is put forward. Next, the calibration algorithm based on real-valued time-delay neural network, which can take the system impairments and signal distortions into consideration, is proposed to retrieve two baseband signals, simultaneously. Finally, the six-port receiver is tested under the common modulated signals, and the measured error vector magnitudes between the transmitted and the received signals are all less than 2%.

Global Mittag-Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons

This paper talks about the stability and synchronization problems of fractional-order quaternion-valued neural networks (FQVNNs) with linear threshold neurons. On account of the non-commutativity of quaternion multiplication resulting from Hamilton rules, the FQVNN models are separated into four real-valued neural network (RVNN) models. Consequently, the dynamic analysis of FQVNNs can be realized by investigating the real-valued ones. Based on the method of M-matrix, the existence and uniqueness of the equilibrium point of the FQVNNs are obtained without detailed proof. Afterwards, several sufficient criteria ensuring the global Mittag-Leffler stability for the unique equilibrium point of the FQVNNs are derived by applying the Lyapunov direct method, the theory of fractional differential equation, the theory of matrix eigenvalue, and some inequality techniques. In the meanwhile, global Mittag-Leffler synchronization for the drive–response models of the addressed FQVNNs are investigated explicitly. Finally, simulation examples are designed to verify the feasibility and availability of the theoretical results.

A Fully Complex‐Valued Gradient Neural Network for Rapidly Computing Complex‐Valued Linear Matrix Equations

This paper concerns online solution of complex-valued linear matrix equations in the complex domain. Differing from the real-valued neural network, which is only designed for solving real-valued linear matrix equations in the real domain, a fully complex-valued Gradient neural network (GNN) is developed for computing complex-valued linear matrix equations. The fully complex-valued GNN model has the merit of reducing the unnecessary complexities in theoretical analysis and realtime computation, as compared to the real-valued neural network. Besides, the convergence analysis of the proposed complex-valued GNN model is presented, and simulation experiments are performed to substantiate the effectiveness and superiority of the proposed complex-valued GNN model for online computing the complex-valued linear matrix equations in the complex domain.

Global stability of Clifford-valued recurrent neural networks with time delays

In this paper, we study an issue of stability analysis for Clifford-valued recurrent neural networks (RNNs) with time delays. As an extension of real-valued neural network, the Clifford-valued neural network, which includes familiar complex-valued neural network and quaternion-valued neural network as special cases, has been an active research field recently. To the best of our knowledge, the stability problem for Clifford-valued systems with time delays has still not been solved. We first explore the existence and uniqueness for the equilibrium of delayed Clifford-valued RNNs, based on which some sufficient conditions ensuring the global asymptotic and exponential stability of such systems are obtained in terms of a linear matrix inequality (LMI). The simulation result of a numerical example is also provided to substantiate the effectiveness of the proposed results.

A Real Valued Neural Network Based Autoregressive Energy Detector for Cognitive Radio Application.

A real valued neural network (RVNN) based energy detector (ED) is proposed and analyzed for cognitive radio (CR) application. This was developed using a known two-layered RVNN model to estimate the model coefficients of an autoregressive (AR) system. By using appropriate modules and a well-designed detector, the power spectral density (PSD) of the AR system transfer function was estimated and subsequent receiver operating characteristic (ROC) curves of the detector generated and analyzed. A high detection performance with low false alarm rate was observed for varying signal to noise ratio (SNR), sample number, and model order conditions. The proposed RVNN based ED was then compared to the simple periodogram (SP), Welch periodogram (WP), multitaper (MT), Yule-Walker (YW), Burg (BG), and covariance (CV) based ED techniques. The proposed detector showed better performance than the SP, WP, and MT while providing better false alarm performance than the YW, BG, and CV. Data provided here support the effectiveness of the proposed RVNN based ED for CR application.