Multistage Volterra Filters

In this paper, we propose a multistage Volterra filter and show it is equivalent to the partially decoupled Volterra per as formulated in [1]. Using this approach. we may readily derive a partially decoupled parallel algorithm for adaptation of filter's coefficients and upper bounds for each of the step sizes. The approach greatly simplifies the derivation given in [1].

A Probabilistic Trust Model and Control Algorithm to Protect 6G Networks against Malicious Data Injection Attacks in Edge Computing Environments

Future 6G communications are envisioned to enable a large catalogue of pioneering applications.These will range from networked Cyber-Physical Systems to edge computing devices,establishing real-time feedback control loops critical for managing Industry 5.0 deployments,digital agriculture systems,and essential infrastructures.The provision of extensive machine-type communications through 6G will render many of these innovative systems autonomous and unsupervised.While full automation will enhance industrial efficiency significantly,it concurrently introduces new cyber risks and vulnerabilities.In particular,unattended systems are highly susceptible to trust issues:malicious nodes and false information can be easily introduced into control loops.Additionally,Denialof-Service attacks can be executed by inundating the network with valueless noise.Current anomaly detection schemes require the entire transformation of the control software to integrate new steps and can only mitigate anomalies that conform to predefined mathematical models.Solutions based on an exhaustive data collection to detect anomalies are precise but extremely slow.Standard models,with their limited understanding of mobile networks,can achieve precision rates no higher than 75%.Therefore,more general and transversal protection mechanisms are needed to detect malicious behaviors transparently.This paper introduces a probabilistic trust model and control algorithm designed to address this gap.The model determines the probability of any node to be trustworthy.Communication channels are pruned for those nodes whose probability is below a given threshold.The trust control algorithmcomprises three primary phases,which feed themodel with three different probabilities,which are weighted and combined.Initially,anomalous nodes are identified using Gaussian mixture models and clustering technologies.Next,traffic patterns are studied using digital Bessel functions and the functional scalar product.Finally,the information coherence and content are analyzed.The noise content and abnormal information sequences are detected using a Volterra filter and a bank of Finite Impulse Response filters.An experimental validation based on simulation tools and environments was carried out.Results show the proposed solution can successfully detect up to 92%of malicious data injection attacks.

Neural Volterra filter for chaotic time series prediction

A new second-order neural Volterra filter （SONVF） with conjugate gradient （CG） algorithm is proposed to predict chaotic time series based on phase space delay-coordinate reconstruction of chaotic dynamics system in this paper, where the neuron activation functions are introduced to constraint Volterra series terms for improving the nonlinear approximation of second-order Volterra filter （SOVF）. The SONVF with CG algorithm improves the accuracy of prediction without increasing the computation complexity. Meanwhile, the difficulty of neuron number determination does not exist here. Experimental results show that the proposed filter can predict chaotic time series effectively, and one-step and multi-step prediction performances are obviously superior to those of SOVF, which demonstrate that the proposed SONVF is feasible and effective.

Dual loop feedback pre-distortion in satellite communication

Since the satellite communication goes in the trend of high-frequency and fast speed, the coefficients updating and the precision of the traditional pre-distortion feedback methods need to be further improved. On this basis, this paper proposes dual loop feedback pre-distortion, which uses two first-order Volterra filter models to reduce the computing complexity and a dynamic error adjustment model to construct a revised feedback to ensure a better pre-distortion performance. The computation complexity, iterative convergence speed and precision of the proposed method are theoretically analyzed. Simulation results show that this dual loop feedback pre-distortion can speed the updating of coefficients and ensure the linearity of the amplifier output.

Flower Pollination Heuristics for Nonlinear Active Noise Control Systems

In this paper,a novel design of the flower pollination algorithm is presented for model identification problems in nonlinear active noise control systems.The recently introduced flower pollination based heuristics is implemented to minimize the mean squared error based merit/cost function representing the scenarios of active noise control system with linear/nonlinear and primary/secondary paths based on the sinusoidal signal,random and complex random signals as noise interferences.The flower pollination heuristics based active noise controllers are formulated through exploitation of nonlinear filtering with Volterra series.The comparative study on statistical observations in terms of accuracy,convergence and complexity measures demonstrates that the proposed meta-heuristic of flower pollination algorithm is reliable,accurate,stable as well as robust for active noise control system.The accuracy of the proposed nature inspired computing of flower pollination is in good agreement with the state of the art counterpart solvers based on variants of genetic algorithms,particle swarm optimization,backtracking search optimization algorithm,fireworks optimization algorithm along with their memetic combination with local search methodologies.Moreover,the central tendency and variation based statistical indices further validate the consistency and reliability of the proposed scheme mimic the mathematical model for the process of flower pollination systems.

A Humanoid Method for Extracting Abnormal Engine Sounds from Engine Acoustics Based on Adaptive Volterra Filter

The improvement of SNR （Signal-to-Noise Ratio） of abnormal engine sounds is of great help in improving the accuracy of engine fault diagnosis. By imitating the way that human technicians use to distinguish abnormal engine sounds from engine acoustics, a humanoid abnormal sound extracting method is proposed. By implementing adaptive Volterra filter in the canonical Adaptive Noise Cancellation （ANC） system, the proposed method is capable of tracing the engine baseline sound which exhibits an intrinsic nonlinear dynamics. Besides, by introducing a template noise tailored from the records of engine baseline sound and taking it as virtual input of the adaptive Volterra filter, the priori knowledge of engine baseline sound, such as inherent correlation, periodicity or phase information, and stochastic factors, is taken into consideration. The hybrid simulations prove that the proposed method is functional. Since the method proposed is essentially a single-sensor based ANC, hopefully, it may become an effective way to extricate the dilemma that canonical dual-sensor based ANC encounters when it is used in extracting fault-featured signals from observed signals.

Cross-Target Transfer Algorithm Based on the Volterra Model of SSVEP-BCI

In general, a large amount of training data can effectively improve the classification performance of the Steady-State Visually Evoked Potential(SSVEP)-based Brain-Computer Interface(BCI) system. However, it will prolong the training time and considerably restrict the practicality of the system. This study proposed a SSVEP nonlinear signal model based on the Volterra filter, which could reconstruct stable reference signals using relatively small number of training targets by transfer learning, thereby reducing the training cost of SSVEP-BCI. Moreover,this study designed a transfer-extended Canonical Correlation Analysis(t-eCCA) method based on the model to achieve cross-target transfer. As a result, in a single-target SSVEP experiment with 16 stimulus frequencies,t-eCCA obtained an average accuracy of 86.96%˙12.87% across 12 subjects using only half of the calibration time,which exhibited no significant difference from the representative training classification algorithms, namely, extended canonical correlation analysis(88.32%±13.97%) and task-related component analysis(88.92%±14.44%), and was significantly higher than that of the classic non-training algorithms, namely, Canonical Correlation Analysis(CCA) as well as filter-bank CCA. Results showed that the proposed cross-target transfer algorithm t-eCCA could fully utilize the information about the targets and its stimulus frequencies and effectively reduce the training time of SSVEP-BCI.

Volterra filter modeling of a nonlinear discrete-time system based on a ranked differential evolution algorithm

This paper presents a ranked differential evolution(RDE) algorithm for solving the identification problem of nonlinear discrete-time systems based on a Volterra filter model. In the improved method, a scale factor, generated by combining a sine function and randomness, effectively keeps a balance between the global search and the local search. Also, the mutation operation is modified after ranking all candidate solutions of the population to help avoid the occurrence of premature convergence. Finally, two examples including a highly nonlinear discrete-time rational system and a real heat exchanger are used to evaluate the performance of the RDE algorithm and five other approaches. Numerical experiments and comparisons demonstrate that the RDE algorithm performs better than the other approaches in most cases.

An approach for parameter estimation of combined CPPM and LFM radar signal

In this paper, the problem of parameter estimation of the combined radar signal adopting chaotic pulse position modulation （CPPM） and linear frequency modulation （LFM）, which can be widely used in electronic countermeasures, is addressed. An approach is proposed to estimate the initial frequency and chirp rate of the combined signal by exploiting the second-order cyclostationarity of the intra-pulse signal. In addition, under the condition of the equal pulse width, the pulse repetition interval （PRI） of the combined signal is predicted using the low-order Volterra adaptive filter. Simulations demonstrate that the proposed cyclic autocorrelation Hough transform （CHT） algorithm is theoretically tolerant to additive white Gaussian noise. When the value of signal noise to ratio （SNR） is less than 4 dB, it can still estimate the intra-pulse parameters well. When SNR = 3 dB, a good prediction of the PRI sequence can be achieved by the Volterra adaptive filter algorithm, even only 100 training samples.