Adaptive polynomial filters

Journal ArticleWhile linear filter are useful in a large number of applications and relatively simple from conceptual and implementational view points. there are many practical situations that require nonlinear processing of the signals involved. This article explains adaptive nonlinear filters equipped with polynomial models of nonlinearity. The polynomial systems considered are those nonlinear systems whose output signals can be related to the input signals through a truncated Volterra series expansion, or a recursive nonlinear difference equation. The Volterra series expansion can model a large class of nonlinear systems and is attractive in filtering applications because the expansion is a linear combination of nonlinear functions of the input signal. The basic ideas behind the development of gradient and recursive least-squares adaptive Volterra filters are first discussed. followed by adaptive algorithms using system models involving recursive nonlinear difference equations. Such systems are attractive because they may be able to approximate many nonlinear systems with great parsimony in the use pf coefficients. Also discussed are current research trends and new results and problem areas associated with these nonlinear filters. A lattice structure for polynomial models is also described

A Study on the Suitability of Genetic Algorithm for Adaptive Channel Equalization

Adaptive algorithms such as Least-Mean-Square (LMS) based channel equalizer aim to minimize the Intersymbol Interference (ISI) present in the transmission channel. However the adaptive algorithms suffer from long training time and undesirable local minima during training mode. These disadvantages of the adaptive algorithms for channel equalization have been discussed in the literature. In this paper, we propose a new adaptive channel equalizer using Genetic Algorithm (GA) which is essentially a derivative free optimization tool. This algorithm is suitably used to update the weights of the equalizer. The performance of the proposed channel equalizer is evaluated in terms of mean square error (MSE) and convergence rate and is compared with its LMS and RLS counter parts. It is observed that the new adaptive equalizer based GA offer improved performance so far as the accuracy of reception is concerned.DOI:http://dx.doi.org/10.11591/ijece.v2i3.31

Sparse Volterra and Polynomial Regression Models: Recoverability and Estimation

Volterra and polynomial regression models play a major role in nonlinear system identification and inference tasks. Exciting applications ranging from neuroscience to genome-wide association analysis build on these models with the additional requirement of parsimony. This requirement has high interpretative value, but unfortunately cannot be met by least-squares based or kernel regression methods. To this end, compressed sampling (CS) approaches, already successful in linear regression settings, can offer a viable alternative. The viability of CS for sparse Volterra and polynomial models is the core theme of this work. A common sparse regression task is initially posed for the two models. Building on (weighted) Lasso-based schemes, an adaptive RLS-type algorithm is developed for sparse polynomial regressions. The identifiability of polynomial models is critically challenged by dimensionality. However, following the CS principle, when these models are sparse, they could be recovered by far fewer measurements. To quantify the sufficient number of measurements for a given level of sparsity, restricted isometry properties (RIP) are investigated in commonly met polynomial regression settings, generalizing known results for their linear counterparts. The merits of the novel (weighted) adaptive CS algorithms to sparse polynomial modeling are verified through synthetic as well as real data tests for genotype-phenotype analysis.Comment: 20 pages, to appear in IEEE Trans. on Signal Processin

Kernel mapping for mitigating nonlinear impairments in optical short-reach communications

Nonlinear impairments induced by the opto-electronic components are one of the fundamental performance-limiting factors in high-speed optical short-reach communications, significantly hindering capacity improvement. This paper proposes to employ a kernel mapping function to map the signals in a Hilbert space to its inner product in a reproducing kernel Hilbert space, which has been successfully demonstrated to mitigate nonlinear impairments in optical short-reach communication systems. The operation principle is derived. An intensity modulation/direct detection system with 1.5-mu m vertical cavity surface emitting laser and 10-km 7-core fiber achieving 540.68-Gbps (net-rate 505.31-Gbps) has been carried out. The experimental results reveal that the kernel mapping based schemes are able to realize comparable transmission performance as the Volterra filtering scheme even with a high order. (C) 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreemen

Low-complexity RLS algorithms using dichotomous coordinate descent iterations

In this paper, we derive low-complexity recursive least squares (RLS) adaptive filtering algorithms. We express the RLS problem in terms of auxiliary normal equations with respect to increments of the filter weights and apply this approach to the exponentially weighted and sliding window cases to derive new RLS techniques. For solving the auxiliary equations, line search methods are used. We first consider conjugate gradient iterations with a complexity of O(N-2) operations per sample; N being the number of the filter weights. To reduce the complexity and make the algorithms more suitable for finite precision implementation, we propose a new dichotomous coordinate descent (DCD) algorithm and apply it to the auxiliary equations. This results in a transversal RLS adaptive filter with complexity as low as 3N multiplications per sample, which is only slightly higher than the complexity of the least mean squares (LMS) algorithm (2N multiplications). Simulations are used to compare the performance of the proposed algorithms against the classical RLS and known advanced adaptive algorithms. Fixed-point FPGA implementation of the proposed DCD-based RLS algorithm is also discussed and results of such implementation are presented

Multi-Agent Feedback Enabled Neural Networks for Intelligent Communications

In the intelligent communication field, deep learning (DL) has attracted much attention due to its strong fitting ability and data-driven learning capability. Compared with the typical DL feedforward network structures, an enhancement structure with direct data feedback have been studied and proved to have better performance than the feedfoward networks. However, due to the above simple feedback methods lack sufficient analysis and learning ability on the feedback data, it is inadequate to deal with more complicated nonlinear systems and therefore the performance is limited for further improvement. In this paper, a novel multi-agent feedback enabled neural network (MAFENN) framework is proposed, consisting of three fully cooperative intelligent agents, which make the framework have stronger feedback learning capabilities and more intelligence on feature abstraction, denoising or generation, etc. Furthermore, the MAFENN frame work is theoretically formulated into a three-player Feedback Stackelberg game, and the game is proved to converge to the Feedback Stackelberg equilibrium. The design of MAFENN framework and algorithm are dedicated to enhance the learning capability of the feedfoward DL networks or their variations with the simple data feedback. To verify the MAFENN framework’s feasibility in wireless communications, a multi-agent MAFENN based equalizer (MAFENN-E) is developed for wireless fading channels with inter-symbol interference (ISI). Experimental results show that when the quadrature phase-shift keying (QPSK) modulation scheme is adopted, the SER performance of our proposed method outperforms that of the traditional equalizers by about 2 dB in linear channels. When in nonlinear channels, the SER performance of our proposed method outperforms that of either traditional or DL based equalizers more significantly, which shows the effectiveness and robustness of our proposal in the complex channel environment

ADAPTIVE AND NONLINEAR SIGNAL PROCESSING

1996/1997X Ciclo1967Versione digitalizzata della tesi di dottorato cartacea

Advanced DSP Techniques for High-Capacity and Energy-Efficient Optical Fiber Communications

The rapid proliferation of the Internet has been driving communication networks closer and closer to their limits, while available bandwidth is disappearing due to an ever-increasing network load. Over the past decade, optical fiber communication technology has increased per fiber data rate from 10 Tb/s to exceeding 10 Pb/s. The major explosion came after the maturity of coherent detection and advanced digital signal processing (DSP). DSP has played a critical role in accommodating channel impairments mitigation, enabling advanced modulation formats for spectral efficiency transmission and realizing flexible bandwidth. This book aims to explore novel, advanced DSP techniques to enable multi-Tb/s/channel optical transmission to address pressing bandwidth and power-efficiency demands. It provides state-of-the-art advances and future perspectives of DSP as well

Reduced Fuzzy Recursive Least-Squares Algorithm For Real Time Estimation

Adaptive filtering is an online signal processing application that is capable of estimating parameters for the characterization of a real time system. The estimation is done based on the mean-square error (MSE) minimization of the difference between some desired output and the output of the adaptive filter. The unknown transfer function is assumed to be a known structure and is realized by three different structures which are commonly used in conventional adaptive filtering: (i) the finite-duration impulse response (FIR) filter, (ii) the infinite-duration impulse response (IIR) filter, and (iii) the nonlinear filter