Renato Candido

Transient and Steady-State Analysis of the Affine Combination of Two Adaptive Filters

In this paper, we propose an approach to the transient and steady-state analysis of the affine combination of one fast and one slow adaptive filters. The theoretical models are based on expressions for the excess mean-square error (EMSE) and cross-EMSE of the component filters, which allows their application to different combinations of algorithms, such as least mean-squares (LMS), normalized LMS (NLMS), and constant modulus algorithm (CMA), considering white or colored inputs and stationary or nonstationary environments. Since the desired universal behavior of the combination depends on the correct estimation of the mixing parameter at every instant, its adaptation is also taken into account in the transient analysis. Furthermore, we propose normalized algorithms for the adaptation of the mixing parameter that exhibit good performance. Good agreement between analysis and simulation results is always observed.

A transient analysis for the convex combination of adaptive filters

Combination schemes are gaining attention as an interesting way to improve adaptive filter performance. In this paper we pay attention to a particular convex combination scheme with nonlinear adaptation that has recently been shown to be universal -i.e., to perform at least as the best component filter- in steady-state; however, no theoretical model for the transient has been provided yet. By relying on Taylor Series approximations of the nonlinearities, we propose a theoretical model for the transient behavior of such convex combinations. In particular, we provide expressions for the time evolution of the mean and the variance of the mixing parameter, as well as for the mean square overall filter convergence. The accuracy of the model is analyzed for the particular case of a combination of two LMS filters with different step sizes, explaining also how our results can help the designer to adjust the free parameters of the scheme.

Affine combinations of adaptive filters

We extend the analysis presented in for the affine combination of two least mean-square (LMS) filters to allow for colored inputs and nonstationary environments. Our theoretical model deals, in a unified way, with any combinations based on the following algorithms: LMS, normalized LMS (NLMS), and recursive-least squares (RLS). Through the analysis, we observe that the affine combination of two algorithms of the same family with close adaptation parameters (step-sizes or forgetting factors) provides a 3 dB gain in relation to its best component filter. We study this behavior in stationary and nonstationary environments. Good agreement between analytical and simulation results is always observed. Furthermore, a simple geometrical interpretation of the affine combination is investigated. A model for the transient and steady-state behavior of two possible algorithms for estimation of the mixing parameter is proposed. The model explains situations in which adaptive combination algorithms may achieve good performance.

Channel equalization for synchronization of chaotic maps

Abstract Many communication systems applying synchronism of chaotic systems have been proposed as an alternative spread spectrum modulation that improves the level of privacy in data transmission. However, due to the lack of robustness of chaos synchronization, even minor channel imperfections are enough to hinder communication. In this paper, we propose an adaptive equalization scheme based on a modified normalized least-mean-squares (NLMS) algorithm, which enables chaotic synchronization when the communication channel is not ideal. As an example of application, this scheme is used to recover a binary sequence modulated by a chaotic signal generated by the Henon map. Simulation results show that the modified NLMS can successfully equalize the channel in different scenarios.

Do chaos-based communication systems really transmit chaotic signals?

Many communication systems based on the synchronism of chaotic systems have been proposed as an alternative spread spectrum modulation that improves the level of privacy in data transmission. However, depending on the map and on the encoding function, the transmitted signal may cease to be chaotic. Therefore, the sensitive dependence on initial conditions, which is one of the most interesting properties for employing chaos in telecommunications, may disappear. In this paper, we numerically analyze the chaotic nature of signals modulated using a system that employs the Ikeda map. Additionally, we propose changes in the communication system in order to guarantee that the modulated signals are in fact chaotic. HighlightsWe analyze a chaos-based communication system to verify if the signals are chaotic.An analysis concerning the presence of co-existing attractors in the Ikeda map is performed.We compute Lyapunov exponents of the orbits of the Ikeda map, including an encoded message.We propose a strategy to guarantee a truly chaos-based system.

A statistical analysis of the dual-mode CMA

Blind equalization algorithms with good convergence and tracking properties and numerical robustness are desired to ensure the good performance of communications systems. In this paper, we present transient and steady-state analyses for the dual-mode constant modulus algorithm (DM-CMA), a version of CMA that avoids its well-known divergence problem. We show that DM-CMA is able to avoid divergence without degradation of mean-square performance. Good agreement between analytical and simulation results is observed.

On combinations of CMA equalizers

We extend the affine combination of one fast and one slow least mean-square (LMS) filter to blind equalization, considering the combination of two constant modulus algorithms (CMA). We analyze the proposed combination in stationary and nonstationary environments verifying that there are situations where the absence of the restriction on the mixing parameter can be advantageous for the combination. Furthermore, we propose a combination of two CMAs with different initializations. Preliminary simulations show that this scheme can avoid local minima and eventually can present a faster convergence rate than that of its components.

New Trends in Chaos-Based Communications and Signal Processing

In the last decades many possible applications of nonlinear dynamics in communication systems and signal processing have been reported. Conversely, techniques usually employed by the signal processing and communication systems communities, as correlation, power spectral density analysis, and linear filters, among others have been used to characterize chaotic dynamical systems. This chapter presents four works that aim to use tools from both fields to generate new and interesting results: (1) a message authentication system based on chaotic fingerprint; (2) a study of the spectral characteristics of the chaotic orbits of the Henon map; (3) an investigation of the chaotic nature of the signals generated by a filtered Henon map, and (4) a communication system that presents equalization and a switching scheme between chaos-based and conventional modulations.

Combined Filtering Architectures for Complex Nonlinear Systems

Abstract In this chapter, we review the use of combination approaches to improve the performance of nonlinear adaptive systems. In particular, we analyze two different strategies to take advantage of the approach: (1) combining adaptive filters with the same structure but different parameters with the goal of simplifying parameter selection and/or improve the performance of the filter; (2) exploit the combination strategy as a way to simplify the selection of the nonlinear filter structure, by choosing the relevant nonlinear elements and suppressing the unnecessary ones. In both cases, combination approaches can be used to deal with the lack of the necessary statistical information for an optimal adjustment of the filter and its structure. The versatility of the combination approach is demonstrated by reviewing existing works that involve different nonlinear technologies, such as Volterra, functional-link and kernel adaptive filters. Some novel schemes are presented with the goal of improving the filter structure, and their advantages are discussed with several numerical examples in the context of nonlinear echo cancelation, signal prediction and system identification.

Equalização de canais de comunicação para a sincronização de mapas

Ha varios sistemas de comunicacao baseados em sincronismo caotico propostos na literatura. Entretanto, devido a pouca robustez do sincronismo caotico, na maioria dos casos uma pequena imperfeicao no canal e suficiente para impedir a comunicacao. Neste artigo, e proposto um esquema de equalizacao adaptativa para recuperar uma sequencia binaria modulada por um sinal caotico, que por sua vez e gerado por um mapa de Henon. O esquema proposto utiliza o algoritmo NLMS (Normalized Least-Mean-Squares) com uma modificacao para permitir a sincronizacao caotica mesmo quando o canal de comunicacao nao e ideal. Os resultados de simulacao mostram que o NLMS e capaz de equalizar o canal de comunicacao em diferentes cenarios.