KIBANGOU , Alain

A broad class of physical systems can be represented using the Volterra model. Particularly, it was shown that a truncated Volterra model could represent any non-linear system, time-invariant with fading memory. This model is thus particularly attractive for non-linear systems modeling and identification purpose. One of the main advantages of...

In this study, we show that the minimum mean square estimate (MMSE) of the parameters of a fifth-order Volterra model can be obtained in closed-form when the input is independent and identically distributed (i.i.d). The derived closed-form expressions of the kernel coefficients can be used for identifying Volterra systems with arbitrary memory....

Recently, tensor signal processing has received an increased attention, particularly in the context of wireless communication applications. The so-called PARAllel FACtor (PARAFAC) decomposition is certainly the most used tensor tool. In general, the parameter estimation of a PARAFAC decomposition is carried out by means of the iterative ALS...

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In this paper, we propose a new tensor-based approach to identify the structure of a block-oriented nonlinear system (Hammerstein, Wiener, and Wiener-Hammerstein systems). The proposed method makes use of one time-domain Volterra kernel of an arbitrary order higher than two, which can be viewed as a tensor. We develop a tensor analysis for...

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In this paper, we consider the problem of identification of nonlinear communication channels using input-output measurements. The nonlinear channel is structured as a LTI-ZMNL-LTI one, i.e. a zero-memory nonlinearity (ZMNL) sandwiched between two linear time-invariant (LTI) subchannels. Considering Volterra kernels of order higher than two as...

In this letter, we present an algorithm for computing the factors of a matrix bilinear decomposition when the factors are constrained to have a Toeplitz and a Vandermonde structure. The proposed algorithm is constituted by a set of recurrence relations derived when the matrix to be decomposed has at least three columns. This algorithm is then...

This letter is concerned with the parameter estimation of linear and nonlinear subsystems of parallel-cascade Wiener systems (PCWS). We first present the relationship between a PCWS and its associated Volterra model. We show that the coefficients of the linear subsystems can be obtained using a joint diagonalization of the third-order Volterra...

In this letter, we first present explicit relations between block-oriented nonlinear representations and Volterra models. For an identification purpose, we show that the estimation of the diagonal coefficients of the Volterra kernels associated with the considered block-oriented nonlinear structures is sufficient to recover the overall model....

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In this paper, we consider the blind equalization problem for nonlinear channels represented by means of a Volterra model. We first suggest a precoding scheme inducing a three-dimensional (3-D) structure for the received data due to code, space, and time diversities. The tensor of received data admits a PARAFAC (parallel factors) decomposition...

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In this paper we introduce a new approach for compensating nonlinear distortions. The usual approaches necessitate the design of devices such as predistorters or nonlinear equalizers for compensating nonlinearities. Our approach consists in viewing the received signal as a linear mixture of distorted signals. Owing to a redundant precoder of...

Nonlinear (NL) and multilinear (ML) systems play a fundamental role in engineering and science. Over the last two decades, active research has been carried out on exploiting the intrinsically multilinear structure of input-output signals and/or models in order to develop more efficient identification algorithms. This has been achieved using the...

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New batch and adaptive methods are proposed to optimize the Volterra kernels expansions on a set of Laguerre functions. Each kernel is expanded on an independent Laguerre basis. The expansion coefficients, also called Fourier coefficients, are estimated in the NMSE sense or by applying the gradient technique. An analytical solution to Laguerre...

Volterra models are very useful for signal and system representation due to their general nonlinear structure and their property of linearity with respect to their parameters, the kernel coefficients. However, when using Volterra models we are confronted with a complexity problem that results from the very large number of parameters required by...

Discrete-time Volterra models are widely used in various application areas. Their usefulness is mainly because of their ability to approximate to an arbitrary precision any fading memory nonlinear system and to their property of linearity with respect to parameters, the kernels coefficients. The main drawback of these models is their parametric...

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This paper proposes two new methods for identifying multiple-input-multiple-output (MIMO) nonlinear systems. Specifically, we are interested in radio over fiber (ROF) uplink communications channels. The electrical optical (E/O) conversion in such systems introduces relevant nonlinear distortion and, consequently, the overall channel can be...