Panos Koukoulas

Nonlinear system identification using Gaussian inputs

The paper is concerned with the identification of nonlinear systems represented by Volterra expansions and driven by stationary, zero mean Gaussian inputs, with arbitrary spectra that are not necessarily white. Procedures for the computation of the Volterra kernels both in the time as well as in the frequency domain are developed based on cross-cumulant information. The derived kernels are optimal in the mean squared error sense for noncausal systems. Order recursive procedures based on minimum mean squared error reduction are derived. More general input output representations that result when the Volterra kernels are expanded in a given orthogonal base are also considered. >

Efficient algorithms for Volterra system identification

In this paper, nonlinear filtering and identification based on finite-support Volterra models are considered. The Volterra kernels are estimated via input-output statistics or directly in terms of input-output data. It is shown that the normal equations for a finite-support Volterra system excited by zero mean Gaussian input have a unique solution if, and only if, the power spectral process of the input signal is nonzero at least at m distinct frequencies, where m is the memory of the system. A multichannel embedding approach is introduced. A set of primary signals defined in terms of the input signal serve to map efficiently the nonlinear process to an equivalent multichannel format. Efficient algorithms for the estimation of the Volterra parameters are derived for batch, as well as for adaptive processing. An efficient order-recursive method is presented for the determination of the Volterra model structure. The proposed methods are illustrated by simulations.

Second-order Volterra system identification

Second-order Volterra system identification is discussed. Crosscumulant information is converted into a Fredholm integral equation. Special emphasis is focused on inputs obtained at the output of a linear filter driven by higher order white noise.

Blind identification of second order Hammerstein series

Blind identification of second order Hammerstein series is considered [1]. The output cumulants up to order 5 are used to determine the Volterra kernels, when the input is a stationary zero mean Gaussian white stochastic process. Both infinite and finite extent kernels are considered.

Subspace projection based blind channel order estimation of MIMO systems

In this paper, a novel algorithm based on subspace projections is developed for blindly estimating the discrete orders of a linear finite-impulse-response (FIR) multiple-input multiple-output (MIMO) system, the number of subsystems that attain each order as well as the total number of inputs. Furthermore, the proposed algorithm applies to single-input multiple-output (SIMO) system order estimation. Simulations in the context of blind channel order estimation show good performance in comparison to existing schemes developed for SIMO systems.

Identification of input-output bilinear systems using cumulants

This paper is concerned with the identification of a discrete input-output bilinear system driven by an independent identically distributed (i.i.d.) stochastic input and corrupted by measurement noise. A novel algorithmic procedure for the direct computation of the unknown model parameters is developed based on crosscumulant information up to third order. Simulations and comparisons with a least squares type identification method are provided.

Input-output identification of nonlinear channels using PSK, QAM and OFDM inputs

Nonparametric identification of baseband and passband complex Volterra systems excited by communication inputs (phase shift keying, PSK; quadrature amplitude modulation, QAM and OFDM) is considered. Closed form expressions are established using multivariate orthogonal polynomials and higher order statistics. First multivariate orthogonal polynomials are used for baseband and passband Volterra models driven by PSK and QAM inputs and closed form expressions are derived. For baseband Volterra models excited with i.i.d. complex Gaussian signals (OFDM), the general 2p+1 order Volterra system is solved using cross-cumulants in time and frequency domain. An order recursive algorithm is presented for the latter case, that does not require a priori knowledge of the systems order. Performance is illustrated by simulations.

Blind identification of Volterra-Hammerstein systems

This paper is concerned with the blind identification of Volterra-Hammerstein systems excited by zero mean white Gaussian inputs. A new method is developed for the determination of the Volterra kernels. Output cumulants of order twice the nonlinearity degree of the system are employed.

A cumulant based algorithm for the identification of input-output quadratic systems

A parameter estimation algorithm is developed for the identification of an input output quadratic model. The excitation is a zero mean white Gaussian input and the output is corrupted by additive measurement noise. Input output crosscumulants up to fifth order are employed and the identification problem of the unknown model parameters is reduced to the solution of succesive linear systems of equations that are solved iteratively. Simulation results are provided for different SNRs illustrating the performance of the algorithm and confirming the theoretical set up.

Third order Volterra system identification

This paper is concerned with third order Volterra system identification. It is shown that crosscumulant information can be converted into a Fredholm integral equation. Closed form expressions for the Volterra kernels are derived using the determinant theory. Finally, special emphasis is focused on i.i.d. inputs.