Sparse Nonlinear MIMO Filtering and Identification

In this chapter system identification algorithms for sparse nonlinear multi input multi output (MIMO) systems are developed. These algorithms are potentially useful in a variety of application areas including digital transmission systems incorporating power amplifier(s) along with multiple antennas, cognitive processing, adaptive control of nonlinear multivariable systems, and multivariable biological systems. Sparsity is a key constraint imposed on the model. The presence of sparsity is often dictated by physical considerations as in wireless fading channel-estimation. In other cases it appears as a pragmatic modelling approach that seeks to cope with the curse of dimensionality, particularly acute in nonlinear systems like Volterra type series. Three dentification approaches are discussed: conventional identification based on both input and output samples, semi–blind identification placing emphasis on minimal input resources and blind identification whereby only output samples are available plus a–priori information on input characteristics. Based on this taxonomy a variety of algorithms, existing and new, are studied and evaluated by simulation

Blind identification of bilinear systems

Journal ArticleAbstract This paper is concerned with the blind identification of bilinear systems excited by higher-order white noise. Unlike prior work that restricted the bilinear system model to simple forms and required the excitation to be Gaussian distributed, the results of this paper are applicable to a more general class of bilinear systems and for the case when the excitation is non-Gaussian. We describe an estimation procedure for the computation of the system parameters using output cumulants of order less than four

An Equivalence Relation between Multiresolution Analysis ofL2(R)

AbstractThis paper is concerned with the development of an equivalence relation between two multiresolution analysis ofL2(R). The relation called unitary equivalence is created by the action of a unitary operator in such a way that the multiresolution structure and the decomposition and reconstruction algorithms remain invariant. A characterization in terms of the scaling functions of the multiresolution analysis is given. Distinct equivalence classes of multiresolution analysis are derived. Finally, we prove that B-splines give rise to nonequivalent examples

State–of–the–art report on nonlinear representation of sources and channels

This report consists of two complementary parts, related to the modeling of two important sources of nonlinearities in a communications system. In the first part, an overview of important past work related to the estimation, compression and processing of sparse data through the use of nonlinear models is provided. In the second part, the current state of the art on the representation of wireless channels in the presence of nonlinearities is summarized. In addition to the characteristics of the nonlinear wireless fading channel, some information is also provided on recent approaches to the sparse representation of such channels

On the Linear Complexity of Nonlinearly Filtered PN-Sequences

Binary sequences of period 2n-1 generated by a linear feedback shift register (LFSR) whose stages are filtered by a nonlinear function f are studied. New iterative formulas are derived for the calculation of the linear complexity of the output sequences. It is shown that these tools provide an efficient mechanism for controlling the linear complexity of the nonlinearly filtered maximal-length sequences

Blind Identification of Volterra-Hammerstein Systems

This paper is concerned with the blind identification of Volterra-Hammerstein systems. Two identification scenarios are covered. The first scenario assumes that, although the input is not available, the statistics of the input are a priori known. This case appears in communication applications where the input statistics of the transmitter are known to the receiver. The second scenario assumes that the input statistics are unknown. In the case of known input statistics, the input is stationary higher order white noise with arbitrary probability density function. Under the scenario of unknown input statistics, the input is restricted to Gaussian white process. New cumulant-based identification methods are described for the above scenarios. The problem is converted into a linear multivariable form and the output cumulants are calculated using Kronecker products. First, initial conditions are determined by a linear system of equations. These correspond to the boundary values of the Volterra kernels. The remaining kernel coefficients can be determined under both identification schemes from a possibly overdetermined system of linear equations. © 2005, IEEE. All rights reserved

EFFICIENT ALGORITHMS FOR THE SOLUTION OF BLOCK LINEAR-SYSTEMS WITH TOEPLITZ ENTRIES

This paper is concerned with the development of fast solvers for block linear systems with Toeplitz entries. Two algorithms are described. The first utilizes block permutations to unravel the nesting structure of the associated matrix. The second has a block Schur type format and features highly parallel potential