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

A sparsity driven approach to cumulant based identification and order determination

The area of blind system identification using Higher-Order-Statistics has gained considerable attention over the last two decades. This paper, motivated by the recent developments in sparse approximations, proposes new algorithms for the blind identification and order determination of sparse systems. The methodology used relies on greedy schemes. In particular, the first algorithm exploits a single step greedy structure, while the second improves performance using a threshold-based selection procedure. Finally, the proposed algorithms are tested on a wide range of randomly generated channels and different output signal lengths. © 2013 Elsevier B.V

Blind identification of second order volterra systems with complex random inputs using higher order cumulants

In this correspondence, closed-form expressions for the blind identification of linear-quadratic Volterra systems are established. The system is excited by a complex valued random sequence and the output cumulants (of order up to 4) are employed. It is assumed that the memory of the linear part is greater than or equal to the memory of the quadratic part. Cumulant-based formulas are developed demonstrating that the system is uniquely identifiable. An SVD based variant with improved performance is also derived. Simulations and comparisons with existing techniques are presented. © 2009 IEEE

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 2 p + 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. © 2009 Elsevier B.V. All rights reserved

Empirical volterra-series modeling of commercial light-emitting diodes

Light-emitting diodes (LEDs) constitute a low-cost alternative for optical data transmission of up to ∼1 Gb/s. What differentiates such applications from, e.g., backhaul optical networks, is the fact that apart from their data throughput, LEDs are generally not as well characterized by the manufacturer as, for example, optical fiber amplifiers. While for simple modulation formats, this lack of knowledge is not a severe impediment; in any other situation, one may face rather complex behaviors of commercial LEDs. In this paper, the main electro-optical characteristics of LEDs are discussed, and it is shown that some popular simple nonlinear models available in the literature are inadequate in describing their dynamics. As a way out of this malady, we present a reverse-engineering approach that is based on Volterra expansions of the electro-optical characteristic function of LEDs, enabling the introduction of a realistic empirical model for commercial devices. © 2006 IEEE

Adaptive algorithms for sparse system identification

In this paper, identification of sparse linear and nonlinear systems is considered via compressive sensing methods. Efficient algorithms are developed based on Kalman filtering and Expectation-Maximization. The proposed algorithms are applied to linear and nonlinear channels which are represented by sparse Volterra models and incorporate the effect of power amplifiers. Simulation studies confirm significant performance gains in comparison to conventional non-sparse methods. © 2011 Elsevier B.V. All rights reserved

Greedy sparsity-promoting algorithms for distributed learning

This paper focuses on the development of novel greedy techniques for distributed learning under sparsity constraints. Greedy techniques have widely been used in centralized systems due to their low computational requirements and at the same time their relatively good performance in estimating sparse parameter vectors/signals. The paper reports two new algorithms in the context of sparsity-aware learning. In both cases, the goal is first to identify the support set of the unknown signal and then to estimate the nonzero values restricted to the active support set. First, an iterative greedy multistep procedure is developed, based on a neighborhood cooperation strategy, using batch processing on the observed data. Next, an extension of the algorithm to the online setting, based on the diffusion LMS rationale for adaptivity, is derived. Theoretical analysis of the algorithms is provided, where it is shown that the batch algorithm converges to the unknown vector if a Restricted Isometry Property (RIP) holds. Moreover, the online version converges in the mean to the solution vector under some general assumptions. Finally, the proposed schemes are tested against recently developed sparsity-promoting algorithms and their enhanced performance is verified via simulation examples. © 2015 IEEE

An adaptive greedy algorithm with application to nonlinear communications

Greedy algorithms form an essential tool for compressed sensing. However, their inherent batch mode discourages their use in time-varying environments due to significant complexity and storage requirements. In this paper two existing powerful greedy schemes developed in the literature are converted into an adaptive algorithm which is applied to estimation of a class of nonlinear communication systems. Performance is assessed via computer simulations on a variety of linear and nonlinear channels; all confirm significant improvements over conventional methods. © 2010 IEEE