Adaptive parallel-cascade truncated volterra filters

Journal ArticleAbstract-This paper studies adaptive truncated Volterra filters employing parallel-cascade structures. Parallel-cascade realizations implement higher order Volterra systems a s a parallel connection of multiplicative combinations of lower order truncated Volterra systems. A normalized LMS adaptive filter is developed, and its performance capabilities are evaluated using a series of simulation experiments. The experimental results indicate that the normalized LMS adaptive parallel-cascade Volterra filter has superior convergence properties over several competing structures. This paper also includes an experiment that demonstrates the capability of the parallel-cascade adaptive system to reduce its implementation complexity by using fewer than the maximum number of branches required for the most general realization of the system

Efficient block-adaptive parallel-cascade quadratic filters

Journal ArticleAbstract-This brief presents computationally efficient block-adaptive algorithms for quadratic filters employing parallel-cascade realizations of the system model. Parallel-cascade realizations implement higher order Volterra systems using a parallel connection of multiplicative combinations of lower order systems. Such realizations are modular and therefore well-suited for very large scale integrate circuit implementation. They also permit efficient approximations of truncated Volterra systems. Mixed frequency- and time-domain realizations of the least-mean-square (LMS) adaptive filter, as well as that of a normalized LMS adaptive filter, are presented in this brief. The adaptive normalized LMS parallel-cascade quadratic filter has the advantages of computational simplicity and superior performance over its direct form, and unnormalized adaptive parallel-cascade counterparts

Analysis of Different Low Complexity Nonlinear Filters for Acoustic Echo Cancellation

Linear filters are often employed in most signal processing applications. As a matter of fact, they are well understood within a uniform theory of discrete linear systems. However, many physical systems exhibit some nonlinear behaviour, and in certain situations linear filters perform poorly. One case is the problem of acoustic echo cancellation, where the digital filter employed has to identify as close as possible the acoustic echo path that is found to be highly nonlinear. In this situation a better system identification can be achieved by a nonlinear filter. The problem is to find a nonlinear filter structure able to realize a good approximation of the echo path without any significant increase of the computational load. Conventional Volterra filters are well suited for modelling that system but they generally need too many computational resources for a real time implementation. In this paper we consider some low complexity nonlinear filters in order to find out a filter structure able to achieve performances close to those of the Volterra filter, but with a reduced increase of the computational load in comparison to the linear filters commonly employed in commercial acoustic echo cancellers

Analysis of Different Low Complexity Nonlinear Filters for Acoustic Echo Cancellation

Linear filters are often employed in most signal processing applications. As a matter of fact, they are well understood within a uniform theory of discrete linear systems. However, many physical systems exhibit some nonlinear behaviour, and in certain situations linear filters perform poorly. One case is the problem of acoustic echo cancellation, where the digital filter employed has to identify as close as possible the acoustic echo path that is found to be highly nonlinear. In this situation a better system identification can be achieved by a nonlinear filter. The problem is to find a nonlinear filter structure able to realize a good approximation of the echo path without any significant increase of the computational load. Conventional Volterra filters are well suited for modelling that system but they generally need too many computational resources for a real time implementation. In this paper we consider some low complexity nonlinear filters in order to find out a filter structure able to achieve performances close to those of the Volterra filter, but with a reduced increase of the computational load in comparison to the linear filters commonly employed in commercial acoustic echo cancellers

Parallel-cascade realizations and approximations of truncated volterra systems

Journal ArticleAbstract This paper introduces parallel-cascade realizations of truncated Volterra systems with arbitrary, but finite order of nonlinearity. Parallel-cascade realizations implement higher-order Volterra systems using parallel and multiplicative combinations of lower-order Volterra systems. Such realizations are very modular and therefore well-suited for VLSI implementation. A Systematic way of approximating higher-order Volterra systems in parallel-cascade form using a reduced number of branches and a bound on the mean-square error in the output signals caused by such approximate realizations are derived in this paper. A variation of the parallel-cascade structure in which a pth order Volterra filter is implemented as a parallel combination of linear filters whose outputs are raised to the pth power is also described in this paper

Parallel-cascade realizations and approximations of truncated volterra systems

Journal ArticleThis paper introduces parallel-cascade realizations of truncated Volterra systems with arbitrary, but finite order of nonlinearity. Parallel-cascade realizations implement higher-order Volterra systems using parallel and multiplicative combinations of lower-order Volterra systems. Such realizations are very modular and therefore well-suited for VLSI implementation. A systematic way of approximating higher-order Volterra systems in parallel-cascade form using a reduced number of branches and a bound on the mean-square error in the output signals caused by such approximate realizations are derived in this paper. A variation of the parallel-cascade structure in which a pth order Volterra filter is implemented as a parallel combination of linear filters whose outputs are raised to the pth power is also described in this paper

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 Digital Predistortion Scheme Exploiting Degrees-of-Freedom for Massive MIMO Systems

The primary source of nonlinear distortion in wireless transmitters is the power amplifier (PA). Conventional digital predistortion (DPD) schemes use high-order polynomials to accurately approximate and compensate for the nonlinearity of the PA. This is not practical for scaling to tens or hundreds of PAs in massive multiple-input multiple-output (MIMO) systems. There is more than one candidate precoding matrix in a massive MIMO system because of the excess degrees-of-freedom (DoFs), and each precoding matrix requires a different DPD polynomial order to compensate for the PA nonlinearity. This paper proposes a low-order DPD method achieved by exploiting massive DoFs of next-generation front ends. We propose a novel indirect learning structure which adapts the channel and PA distortion iteratively by cascading adaptive zero forcing precoding and DPD. Our solution uses a 3rd order polynomial to achieve the same performance as the conventional DPD using an 11th order polynomial for a 100x10 massive MIMO configuration. Experimental results show a 70% reduction in computational complexity, enabling ultra-low latency communications.Comment: IEEE International Conference on Communications 201

Lattice algorithms for recursive least squares adaptive second-order volterra filtering

Journal ArticleThis paper presents two computationally efficient recursive least-square (RLS) lattice algorithms for adaptive nonlinear filtering based on a truncated second-order Volterra system model. The lattice formulation transforms the nonlinear filtering problem into an equivalent multichannel, linear filtering problem and then generalizes the lattice solution to the nonlinear filtering problem. One of the algorithms is a direct extension of the conventional RLS lattice adaptive linear filtering algorithm to the nonlinear case. The other algorithms is based on the QR decomposition of the prediction error covariance matrices using orthogonal transformations. Several experiments demonstrating and comparing the properties of the two algorithms in finite and "infinite" precision environments are included in the paper. The results indicate that both the algorithms retain the fast convergence behavior of the RLS Volterra filters and are numerically stable