Fast Newton Transversal Filter Research Articles

Efficient adaptive filtering algorithm for IQ imbalance compensation Tx/Rx systems

This study addresses the problem of in-phase and quadratic-phase (IQ) imbalance in digital transmitter and receiver communication systems. Recently, several adaptive and non-adaptive solutions to this problem have been proposed. In this study, an adaptive solution to this problem is given. The authors propose a new robust two-channel adaptive algorithm to compensate the IQ imbalance problem of quadratic receivers. The new algorithm is based on the combination between the backward blind source separation (BBSS) structure and the fast Newton transversal filter (FNTF) technique to form a two-channel algorithm that cancels the noisy IQ signal adaptively. The combination of the Newton recursion of the FNTF algorithm with the BBSS principle shows the efficiency of the new algorithm to enhance the output signal to interference ratio and allows distortion correction at the output. Simulation results show the efficiency of the new algorithm to compensate the IQ imbalance problem in comparison with the conventional two-channel normalised least mean square algorithm.

A new fast Newton‐type adaptive filtering algorithm for stereophonic acoustic echo cancellation (SAEC)

AbstractThis paper addresses the problem of acoustic echo cancellation. We propose a new version of the fast Newton transversal filter algorithm for stereophonic acoustic echo cancellation applications. This algorithm can be viewed as an efficient implementation of the extended two‐channel fast transversal filter algorithm. Moreover, it fits naturally within the frame of the fast version of the recursive least‐squares (RLS) algorithm, applied to the two‐channel case. To stabilize the proposed two‐channel algorithm, we have adapted and then applied a new numerical stabilization technique that has been proposed recently. The computational complexity of the proposed two‐channel algorithm is less than half the complexity of the fastest two‐channel RLS versions and very close to that of the two‐channel normalized least mean squares algorithm when its predicting part length is chosen to be small. Simulation results and comparisons in term of complexities, convergence speed and tracking with the two‐channel algorithms are presented. Copyright © 2009 John Wiley & Sons, Ltd.

Pairwise Optimal Weight Realization—Acceleration Technique for Set-Theoretic Adaptive Parallel Subgradient Projection Algorithm

The adaptive parallel subgradient projection (PSP) algorithm was proposed in 2002 as a set-theoretic adaptive filtering algorithm providing fast and stable convergence, robustness against noise, and low computational complexity by using weighted parallel projections onto multiple time-varying closed half-spaces. In this paper, we present a novel weighting technique named pairwise optimal weight realization (POWER) for further acceleration of the adaptive PSP algorithm. A simple closed-form formula is derived to compute the projection onto the intersection of two closed half-spaces defined by a triplet of vectors. Using the formula inductively, the proposed weighting technique realizes a good direction of update. The resulting weights turn out to be pairwise optimal in a certain sense. The proposed algorithm has the inherently parallel structure composed of q primitive functions, hence its total computational complexity O(qrN) is reduced to O(rN) with q concurrent processors (r: a constant positive integer). Numerical examples demonstrate that the proposed technique for r=1 yields significantly faster convergence than not only adaptive PSP with uniform weights, affine projection algorithm, and fast Newton transversal filters but also the regularized recursive least squares algorithm

A numerically stable fast newton-type adaptive filter based on order recursive least squares algorithm

This paper presents a numerically stable fast Newton-type adaptive filter algorithm. Two problems are dealt with in the paper. First, we derive the proposed algorithm from an order-recursive least squares algorithm. The result of the proposed algorithm is equivalent to that of the fast Newton transversal filter (FNTF) algorithm. However, the derivation process is different. Instead of extending a covariance matrix of the input based on the min-max and the max-min criteria, the derivation shown in this paper is to solve an optimum extension problem of the gain vector based on the information of the Mth-order forward or backward predictor. The derivation provides an intuitive explanation of the FNTF algorithm, which may be easier to understand. Second, we present stability analysis of the proposed algorithm using a linear time-variant state-space method. We show that the proposed algorithm has a well-analyzable stability structure, which is indicated by a transition matrix. The eigenvalues of the ensemble average of the transition matrix are proved all to be asymptotically less than unity. This results in a much-improved numerical performance of the proposed algorithm compared with the combination of the stabilized fast recursive least squares (SFRLS) and the FNTF algorithms. Computer simulations implemented by using a finite-precision arithmetic have confirmed the validity of our analysis.

Convergence rate analysis of fast predictor-based least squares algorithm

The numerical stability and convergence rate properties of least mean square (LMS) and recursive least squares (RLS) algorithms have attracted much interest in the literature, however, very few investigations have been reported concerning the fast Newton transversal filter (FNTF) algorithm. The FNTF algorithm spans the range of adaptive algorithms from LMS to RLS and is, therefore, more flexible in implementation. One of the reasons for the lack of analysis of FNTF seems that its derivation is much more complicated since it is based on the min-max principle under the assumption that the input signal is autoregressive of smaller order than that of the filter. Recently, FNTF has been shown to be almost equivalent to the fast predictor-based LS (FPLS) algorithm which is a complexity-reduced version of the PLS algorithm. In this paper, we evaluate the convergence rate of FPLS by considering the eigenvalues of the transition matrix of the state vector and show that the convergence gets slower as the order of the predictor decreases.

The fast subsampled-updating fast Newton transversal filter (FSU FNTF) algorithm for adaptive filtering

The fast Newton transversal filter (FNTF) algorithm starts from the recursive least-squares algorithm for adapting a finite impulse response filter. The FNTF algorithm approximates the Kalman gain by replacing the sample covariance matrix inverse by a banded matrix of total bandwidth 2M+1 (AR(M) assumption for the input signal). In this algorithm, the approximate Kalman gain can still be computed using an exact recursion that involves the prediction parts of two fast transversal filter (FTF) algorithms of order M. We introduce the subsampled updating (SU) approach in which the FNTF filter weights and the Kalman gain are provided at a subsampled rate, say every L samples. Because of its low computational complexity, the prediction part of the FNTF algorithm is kept as such. A Schur type procedure is used to compute various filter outputs at the intermediate time instants, while some products of vectors with Toeplitz matrices are carried out with the FFT. This leads to the fast subsampled-updating FNTF (FSU FNTF) algorithm, an algorithm that is mathematically equivalent to the FNTF algorithm in the sense that exactly the same filter output is produced. However it shows a significantly smaller computational complexity for large filter lengths at the expense of some relatively small delay. The FSU FNTF algorithm (like the FNTF algorithm) has good convergence and tracking properties. This renders the FSU FNTF algorithm very interesting for applications such as acoustic echo cancellation.

Simplified Newton-type adaptive estimation algorithms

A new adaptive estimation algorithm is presented. It is the result of a combination of the LMS and the fast Newton transversal filters (FNTF) class. The main characteristic of the proposed algorithm is its improved convergence rate as compared to LMS, for cases where it is known that LMS behaves poorly. This improved characteristic is achieved in expense of a slight increase in the computational complexity while the overall algorithmic structure is very simple (LMS type). The proposed algorithm seems also to compare relatively well against RLS and FNTF.

A fast Newton multichannel algorithm for decision feedback equalization

Fast Newton transversal filters (FNTF) are a new class of adaptive algorithms unifying NLMS and fast RLS. This is achieved by allowing the algorithm to exploit a priori information about the associated predictors order. This note extends FNTF to the multichannel case and demonstrates the applicability of the resulting algorithm to decision feedback equalization.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The fast Newton transversal filter: an efficient scheme for acoustic echo cancellation in mobile radio

The authors investigate the recently suggested fast Newton family for adaptive filtering in the context of acoustic echo cancellation, with emphasis on the mobile radio case. A distinctive advantage of the fast Newton transversal filter (FNTF) is that it can offer high performance with speech inputs at low computational cost. They discuss possible implementations and compare the FNTF with classical schemes in terms of complexity. A complete numerically stabilized version is presented, and additional features for proper real-time operation with speech are discussed. Experimental comparisons using various signals and real situations show that in all cases, the FNTF behaves similarly to the standard fast RLS transversal filter (FTF) algorithm, whereas its complexity is only slightly higher than that of the normalized LMS (NLMS). Compared with the NLMS, the experiments show that in the context investigated, the latter exhibits inferior performance with respect to convergence and tracking. Thus, they demonstrate that the FNTF is an efficient scheme for acoustic echo cancellation in mobile radio.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>