QR-decomposition-based Least-squares Lattice Research Articles

Reduced Complexity Solution for Weight Extraction in QRD-LSL Algorithms

QR-decomposition-based least-squares lattice (QRD-LSL) algorithms do not provide the transversal weight vector in explicit form. These weights can be computed from the variables of the QRD-LSL algorithm using the Levinson-Durbin (LD) recursion. If the prediction coefficients do not vary over time, a reduced complexity but approximate solution can be obtained. Nonetheless, this approximate solution requires algorithm convergence and infinite memory support (forgetting factor equal to one). To obtain the exact weights at any time instant and for any choice of the forgetting factor, the computational complexity of the true LD recursion increases by an order of magnitude. In this letter, we show that an exact solution can be obtained with a reduced computational complexity and without any added restriction. Simulation results show that the solutions obtained using the proposed method and the exact LD recursion are the same up to the precision used, whereas the weights from the approximate method always deviate from the true solution.

Narrow-band interference rejection in ds/cdma systems using adaptive (qrd-lsl)-based nonlinear acm interpolators

An Mth order adaptive lattice filter automatically generates all M of the outputs that would be provided by M separate transversal filters. This feature may effectively suppress narrow-band interference (NBI) of either unknown or time-varying bandwidth (or number of frequency bands) in direct-sequence code-division multiple access systems for which the order of the interference rejection filter that achieves the optimal performance is unknown or constantly changing. Moreover, a lattice filter may significantly outperform its transversal counterpart in complex jamming environments in which the adaptive lattice filter must suppress multiple jammers, since each stage of a lattice filter adapts to suppress an orthogonal component of the NBI. The paper develops a computationally efficient and numerically stable adaptive QR-decomposition-based least squares lattice (QRD-LSL)-based nonlinear approximate conditional mean interpolator to suppress NBI effectively. Simulation results demonstrate that both the signal-to-noise ratio improvement and the convergence rate achieved by the proposed interpolators outperform those of other existing prediction-based techniques.

Narrow-band interference rejection in DS/CDMA systems using adaptive (QRD-LSL)-based nonlinear ACM interpolators

An Mth order adaptive lattice filter automatically generates all M of the outputs that would be provided by M separate transversal filters. This feature may effectively suppress narrow-band interference (NBI) of either unknown or time-varying bandwidth (or number of frequency bands) in direct-sequence code-division multiple access systems for which the order of the interference rejection filter that achieves the optimal performance is unknown or constantly changing. Moreover, a lattice filter may significantly outperform its transversal counterpart in complex jamming environments in which the adaptive lattice filter must suppress multiple jammers, since each stage of a lattice filter adapts to suppress an orthogonal component of the NBI. The paper develops a computationally efficient and numerically stable adaptive QR-decomposition-based least squares lattice (QRD-LSL)-based nonlinear approximate conditional mean interpolator to suppress NBI effectively. Simulation results demonstrate that both the signal-to-noise ratio improvement and the convergence rate achieved by the proposed interpolators outperform those of other existing prediction-based techniques.

QR-decomposition-based least-squares lattice interpolators

QR-decomposition-based least-squares lattice (QRD-LSL) predictors have been extensively applied in the design of order-recursive adaptive filters. This work presents QRD-LSL interpolators that use both past and future data samples to estimate the present data sample based on a novel decoupling property. We show that the order-recursive QRD-LSL interpolators display better numerical properties and achieve a higher level of computational efficiency than the conventional LSL interpolators. Except for an overall delay needed for physical realization, QRD-LSL interpolators can substantially outperform QRD-LSL predictors while retaining all the desirable features of the latter.

A modified QRD for smoothing and a QRD-LSL smoothing algorithm

This paper introduces a modified QR-decomposition (QRD) that extends the method of QRD to a more general case to solve the least-squares lattice smoothing problems. We show that the conventional QRD is a special form of the modified QRD that occurs when no future data values are used. Within the framework of the modified QRD procedure, an order-recursive QRD based least-squares lattice (QRD-LSL) smoothing algorithm is formulated. The algorithm combines all the desirable features of the standard QRD-LSL filtering algorithm with a more accurate smoothing process. The results of some computer simulations of a channel equalizer are also presented.

A state-space approach to adaptive RLS filtering

Adaptive filtering algorithms fall into four main groups: recursive least squares (RLS) algorithms and the corresponding fast versions; QR- and inverse QR-least squares algorithms; least squares lattice (LSL) and QR decomposition-based least squares lattice (QRD-LSL) algorithms; and gradient-based algorithms such as the least-mean square (LMS) algorithm. Our purpose in this article is to present yet another approach, for the sake of achieving two important goals. The first one is to show how several different variants of the recursive least-squares algorithm can be directly related to the widely studied Kalman filtering problem of estimation and control. Our second important goal is to present all the different versions of the RLS algorithm in computationally convenient square-root forms: a prearray of numbers has to be triangularized by a rotation, or a sequence of elementary rotations, in order to yield a postarray of numbers. The quantities needed to form the next prearray can then be read off from the entries of the postarray, and the procedure can be repeated; the explicit forms of the rotation matrices are not needed in most cases.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>