The QR-Decomposition Based Least-Squares Lattice Algorithm for Adaptive Filtering

Abstract

We derive, from first principles, the least squares lattice algorithm for adaptive filtering based on the QR decomposition (QRD). In common with other lattice algorithms for adaptive filtering, this algorithm only requires O(p) operations for the solution of a p-th order problem. The algorithm has as its root the QRD-based recursive least squares minimisation algorithm and hence is expected to have superior numerical properties when compared with other fast algorithms. This algorithm contains within the QRD-based algorithm for solving the least squares linear prediction problem. These algorithms are presented in two forms: one that involves taking square-roots and one that does not. Some computer simulations of a channel equaliser, using finite-precision arithmetic, are presented in which the lattice algorithms are compared to the more established triangular systolic array ones. The relationship between the QRD- based lattice algorithms and other least square lattice algorithms is briefly discussed. Various extensions to this work are discussed including the multi- channel QRD-based adaptive filtering algorithm that can be used for a wide-band beamforming. Keywords: Great Britain, Digital signal processing.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1990
Accession Number
ADA229790

Entities

People

  • I. K. Proudler
  • J. G. Mcwhirter

Organizations

  • Royal Signals and Radar Establishment

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Adaptive Filters
  • Algorithms
  • Arithmetic
  • Computations
  • Computer Simulations
  • Computers
  • Digital Signal Processing
  • Eigenvalues
  • Equations
  • Floating Point Operations
  • Mathematics
  • Numerical Analysis
  • Probability Distributions
  • Random Variables
  • Simulations
  • Square Roots
  • Two Dimensional

Fields of Study

  • Engineering

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Linear Algebra
  • Phased Array Antenna Design.