An Analysis of Gauss Elimination for Adaptive Beamforming.

Abstract

There are many formulations of the Adaptive Beamforming (ABF) problem. We are motivated to use an algorithm that uses the least number of divisions or square root operations, since these operations are very expensive in time or chip area. One method solves the solution of a Hermitian matrix. The Gauss Elimination (GE) algorithm has no square roots. In this paper, we analyze dynamic range requirements and precision analysis for an integer processor implementation of GE (as opposed to fixed point or floating point), to solve the ABF problem. This analysis differs from the standard Wilkinson analysis which is based on fixed point arithmetic, where the multiplier is formed once per row, whereas the integer formulation requires that we perform explicit divisions on each element of the reduced matrix. We present formulas to determine input quantization, storage wordlengths and accumulator wordlengths for a desired weight precision.

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Document Details

Document Type
Technical Report
Publication Date
Aug 09, 1994
Accession Number
ADA298992

Entities

People

  • Barry J. Kirsch
  • Peter R. Turner

Organizations

  • Naval Air Warfare Center Aircraft Divison

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accumulators
  • Aircrafts
  • Algorithms
  • Arithmetic
  • Cross Correlation
  • Dynamic Range
  • Elimination
  • Engineering
  • Error Analysis
  • Growth Factors
  • Linear Systems
  • Mathematics
  • Numbering Systems
  • Numbers
  • Precision
  • Square Roots
  • Standards

Fields of Study

  • Engineering

Readers

  • Linear Algebra
  • Phased Array Antenna Design.