Efficient fast recursive least-squares adaptive complex filtering using real valued arithmetic

  • Authors:

  • George-Othon Glentis

  • Affiliations:

  • Technological Education Institute of Crete, Branch at Chania, Department of Electronics, Halepa, Chania, Greece

  • Venue:
  • Signal Processing
  • Year:
  • 2005

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Abstract

In this paper, a novel implementation of the fast recursive least squares (FRLS) algorithm for complex adaptive filtering, is presented. Complex signals are treated as pairs of real signals, and operations are re-organized on a real arithmetic basis. A new set of signals and filtering parameters is introduced, which are expressed either as the sum, or as the difference between the real and the imaginary part of the original variables. The algorithmic strength reduction technique is subsequently applied, resulting in significant computational savings. In this way, an efficient, FRLS algorithm is derived, where only two real valued filters are propagated, based on novel three-terms recursions for the time updating of the pertinent parameters. The proposed algorithm is implemented using real valued arithmetic only, whilst reducing the number of the required real valued multiplication operations by 23.5%, at the expense of a marginal 2.9% increase in the number of the real valued additions. The performance of the proposed FRLS algorithm is investigated by computer simulations, in the context of adaptive system identification and adaptive channel equalization.