Applications of fast QR-decomposition based adaptive algorithms in wireless systems

Mohammed Mobien Mohammad

Research output: ThesisDoctoral ThesisCollection of Articles


This thesis presents four contributions: first, it develops new techniques to extend the range of applications of computationally efficient (comparing to recursive least-squares (RLS) algorithm) fast QR-decomposition least-squares (FQRD-LS) algorithms; second, it develops new version of FQRD-LS algorithm for widely-linear (WL) input signal; third, It presents fixed-point analysis of FQRD-LS algorithm; and finally, it applies contant modulus algorithm (CMA) framework to the inverse QR-decomposition recursive least-squares (QRD-RLS) algorithm. The main idea in the new techniques is to make available the adaptive filter coefficients using the internal variables of the FQRD-RLS algorithm. Four applications that result from using these techniques are: system identification, burst-trained equalization, broad-band beamformation, and predistortion. WL adaptive algorithms are well suited for non-circular input signals, which arises for example in adaptive beamforming scenario when number of sources is greater than the number of antennas. In fixed point analysis of FQRD-LS algorithm we present: mathematical expressions for the mean square quantization error (MSQE) of all internal variables of the FQRD-LS algorithms; and derive the conditions that guarantee the stability of FQRD-LS algorithms for the purpose of fixed-point implementation. Finally, we show how to apply the CMA framework toward inverse QRD-RLS algorithm. We show application of CMA based IQRD-RLS algorithm in blind equalization of an optical channel.
Translated title of the contributionApplications of fast QR-decomposition based adaptive algorithms in wireless systems
Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
  • Wichman, Risto, Supervising Professor
Print ISBNs978-952-60-7458-0
Electronic ISBNs978-952-60-7457-3
Publication statusPublished - 2017
MoE publication typeG5 Doctoral dissertation (article)


  • adaptive filters
  • least-squares
  • fast algorithms
  • weight extraction
  • fixed-point analysis
  • system identification
  • digital beam forming
  • pre-distortion
  • channel equalization


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