Adaptive reduced-rank constrained constant modulus algorithms based on joint iterative optimization of filters for beamforming

Lei Wang, Rodrigo C. De Lamare, Masahiro Yukawa

Research output: Contribution to journalArticle

21 Citations (Scopus)


This paper proposes a robust reduced-rank scheme for adaptive beamforming based on joint iterative optimization (JIO) of adaptive filters. The novel scheme is designed according to the constant modulus (CM) criterion subject to different constraints. The proposed scheme consists of a bank of full-rank adaptive filters that forms the transformation matrix, and an adaptive reduced-rank filter that operates at the output of the bank of filters to estimate the desired signal. We describe the proposed scheme for both the direct-form processor (DFP) and the generalized sidelobe canceller (GSC) structures. For each structure, we derive stochastic gradient (SG) and recursive least squares (RLS) algorithms for its adaptive implementation. The GramSchmidt (GS) technique is applied to the adaptive algorithms for reformulating the transformation matrix and improving the performance. An automatic rank selection technique is developed and employed to determine the most adequate rank for the derived algorithms. A detailed complexity study and a convexity analysis are carried out. Simulation results show that the proposed algorithms outperform the existing full-rank and reduced-rank methods in convergence and tracking performance.

Original languageEnglish
Article number5419962
Pages (from-to)2983-2997
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number6
Publication statusPublished - 2010 Jun 1



  • Antenna array
  • Beamforming
  • Constrained constant modulus
  • Reduced-rank

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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