Blind Source Separation Algorithms Using Hyperbolic and Givens Rotations for High-Order QAM Constellations

Syed Awais Wahab Shah, Karim Abed-Meraim, Tareq Y. Al-Naffouri*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


This paper addresses the problem of blind demixing of instantaneous mixtures in a multiple-input multiple-output communication system. The main objective is to present efficient blind source separation (BSS) algorithms dedicated to moderate or high-order quadratic-amplitude modulation (QAM) constellations. Four new iterative batch, BSS algorithms are presented dealing with the multimodulus (MM) and alphabet matched (AM) criteria. For the optimization of these cost functions, iterative methods of Givens and hyperbolic rotations are used. A prewhitening operation is also utilized to reduce the complexity of design problem. It is noticed that the designed algorithms using Givens rotations give satisfactory performance only for a large number of samples. However, for a small number of samples, the algorithms designed by combining both Givens and hyperbolic rotations compensate for the ill-whitening that occurs in this case and thus improves the performance. Two algorithms dealing with the MM criterion are presented for moderate-order QAM signals such as 16-QAM. The other two dealing with the AM criterion are presented for high-order QAM signals. These methods are finally compared with the state-of-the-art batch BSS algorithms in terms of signal-to-interference and noise ratio, symbol error rate, and convergence rate. Simulation results show that the proposed methods outperform the contemporary batch BSS algorithms.

Original languageEnglish (US)
Pages (from-to)1802-1816
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number7
StatePublished - Apr 1 2018


  • Alphabet matched algorithm
  • Givens and hyperbolic rotations
  • blind source separation
  • constant modulus algorithm
  • constellation matched error
  • multimodulus algorithm

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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