Fast Blind Equalizer Exploiting Statistical Features of Symbol Constellations

Naota Takeyama, Jin Mitsugi

Research output: Contribution to journalArticlepeer-review


This paper proposes a fast blind equalization algorithm realized by equating the higher-order statistics of transmitted and received signals’ IQ constellations over wireless channels. The idea is motivated by the fact that the transmitter and the receiver usually pre-share the modulation scheme, which determines the statistical distribution of the IQ constellation. Conventional blind equalizer algorithms are not practical because these optimize the equalizer coefficients with the gradient descent method demanding from hundreds to thousands of iterations to converge. This paper proposes a dimensionless loss function that can be extended to various modulation schemes and applies the Levenberg-Marquardt (LM) algorithm to regularize the Hessian matrix of the loss function automatically. This regu-larization compensates the singularity of the Hessian matrix which enables fast equalizing. The proposed method is evaluated in a MATLAB simulation to reveal that the algorithm can converge within dozens of iterations, achieving about a hundred times faster convergence and about a 30 times faster computation time than conventional blind equalization. The evaluation also reveals that the cause of the singularity of the Hessian matrix is the eigenvector space of equalizer coefficients which works to amplify inter-symbol-interference.

Original languageEnglish
Pages (from-to)909-916
Number of pages8
JournalJournal of information processing
Publication statusPublished - 2022


  • adaptive signal processing
  • blind equalization
  • kurtosis
  • Levenberg-Marquardt algorithm

ASJC Scopus subject areas

  • Computer Science(all)


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