Shrinkage linear and widely linear complex-valued least mean squares algorithms for adaptive beamforming

Yun Mei Shi, Lei Huang, Cheng Qian, H. C. So

Research output: Contribution to journalArticlepeer-review

67 Scopus citations


In this paper, shrinkage linear complex-valued least mean squares (SL-CLMS) and shrinkage widely linear complex-valued least mean squares (SWL-CLMS) algorithms are devised for adaptive beamforming. By exploiting the relationship between the noise-free a posteriori and a priori error signals, the SL-CLMS method is able to provide a variable step size to update the weight vector for the adaptive beamformer, significantly enhancing the convergence speed and decreasing the steady-state misadjustment. On the other hand, besides adopting a variable step size determined by minimizing the square of the augmented noise-free a posteriori errors, the SWL-CLMS approach exploits the noncircular properties of the signal of interest, which considerably improves the steady-state performance. Simulation results are presented to illustrate their superiority over the CLMS, complex-valued normalized LMS, variable step size, recursive least squares (RLS) algorithms and their corresponding widely linear-based schemes. Additionally, our proposed algorithms are more computationally efficient than the RLS solutions though they may have a slightly slower convergence rate.

Original languageEnglish (US)
Article number6963464
Pages (from-to)119-131
Number of pages13
JournalIEEE Transactions on Signal Processing
Issue number1
StatePublished - Jan 1 2015
Externally publishedYes

Bibliographical note

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© 1991-2012 IEEE.


  • Complex-valued least mean squares (CLMS)
  • convergence speed
  • shrinkage
  • steady-state
  • variable step size
  • widely linear


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