Inverse Covariance Matrix Estimation for Low-Complexity Closed-Loop DPD Systems: Methods and Performance

Pablo Pascual Campo, Lauri Anttila, Vesa Lampu, Markus Allen, Yan Guo, Neng Wang, Mikko Valkama

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In this article, we study closed-loop digital predistortion (DPD) systems and associated learning algorithms. Specifically, we propose various low-complexity approaches to estimate and manipulate the inverse of the input data covariance matrix (CM) and combine them with the so-called self-orthogonalized (SO) learning rule. The inherent simplicity of the SO algorithm, combined with the proposed solutions, allows for remarkably reduced complexity in the DPD system while maintaining similar linearization performance compared to other state-of-the-art methods. This is demonstrated with thorough over-the-air (OTA) mmW measurement results at 28 GHz, incorporating a state-of-the-art 64-element active antenna array, and very wide channel bandwidths up to 800 MHz. In addition, complexity analyses are carried out, which together with the measured linearization performance demonstrates favorable performance-complexity tradeoffs in linearizing mmW active array transmitters through the proposed solutions. The techniques can find application in systems where the power amplifier (PA) nonlinearities are time-varying and thus frequent or even constant updating of the DPD is required, good examples being mmW adaptive antenna arrays as well as terminal transmitters in 5G and beyond networks.

Original languageEnglish
Pages (from-to)1474-1489
Number of pages16
JournalIEEE Transactions on Microwave Theory and Techniques
Issue number3
Early online date24 Nov 2021
Publication statusPublished - 2022
Publication typeA1 Journal article-refereed


  • Antenna arrays
  • Antenna measurements
  • Array transmitters
  • autocorrelation function
  • Bandwidth
  • Bussgang theorem
  • closed-loop systems
  • Complexity theory
  • covariance matrix (CM)
  • digital predistortion
  • Estimation
  • Gauss-Newton (GN)
  • Mobile handsets
  • parameter learning
  • power amplifier (PA)
  • Predistortion
  • self-orthogonalization.

Publication forum classification

  • Publication forum level 2

ASJC Scopus subject areas

  • Radiation
  • Condensed Matter Physics
  • Electrical and Electronic Engineering


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