Asymptotic Behavior of Zero-Forcing Precoding based on Imperfect Channel Knowledge for Massive MISO FDD Systems

Donia Ben Amor, Michael Joham, Wolfgang Utschick

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


In this work, we study the asymptotic behavior of the zero-forcing precoder based on the least squares (LS) and the linear minimum mean-square error (LMMSE) channel estimates for the downlink (DL) of a frequency-division-duplex (FDD) massive multiple-input-single-output (MISO) system. We show analytically the rather surprising result that zero-forcing precoding based on the LS estimate leads asymptotically to an interference-free transmission, even if the number of pilots used for DL channel training is less than the number of antennas available at the base station (BS). Although the LMMSE channel estimate exhibits a better quality in terms of the MSE due to the exploitation of the channel statistics, we show that in the case of contaminated channel observations, zero-forcing based on the LMMSE is unable to eliminate the inter-user interference in the asymptotic limit of high DL transmit powers. In order for the results to hold, mild conditions on the channel probing phase are assumed. The validity of our analytical results is demonstrated through numerical simulations for different scenarios.

Original languageEnglish
Title of host publicationICC 2023 - IEEE International Conference on Communications
Subtitle of host publicationSustainable Communications for Renaissance
EditorsMichele Zorzi, Meixia Tao, Walid Saad
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781538674628
StatePublished - 2023
Event2023 IEEE International Conference on Communications, ICC 2023 - Rome, Italy
Duration: 28 May 20231 Jun 2023

Publication series

NameIEEE International Conference on Communications
ISSN (Print)1550-3607


Conference2023 IEEE International Conference on Communications, ICC 2023


  • FDD
  • LMMSE channel estimation
  • LS channel estimation
  • Zero-forcing
  • high SNR
  • interference suppression
  • massive MIMO


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