Differential feedback of geometrical mean decomposition precoder for time-correlated MIMO systems

Hung Chun Chen, Yuan-Pei Lin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


For a time-correlated channel, we consider the differential feedback of the geometrical mean decomposition (GMD) precoder, which is known to be optimal for a number of criteria. When the channel varies slowly, we can expect the optimal GMD precoders of consecutive channel uses to be close. We consider the feedback of the so-called differential precoder and show that it lies in a neighborhood of the identity matrix using matrix perturbation theory. Furthermore, the radius of the neighborhood is shown to be proportional to a time-correlation parameter. Such a characterization allows for subsequent efficient quantization of the differential precoder.We show how to design codewords for the prescribed radius by perturbing the identity matrix and applying QR decomposition on the perturbed matrix. Simulations are given to demonstrate that, with a small feedback rate, the performance of the proposed differential GMD comes close to the case when perfect channel state information is available to the transmitter for slowly time-varying channels like those in indoor andmicrocellular environments.

Original languageEnglish
Article number7895158
Pages (from-to)3833-3845
Number of pages13
JournalIEEE Transactions on Signal Processing
Issue number14
StatePublished - 15 Jul 2017


  • Differential feedback
  • Geometrical mean decomposition (GMD)
  • GMD precoder
  • Limited feedback
  • MIMO

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