Quantifying the power loss when transmit beamforming relies on finite-rate feedback

Shengli Zhou, Zhengdao Wang, Georgios B. Giannakis

Research output: Contribution to journalArticle

170 Scopus citations


Transmit beamforming achieves optimal performance in systems with multiple transmit antennas and a single receive antenna from both the capacity and the received signal-to-noise ratio (SNR) perspectives but ideally requires perfect channel knowledge at the transmitter. In practical systems where the feedback link can only convey a finite number of bits, transmit beamformer designs have been extensively investigated using either the outage probability or the average SNR as the figure of merit. In this paper, we study the symbol error rate (SER) for transmit beamforming with finite-rate feedback in a multi-input single-output setting. We derive an SER lower bound that is tight for good beamformer designs. Comparing this bound with the SER corresponding to the ideal case, we quantify the power loss due to the finite-rate constraint across the entire SNR range.

Original languageEnglish (US)
Pages (from-to)1948-1957
Number of pages10
JournalIEEE Transactions on Wireless Communications
Issue number4
StatePublished - Jul 1 2005


  • Finite-rate feedback
  • Multi-antenna systems
  • Power loss
  • Transmit beamforming

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