Lattice quantization of phases for equal gain transmission

Shang-Ho Tsai*, Yuan-Pei Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Equal gain transmission (EGT) requires only the feedback of phase information and is known to enjoy several implementational advantages compared to maximum ratio transmission (MRT). This paper investigates the use of lattice quantization for quantizing phases in EGT systems. In practice, the feedback rate is finite and the lattices need to be truncated to have finite code rate. The truncation of lattices results in boundary effect; hence, earlier results developed for untruncated lattices, e.g., fast algorithm and mean-square error (MSE) analysis, cannot be applied directly. Exploiting the fact that the quantized signals are phases, we show how to quantize using truncated lattices so that there is no boundary effect. Moreover, we propose efficient methods to convert between lattice codewords and binary digits so that the lattice quantization can be used in practical systems. Furthermore, the mean-square quantization error is analyzed for several useful truncated lattices. We also show how to analyze the signal-to-noise ratio (SNR) loss when the proposed quantization is applied to an EGT system.

Original languageEnglish
Article number6059518
Pages (from-to)822-833
Number of pages12
JournalIEEE Transactions on Signal Processing
Issue number2
StatePublished - 1 Feb 2012


  • Beamforming
  • EGT
  • equal gain transmission
  • Grassmannian
  • lattice
  • Lloyd
  • phase quantization
  • precoding


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