Asymptotic coded BER analysis for MIMO BICM-ID with quantized extrinsic LLR

I. Wei Lai*, Chien Yi Wang, Tzi Dar Chiueh, Gerd Ascheid, Heinrich Meyr

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In this paper, we derive a closed-form expression for the probability density/mass function (PDF/PMF) and the moment generating function (MGF) of the quantized detector soft output, i.e., extrinsic log-likelihood ratio (LLR), for multiple-input multiple-output (MIMO) bit-interleaved coded modulation with iterative decoding (BICM-ID) systems. The effect of either LLR clipping or LLR clipping with rounding, often applied in practical implementations, are considered. Using the derived expression, we analyze the asymptotic coded bit error rate (BER) for MIMO BICM-ID systems with the two quantization operations under a flat Rayleigh fading channel. The error rate degradation caused by quantizing the extrinsic LLR is then interpreted as an additional signal-to-noise ratio (SNR) loss. Rather than Monte Carlo simulations, this theoretical treatment provides a more convenient alternative to determining the clipping level and optimal word-length (the number of bits needed to represent signals) for LLR in a BICM-ID implementation. Finally, several other applications of this proposed theoretical analysis are also demonstrated.

Original languageEnglish
Article number6253203
Pages (from-to)2820-2828
Number of pages9
JournalIEEE Transactions on Communications
Issue number10
Publication statusPublished - 2012
Externally publishedYes


  • Bit-interleaved coded modulation (BICM)
  • Bit-interleaved coded modulation with iterative decoding (BICM-ID)
  • design space exploration
  • error rate analysis
  • fixed-point arithmetic
  • iterative receiver
  • LLR clipping
  • multiple-input multiple-output (MIMO)
  • quantization
  • rounding
  • sphere decoder

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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