Nearest neighbor decoding in MIMO block-fading channels with imperfect CSIR

A. Taufiq Asyhari, Albert Guillén I Fàbregas

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


This paper studies communication outages in multiple-input multiple-output (MIMO) block-fading channels with imperfect channel state information at the receiver (CSIR). Using mismatched decoding error exponents, we prove the achievability of the generalized outage probability, the probability that the generalized mutual information (GMI) is less than the data rate, and show that this probability is the fundamental limit for independent and identically distributed (i.i.d.) codebooks. Then, using nearest neighbor decoding, we study the generalized outage probability in the high signal-to-noise ratio (SNR) regime for random codes with Gaussian and discrete signal constellations. In particular, we study the SNR exponent, which is defined as the high-SNR slope of the error probability curve on a logarithmic-logarithmic scale. We show that the maximum achievable SNR exponent of the imperfect CSIR case is given by the SNR exponent of the perfect CSIR case times the minimum of one and the channel estimation error diversity. Random codes with Gaussian constellations achieve the optimal SNR exponent with finite block length as long as the block length is larger than a threshold. On the other hand, random codes with discrete constellations achieve the optimal SNR exponent with block length growing with the logarithm of the SNR. The results hold for many fading distributions, including Rayleigh, Rician, Nakagami-m, Nakagami-q and Weibull as well as for optical wireless scintillation distributions such as lognormal-Rice and gamma-gamma.

Original languageEnglish
Article number6157055
Pages (from-to)1483-1517
Number of pages35
JournalIEEE Transactions on Information Theory
Issue number3
Publication statusPublished - 27 Feb 2012
Externally publishedYes


  • Block-fading channels
  • channel state information
  • diversity
  • error exponent
  • generalized mutual information (GMI)
  • imperfect channel state information
  • MIMO
  • multiple antenna
  • nearest neighbor decoding
  • outage probability
  • SNR exponent

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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