Locally Diverse Constellations from the Special Orthogonal Group

David A. Karpuk, Camilla Hollanti

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)
153 Downloads (Pure)


To optimize rotated multidimensional constellations over a single-input single-output Rayleigh fading channel, a family of rotation matrices is constructed for all dimensions which are a power of 2. This family is a one-parameter subgroup of the group of rotation matrices, and is located using a gradient descent scheme on this Lie group. The parameter defining the family is chosen to optimize the cutoff rate of the constellation. The optimal rotation parameter is computed explicitly for low signal-to-noise ratios. These rotations outperform full-diversity algebraic rotations in terms of cutoff rate at low signal-to-noise ratio (SNR) and bit error rate at high SNR in dimension n = 4. However, a quadrature amplitude modulation (QAM) constellation rotated by such a matrix lacks full diversity, in contrast with the conventional wisdom that good signal sets exhibit full diversity. A new notion of diversity, referred to as local diversity, is introduced to attempt to account for this behavior. Roughly, a locally fully diverse constellation is fully diverse only in small neighborhoods. A local variant of the minimum product distance is also introduced and is shown experimentally to be a superior predictor of constellation performance than the minimum product distance in dimension n = 4.

Original languageEnglish
Article number7433476
Pages (from-to)4426-4437
Number of pages12
JournalIEEE Transactions on Wireless Communications
Issue number6
Publication statusPublished - 1 Jun 2016
MoE publication typeA1 Journal article-refereed


  • capacity
  • cutoff rate
  • full diversity
  • Lie groups
  • non-uniform constellations
  • Rayleigh fading channel
  • rotated constellations


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