On orthogonal designs and space-time codes

Francis Lu*, P. Vijay Kumar, Habong Chung

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

12 Scopus citations


Orthogonal-design-based space-time (ODST) codes of size (n × n) offer maximum diversity gain advantage and a simple yet optimal decoding algorithm under an arbitrary signal alphabet or constellation A. However, these designs only exist for n = 2, 4, 8 when A is real and for n = 2 when A is complex. In this letter, we address the question of the existence of ODST codes of other sizes when A is restricted to be a proper subset of either real or complex numbers. We refer to these as restricted-alphabet ODST (RA-ODST) codes. We show that real RA-ODST codes of size greater than 8 that also guarantee maximum diversity advantage do not exist. Without the diversity requirement, RA-ODST codes exist only when A = {a, -a}, 0 < a ∈ ℝ. Examples of such codes are provided. In the complex case, under the added requirement of maximum diversity advantage, we prove the nonexistence of complex RA-ODST codes under fairly simple assumptions regarding the signal alphabet.

Original languageEnglish
Pages (from-to)220-222
Number of pages3
JournalIEEE Communications Letters
Issue number4
StatePublished - 1 Apr 2004
Event2002 IEEE International Symposium on Information Theory - Lausanne, Switzerland
Duration: 30 Jun 20025 Jul 2002


  • Fading channel
  • Multi-input-multi-output (MIMO) systems

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