Multiple-symbol differential detection for MPSK space-time block codes: Decision metric and performance analysis

Chunjun Gao, Alexander M. Haimovich, Debang Lao

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


Approximately 3 dB signal-to-noise ratio (SNR) loss is always paid with conventional differential space-time block codes (STBCs), compared with coherent STBCs. In this paper, a multiple-symbol differential detection (MSDD) technique is proposed for M-ary phase-shift keying (PSK) STBCs. The new scheme can greatly narrow the 3-dB performance gap by extending the observation interval for differential decoding. The technique uses maximum-likelihood sequence detection instead of traditional symbol-by-symbol detection, and is carried out on the slow, flat Rayleigh fading channel. A generalized decision metric is derived for an observation interval of arbitrary length. It is shown that for a moderate number of symbols, MSDD provides approximately 1.5 dB performance improvement over conventional differential detection. In addition, a closed-form pairwise error probability and approximate bit-error probability (BEP) are derived for multiple-symbol differential binary PSK STBC. Results show that the theoretical BEP matches simulation results well. The BEP is shown to converge asymptotically with the number of symbols in the observation interval to that of the differential scheme with coherent detection.

Original languageEnglish (US)
Pages (from-to)1502-1510
Number of pages9
JournalIEEE Transactions on Communications
Issue number8
StatePublished - Aug 2006

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


  • Bit-error rate (BER)
  • Decision metric
  • Multiple-symbol differential detection (MSDD)
  • Pairwise error probability (PEP)
  • Space-time block code (STBC)


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