Equalization techniques for distributed space-time block codes with amplify-and-forward relaying

Hakam Mheidat, Murat Uysal, Naofal Al-Dhahir

Research output: Contribution to journalArticlepeer-review


In this paper, we investigate equalization methods for cooperative diversity schemes over frequency-selective fading channels. Specifically, we consider three equalization schemes proposed originally for conventional space-time block codes (STBC) [1]-[3] and extend them to distributed STBC in a cooperative transmission scenario with amplify-and-forward relaying. The distributed STBC equalization schemes are named after their original counterparts as distributed time-reversal (D-TR) STBC, distributed single-carrier (D-SC) STBC, and distributed orthogonal frequency division multiplexed (D-OFDM) STBC. The underlying orthogonality of distributed STBC results in decoupled data streams at the receiver side allowing low-complexity implementations. Without loss of generality, we consider a single-relay scenario where the source-to-relay S → R, relay-to-destination R → D, and source-to-destination S → D links experience possibly different channel delay spreads. Under the assumption of perfect power control for the relay terminal and high signal-to-noise ratio (SNR) for the underlying links, our performance analysis demonstrates that D-TR-STBC, D-SC-STBC, and coded D-OFDM-STBC schemes are able to achieve a maximum diversity order of min(L1, L3+ L2 + 2 where L1, L2, and L3 are the channel memory lengths for S → R, S → D, and R → D→ links, respectively. This illustrates that the minimum of the multipath diversity orders experienced in S → R and R → D links becomes the performance bottleneck for the relaying path. For the case of a nonfading relaying path where line-of-sight propagation is possible in either one of these underlying links, we demonstrate that diversity orders of L1+L2+2 and L3+L2 +2 are achievable assuming nonfading S → R and R → D links, respectively. An extensive Monte Carlo simulation study is presented to corroborate the analytical results and to provide detailed performance comparisons among the three candidate equalization schemes.

Original languageEnglish (US)
Pages (from-to)1839-1852
Number of pages14
JournalIEEE Transactions on Signal Processing
Issue number5 I
StatePublished - May 2007


  • Cooperative diversity
  • Distributed space-time block coding (STBC)
  • Equalization
  • Fading channels
  • Pairwise error probability

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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