Communications in Information and Systems

Volume 5 (2005)

Number 1

Construction and analysis of a new quaternionic space-time code for 4 transmit antennas

Pages: 97 – 122



N. Al-Dhahir (University of Texas at Dallas, Texas, U.S.A.)

Robert Calderbank (Princeton University, New Jersey, U.S.A.)

Sushanta Das (University of Texas at Dallas, Texas, U.S.A.)

S. Diggavi (EPFL, Laussane, Switzerland)


We present a novel full-rate full-diversity orthogonal space-time block code for QPSK modulation and 4 transmit antennas based on quaternionic algebra. The code does not result in constellation expansion unlike other full-rate full-diversity codes in the literature. The quaternionic structure of the code is exploited to reduce the complexity of maximum likelihood (ML) coherent decoding from a size-256 search to a size-16 search. Furthermore, we show how to modify this low-complexity coherent ML decoding rule to derive a non-coherent differential ML decoding rule. Due to the orthogonality of the code, ML differential decoding results in the minimum SNR loss of 3 dB from coherent ML decoding. Finally, extensive simulation results in a WiMAX 802.16 broadband wireless access environment demonstrate that the proposed code increases the cell coverage area by 1.5 and 2.6 folds compared to single-antenna transmission at $10^{−3}$ bit error rate when combined with 1 and 2 receive antenna(s), respectively.

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