Decoding of Differential OSTBC with Non-Unitary Constellations Using Multiple Received Data Blocks

In this paper, we propose a maximum likelihood~(ML) decoder for differentially encoded orthogonal space-time block codes (OSTBCs) based on multiple received data blocks. The proposed ML decoder differs from the existing ML decoders of differential OSTBC as follows: 1) Most existing ML decoders are derived on the basis of \emph{two} consecutively received data matrices, whereas the proposed decoder takes \emph{multiple} consecutively received data matrices into account. 2) One existing ML decoder considers multiple consecutively received specific differential OSTBC using \emph{two} transmit antennas and is applicable to $M$-PSK constellation only, whereas the proposed ML decoder works with arbitrary differential OSTBCs using arbitrary number of transmit and receive antennas and arbitrary constellations which do not include zero. We have also derived an upper bound of the pairwise error probability (PEP) of the proposed ML decoder for differentially encoded orthogonal STBC (OSTBC) with $M$-QAM constellation over Rayleigh fading channels.