  In a distributed space-time coding scheme, based on the relay channel model,
the relay nodes co-operate to linearly process the transmitted signal from the
source and forward them to the destination such that the signal at the
destination appears as a space time block code. Recently, a code design
criteria for achieving full diversity in a partially-coherent environment have
been proposed along with codes based on differential encoding and decoding
techniques. For such a set up, in this paper, a non-differential encoding
technique and construction of distributed space time block codes from unitary
matrix groups at the source and a set of diagonal unitary matrices for the
relays are proposed. It is shown that, the performance of our scheme is
independent of the choice of unitary matrices at the relays. When the group is
cyclic, a necessary and sufficient condition on the generator of the cyclic
group to achieve full diversity and to minimize the pairwise error probability
is proved. Various choices on the generator of cyclic group to reduce the ML
decoding complexity at the destination is presented. It is also shown that, at
the source, if non-cyclic abelian unitary matrix groups are used, then
full-diversity can not be obtained. The presented scheme is also robust to
failure of any subset of relay nodes.
