Non-Differential DSTBCs for Partially-Coherent Cooperative Communication

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, wherein the destination has the knowledge of channels from the relays to itself, but not the channels from the source to the relays, 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 (a set of diagonal unitary matrices forming a group) 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. It is also shown that, at the source, if non-cyclic abelian unitary matrix groups are used, then full-diversity can not be obtained.