Low complexity distributed STBCs with unitary relay matrices for any number of relays

Jing and Hassibi introduced a distributed space time block coding scheme for symbol synchronous, coherent, amplify and forward relay networks with half duplex constrained relay nodes. In this two phase transmission scheme, the source transmits a vector of complex symbols to the relays during the first phase and each relay applies a pre-assigned unitary transformation to the received vector or its conjugate before transmitting it to the destination during the second phase. The destination then perceives a certain structured distributed space time block code (DSTBC) whose maximum likelihood (ML) decoding complexity in general, is very high. In this paper, explicit constructions of minimum delay, full diversity, four group ML decodable DSTBCs with unitary relay matrices are provided for even number of relay nodes. Prior constructions of DSTBCs with the same features were either limited to power of two number of relay nodes or had non-unitary relay matrices which leads to large peak to average power ratio of the relay's transmitted signals. For the case of odd number of relays, constructions of minimum delay, full diversity, two group ML decodable DSTBCs are given.