A New Class of Space-Time Codes via Orthogonal Designs, Circulant Basis, and Kronecker Product

We present a unified algebraic structure of space-time block codes (STBC) with orthogonality called orthogonality-embedded space-time (OEST) codes. Previously known codes, including orthogonal, quasi-orthogonal, semi-orthogonal, and non-orthogonal rate-one circulant space-time codes, are special cases of OEST codes. To construct OEST codes, the generalized complex or real orthogonal designs are employed with two main differences: (1) each data symbol is replaced by a circulant matrix; (2) the scalar product is replaced by the Kronecker product. We show that each group of transmitted symbols embedded in the circulant matrices can be separately detected without any interference from other groups. Signal rotations are used to obtain full diversity and optimal coding gain