Equivalent codes and optimality of orthogonal space-time block codes

An equivalent model of a multiple-input multiple-output (MIMO) communication system with orthogonal space-time block coding (OSTBC) is proposed based on a newly found connection between OSTBCs and Euclidian codes. A new asymptotic upper bound on the symbol error rate (SER) of OSTBC, which is based on distance spectra of the introduced equivalent Euclidian codes, is derived. Based on this upper bound, new general design criteria for OSTBCs are proposed. Some bounds relating distance properties, dimensionality, and cardinality of OSTBCs with constituent signals of equal energy are given, and a new optimal signal constellation for the Alamouti code with cardinality M = 8 is designed.