  An equivalent model for a multi-input multi-output (MIMO) communication
system with orthogonal space-time block codes (OSTBCs) is proposed based on a
newly revealed connection between OSTBCs and Euclidean codes. Examples of
distance spectra, signal constellations, and signal coordinate diagrams of
Euclidean codes equivalent to simplest OSTBCs are given. A new asymptotic upper
bound for the symbol error rate (SER) of OSTBCs, based on the distance spectra
of the introduced equivalent Euclidean codes is derived, and new general design
criteria for signal constellations of the optimal OSTBC are proposed. Some
bounds relating distance properties, dimensionality, and cardinality of OSTBCs
with constituent signals of equal energy are given, and new optimal signal
constellations with cardinalities M = 8 and M = 16 for Alamouti's code are
designed. Using the new model for MIMO communication systems with OSTBCs, a
general methodology for performance analysis of OSTBCs is developed. As an
example of the application of this methodology, an exact evaluation of the SER
of any OSTBC is given. Namely, a new expression for the SER of Alamouti's OSTBC
with binary phase shift keying (BPSK) signals is derived.
