Equivalent Codes, Optimality, and Performance Analysis of OSTBC: Textbook Study

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. Index Terms Euclidean codes, group codes, MIMO, optimal constellations, OSTBC, SER, signal coordinate diagrams, spherical codes.