Euclidean and Space–Time Block Codes: Relationship, Optimality, Performance Analysis Revisited

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