An insight into space–time block codes using Hurwitz–Radon families of matrices

It is shown that for four-transmitter systems, a family of four-by-four unit-rate complex quasi-orthogonal space–time block codes, where each entry equals a symbol variable up to a change of sign and/or complex conjugation, can be generated from any two independent codes via elementary operations. The two independent groups of codes in the family generally have different properties of diversity, but the codes in each group have the same diversity provided that the differential symbol constellation is symmetric. It is also shown that for four-transmitter systems, an eight-by-four unit-rate complex linear dispersion space–time block code can be constructed by using Hurwitz–Radon families of matrices of size eight such that diversity three is guaranteed even when all symbols are independently selected from any given constellation. This code is so far the only known unit-rate linear dispersion code that has diversity no less than three for four transmitters under any given constellation.