Constellation space invariance of space-time block codes with application to optimal antenna subset selection

We prove a new constellation space invariance property of space-time block codes (STBC) based on generalized orthogonal designs. In the flat block-fading channel case, it is shown that the internal structure of the vector space of the input constellation remains invariant to the combined effect of the STBC and the channel, except for a scaling factor. Using the established property, we prove that the exact error probability of the maximum likelihood (ML) decoder is a decreasing function of the Frobenius norm of the channel matrix in the general case when the channel, STBC, and input signal constellations are arbitrary. The constellation space invariance property is then applied to the problem of antenna subset selection in multiple-input multiple-output (MIMO) systems. We study the popular norm-based antenna subset selection method which is known to minimize an upper bound on the pairwise probability of error at the output of the ML decoder. The strict optimality of this approach is established by proving that it minimizes the exact probability of error as well.