Constellation space invariance of space-time block codes with application to optimal ML decoding

We prove an interesting property of space-time block codes (STBCs) that are based on generalized orthogonal designs. It is shown that, for flat block-fading channels with an arbitrary number of transmit and receive antennas, the internal structure of the inner product space of the input constellation remains invariant to the combined effect of the STBC and the channel, except for a scaling factor. The established constellation space invariance property sheds a new light on the mechanism of ML decoding of STBCs and, in particular, provides a simple explanation of why the optimal decoding can be reduced to symbol-by-symbol decoding. New simple expressions for the ML decoder are obtained which clarify its intrinsic structure.