Mean-square-error optimality of orthogonal space-time block codes

Linear space-time block coding (STBC) is a conceptually simple transmission technique for channels with multiple transmit and receive antennas. In this letter, we study a subclass of linear STBC, namely orthogonal STBC (OSTBC), with the primary goal of contributing toward a complete understanding of OSTBC. In particular, we prove that OSTBC is optimal in a minimum mean-square-error (mse) sense, provided that a zero-forcing detector is used at the receiver. As a by-product, we also obtain a concise characterization of linear and orthogonal STBCs as well as the relationship between them. The ruse optimality of OSTBC shown in this letter can be used as a way of introducing this coding scheme from first principles.