Geometrical properties of orthogonal space-time codes

We discuss the geometrical properties of a transmission scheme with orthogonal space-time codes. In particular, we show that the transmission channel can be interpreted as the rotation of a vector of transmit symbols in an Euclidean space, together with an attenuation and additive noise. We show that the receiver - as intuitively obvious - essentially has to perform a back-rotation. This geometrical interpretation applies to real vector spaces of signals, i.e., the complex transmit and receive symbols have to be split up into their real and imaginary parts.