On orthogonal space-time block codes and transceiver signal linearization

We present a necessary and sufficient condition for any orthogonal space-time block code (STBC) to allow transceiver signal linearization (as in the well-known case of the Alamouti scheme). Then, we show that all square orthogonal STBC's that satisfy the condition have rate that goes to zero linearly with the number of transmit antennas. Hence, multiple-antenna systems with orthogonal STBC's and satisfactory rate are possible only if we abandon the linearization property or utilize non-square codes (except for the 2 x 2 Alamouti code).