Alamouti scheme´s generalization

The Orthogonal spacetime block code proposed by Alamouti [1], which is a promising scheme for information transmission over Rayleigh-fading channels using two transmit antennas due to its favorable characteristics of having full transmit diversity, full rate and a simple maximum-likelihood (ML) decoding algorithm, motivates searches for similar schemes using more than two transmit antennas. Many authors extended the theory of classical orthogonal designs to the theory of generalized, real, or complex orthogonal designs and then applied it to construct spacetime block codes (STBCs) with the maximum possible diversity order while having a simple decoding algorithm for any given number of transmit and receive antennas. These codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as PAM. Unfortunatly, for any arbitrary complex constellation such as PSK and QAM, spacetime block codes were penelized by a rate strictly inferior to one for transmission with more than two antennas. In this correspondence we study the Alamouti code and its generalization, for both real and complex constellations, for any number of transmit antennas.