Full Diversity Group Decodable Orthogonal Linear Dispersion Codes for MISO Flat Fading Channels

We consider a flat fading wireless link having multiple $M$ transmitter antennas and a single receiver antenna (MISO). This system is often useful in mobile downlink communications for which the mobile receiver may not be able to support multiple antennas. For such a system, we propose a novel and very simple design of full diversity two-group and four-group decodable block diagonal linear dispersion codes with rate one for any number of the transmitter antennas. For $M=2^{n}$ and $M=2^{n}-1$, we also prove that for $K-{\rm ary}$ Quadrature Amplitude Modulation (QAM) transmission equipped with a maximum likelihood (ML) detector, our proposed code minimizes the worst case average pair-wise error probability, i.e., it achieve optimal coding gain.