Achieving maximum spatial diversity with decouple-and-forward relaying in dual-hop OSTBC transmissions

In this letter, we prove that decouple-and-forward (DCF) relaying for dual-hop orthogonal space-time block code (OSTBC) transmissions achieves the maximum diversity order attainable by dual-hop MIMO relaying systems. Decoupling at the relay transforms received OSTBC signals into independent and maximal-ratio combined single-input single-output (SISO) signals, which provides the receive diversity gain, and also enables the relay to use OSTBCs again so as to achieve the transmit diversity gain. In obtaining the diversity order, DCF relaying needs a coherence interval of the length of OSTBC transmissions, which is shorter than the requirement assumed in other works that provide the maximum diversity. Numerical results are also presented to verify the proof and give an insight to the relationship between the diversity order and antenna configurations.