Decode-and-forward relaying based on orthogonal complementary codes

In this note, we propose a full-duplex decode-and-forward cooperative diversity scheme based on code division with orthogonal complementary codes. We consider a simple case in which a single user is assisted by a single relay to achieve cooperative diversity. When the cooperation is full-duplex, the operational delay of the relay makes the channel asynchronous and this may cause multiple-access interference (MAI) between the user and relay. The orthogonal complementary codes have perfect autocorrelation and cross-correlation properties that provide MAI-free operation in asynchronous channels. In the proposed scheme, the user and relay terminals spread their messages with complementary codes and the spread messages can reach the destination without interfering with each other. The numerical results reveal that the proposed scheme reaches the same bit-error-rate performance in both synchronous and asynchronous channels. The results are also compared with the conventional orthogonal code sets, such as Hadamard sets, which fail to provide diversity.