Efficient Quatenion-Based Fast-Decodable Space Time Codes

Abstract:
Design of a low-complexity optimal decoder for quaternion orthogonal designs (QODs) bas been an open research problem. In this paper, we identify the main issue with the conventional maximum-likelihood (ML) decoder based on quaternion-norm that obstructs the existence of decoupled decoding at the receiver. An optimal decoder which has both characteristics, i.e., linear and decoupled, is found using transmit precoding to realize an effective channel at the receiver that simpllfies the criterion and ultimately leads to a low-complexity decoder for all QODs. Tbe proposed solution is then successfully applied to a wide range of quaternion designs where the conventional ML decoder fails to provide decoupled decoding. Simulation results of these designs validate the optimality of the proposed generalized decoder. Overall, the bit error rate (BER) curves exhibit the trend of diversity-multiplexing tradeoff, i.e., the coded matrices of low code rate outperform the ones of higher code rate in terms of diversity.