Multiple Symbol Differential Sphere Detection and Decision Feedback Differential Detection Conceived for Differential QAM
Multiple symbol differential sphere detection (MSDSD) relies on the knowledge of channel correlation. More explicitly, for differential phase shift keying (DPSK) the transmitted symbols' phases form a unitary matrix, which can be separated from the channel's correlation matrix by the classic multiple symbol differential detection (MSDD) so that a lower triangular matrix extracted from the inverted channel correlation matrix is utilized for the MSDSD's sphere decoding. However, for differential quadrature amplitude modulation (DQAM) the transmitted symbols' amplitudes cannot form a unitary matrix, which implies that the MSDD's channel correlation matrix becomes amplitude dependent and remains unknown unless all the data carrying symbol amplitudes are detected. To tackle this open problem, in this paper, we propose to determine the MSDD's nonconstant amplitude dependent channel correlation matrix with the aid of a sphere decoder (SD) so that the classic MSDSD algorithms that were originally conceived for DPSK may also be invoked for DQAM detection. As a result, our simulation results demonstrate that the MSDSD aided DQAM schemes substantially outperform their DPSK counterparts. However, the price paid is that the detection complexity of MSDSD is also significantly increased. To mitigate this, we then propose a reduced complexity MSDSD search strategy specifically conceived for DQAM constellations, which separately map bits to their ring amplitude index and phase index. Furthermore, the classic decision feedback differential detection (DFDD) conceived for DQAM relies on a constant channel correlation matrix, which implies that these DFDD solutions are suboptimal and that they are not equivalent to the optimum MSDD operating in decision feedback mode. With the advent for solving the open problem of MSDSD aided DQAM, we further propose to improve the conventional DFDD aided DQAM solutions in this paper.
IEEE Transactions on Vehicular Technology