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.