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 PSK (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 QAM (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. In order to tackle this open problem, in this paper, we propose to determine the MSDD’s non-constant amplitudedependent channel correlation matrix with the aid of a sphere decoder, 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. In order 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 sub-optimal and 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