Multiple-Symbol Differential Sphere Detection and Decision-Feedback Differential Detection Conceived for Differential QAM

Abstract

Abstract-Multiple-Symbol Differential Sphere Detection (MS-DSD) 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.

Sixty Years of Coherent Versus Non-Coherent Tradeoffs and the Road From 5G to Wireless Futures

“…In order to mitigate this problem, a dynamic MSDSD algorithm was conceived for DQAM by Xu et al [206] in 2016, where the optimal estimation of a submatrix of the channel correlation matrix is carried out at each step of SD, so that the holistic channel correlation matrix may be recovered, once the SD is terminated. Moreover, the associated DFDD solution becomes equivalent to the optimal MSDD of [42] operating in the decision-feedback mode, which substantially outperforms the previous solutions of [185], [198], [199].…”

Single-RF Index Shift Keying Aided Differential Space–Time Block Coding

“…where the differential encoding of the unitary matrices is also given by (3), while the absolute-amplitude is invoked in the same way as in ADPSK [4]- [6]. More explicitly, γ n−1 in X n−1 = γ n−1 X n−1 of (32) , and then thanks to the normalization of 1 Γn−1 in (32), the transmitted ring-amplitudes always assume the absolute-amplitude of Γ n = γ n−1 .…”

“…In Single-Input Single-Output (SISO) channels, Differential Phase Shift Keying (DPSK) [1], [2], Differential Amplitude Phase Shift Keying (DAPSK) [3]- [5] and Absolute-amplitude Differential Phase Shift Keying (ADPSK) [4]- [6] constitute low-complexity alternatives to coherent PSK/QAM schemes. In Multiple-Input Multiple-Output (MIMO) channels, Differential Space-Time Modulation (DSTM) that dispenses with high-complexity channel estimation has also attracted substantial research interests.…”

Regularized WDFDC Receivers for Selective Detect-and-Forward Multi-Relaying Systems

“…The linear-prediction DFDC receiver of [21] has the additional benefit of maintaining good performance in the presence of frequency offsets. The DFDC receiver was also considered for differential quadrature amplitude modulation (DQAM) [22]. In [23], iterative decoding techniques based on DFDC detection were applied to massive MIMO system.…”