Reduced-Complexity Soft-Decision Multiple-Symbol Differential Sphere Detection

Unlike a generic PSK/QAM detector, which may visit a constellation diagram only once, a depth-first Sphere Decoder (SD) has to re-visit the same constellation diagram multiple times. Therefore, in order to prevent the SD from repeating the detection operations, the Schnorr-Euchner search strategy of Schnorr and Euchner may be invoked for optimizing the nodes\´ search-order, where the ideal case is for the SD to visit the constellation nodes in a zigzag fashion. However, when the hard-decision Multiple-Symbol Differential Sphere Detection (MSDSD) of Lampe et al. is invoked for using multiple receive antennas , the Schnorr-Euchner search strategy has to visit and sort all the constellation points. A similar situation is encountered for the soft-decision MSDSD of Pauli et al., when the a priori LLRs gleaned from the channel decoder are taken into account. In order to tackle these open problems, in this paper, we propose a correlation process for the hard-decision MSDSD of Lampe et al. and a reduced-complexity design for the soft-decision MSDSD of Pauli et al., so that the Schnorr-Euchner search strategy always opts for visiting the constellation points in a zigzag fashion. Our simulation results demonstrate that a substantial complexity reduction is achieved by our reduced-complexity design without imposing any performance loss. Explicitly, up to 88.7% complexity reduction is attained for MSDSD aided D16PSK. This complexity reduction is quite substantial, especially when the MSDSD is invoked several times- during turbo detection. Furthermore, in order to offer an improved solution and a comprehensive study for the soft-decision MSDSD, we also propose to modify the output of the SD to harmonize its operation with the near-optimum Approx-Log-MAP. Then the important subject of coherent versus noncoherent is discussed in the context of coded systems, which suggests that MSDSD aided DPSK is an eminently suitable candidate for turbo detection assisted coded systems operating at high Doppler frequencies.