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Multi-dimensional spatial modulation is a multipleinput/ multiple-output wireless transmission technique, that uses only a few active antennas simultaneously. The computational complexity of the optimal maximum-likelihood (ML) detector at the receiver increases rapidly as more transmit antennas or larger modulation orders are employed. ML detection may be infeasible for higher bit rates. Many suboptimal detection algorithms for spatial modulation use two-stage detection schemes where the set of active antennas is detected in the first stage and the transmitted symbols in the second stage. Typically, these detection schemes use the ML strategy for the symbol detection. In this work, we consider a suboptimal detection algorithm for the second detection stage. This approach combines equalization and list decoding. We propose an algorithm for multi-dimensional signal constellations with a reduced search space in the second detection stage through set partitioning. In particular, we derive a set partitioning from the properties of Hurwitz integers. Simulation results demonstrate that the new algorithm achieves near-ML performance. It significantly reduces the complexity when compared with conventional two-stage detection schemes. Multi-dimensional constellations in combination with suboptimal detection can even outperform conventional signal constellations in combination with ML detection.
This work proposes a suboptimal detection algorithm for generalized multistream spatial modulation. Many suboptimal detection algorithms for spatial modulation use two-stage detection schemes where the set of active antennas is detected in the first stage and the transmitted symbols in the second stage. For multistream spatial modulation with large signal constellations the second detection step typically dominates the detection complexity. With the proposed detection scheme, the modified Gaussian approximation method is used for detecting the antenna pattern. In order to reduce the complexity for detecting the signal points, we propose a combined equalization and list decoding approach. Simulation results demonstrate that the new algorithm achieves near-maximum-likelihood performance with small list sizes. It significantly reduces the complexity when compared with conventional two-stage detection schemes.
Four-Dimensional Hurwitz Signal Constellations, Set Partitioning, Detection, and Multilevel Coding
(2021)
The Hurwitz lattice provides the densest four-dimensional packing. This fact has motivated research on four-dimensional Hurwitz signal constellations for optical and wireless communications. This work presents a new algebraic construction of finite sets of Hurwitz integers that is inherently accompanied by a respective modulo operation. These signal constellations are investigated for transmission over the additive white Gaussian noise (AWGN) channel. It is shown that these signal constellations have a better constellation figure of merit and hence a better asymptotic performance over an AWGN channel when compared with conventional signal constellations with algebraic structure, e.g., two-dimensional Gaussian-integer constellations or four-dimensional Lipschitz-integer constellations. We introduce two concepts for set partitioning of the Hurwitz integers. The first method is useful to reduce the computational complexity of the symbol detection. This suboptimum detection approach achieves near-maximum-likelihood performance. In the second case, the partitioning exploits the algebraic structure of the Hurwitz signal constellations. We partition the Hurwitz integers into additive subgroups in a manner that the minimum Euclidean distance of each subgroup is larger than in the original set. This enables multilevel code constructions for the new signal constellations.