Low-Complexity Detection for Multi-Dimensional Spatial Modulation Schemes

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.