Constellation design for spatial modulation

Conventional amplitude-phase modulations (APMs) are designed such that the minimum Euclidean distance between constellation points is maximized. Unlike these modulations, the error performance of spatial modulation (SM) is not only a function of the Euclidean distances but also the energy of each symbol, i.e. constellation point. Therefore, conventional APM schemes that are designed solely based on the notion of Euclidean distance are not necessarily suitable for SM transmission. In this paper, the constellation design for SM is investigated and it is shown that, by a proper constellation design, a significant performance gain is obtained compared to the well-known phase shift keying (PSK) or quadrature amplitude modulation (QAM). It is shown that in many cases multi-ring star-QAM is a suitable constellation for SM. However, when the number of transmit antennas is large, the numerically derived constellation converges to the conventional phase shift keying (PSK) constellation, especially at small number of receive antennas.