Constellation Randomization Achieves Transmit Diversity for Single-RF Spatial Modulation

The performance of spatial modulation (SM) is known to be dominated by the minimum Euclidean distance (MED) in the received SM constellation. In this paper, a symbol-scaling technique is proposed for SM in the multiple-input-multiple-output (MIMO) channel that enhances the MED to improve the performance of SM. This is achieved by forming fixed sets of candidate prescaling factors for the transmit antennas (TAs), which are randomly generated and are known at both the transmitter and the receiver. For a given channel realization, the transmitter chooses the specific set of factors that maximizes the MED. Given the channel state information (CSI) readily available at the receiver for detection, the receiver independently chooses the same set of prescaling factors and uses them for the detection of both the antenna index (AI) and the symbol of interest. We analytically calculate the attainable gains of the proposed technique, in terms of its transmit diversity order, based on both the distribution of the MED and on the theory of classical order statistics. Furthermore, we show that the proposed scheme offers a scalable performance-complexity tradeoff for SM by varying the number of candidate sets of prescaling factors, with significant performance improvements, compared to conventional SM.