It is widely recognised that traditional single RFchain aided spatial modulation (SM) does not offer any transmit diversity gain. As a remedy, constellation randomization (CR), relying on transmit pre-scaling (TPS), has been shown to provide transmit diversity for single RF-chain aided SM. In this paper we propose a low-complexity approach to SM with the aid of constellation randomization (SM-CR) that considerably improves the transmit diversity gain of SM at a reduced computational burden compared to conventional SM-CR. While conventional SM-CR performs a full search amongst a set of candidate TPS factors in order to achieve the maximum minimum Euclidean distance (MED) in the received SM constellation, here we propose a thresholding approach, where instead of the maximum MED the TPS aims to satisfy a specific MED threshold. This technique offers a significant complexity reduction with respect to the full maximization of SM-CR, since the search for TPS is terminated once a TPS set is found that satisfies the MED threshold. Our analysis and results demonstrate that a scalable trade-off can be achieved between transmit diversity and complexity by appropriately selecting the MED threshold, where a significant complexity reduction is attained, while achieving a beneficial transmit diversity gain for the single-RF SM.
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