A Scalable Performance–Complexity Tradeoff for Constellation Randomization in Spatial Modulation

It is widely recognized that traditional single radio frequency (RF)-chain-aided spatial modulation (SM) does not offer any transmit diversity gain. As a remedy, constellation randomization (CR), relying on transmit prescaling (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 with conventional SM-CR. While conventional SM-CR performs a full search among a set of candidate TPS factors 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 tradeoff 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.