AbstractOffset spatial modulation (OSM) is an attractive variant in the family of spatial modulation technology, which is capable of reducing the frequency of radio frequency chain switching in practical implementations. This paper elaborates on the benefits of adaptive power allocation (PA) conceived for OSM systems. First, a closed‐form solution of the optimal PA algorithm is derived for the case of two transmit antennas, which maximizes the minimum Euclidean distance (ED) between the received signal points. Moreover, based on the above solutions, a low‐complexity iterative PA algorithm is proposed for larger numbers of transmit antennas, by exploiting the EDs of a few dominant error vectors. Furthermore, for striking a flexible trade‐off between the bit error performance and complexity, an iterative convex approximation based PA algorithm is also developed. Finally, simulation results are presented to show that the proposed PA algorithms provide considerable improvements on the original OSM in terms of the bit error rate.