Spatial modulation (SM) is an efficient transmission scheme based on multiple‐input multiple‐output systems. SM, by nature, requires coherent detection to achieve optimal error performance. This requires that the receiver has full knowledge of the channel state information (CSI), however, determining the CSI results in an increase in the detection complexity at the receiver. Differential modulation systems are capable of performing detection without knowledge of the CSI at the receiver, however, they suffer a 3 dB error performance penalty as compared to their coherent counterparts. In this study, the authors present a generalised differential scheme for SM (GD‐SM) based on generalised differential modulation, which is capable of reducing the performance penalty incurred through optimal power allocation. Furthermore, they extend the architecture of GD‐SM and optimal power allocation to conventional differential SM. The architecture of the proposed systems, advantageously permits the use of either M ‐ary quadrature amplitude modulation or M ‐ary phase shift keying constellations. Simulation and theoretical results demonstrate that GD‐SM incurs only about 0.5 dB performance loss as compared to coherent SM when the frame length is 400.