In this treatise, first of all, we conceive a generic multiple-symbol differential sphere detection (MSDSD) solution for both single- and multiple-antenna-based noncoherent schemes in both uncoded and coded scenarios, where the high-mobility aeronautical Ricean fading features are taken into account. The bespoke design is the first MSDSD solution in the open literature that is applicable to the generic differential space-time modulation (DSTM) for transmission over Ricean fading. In the light of this development, the recently developed differential spatial modulation and its diversity counterpart of differential space-time block coding using index shift keying are specifically recommended for aeronautical applications owing to their low-complexity single-RF and finite-cardinality features. Moreover, we further devise a noncoherent decision-feedback differential detection and a channel-state information estimation aided coherent detection, which also take into account the same Ricean features. Finally, the advantages of the proposed techniques in different scenarios lead us to propose for the aeronautical systems to adaptively: 1) switch between coherent and non-coherent schemes; 2) switch between single- and multiple-antenna-based schemes as well as; and 3) switch between high-diversity and high-throughput DSTM schemes.