We show that certain signal constellations invoked for classic differential encoding result in a phenomenon we term as the unbounded differential constellation size (UDCS). Various existing differential transmission schemes that suffer from this issue are identified. Then, we propose an enhanced algebraic field extension-based differential spatial modulation (AFE-DSM) scheme and its enhanced counterpart that strikes a diversityrate tradeoff (AFE-DSM-DR), both of which overcome the UDCS issue without compromising its full transmit diversity advantage. Furthermore, the proposed schemes are extended to incorporate amplitude and phase shift keying (APSK) in order to exploit all the available degrees of freedom. Additionally, we propose a pair of detection schemes specially designed for APSK-aided differential transmission schemes. Explicitly, we conceive the buffered minimum mean squared error (B-MMSE) detector and buffered maximum likelihood (B-ML) detector, which exploit the knowledge of previously detected symbols in order to further improve the detection performance. Our simulation results have shown that the proposed detectors are capable of bridging the performance gap between the conventional differential detector (CDD) and the coherent detector that has full channel state information. Specifically, when employing the proposed APSKaided AFE-DSM scheme operating at a rate of 2 b per channel use, the B-MMSE and B-ML detectors are observed to give about 3-and 3.5-dB signal-to-noise ratio gain with respect to their CDD counterpart at a bit error ratio of 10(-5).