A multiple‐symbol differential detection scheme based on the ML criterion is adopted to MAPSK, and the decision rule to estimate the transmitted signals is constructed theoretically, including terms for the channel noise power. SER performance of star QAM and (4,12) QAM, which are typical constellations for 16APSK, under the decision rule is evaluated. It is confirmed that the performance of this decision rule is better than that using the former rule. In addition, we introduce the (M,L) algorithm into this detection scheme to reduce tree search and confirm its performance by computer simulation. Finally, the performance shows good proximity to that of the ideal coherent detection on the AWGN channel. © 2001 Scripta Technica, Electron Comm Jpn Pt 1, 84(10): 27–35, 2001