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Differentially encoded and noncoherently detected transceivers exhibit low complexity since they dispense with a complex channel estimation. In pursuit of high bandwidth efficiency, differential amplitude/phase (A/P)-shift keying (DAPSK) was devised using constellations of multiple concentric rings. To increase resilience against the typical high-Doppler-induced performance degradation of DAPSK and/or to enhance the maximum achievable error-free transmission rate for DAPSK-modulated systems, multiple-symbol differential detection (MSDD) may be invoked. However, the complexity of the maximum a posteriori (MAP) MSDD exponentially increases with the detection window size and hence may become excessive upon increasing the window size, particularly in the context of an iterative detection-aided channel-coded system. To circumvent this excessive complexity, we conceive a decomposed two-stage iterative A/P detection framework, where the challenge of having a nonconstant-modulus constellation is tackled with the aid of a specifically designed information exchange between the independent A/P detection stages, thus allowing the incorporation of reduced-complexity sphere detection (SD). Consequently, a near-MAP-MSDD performance can be achieved at significantly reduced complexity, which may be five orders of magnitude lower than that of the traditional MAP-MSDD in the 16-DAPSK scenario that was considered.