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The use of multi-level (QAM-type) modulations in mobile communications affected by fading and Doppler shift imposes a tight control on the carrier frequency offset if quasi-coherent detection is a goal. This aspect is taken into account by the receiver herein proposed. A 16-DAPSK (differential amplitude phase shift-keying) scheme is considered, with one bit being absolutely encoded in amplitude and the other two bits differentially encoded in phase by a 8-state Ungerboeck trellis-code. To estimate the frequency offset the receiver includes a bank of stochastic nonlinear filters, an innovations processor and a modified Kay algorithm. Sequence detection is performed by a gain estimator and a Viterbi algorithm fed by the frequency-corrected input samples. The receiver can cope with considerable phase drifts within the symbol interval, which allows significant Doppler shifts or the operation of free-running oscillators with moderate frequency stabilities and large symbol durations.