Most existing studies on modulation recognition for orthogonal frequency-division multiplexing (OFDM) signals operate under the idealized assumption of perfect synchronization, thereby overlooking the practical challenges posed by real-world wireless environments. Such assumptions neglect the detrimental effects of timing and carrier frequency offsets, which inevitably arise in practice and can severely degrade recognition accuracy. In this work, we address this gap by proposing a novel modulation recognition framework tailored for coded OFDM signals operating under imperfect synchronization conditions over unknown channel coefficients. The core of the proposed approach is a maximum-likelihood (ML) formulation that jointly estimates the transmitted modulation format, the underlying channel response, and the synchronization parameters-namely, the timing and carrier frequency offsets. To efficiently solve this inherently coupled estimation problem, we adopt an expectation-maximization (EM) algorithm, which alternates between soft-data detection and parameter refinement. Unlike conventional schemes that rely exclusively on known pilot symbols for parameter estimation, our method leverages the soft outputs of a bit-interleaved coded modulation with iterative decoding (BICM-ID) receiver as virtual pilots. These decoder-generated reliability values are recursively fed back into the EM process, enabling continuous improvement of modulation recognition, synchronization, and channel estimates without requiring additional pilot overhead. Extensive simulation results demonstrate that the proposed scheme achieves superior modulation recognition accuracy compared to traditional synchronization-agnostic methods, particularly in scenarios with moderate-to-severe timing and frequency misalignments.
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