This study discusses synchronisation in phase noise-impaired spectrally efficient communication systems employing high-order modulations. In particular, an iterative receiver, where demodulation and decoding are separate from maximum a posteriori probability (MAP) synchronisation, is presented. The authors' separate approach is tailored to the design of pragmatic iterative receiver schemes employing 'off-the-shelf' demodulation and decoding blocks. This allows full compatibility with already existing systems, which is attractive from the implementation viewpoint. The proposed MAP synchronisation algorithm also requires very limited knowledge of the phase noise process and achieves near coherent performance with moderate computational comple...