In this paper, we consider a single-carrier modulation combined with frequency-domain equalisation block transmission with residual frequency errors. We employ a frequency-domain iterative decision feedback equalisation (DFE) denoted iterative block-decision feedback equalisation (IB-DFE), which is combined with a decision-directed carrier frequency offset (CFO) estimator. This estimator produces a CFO estimate within each iteration of the equaliser, which is used to compensate for the CFO. As the analytical study of the IB-DFE is very hard because of the feedback chain, IB-DFE receivers with joint symbol detection and carrier frequency synchronisation are also very difficult to tackle. To address this problem, we propose three new models. One models the decision-directed CFO estimator, another models the IB-DFE and finally one makes use of the previous two models to jointly characterise equalisation and carrier frequency synchronisation. In addition, a novel graphical tool for the convergence evaluation of the iterative receiver is included. Finally, we validate our models using Monte Carlo simulations and conclude that they are accurate for small and moderate residual CFO values.