In this paper we consider the use of single carrier (SC) modulations combined with frequency-domain equalisation (FDE) in future broadband wireless systems. We propose iterative receiver structures with joint equalisation and carrier synchronisation. The proposed receivers can be regarded as modified frequency-domain turbo equalisers where we perform a decision-directed frequency offset estimation within each iteration of the turbo equaliser. Our performance results show that the proposed receiver structure has good bit error rate (BER), even with moderate frequency offsets and in severely time-dispersive channels. Moreover, our receiver has a relatively low implementation complexity, due to its fast Fourier transform (FFT)-based frequency-domain implementation.