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It is widely accepted that SC-FDE (Single-Carrier with Frequency-Domain Equalization) is an excellent candidate for broadband wireless systems, especially when an efficient power amplification is intended. If grossly nonlinear power amplifiers are employed, conventional QPSK (Quaternary Phase Shift Keying) or QAM (Quadrature Amplitude Modulation) modulations should be replaced by offset modulations such as OQPSK (Offset QPSK) and OQAM (Offset QAM). In fact, offset signals have much lower dynamic range than non-offset signals, with OQPSK signals being able to have an almost constant envelope. This paper considers frequency-domain receiver design for OQPSK and OQAM schemes. It is shown that FDE (Frequency Domain Equalization) designed for non-offset modulations are not suitable for offset modulations due to the residual IQI (In-phase/Quadrature Interference), i.e. the interference between in-phase (I) and quadrature (Q) components at the sampling instants. Therefore, we propose several FDE designs where there is no IQI in the sampling instants as well as iterative FDE receivers with IQI cancellation. Our receivers have excellent performance, with the linear designs significantly outperforming linear FDE for non-offset modulations and the iterative designs with performance close to the MFB (Matched Filter Bound).