The transmitted signals in multi-input, multi-output (MIMO) systems employing singular value decomposition (SVD) techniques can have large envelope fluctuations, even when single-carrier modulations are employed, which leads to amplification difficulties and makes them prone to nonlinear distortion effects. In this paper we consider the use of MIMO-SVD techniques with single-carrier with frequency-domain equalization (SC-FDE) modulations, together with strongly nonlinear amplifiers. The singular modes are interleaved among the antennas, which allows improved performance. To achieve this potential performance, we propose an iterative frequency-domain receiver that combines equalization with cancellation of nonlinear distortion effects. Our performance results show that the proposed receivers can have excellent performance with just a few iterations, making this technique particularly interesting for point-to-point communications with multiple antennas at the transmitter and the receiver.