Single-carrier multi-input, multi-output (MIMO) systems are known to have low envelope fluctuations. However, the introduction of higher order modulations, such as M-ary quadrature amplitude modulation (M-QAM), and singular value decomposition (SVD) techniques, can lead to large envelope fluctuations, making the signals prone to nonlinear distortion effects during amplification.For this work we consider a MIMO-SVD system employing single-carrier with frequency-domain equalization (SC-FDE) and M-QAM constellations with M>4, together with strongly nonlinear amplifiers. To increase performance of the SVD technique, we interleave the singular modes among the antennas. Moreover, to handle the nonlinear distortion, we propose an iterative frequency-domain receiver that combines equalization with cancellation of nonlinear distortion effects.The performance results show that the proposed receivers can achieve excellent performance with only a few iterations, which makes this technique appealing for MIMO point-to-point communication systems.11A preliminary version of this work was published in ICUMT 2018.