For weakly coupled mode-division multiplexed (MDM) transmission systems, we design and implement optical coherent receiver prototypes with real-time multiple-input multiple-output (MIMO) digital signal processing to equalize two degenerate linearly polarized modes with dual polarization. Using field programmable gate array circuits, we implement real-value 8 x 2 MIMO adaptive equalization with externally separated phase compensators based on the least mean square algorithm, which enables not only training equalization but also fast carrier-phase tracking. With the optical coherent MIMO receiver prototype, we demonstrate real-time weakly coupled 10 x MDM wavelength-division multiplexed dual-polarization quadrature phase shift keying transmission over 48-km few-mode fibers. This report shows a record number of multiplexed spatial modes, namely, 10 modes with dual polarization, in real-time MDM transmission experiments. (C) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement