The exponential growth of network traffic within data centers and high-performance computing generates a growing volume of fiber cabling. This raises the need for spectrally efficient communication scheme, which allows easy integration of optics and electronics. In this paper, we suggest a mode group division multiplexing scheme based upon intensity-modulated silicon photonics (SiP) Mach-Zehnder modulators (MZMs) coupled to standard graded-index multi-mode fiber directly detected using multi-segment concentric photo-detector. In addition, we have theoretically derived the bit and power loading of such a system in a closed-loop multiple-input multiple-output (MIMO) formation using convex optimization with two possible types of architectures: the vertical Bell Labs layered space-time architecture (V-BLAST) with minimum mean square error and successive interference cancellation (MMSE-SIC); and singular value decomposition (SVD). Our optimization problem maximizes the system's capacity under peak amplitude, power consumption, and BER constraints. Simulation results have shown the superiority of a V-BLAST MMSE-SIC over the SVD architecture in terms of total spectral efficiency for a 4 × 4 MIMO short reach low driving voltage conventional SiP-based MZM system.