  The use of multidimensional modulations can decrease the energy consumption
of optical links. In this paper, we propose and study Mode Vector Modulation
(MVM), a generalized polarization modulation scheme for transmission over
multimode/multicore optical fibers or free space. Similar to Polarization Shift
Keying (PolSK) and Stokes Vector Modulation (SVM), MVM can be used in
conjunction with direct detection and, therefore, is suitable for
next-generation, short-haul optical interconnects. This paper focuses on the
MVM transceiver architecture, the back-to-back performance of
optically-preamplified MVM direct detection (DD) receivers, the optimized
geometric shaping of the MVM constellation, and the related bit-to-symbol
mapping. We show that MVM DD outperforms conventional single-mode,
direct-detection-compliant, digital modulation formats by several dBs in terms
of receiver sensitivity and the SNR gain increases with the number of spatial
degrees of freedom (SDOFs) N.
