We propose long-haul space-division-multiplexing (SDM) transmission systems employing parallel multiple-input multiple-output (MIMO) frequency-domain equalization (FDE) and transmission fiberwith lowdifferentialmode delay (DMD). We first discuss the advantages of parallel MIMO FDE technique in long-haul SDMtransmission systems in terms of the computational complexity, and then, compare the complexity required for parallel MIMO FDE as well as the conventional time-domain equalization techniques. Proposed parallel MIMO FDE that employs low baud rate multicarrier signal transmission with a receiver-side FDE enables us to compensate for 33.2-ns DMD with considerably low-computational complexity. Next, we describe in detail the newly developed fiber and devices we used in the conducted experiments. A graded-index (GI) multicore few-mode fiber (MC-FMF) suppressed the accumulation of DMD as well as intercore crosstalk. Mode dependent loss/gain effect was also mitigated by employing both a ring-core FM erbium-doped fiber amplifier and a free-space optics type gain equalizer. By combining these advanced techniques together, we finally demonstrate 12-core x 3 mode dense SDM transmission over 527-km GI MC-FMF without optical DMD management.