Three novel designs of adaptively modulated optical orthogonal frequency division multiplexing modems using subcarrier modulation (AMOOFDM-SCM) are proposed, for the first time, each of which requires a single inverse fast Fourier transform/fast Fourier transform (IFFT/FFT) operation. These designs not only significantly simplify the AMOOFDM-SCM modem configurations, but also offer extra unique network features such as input/output reconfigurability. Investigations show that these three modems are capable of supporting more than 60 Gb/s AMOOFDM-SCM signal transmission over 20, 40 and 60 km single mode fibre (SMF)-based intensity modulation and direct detection (IMDD) transmission links without optical amplification and chromatic dispersion compensation.