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An adaptively modulated optical orthogonal frequency division multiplexing (AMOOFDM) modem using subcarrier modulation (SCM) (AMOOFDM-SCM) is proposed, for the first time, which consists of two conventional AMOOFDM modems in parallel with one operating at the baseband and the other being modulated onto an intermediate radio frequency (RF) carrier. Numerical simulations of the transmission performance of the AMOOFDM-SCM modems are undertaken in single-channel, optical amplifier-free, worst-case multimode fibre (MMF) links using intensity modulation and direct detection. It is shown that, based on practically available RF components, at least 64 Gb/s over 500 m and 37 Gb/s over 1000 m AMOOFDMSCM signal transmission is feasible in the aforementioned MMF links having 3-dB bandwidths as small as 292.5 MHz.km. In addition, when compared against the AMOOFDM technique, for achieving a required signal transmission capacity, AMOOFDMSCM also reveals significantly relaxed requirements on key component parameters, improved flexibility and robustness and more efficient use of MMF link spectral properties.