  Faster-than-Nyquist non-orthogonal frequency-division multiplexing
(FTN-NOFDM) is robust against the steep frequency roll-off by saving signal
bandwidth. Among the FTN-NOFDM techniques, the non-orthogonal matrix precoding
(NOM-p) based FTN has high compatibility with the conventional orthogonal
frequency division multiplexing (OFDM), in terms of the advanced digital signal
processing already used in OFDM. In this work, by dividing the single band into
multiple sub-bands in the NOM-p-based FTN-NOFDM system, we propose a novel
FTN-NOFDM scheme with adaptive multi-band modulation. The proposed scheme
assigns different quadrature amplitude modulation (QAM) levels to different
sub-bands, effectively utilizing the low-pass-like channel and reducing the
complexity. The impacts of sub-band number and bandwidth compression factor on
the bit-error-rate (BER) performance and implementation complexity are
experimentally analyzed with a 32.23-Gb/s and 20-km intensity modulation-direct
detection (IM-DD) optical transmission system. Results show that the proposed
scheme with proper sub-band numbers can lower BER and greatly reduce the
complexity compared to the conventional single-band way.
