In this paper, we propose a faster-than-Nyquist (FTN) non-orthogonalfrequency-division multiplexing (NOFDM) scheme for visible light communications(VLC) where the multiplexing/demultiplexing employs the inverse fractionalcosine transform (IFrCT)/FrCT. Different to the common fractional Fouriertransform-based NOFDM (FrFT-NOFDM) signal, FrCT-based NOFDM (FrCT-NOFDM) signalis real-valued which can be directly applied to the VLC systems without theexpensive upconversion. Thus, FrCT-NOFDM is more suitable for thecost-sensitive VLC systems. Meanwhile, under the same transmission rate,FrCT-NOFDM signal occupies smaller bandwidth compared to OFDM signal. When thebandwidth compression factor $\alpha$ is set to $0.8$, $20\%$ bandwidth savingcan be obtained. Therefore, FrCT-NOFDM has higher spectral efficiency andsuffers less high-frequency distortion compared to OFDM, which benefits thebandwidth-limited VLC systems. As the simulation results show, bit error rate(BER) performance of FrCT-NOFDM with $\alpha$ of $0.9$ or $0.8$ is better thanthat of OFDM. Moreover, FrCT-NOFDM has a superior security performance. Inconclusion, FrCT-NOFDM shows great potential for application in the future VLCsystems.
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