LAUSR

In this paper, we propose a faster-than-Nyquist non-orthogonal frequency-division multiplexing (NOFDM) scheme for visible light communications (VLCs) where the multiplexing/demultiplexing employs the inverse fractional cosine transform (IFrCT)/FrCT. Different to the common fractional Fourier transform-based NOFDM (FrFT-NOFDM) signal, FrCT-based NOFDM (FrCT-NOFDM) signal is real-valued, which can be directly applied to the VLC systems without the expensive up-conversion and thus it is more suitable for the cost-sensitive VLC systems. Under the same transmission rate, FrCT-NOFDM signal occupies smaller bandwidth compared to OFDM signal. When the bandwidth compression factor $\alpha$ is set to 0.8, 20% bandwidth saving can be obtained. Therefore, FrCT-NOFDM has higher spectral efficiency and suffers less high-frequency distortion compared to OFDM, which benefits the bandwidth-limited VLC systems. As the simulation results show, bit error rate performance of FrCT-NOFDM with $\alpha$ of 0.9 or 0.8 is better than that of OFDM. Meanwhile, FrCT-NOFDM has a superior security performance. In conclusion, FrCT-NOFDM shows the potential for application in the future VLC systems.