Faster-than-Nyquist (FTN) signal achieves higher spectral efficiency and capacity compared to Nyquist signal due to its smaller pulse interval or narrower subcarrier spacing. Shannon limit typically defines the upper-limit capacity of Nyquist signal. To the best of our knowledge, the mathematical expression for the capacity limit of FTN non-orthogonal frequency-division multiplexing (NOFDM) signal is first demonstrated in this paper. The mathematical expression shows that FTN NOFDM signal has the potential to achieve a higher capacity limit compared to Nyquist signal. In this paper, we demonstrate the principle of FTN NOFDM by taking fractional cosine transform-based NOFDM (FrCT-NOFDM) for instance. FrCT-NOFDM is first proposed and implemented by both simulation and experiment. When the bandwidth compression factor $alpha$ is set to $0.8$ in FrCT-NOFDM, the subcarrier spacing is equal to $40%$ of the symbol rate per subcarrier, thus the transmission rate is about $25%$ faster than Nyquist rate. FTN NOFDM with higher capacity would be promising in the future communication systems, especially in the bandwidth-limited applications.
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