Capacity limit for faster-than-Nyquist non-orthogonal frequency-division multiplexing signals

Abstract

Faster-than-Nyquist (FTN) signal can achieve higher spectral efficiency and capacity than Nyquist signal. For Nyquist signal, the capacity limit was shown in the pioneering work of Shannon. However, different from Nyquist signal, FTN signal has a smaller pulse interval or narrower subcarrier spacing. What is the capacity limit of FTN signal? In this paper, to the best of our knowledge, we first give the mathematical expression for the capacity limit of FTN non-orthogonal frequency-division multiplexing (NOFDM) signal, which can be also applied to FTN non-orthogonal time-division multiplexing signal. The mathematical expression shows that the capacity limit for FTN signal is higher than Shannon limit for Nyquist signal. Meanwhile, we demonstrate the principle of FTN NOFDM by taking fractional cosine transform-based NOFDM (FrCT-NOFDM) for instance. As far as we know, FrCT-NOFDM is first proposed in this paper. The simulations and experiments have been demonstrated to verify the feasibility of FrCT-NOFDM. When the bandwidth compression factor alpha is set to 0.8, the subcarrier spacing is equal to 40% of the symbol rate per subcarrier. The transmission rate is about 25% faster than Nyquist rate and the capacity limit is 25% higher than Shannon limit.