We consider the multicarrier faster-than-Nyquist (MFTN) signaling under low complexity symbol-by-symbol detection, where the lattice structure and time-frequency spacing play key roles in determining the system performance. Specifically, the energy of intersymbol interference (ISI) and intercarrier interference (ICI) introduced by time-frequency packing is taken as a figure of merit. In this regard, we firstly prove the asymptotical equivalence of the hexagonal MFTN and conventional rectangular MFTN signaling systems when the time packing factor is small enough, and we also reveal the potential benefit of hexagonal MFTN with respect to conventional rectangular MFTN for moderate time-frequency spacing. Then, an optimal MFTN signaling scheme under the given signaling efficiency is proposed. By jointly optimizing the lattice structure and time-frequency spacing to minimize the interference energy, we show that the optimal time-frequency spacing can be accurately obtained with substantially reduced complexity than conventional exhaustive search scheme. Finally, we demonstrate that there is a good match between minimizing the interference energy and maximizing the achievable spectral efficiency, which is also considered to be an important figure for MFTN signaling system. Our theoretical analysis and numerical results validate that the proposed scheme outperforms conventional MFTN signaling system.
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