Spectrum Broadening of Faster-Than-Nyquist Signaling Using GTMH Precoding

As a promising technique to eliminate the intersymbol interference (ISI) caused by the faster-than-Nyquist (FTN) signaling, the G-to-minus-half (GTMH) precoding could result in severe spectrum broadening and reduce the spectrum efficiency. Combining the baseband-shaping filter with the precoding matrix, we define the transfer function of the FTN signaling using the GTMH precoding. By further analyzing the effect of the GTMH precoding on the transfer function, we prove how the FTN signaling makes its ISI matrix ill-conditioned. Then, we reveal the relationship between the transfer function and the eigenvalues of the ISI matrix. The derivation shows that due to the minimal eigenvalues of the ill-conditioned ISI matrix, the inverse operation of the GTMH precoding gives in the maximal elements for the transfer function, thereby resulting in the spectrum broadening. Furthermore, we present and validate the spectrum-broadening ratio and the maximum spectrum efficiency improvement of the GTMH precoding, which serve as additional evaluative tools for the GTMH precoding of the FTN signaling, complementing the conventional bit-error-ratio-based evaluation methodology.