  Faster-than-Nyquist (FTN) signaling is a promising non-orthogonal pulse
modulation technique that can improve the spectral efficiency (SE) of next
generation communication systems at the expense of higher detection complexity
to remove the introduced inter-symbol interference (ISI). In this paper, we
investigate the detection problem of ultra high-order quadrature-amplitude
modulation (QAM) FTN signaling where we exploit a mathematical programming
technique based on the alternating directions multiplier method (ADMM). The
proposed ADMM sequence estimation (ADMMSE) FTN signaling detector demonstrates
an excellent trade-off between performance and computational effort enabling
successful detection and SE gains for QAM modulation orders as high as 64K
(65,536). The complexity of the proposed ADMMSE detector is polynomial in the
length of the transmit symbols sequence and its sensitivity to the modulation
order increases only logarithmically. Simulation results show that for 16-QAM,
the proposed ADMMSE FTN signaling detector achieves comparable SE gains to the
generalized approach semidefinite relaxation-based sequence estimation
(GASDRSE) FTN signaling detector, but at an experimentally evaluated much lower
computational time. Simulation results additionally show SE gains for
modulation orders starting from 4-QAM, or quadrature phase shift keying (QPSK),
up to and including 64K-QAM when compared to conventional Nyquist signaling.
The very low computational effort required makes the proposed ADMMSE detector a
practically promising FTN signaling detector for both low order and ultra
high-order QAM FTN signaling systems.
