  Conventional OFDM, adopted in LTE-A systems, cannot provide the quality of
service requirements sought in 5G systems because of extreme natural channel
impairments caused by higher Doppler spreads and unexpected artificial
impairments caused by multi-source transmission, to be brought by 5G, and by
synchronization relaxation for closed-loop signaling overhead reduction in some
5G applications. These severe impairments induce a strong loss of orthogonality
between subcarriers and OFDM symbols and, therefore, lead to a dramatic
increase in ICI and ISI. To be well armed against these dramatic impairments,
we, in the present paper, optimize the transmit/receive waveforms for FBMC
systems, with hexagonal time-frequency lattices, operating over severe doubly
dispersive channels, accounting for both natural and artificial impairments.
For this, we exploit the POPS paradigm, recently proposed for rectangular
time-frequency lattices, to design offline waveforms maximizing the SINR for
hexagonal time-frequency lattices. We show that FBMC, with hexagonal lattices,
offers a strong improvement in SIR with respect to conventional OFDM and an
improvement of 1dB with respect to POPS-FBMC, with classical rectangular
lattices. Furthermore, we show that the hexagonal POPS-FBMC brings more
robustness to frequency synchronization errors and offers a 10dB reduction in
OOB emissions with respect to rectangular POPS-FBMC.
