Prototype waveform optimization for an OFDM/OQAM system with hexagonal time-frequency lattice structure

This paper deals with the optimization of the time-frequency localization of the prototype waveform for OFDM/OQAM with hexagonal time-frequency lattice. The set of orthonormal waveforms among which the optimally localized one should be searched are obtained as the orthonormalization of mother functions well localized in time-frequency. To preserve as much as possible the good localization of the original mother functions, the canonical form of the orthonormalization procedure is used. For an easy and systematic way to generate well localized mother functions, we use the orthonormal base of Hermite functions, which are known to provide, in decreasing order, the best time-frequency localization. To preserve the pi/3 rotational invariance of the hexagonal lattice in the ambiguity function of each candidate prototype function, only Hermite functions with indices multiple of 6 are allowed. The obtained numerical results show that the optimized prototype waveform outperforms in localization the best localized waveform for OFDM/OQAM with square time-frequency lattice.