A time-frequency division multiplexing communications system with hexagonal lattice structure

In this paper, we propose a time-frequency division multiplexing (TFDM) communications system for multiple users which uses prolate spheroidal wave functions (PSWFs) as the transmission basis. A hexagonal time-frequency lattice provides optimal packing of the data in a fixed time-bandwidth support. We show that when using chirp modulation created by fractional Fourier transform (FrFT) the resulting system is robust to noise. The chirps having an instantaneous frequency with the angle of π/3 with respect to the time sets a hexagonal lattice structure. The reconstruction of the data can be done efficiently by windowing and filtering. We illustrate the performance of the proposed TFDM system in the presence of additive white Gaussian noise by means of simulations.