Asymptotic Equivalence of Two Multicarrier Transmission Schemes in Terms of Robustness Against Time–Frequency Dispersive Channels

Digital signal transmission can be viewed as lattice-tiling over a time-frequency plane. Corresponding to a rectangular lattice and a hexagonal lattice, there are two multicarrier transmission schemes, i.e., the Weyl-Heisenberg (W-H) system and the hexagonal Gabor (H-G) system, respectively. In the previous works, the transmission pulse shape and the time-frequency lattice parameters of the above two systems were optimized to obtain the best robustness against time-frequency dispersive channels. In this paper, by virtue of elliptic integral theory, we theoretically prove that the optimized W-H system and H-G system are asymptotically equivalent to each other in the sense of achieving the same energy perturbation as signaling efficiency approaches 0 or +??. Moreover, it is shown that, for moderate signaling efficiencies, the superiority of the H-G system over the W-H system is virtually limited. Numerical results are provided to support the theoretical analysis.