Global optimality of conventional OFDM for the zero-Doppler A-ACF problem

Determine whether an OFDM-equivalent monomial unitary transformation attains the global optimum of the zero-Doppler aperiodic-autocorrelation-function delay-slice peak-to-sidelobe-ratio problem within the class of unitary waveforms.

Background

The paper studies unitary transformations of fully occupied OFDM frames to optimize the zero-Doppler delay-slice PSLR. For the periodic autocorrelation function, prior analysis establishes the optimality of conventional OFDM under QAM/PSK signaling, whereas the corresponding aperiodic-autocorrelation analysis cited by the paper establishes only local optimality under an expected integrated sidelobe-power criterion.

In the authors’ numerical experiments, training under the A-ACF criterion converges toward an approximately monomial unitary matrix, consisting primarily of a permutation and per-subcarrier phase rotations. This behavior provides numerical evidence for, but does not prove, global optimality for the specific zero-Doppler A-ACF delay-slice PSLR objective. The unresolved problem is therefore to establish or refute the conjectured global optimum over the full unitary waveform class.