Shaping Delay-Doppler Ambiguity in Practical OFDM-ISAC

Abstract: Orthogonal frequency-division multiplexing (OFDM) is a key waveform for integrated sensing and communication (ISAC). Existing OFDM ambiguity analyses, however, typically assume fully occupied data-only waveforms, whereas practical frames contain direct-current and edge-guard nulls, fixed pilots, and random payload symbols. This mixed resource structure reshapes the self-ambiguity function and induces prominent sidelobes in the sensing region of interest (ROI). We therefore propose ROI-oriented deep block-unitary precoded OFDM (DBU-OFDM), which combines resource-specific trainable unitary transformations with dedicated sensing subcarriers to suppress ROI sidelobes while preserving the prescribed resource support. We develop a constraint-preserving parameterization capable of representing arbitrary unitary matrices and an ROI-aware sensing-support initialization. We prove periodic autocorrelation function (P-ACF) invariance under phase-only optimization and zero-delay Doppler-cut invariance under arbitrary unitary transformations. Numerical results corroborate the P-ACF optimality of cyclic-prefix OFDM (CP-OFDM) and provide numerical support for the conjecture that conventional OFDM is globally optimal in the considered aperiodic autocorrelation function (A-ACF) setting. Unitary pilot optimization improves the ROI peak-to-sidelobe ratio by over 2 dB, while combining it with dedicated sensing subcarriers yields gains ranging from several to tens of dB. Under the considered configuration, the A-ACF mode also provides substantially greater ROI ambiguity-shaping capability than the P-ACF mode.