Shaping Delay-Doppler Ambiguity in Practical OFDM-ISAC

Orthogonal frequency-division multiplexing (OFDM) serves as a pivotal waveform for integrated sensing and communication (ISAC), yet common analyses of OFDM ambiguity typically presume fully occupied data-only waveforms. Practical frames, however, often contain direct-current and edge-guard nulls, fixed pilots, and random payload symbols, which alter the self-ambiguity function and create significant sidelobes within the sensing region of interest (ROI). To address these challenges, we introduce ROI-oriented deep block-unitary precoded OFDM (DBU-OFDM), which integrates resource-specific trainable unitary transformations with dedicated sensing subcarriers to mitigate ROI sidelobes while maintaining prescribed resource support. This work develops a constraint-preserving parameterization capable of representing arbitrary unitary matrices along with an ROI-aware sensing-support initialization. We demonstrate periodic autocorrelation function (P-ACF) invariance through phase-only optimization and zero-delay Doppler-cut invariance using arbitrary unitary transformations. Numerical simulations affirm the P-ACF optimality of cyclic-prefix OFDM (CP-OFDM) and support the hypothesis that traditional OFDM is globally optimal within the aperiodic autocorrelation function (A-ACF) framework. Unitary pilot optimization can enhance the ROI peak-to-sidelobe ratio by over 2 dB, and its combination with dedicated sensing subcarriers results in significant gains ranging from several to tens of dB. Moreover, the A-ACF mode demonstrates substantially improved ROI ambiguity-shaping capabilities compared to the P-ACF mode.