When Do Pilots Matter for OFDM Sensing? Pilot-Data Resource Design for ISAC

RESUMO

Practical OFDM-based integrated sensing and communication (ISAC) signals contain deterministic pilots and random data payloads, yet how these two types of resources jointly affect matched-filter sensing performance remains insufficiently understood. This paper establishes an analytical and optimization framework for pilot-data (P-D) OFDM sensing. We first derive a closed-form mean-square periodic autocorrelation function (MS P-ACF), which characterizes the respective contributions of the average subcarrier power spectrum and data-symbol randomness to sensing sidelobes. Based on this result, we reveal that pilot placement has no impact on normalized sidelobes under uniform power allocation or on the normalized global expected integrated sidelobe level (EISL), whereas it becomes an effective design degree of freedom for reshaping sidelobes under nonuniform power allocation. We further derive the globally optimal two-level pilot-data power allocation for global EISL minimization and characterize pilot placement for peak sidelobe suppression. For region-of-interest (ROI) sensing, we jointly optimize pilot placement and subcarrier power allocation to minimize the normalized ROI-EISL. A strictly uniform pilot placement is proved globally optimal under specified conditions, while a bisection-and-branch-and-bound algorithm is developed for general resource configurations. Numerical results validate the theoretical analysis and demonstrate that the proposed design reduces the ROI sidelobe level by up to 2.19 dB compared with optimized uniform-pilot OFDM, while improving ranging accuracy at an SNR of -10 dB by 84.3$\%$. These results reveal when and how pilot placement can be exploited to regulate the sensing behavior of random OFDM communication signals, providing practical resource-design principles for OFDM-based ISAC.