Fundamental Limits for Near-Field Sensing -- Part I: Narrow-Band Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909979142782976 |
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| author | Wei, Tong Mishra, Kumar Vijay R., Bhavani Shankar M. Ottersten, Björn |
| author_facet | Wei, Tong Mishra, Kumar Vijay R., Bhavani Shankar M. Ottersten, Björn |
| contents | Extremely large-scale antenna arrays (ELAAs) envisioned for 6G enable high-resolution sensing. However, the ELAAs worked in extremely high frequency will push operation into the near-field region, where spherical wavefronts invalidate classical far-field models and alter fundamental estimation limits. The purpose of this and the companion paper (Part II) is to develop the theory of fundamental limits for near-field sensing systems in detail. In this paper (Part I), we develop a unified narrow-band near-field signal model for joint parameter sensing of moving targets using the ELAAs. Leveraging the Slepian--Bangs formulation, we derive closed-form Cram'er--Rao bounds (CRBs) for joint estimation of target position, velocity, and radar cross-section (RCS) under the slow-time sampling model. To obtain interpretable insights, we further establish explicit far-field and near-field approximations that reveal how the bounds scale with array aperture, target range, carrier wavelength, and coherent integration length. The resulting expressions expose the roles of self-information terms and their cross terms, clarifying when Fresnel corrections become non-negligible and providing beamformer and algorithm design guidelines for near-field sensing with ELAAs. Simulation results validate the derived CRBs and their far-field and near-field approximations, demonstrating accurate agreement with the analytical scaling laws across representative array sizes and target ranges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24958 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fundamental Limits for Near-Field Sensing -- Part I: Narrow-Band Systems Wei, Tong Mishra, Kumar Vijay R., Bhavani Shankar M. Ottersten, Björn Signal Processing Extremely large-scale antenna arrays (ELAAs) envisioned for 6G enable high-resolution sensing. However, the ELAAs worked in extremely high frequency will push operation into the near-field region, where spherical wavefronts invalidate classical far-field models and alter fundamental estimation limits. The purpose of this and the companion paper (Part II) is to develop the theory of fundamental limits for near-field sensing systems in detail. In this paper (Part I), we develop a unified narrow-band near-field signal model for joint parameter sensing of moving targets using the ELAAs. Leveraging the Slepian--Bangs formulation, we derive closed-form Cram'er--Rao bounds (CRBs) for joint estimation of target position, velocity, and radar cross-section (RCS) under the slow-time sampling model. To obtain interpretable insights, we further establish explicit far-field and near-field approximations that reveal how the bounds scale with array aperture, target range, carrier wavelength, and coherent integration length. The resulting expressions expose the roles of self-information terms and their cross terms, clarifying when Fresnel corrections become non-negligible and providing beamformer and algorithm design guidelines for near-field sensing with ELAAs. Simulation results validate the derived CRBs and their far-field and near-field approximations, demonstrating accurate agreement with the analytical scaling laws across representative array sizes and target ranges. |
| title | Fundamental Limits for Near-Field Sensing -- Part I: Narrow-Band Systems |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2512.24958 |