Cramér-Rao Lower Bound Analysis of Positioning With Planar Large Intelligent Surfaces Under Rician Channel
Bibliographic record
Abstract
In this paper we derive the Fisher information matrix (FIM) and Cramér-Rao lower bound (CRLB) for positioning a terminal with a planar large intelligent surface (LIS), under Rician channel. For a disk-shaped continuous LIS and a terminal located on the central perpendicular line (CPL) of the LIS, we obtain expressions for the CRLBs in the form of a single integration. For the situation that the terminal is far from the LIS compared to the LIS radius and the situation with an asymptotically large LIS, closed-form approximations of the CRLBs are derived, based on which scalings and properties of the positioning precision with respect to different system parameters are obtained. For positioning a terminal with arbitrary location, we derive closed-form expressions of the CRLBs when the terminal is far from the LIS and the wavelength is small. When the surface area is small and the path-loss exponent is not larger than 5, the CRLBs of a CPL-terminal are smaller than those of a non-CPL terminal for all three dimensions, while the reverse may occur when the surface area grows large enough. We also carry out a comparative study of the continuous and discrete models of the LIS. Numerical results are presented to validate the precision of our theoretical analysis and approximated performance.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".