Spatial Degrees of Freedom in Distance Domain of Continuous Aperture for Broadside case in Near-Field Region
Bibliographic record
Abstract
Extremely large apertures in the near-field region unlock additional spatial resources in the distance domain, which enables the spatial multiplexing of multiple users even when they share the same angular direction—a capability unattainable in the far-field regime. A fundamental question remains unanswered: "What is the spatial degree of freedom of spatial multiplexing in the distance domain?"To address this, we investigate the spatial degree of freedom (DoF) in the distance domain of a large continuous aperture by considering the line-of-sight (LoS) channel between the aperture and a linear array, whose elements lie in the same direction but are located at different distances relative to the aperture. For simplicity of analysis, we consider the case where the linear array is in the broadside of the aperture. By reformulating the channel as an integral operator with a Hermitian convolution kernel, we derive a closed-form expression for the spatial DoF via the Fourier transform. Analytical and simulation results reveal that the spatial DoF in the distance domain of the aperture is predominantly determined by the aperture’s extreme boundaries rather than its detailed shape.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
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".