Linear Receive Beamforming for CAPA Systems
Bibliographic record
Abstract
The performance of linear receive beamforming in continuous-aperture array (CAPA)-based uplink communications is analyzed. Three continuous beamforming techniques are proposed under the criteria of maximum-ratio combining (MRC), zero-forcing (ZF), and minimum mean-squared error (MMSE). i) ForMRC beamforming, a closed-form expression for the beamformer is derived to maximize per-user signal power. The achieved uplink rate and mean-squared error (MSE) in detecting received data symbols are analyzed. ii) ForZF beamforming, a closed-form beamformer is derived based on channel correlation to eliminate interference. As a further advance, its optimality in maximizing effective channel gain while ensuring zero inter-user interference is proven. iii)MMSE beamformingis established as the optimal linear receive approach for CAPAs in terms of maximizing per-user rate and minimizing MSE. Closed-form expressions are derived for the MMSE beamformer and the achievable sum-rate and sum-MSE. It is mathematically proven that all proposed beamformers lie within the signal subspace spanned by users’ spatial responses. Numerical results demonstrate that CAPAs outperform conventional spatially-discrete arrays (SPDAs) by achieving higher sum-rates and lower sum- MSEs under the proposed linear beamforming techniques.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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) | 0.007 | 0.003 |
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".