Linear Receive Beamforming for CAPA Systems
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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) For <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MRC beamforming</i>, 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) For <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ZF beamforming</i>, 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) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MMSE beamforming</i> is 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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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it