Beamforming with limited feedback in amplify-and-forward cooperative networks - [transactions letters]
Bibliographic record
Abstract
A relay selection approach has previously been shown to outperform repetition-based scheduling for both amplify-and-forward (AF) and decode-and-forward (DF) cooperative networks. The selection method generally requires some feedback from the destination to the relays and the source, raising the issue of the interplay between performance and feedback rate. In this letter, we treat selection as an instance of limited feedback distributed beamforming in cooperative AF networks, and highlight the differences between transmit beamforming in a traditional multi-input single-output (MISO) system and the distributed case. Specifically, Grassmannian line packing (GLP) is no longer the optimal codebook design, and orthogonal codebooks are no longer equivalent to each other. We derive the high signal-to-noise ratio expressions for outage probability and probability of symbol error for unlimited-feedback and selection schemes, which are then used for performance comparisons. The selection protocol is compared to a limited-feedback distributed beamformer that assigns codebooks based on the Generalized Lloyd algorithm (GLA), and one that uses random beam-vectors. The main conclusion is that the performance improvement to be seen using the very complex GLA is small, and that many more feedback bits are required with random beamforming than selection for the same performance. These results indicate that the selection protocol is a very attractive protocol, with low complexity, that provides excellent performance relative to other known methods.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 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 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| 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".