Beamforming with Limited Feedback in Amplify-and-Forward Cooperative Networks
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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 paper, 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, Grassmanian 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. The gap in performance between unlimited-feedback and selection beamforming is found analytically to grow rapidly with the number of relays. We compare the selection protocol 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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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 | 0.001 | 0.000 |
| 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 | 0.000 |
| 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