Achievable Rate Region under Joint Distributed Beamforming and Power Allocation for Two-Way Relay Networks
Bibliographic record
Abstract
We obtain the achievable beamforming rate region for a two-way cooperative network consisting of two transceivers and multiple relays, all single-antenna nodes. Assuming that the relay beamforming weights as well as the transceiver transmit powers are the design parameters, this region is characterized under a constraint on the total (network) transmit power consumption. Using the shape of the rate region, we then use a sum-rate maximization approach to obtain the jointly optimal relay beamforming weights and transceiver transmit powers. Interestingly, we show that the sum-rate maximization approach yields the same solution as the max-min fair design approach does. Using this relationship, we further present a semi-closed-form solution to the underlying distributed beamforming problem. We then prove that the transmit power of any of the two transceivers can be obtained as the solution to a one-dimensional optimization problem using a simple bisection method which enjoys a low computational complexity. Furthermore, we extend these results to obtain the relay beamforming weights and transceiver transmit powers corresponding to any point on the boundary of the rate region, through a weighted sum-rate maximization approach.
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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 | 0.006 | 0.020 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".