Dual Methods for Power Allocation for Radios Coexisting in Unlicensed Spectra
Bibliographic record
Abstract
The power allocation that maximizes the sum rate of transceivers operating in the same frequency band is a difficult non-convex problem. Lack of a convex structure excludes the direct application of Lagrangian dual techniques as the duality gap might not be zero. This paper advances current knowledge by introducing three significant steps in finding a solution. First, we show that for transceivers operating under a total power constraint, the maximum sum rate occurs at the boundary of the feasible set formed by the hyper plane representing the power constraint. This conclusion is nontrivial considering that we are dealing with an interference limited system. Second, we prove that the duality gap is zero for this problem, despite the lack of concavity of the objective. We do this by showing that the maximum sum rate is concave in the power constraint. Third, we propose an iterative algorithm that finds the optimal power allocation by solving the dual problem. Simulation results are provided to support the theorems proven in the paper as well as to demonstrate the convergence of the algorithm to the global maximum sum rate. Results of the algorithm are also compared with solutions based on Game theory.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".