Tier Association Probability and Spectrum Partitioning for Maximum Rate Coverage in Multi-Tier Heterogeneous Networks
Bibliographic record
Abstract
For a wireless multi-tier heterogeneous network with orthogonal spectrum allocation across tiers, we optimize the association probability and the fraction of spectrum allocated to each tier so as to maximize rate coverage. In practice, the association probability can be controlled using a biased received signal power. The optimization problem is non-convex and we are forced to explore locally optimal solutions. We make two contributions in this paper: first, we show that there exists a relation between the first derivatives of the objective function with respect to each of the optimization variables. This can be used to simplify numerical solutions to the optimization problem. Second, we explore the optimality of the intuitive solution that the fraction of spectrum allocated to each tier should be equal to the tier association probability. We show that, in this case, a closed-form solution exists. Importantly, our numerical results show that there is essentially zero performance loss. The results also illustrate the significant gains possible by jointly optimizing the user association and the resource allocation.
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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 | 0.003 | 0.011 |
| 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 | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".