Percentile Optimization in Wireless Networks—Part II: Beamforming for Cell-Edge Throughput Maximization
Bibliographic record
Abstract
Part I of this two-part paper focused on the formulation of percentile problems, complexity analysis, and development of power control algorithms via the quadratic fractional transform (QFT) and logarithmic fractional transform (LFT) for sum-least- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> -percentile (SLqP) rate maximization problems. In this second part, we first tackle the significantly more challenging problems of optimizing SLqP rate via beamforming in a multiuser, multiple-input multiple-output (MUMIMO) network to maximize cell-edge throughput. To this end, we first propose an adaptation of the QFT algorithm presented in Part I that enables optimization of the complex-valued multidimensional beamforming weights for the SLqP rate utility function. We also introduce a new class of problems which we term as sum-greatest- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> -percentile weighted mean squared error (SGqP-WMSE) minimization. We show that this class subsumes the well-known sum-weighted mean squared error (WMMSE) minimization and max-WMSE minimization problems. We demonstrate an equivalence between this class of problems and the SLqP rate maximization problems, and show that this correspondence can be exploited to obtain stationary-point solutions for the aforementioned beamforming problem. Next, we develop extensions for the QFT and LFT algorithms from Part I to optimize ergodic <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">long-term average</i> or ergodic SLqP utility. Finally, we also consider related problems which can be solved using the proposed techniques, including hybrid utility functions targeting optimization at specific subsets of users within cellular networks.
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How this classification was reachedexpand
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 | 0.000 | 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 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".