Low-Complexity ADMM-Based Algorithm for Robust Multi-Group Multicast Beamforming in Large-Scale Systems
Bibliographic record
Abstract
We design an efficient robust multi-group multicast beamforming scheme for massive multiple-input multiple-output (MIMO) systems. Assuming only estimates of the channel covariance matrices are available at the base station with a bounded error, we formulate the robust quality-of-service (QoS) problem, which is to minimize the transmit power subject to the worst-case minimum signal-to-interference-plus-noise-ratio (SINR) guarantee. We directly solve the worst-case SINR problem and convert the robust QoS constraint into a number of non-convex constraints. Based on the recent convergence result of the alternating direction method of multipliers (ADMM) for non-convex problems, we develop an ADMM-based fast algorithm to directly tackle the reformulated non-convex problem with a convergence guarantee. The algorithm contains two layers of ADMM procedures. We design the outer-layer ADMM to decompose the problem into three convex subproblems and solve them alternatingly. We further develop an inner-layer consensus-ADMM-based algorithm to efficiently solve one subproblem. By exploring each subproblem structure and developing the special optimization techniques, we obtain closed-form or semi-closed-form solutions to each subproblem. These results lead to a fast iterative algorithm, which is guaranteed to converge to a stationary point of the original robust QoS problem. Simulation shows that our proposed algorithm provides a favorable performance compared with existing alternative methods with magnitudes of computational complexity reduction.
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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 | 0.001 | 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 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".