On Stochastic Feedback Control for Multi-Antenna Beamforming: Formulation and Low-Complexity Algorithms
Bibliographic record
Abstract
Based on the Gauss-Markov channel model, we investigate the stochastic feedback control for transmit beamforming in multiple-input-single-output systems and design practical implementation algorithms leveraging techniques in dynamic programming and reinforcement learning. We first validate the Markov decision process formulation of the underlying feedback control problem with a 4R-variable (4R-V) state, where R is the number of the transmit antennas. Due to the high complexity of finding an optimal feedback policy under the 4R-V state, we consider a reduced 2-V state. As opposed to a previous study that assumes the feedback problem under such a 2-V state remaining an MDP formulation, our analysis indicates that the underlying problem is no longer an MDP. Nonetheless, the approximation as an MDP is shown to be justifiable and efficient. Based on the quantized 2-V state and the MDP approximation, we propose practical implementation algorithms for feedback control with unknown state transition probabilities. In particular, we provide model-based offline and online learning algorithms, as well as a model-free learning algorithm. We investigate and compare these algorithms through extensive simulations and provide their efficiency analysis. According to these results, the application rule of these algorithms is established under both statistically stable and unstable channels.
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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 | 0.000 |
| 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".