A Two-Way Network Beamforming Approach Based on Total Power Minimization With Symmetric Relay Beamforming Matrices
Bibliographic record
Abstract
We study the total transmit power minimization problem for a two-way relay network under two constraints on the transceivers' received signal-to-noise-ratios. The network considered herein consists of multiple multi-antenna relay nodes and two single-antenna transceivers. Each relay transforms the vector of its received signals, by multiplying this vector with a complex beamforming matrix, thereby obtaining a new vector whose entries are transmitted over different antennas of that relay. Assuming the relay beamforming matrices and the transceivers' transmit powers as the design parameters, we first study the total power minimization problem under the assumption that the relay beamforming matrices are symmetric. Under such an assumption, we show that the total power minimization problem is amenable to a semi-closed-form solution, and thus, it can be solved efficiently. We then consider the case, where the relay beamforming matrices may not be symmetric and show that in this case, the total power minimization problem can be solved using a computationally prohibitive algorithm which involves a 2-D search over a grid in the space of the transceivers' transmit powers and semi-definite programming at each vertex of this grid. Our numerical results show that the symmetric assumption on the relay beamforming matrices incurs only insignificant loss, while this assumption allows us to significantly reduce the computational burden of solving the total power minimization problem.
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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 | 0.001 | 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 | 0.002 | 0.000 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.001 |
| 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".