Symmetric beamforming for multi-antenna two-way relay networks
Bibliographic record
Abstract
This paper addresses the problem of total power minimization of a two-way relay network, where two single-antenna nodes exchange information through multiple multi-antenna relays with symmetric beamforming matrices. More specifically, each relay multiplies the vector of its received signals with a symmetric beamforming matrix to obtain the vector of its transmit signals and broadcasts the elements of the so-obtained transmit signal vector on its different antennas. Considering the two-time-slot multiple access broadcast (MABC) scheme, we aim to minimize the total transmit power subject to signal-to-noise- ratio (SNR) requirements by optimally determining the transceivers' transmit powers and the relay beamforming matrices. We prove that this power minimization problem has a semi-closed-form solution. That is, the symmetric beamforming matrices can be obtained in closed-forms given a certain intermediate parameter. This parameter can also be obtained using Newton-Raphson method or a bisection technique. Our simulation results show that the average total power consumed in the network is twice the average total relay power, which is in average twice the average power of each of the transceivers. Our numerical examples also show that concentrating all the antennas in a few relays reduces the total power consumption as apposed to having a large number of relays with very few antennas.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".