Total power minimization for two-way networks with multi-antenna relays
Bibliographic record
Abstract
We consider a two-way relay network consisting of two single-antenna transceivers and multiple multi-antenna relays. Assuming a multiple access broadcast (MABC) relaying scheme, we aim to jointly obtain the optimal relay beamforming matrices as well as the optimal transceiver transmit powers which minimize the total transmit power under given signal-to-noise-ratio (SNR) constraints at the transceivers. We show that the relay beamforming matrices have special structures which can be exploited to reduce the computational complexity of the optimization problem. We use this structure to re-cast the total power minimization problem as an unconstrained optimization problem with a dimensionality which is smaller than that of the original problem, when number of antennas in the relays is larger than 2. We then show this unconstrained problem can be solved using a two-dimensional search over the feasible set of the transceivers' transmit powers. Indeed, the feasible set is quantized into a sufficiently fine grid. At each vertex of this grid, a quadratically constrained quadratic problem (QCQP) is solved to find the optimal values of the relay beamforming matrices corresponding to that vertex. This QCQP can be rewritten as a semi-definite relaxation (SDR) method which is guaranteed to have a rank-one solution. Once the beamforming matrices are obtained for all vertices of the grid, the vertex which results in the lowest value for the total transmit power, yields the optimal values of the transceivers' transmit powers and the optimal relay beamforming matrices.
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| 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) | 0.002 | 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 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".