Cooperative Beamforming for Single-Carrier Frequency-Domain Equalization Systems with Multiple Relays
Bibliographic record
Abstract
We consider cooperative beamforming (BF) for block-based single-carrier frequency-domain equalization (SC- FDE) in a wireless network consisting of one single-antenna source, one single-antenna destination, and multiple multi- antenna relays. Adopting the minimum mean squared error as optimality criterion, the optimal frequency-domain linear equalization (LE) and decision-feedback equalization (DFE) receivers are derived and corresponding objective functions for relay BF matrix optimization are specified. For a sum relay power constraint, we obtain the structure of the optimal relay BF matrices in closed form. While the structure of the optimal relay BF matrices is identical for LE and DFE as well as for an idealized matched filter receiver, the solution of the remaining power allocation problem depends on the adopted receiver. The power allocation problem is shown to be convex for all considered receivers and an efficient numerical algorithm for finding the optimal power allocation is provided. Furthermore, to reduce complexity, two suboptimal power allocation schemes assigning identical powers to all relays and/or frequencies are proposed and shown to lead to only a small loss in performance and a remarkable robustness against imperfect channel state information.
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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 | 0.000 | 0.001 |
| Open science | 0.002 | 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".