Jointly Optimal Precoder and Power Allocation for an Amplify-and-Forward Half-Duplex Relay System
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Bibliographic record
Abstract
This paper investigates the optimal precoder design and power allocation between the source and relay for a half-duplex single-relay non-orthogonal amplify-and-forward (NAF) system. Based on the pair-wise error probability (PEP) analysis, an optimal class of 2 × 2 precoders is first derived for the traditional power allocation scheme, where one-third of the system power is spent at the relay node, while two-thirds are spent at the source node. Different from optimal unitary precoders proposed earlier, the derived class of precoders indicates that the source should spend all its power transmitting a superposition of the symbols in the broadcast phase, while being silent in the cooperative phase, for optimal asymptotic performance. We then further address the problem of jointly optimal precoder and power allocation for the system under consideration. It is shown that the total power should be equally distributed to the source and the relay, and the source should again spend no power during the cooperative phase for the best asymptotic performance. Analytical and simulation results reveal that the proposed precoders not only exploit full cooperative diversity, but also provide significant coding gain over the optimal unitary precoders. For instance, a coding gain of around 1dB can be attained at the practical BER level of 10 − 5 for various modulation schemes.
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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 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 it