Maximum-Likelihood Detector for Differential Amplify-and-Forward Cooperative Networks
Bibliographic record
Abstract
The exact maximum-likelihood (ML) detector for amplify-and-forward (AF) cooperative networks employing M-ary differential phase-shift keying (DPSK) in Rayleigh fading is derived in a single-integral form, which serves as a benchmark for differential AF networks. Two algorithms are then developed to reduce the complexity of the ML detector. Specifically, the first algorithm can eliminate a number of candidates in the ML search, while causing no loss of optimality of ML detection. In high signal-to-noise ratios (SNRs), this algorithm almost surely identifies a single candidate that amounts to the ML estimate of the signal. For low to medium SNRs with multiple candidates determined, we then derive an accurate closed-form approximation for the integral involved in the likelihood function, which only requires a five-sample evaluation per symbol candidate. Finally, combining these algorithms, we propose a closed-form approximate ML detector, which achieves an almost identical bit-error-rate (BER) performance to the exact ML detector at practical complexity. In particular, it is shown that the proposed approximate ML detector is far less complex than the well-known diversity combiner in high SNRs, while achieving approximately 1.7-dB gain in the 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> BER when the relay is closer to the destination.
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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 | 0.000 | 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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".