Log-Likelihood Ratio Calculation for Pilot Symbol Assisted Coded Modulation Schemes With Residual Phase Noise
Bibliographic record
Abstract
This paper presents a novel log-likelihood ratio (LLR) calculation for high order coded modulation schemes over an additive white Gaussian noise channel at the presence of residual phase noise (RPN). Residual phase noise is known to significantly degrade the error rate performance of such systems, particularly at lower error rates, resulting in an early error floor. To model RPN, we consider the commonly used pilot symbol assisted modulation schemes for carrier recovery. We derive the exact formula for the calculation of LLR for such systems. To simplify the implementation, we also derive an approximation of LLR which reduces the complexity significantly with almost no loss in performance. The simulation results are presented for coded modulation schemes based on quadrature amplitude modulations and low-density parity-check codes. The simulations demonstrate significant performance improvement in the error rate as a result of using the new LLR calculation instead of the conventional calculation of LLR which ignores the RPN.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| 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 | 0.001 |
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".