Code-Aided Time Synchronization of Turbo-Coded Square-QAM-Modulated Transmissions: Closed-Form Cramer-Rao Lower Bounds
Bibliographic record
Abstract
This paper tackles the problem of code-aided (CA) timing recovery in turbo-coded square-QAM transmissions. Owing to a simple recursive construction process, some hidden properties of Gray-coded (GC) square-QAM constellations are demystified and the code bits' a priori log- likelihood ratios (LLRs) are explicitly incorporated in the log-likelihood function (LLF). Then, by splitting the underlying LLF into the sum of two analogous terms, we derive for the very first time the closed-form expressions for the exact Cramer-Rao lower bounds (CRLBs) of the underlying turbo synchronization problem. Computer simulations will show that the new closed-form CRLBs coincide exactly with their empirical counterparts evaluated previously using exhaustive Monte-Carlo simulations. They will also show unambiguously the remarkable performance improvements of the CA scheme against the traditional non-data-aided (NDA) one. Over a wide range of practical SNRs, the new CA CRLBs reach those of the completely data-aided (DA) scheme in which all the transmitted symbols are perfectly known to the receiver.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.003 | 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".