Cramer–Rao lower bound for data-aided and non-data-aided synchronisation of ultra-wideband signals with clock offset
Bibliographic record
Abstract
The Cramér–Rao lower bound (CRLB) for the data-aided (DA) and non-data-aided (NDA) estimation of ultra-wideband (UWB) multipath channel parameters has been previously derived in the literature based on the assumption of a perfectly synchronised clock frequency between the transmitter and the receiver. These results are extended by considering the practical case where there is an initial unknown clock frequency offset that needs to be jointly estimated as part of a successful acquisition of the UWB signal. Intuitively, the additional uncertainty of the clock offset should inflate the CRLB for the estimation of the UWB channel parameters. However, as shown here, this is only valid for a small number of multipath components. As the number of multipath components is increased, the inflation of the CRLB of the channel parameter estimation because of the unknown clock offset becomes negligible. This is of practical significance for UWB propagation channels as they are typically characterised by a large number of multipath components.
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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 | 0.007 | 0.042 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
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".