Generalized CRLB for DA and NDA Synchronization of UWB Signals with Clock Offset
Bibliographic record
Abstract
In this paper the Cramer-Rao lower bound (CRLB) of an ultra-wideband (UWB) pulse amplitude modulated (PAM) signal with time hopping (TH) code is derived for the practical case where there is an initial unknown relative clock offset between the transmitter and receiver. However, it is assumed that there is a priori information about the probability density function of clock offset. CRLB expressions are developed for both the data- aided (DA) case with an assumed deterministic pilot for synchronization and for the non data-aided (NDA) case based on blind synchronization. It is shown that the influence of the unknown clock offset on the synchronization performance becomes negligible as the number of multipath components increases emphasizing an advantage in UWB links where the multipath is typically rich. Another observation made is that as the SNR decreases, the difference in the CRLB for the NDA and DA cases increases emphasizing the significance of a pilot. Having a priori information helps to achieve a lower CRLB for the timing or clock offset estimation. This improvement is significant in the case of NDA. Finally at very low SNR CRLB of the clock offset converges to the variance of clock offset based on only a priori information.
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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 | 0.003 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".