Cramer-Rao Lower Bounds for Angular Parameters Estimates from Incoherently Distributed Signals Generated by Noncircular Sources
Bibliographic record
Abstract
In this paper, we derive for the first time analytical expressions for the stochastic Cramér- Rao lower bound (CRLB or CRB) of the angular parameters (central DOAs and angular spreads) estimates from incoherently distributed (ID) signals generated by noncircular sources. The new CRBs of the angular parameters are compared to those obtained from circular ID signals. The CRB of the central DOAs, however, are compared to those obtained from both circular and noncircular point sources. It will be shown that the CRB of both the central DOAs and the angular spreads obtained assuming noncircular ID sources are lower than those obtained using circular ID sources. This illustrates the potential gain that the noncircularity characteristic of the sources provides for the estimation of the angular parameters, especially in presence of different sources' distributions and for high angular spreads. Finally, the CRBs derived assuming noncircular ID signals decrease as the noncircularity rate increases. Furthermore, this decrease is more prominent at low DOA separations where the CRBs are sensitive to the noncircularity phase separation
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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 | 0.049 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| 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".