Closed form expression for the Cramér-Rao lower bound for the DOA estimates from spatially and temporally correlated narrowband signals considering noncircular sources
Bibliographic record
Abstract
In this paper, we derive for the first time an explicit expression for the stochastic Cramér-Rao lower bound (CRLB or CRB) of the DOA estimates from spatially and temporally correlated signals generated from noncircular sources. The new CRB is compared to those of circular temporally correlated and noncircular independent and identically distributed (iid) signals. It will be shown that the CRB obtained assuming both noncircular sources and temporally correlated signals is lower than the CRBs derived considering only one of these two assumptions. This illustrates the potential gain that both the noncircularity and the temporal correlation provide when considered together. It will also be proved that the difference between the three CRBs increases with the number of snapshots. However, as the signal-to-noise ratio (SNR) increases, the CRBs merge together and decrease linearly. Moreover, we notice that in low SNR values the temporal correlation is more informative about the unknown DOA parameters than the noncircularity. Finally, we show the dependence of the CRB on the noncircularity rate, the noncircularity phase separation and the DOA 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 | 0.003 | 0.019 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.013 | 0.008 |
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".