A Notion of Diversity Order in Distributed Radar Networks
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Bibliographic record
Abstract
We introduce the notion of diversity order in distributed radar networks. Our goal is to analyze the tradeoff between distributed detection, using <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> sensors, and centralized detection, using collocated antennas. The diversity order is representative of the degrees of freedom available in the system. In contrast with the asymptotically high signal-to-noise ratio (SNR) definition in wireless communications, we define the diversity order of a distributed radar network as the slope of the probability of detection (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> ) versus SNR curve at P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> = 0.5. We analyze an optimal joint detection system and prove that its corresponding Neyman-Pearson (NP) test statistic follows a Gamma distribution and that, for large <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> , its diversity order grows as ¿K. For a fully distributed system using the NP fusion rule, we prove that the test statistic follows a binomial distribution and that the diversity order is also on the order of ¿K. In more practical systems where the fusion center uses a fixed fusion rule, the largest growth in diversity order is achieved by the OR rule, and it only grows as log(K). We provide the results of simulations to confirm the theory developed.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 it