Belief Propagation on Factor Graphs for Cooperative Spectrum Sensing in Cognitive Radio
Bibliographic record
Abstract
In this paper, we present a probabilistic inference approach for cooperative spectrum sensing. We probabilistically model the cooperative sensing system on a representative factor graph, and approach the decision fusion problem as one of probabilistic inference on a factor graph that can be tackled by message passing algorithms like belief propagation. This approach allows for the rigorous modeling of all unknown quantities, such as channel effects, and correlations among random variables in the cooperative sensing system. Using belief propagation, we compute the likelihoods of the null and alternative hypotheses based on all observations at the fusion center, and apply the likelihood ratio test (LRT) based on the Neyman-Pearson (NP) theorem for optimal decision making. Unlike most studies in this field, we consider non-ideal transmission channels between secondary users and fusion center, as well as the presence of fading in links between primary and secondary users. We apply the proposed approach for both hard and soft local decisions and through simulation results illustrate the performance improvement achieved by the proposed NP-based LRT cooperative sensing scheme. A useful side result is that the well-known M-out-of-K collaborative sensing method is shown to be optimal for identical independent channels from the primary transmitter to each secondary user, and from each secondary user to the fusion center.
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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 | 0.004 | 0.019 |
| 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 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".