Asymptotic Performance of Energy Detector in Fading and Diversity Reception
Bibliographic record
Abstract
Missed-detection probability expressions for energy detectors often involve infinite series and do not provide quick insights into the effects of operating conditions. To overcome these limitations, we develop novel asymptotic analyses by proposing an approximate probability density function (PDF) of a random variable β, which, in general, can characterize fading channels in diverse operating conditions. The coefficients of the proposed approximate PDF of β are obtained by matching the coefficients of the approximate PDF's series expansion (or coefficients of the approximate PDF's moment generating function (MGF)) with those of the exact PDF (or MGF) of β. By using the proposed approximation, a unified closed-form asymptotic missed-detection probability is derived. Its usefulness is then demonstrated for fading channels without and with antenna diversity, for cooperative detection, and in co-channel interference. For each case, the sensing gain, which reveals the effect of the operating conditions on the detection performance, is determined explicitly. Furthermore, the asymptotic complementary area under the receiver operating characteristic curve, an alternative performance metric, is derived, and found to reveal the sensing gain. Numerical results verify the accuracy of our derived asymptotic expressions over a wider signal-to-noise ratio (SNR) range compared to the existing asymptotic solution, which is accurate only for high SNRs.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".