On the Approximation of the Generalized-K PDF by a Gamma PDF Using the Moment Matching Method
Bibliographic record
Abstract
Using the Nakagami probability density function (PDF) to model multipath fading and the Gamma PDF to model shadowing, in a wireless channel, has led to a closed-form expression for the composite fading PDF, known as the generalized-.fi" PDF (also called Gamma-Gamma PDF). However, further derivations have shown that the cumulative distribution function (CDF) and the characteristic function of the generalized-K PDF contain special functions that are involved to handle. In this paper, an approximation of the generalized-K PDF by the familiar gamma PDF is introduced. The parameters of the approximating Gamma PDF are computed using the moment matching method. The accuracy of this approximation in the lower and upper tail regions is enhanced by adjusting the parameters of the approximating gamma distribution in each region. The CDF and the complementary CDF plots show that this approximation is sufficiently accurate for both integer and non-integer practical values of the multipath fading and shadowing parameters. The region-wise approximation obtained by the adjusted moment matching method is used to well- approximate the PDF of the sum of identically and independent generalized-K random variables. Applications of the obtained results arise in distributed antenna systems (DASs), cooperative relay networks, radar, and sonar systems.
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 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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".