Generalized Asymptotic Measures for Wireless Fading Channels with a Logarithmic Singularity
Bibliographic record
Abstract
In wireless channels, the received signal to noise ratio (SNR) can be represented as γ = βγ̅, where γ is the average SNR and β is a random variable with probability density function (PDF) f(β). In this paper, we analyze the high SNR performance of wireless channels with a logarithmic singularity. That is, f(β) = aβt+ bβμlog(β) + ··· near β = 0. This logarithmic singularity (LS) is critically important in determining the high SNR performance and appears to have been completely overlooked. Important special cases include Gamma-Gamma and Generalized-K channels. For instance, the GG has been used to model scattering, reflection, and diffraction and optical, navigation and relay channels [1]. This versatility highlights the importance of LS wireless channels. Classical asymptotic or high SNR analysis is developed by expanding f(β) = aβt+ · · · near β = 0 and expressing the diversity and coding gain as direct functions of a and t. However, as this monomial expansion does not hold for LS channels, we develop generalized asymptotic performance measures for outage and error rates. The results show significantly improved accuracy in the SNR range of 1025 dB. For this range, our new asymptotic expressions achieve much better accuracy than the conventional ones that ignore this singularity.
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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 | 0.002 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".