SINR Outage Evaluation: Saddle Point Approximation Using Normal Inverse Gaussian Distribution
Bibliographic record
Abstract
Signal-to-noise-plus-interference ratio (SINR) outage probability is among one of the key performance metrics of a wireless network. In this paper, we propose a semi-analytical method based on the saddle point approximation (SPA) technique to calculate the SINR outage of a wireless system whose SINR can be modeled in the form (Σi=1MXi/(1 + Σi=1NYi)) where Xi denotes the useful signal power and Yidenotes the power of the interference signal. Both M and N can also be random variables. The proposed approach is based on the saddle point approximation to cumulative distribution function as given by Wood-Booth-Butler formula. The approach is applicable whenever the cumulant generating function of the received signal and interference exists, and it allows us to tackle distributions with large skewness and kurtosis with higher accuracy. In this paper, we exploit a four parameter normal-inverse Gaussian (NIG) distribution as a base distribution. Given that the skewness and kurtosis satisfy a specific condition, NIG-based SPA works reliably. When this condition is violated, we recommend SPA based on normal or symmetric NIG distribution, both special cases of NIG distribution, at the expense of reduced accuracy. For the purpose of demonstration, we apply SPA for the SINR outage evaluation of a typical user experiencing a downlink coordinated multi-point transmission from the base stations that are modeled by homogeneous Poisson point process. Numerical results are presented to illustrate the accuracy of the proposed set of approximations.
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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 | 0.006 |
| 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 | 0.001 |
| 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".